Test Bank for College Algebra Graphs and Models, 7th Edition by Marvin L. Bittinger Judith A. Beeche

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write equations of the horizontal and the vertical lines that pass through the given point.

1) (2, -8.31) A) horizontal: y = 8.31; B) horizontal: y = -2; vertical: x = -2 vertical: x = 8.31 C) horizontal: y = -8.31x; D) horizontal: y = -8.31; vertical: x = 2y vertical: x = 2

1)

By graphing the function, visually estimate its domain and range.

2) g(x) = x2 - 1

2)

Write an equation in slope-intercept form for the line shown.

3)

3)

A) Domain: [1, ); range: [1, ) C) Domain: (- , ); range: (- , )

A) x = -2

B) Domain: [1, ); range: (- , ) D) Domain: (- , ); range :[-1, )

B) y = -2

C) x = 2

D) y = 2

Solve the problem.

4) Helen Weller invested $13,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the average return on the two investments amounts to 13%?

A) $10,000 B) $13,000 C) $9,000 D) $6,500 Solve the equation.

5) 3(3x + 7) = 2(x + 7) A) - 1

7 C) 11

B) -7

5) D) 7

Solve the problem.

6) A shipping company has determined that their drivers in Montana on average travel 75 miles on a single delivery route for mail order products. This is five times the distance of an average route for their drivers in New Jersey. How far, on average, is the route in New Jersey?

A) 150 mi B) 375 mi C) 15 mi D) 75 mi

1

4)

6)

7) Water accounts for 60% of a man's weight. Stan weighs 167 lb. How much of his body weight is water?

A) 84 lb B) 100 lb C) 134 lb D) 167 lb Graph the function.

1 8) f(x) = x - 3 5

7)

8)

A)

B)

C)

D)

2

Find the slope of the line containing the given points.

1 1 1 1 9) , , , 8 2 4 4 A) -1

9)

B) not defined

C) -2

Find the domain of the function.

10) f(x) = x + 5 A) all real numbers, or (- , ) C) {x|x 5}, or [5, )

D) 2

10)

B) {x|x -5}, or [-5, ) D) {x|x 5}, or (- , 5) (5, )

Write a slope-intercept equation for a line with the given characteristics.

7 11) m = ; passes through (0, 5) 6 A) y =

7 x+5 6

B) y = 5x -

7 6

C) y = 5x +

11) 7 6

D) y =

7 x-5 6

By graphing the function, visually estimate its domain and range.

12) f(x) = x - 6 A) Domain: [6, ); range: [6, ) B) Domain: [0, ); range = [6, ) C) Domain: [0, ); range: [0, ) D) Domain: [6, ); range: (0, ) Find the slope of the line.

13)

A)

9 11

12)

13)

B)

11 9

C) -

11 9

Find the slope and the y-intercept of the line with the given equation.

14) f(x) = 8.2 - x A) 8.2; (0, -1) B) 1; (0, 8.2) C) -1; (0, 8.2)

D) -

9 11

D) -1; (8.2, 0)

Solve the problem.

15) The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 500 parts are produced, the cost is $2,700.

What is the average cost per part?

A) $0.17 per part B) $7.00 per part C) $6.00 per part D) $4.80 per part

3

14)

15)

Write a slope-intercept equation for a line with the given characteristics.

16) Passes through (5, 1) and (8, -3) 4 23 4 23 65 xA) y = x + B) y = - x + C) y = 3 3 3 3 11

4 65 xD) y = 11 11

16)

Solve the problem.

17) The function h described by h(t) = -16t2 + 33.1t + 124.26 gives the height of a ball thrown upward with a speed of 33.1 feet per second from a 124.26 ft high window t seconds after it is thrown until it hits the ground. Find the height of the ball 1.5 seconds after it is thrown.

A) 38.61 ft B) 110.61 ft C) 209.91 ft D) 137.91 ft

17)

Express the data in the graph as ordered pairs, letting the first coordinate represent the year and the second coordinate the amount.

18) Total Advertisement Spending for Soccer Tournament 18)

$300 $250 $200 152.69

155.23

156.99 158.13

160.08

162.82

$150 $100 $50

2003

2004

2005 2006 Year

2007

2008

A) (152.69, 2003), (155.23, 2004), (156.99, 2005), (158.13, 2006), (160.08, 2007), (162.82, 2008) B) (2003, 155.23), (2004, 152.69), (2005, 156.99), (2006, 160.08), (2007, 158.13), (2008, 162.82) C) (2003, 152.69), (2004, 155.23), (2005, 156.99), (2006, 158.13), (2007, 160.08), (2008, 162.82) D) (1, 152.69), (2, 155.23), (3, 156.99),( 4, 158.13), (5,160.08), (6, 162.82) Find the domain of the function.

3 19) f(x) = 4 - x A) {x|x 4}, or (- , 4) (4, ) C) {x|x > 4}, or ( 4, )

19) B) all real numbers, or (- , ) D) {x|x 4}, or (- , 4]

Solve the problem.

20) In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 20° less than that of angle C. Find the measure of the angles.

A) 80°, 20° and 40° B) 80°, 20° and 80° C) 120°, 20° and 80° D) 120°, 20° and 40°

4

20)

Determine the slope, if it exists, of the graph of the given linear equation.

4 21) y = 7 A) m = 0

C) m = -

B) not defined

4 7

21) D) m =

4 7

Solve the problem.

22) The function H described by H(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose humerus is 30.8 cm long.

A) 13.22 cm B) 105.03 cm C) 156.18 cm D) 43.43 cm Plot the two points given by the ordered pairs.

23) A(2, -1), B(-5, 5)

22)

23)

A)

B)

5

C)

D)

Write equations of the horizontal and the vertical lines that pass through the given point.

4 24) -1, 5 A) horizontal: y =

4 x; 5

B) horizontal: y = -1; 4 vertical: x = 5

vertical: x = -1y

C) horizontal: y =

24)

4 ; 5

D) horizontal: y = -

vertical: x = -1

4 ; 5

vertical: x = -1

Find the slope and the y-intercept of the line with the given equation.

2 x 25) f(x) = 2 13 A)

2 ; (0, -2) 13

Solve the equation.

26) 6x + 2 = 2x - 6 A) -8

B) 2; 0, -

2 13

C) -

2 ; (0, 2) 13

25) D) -

2 ; (2, 0) 13

26)

3 B) 2

C) 2

D) -2

Answer the question.

27) The points (-3, 4), (0, 7), ( 2, -1), and ( 5, 2) are the vertices of a quadrilateral. Is the quadrilateral a rectangle?

A) Yes B) No

6

27)

Solve the problem.

28) Find the average rate of change.

28)

Monthly Cellular Phone Charge in Dollars

Minutes Cellular Phone is Used

A) $1.11 per min

B) $-0.25 per min

C) $-4.00 per min

Is the following correspondence a function?

29) -9 -8 -18 -15 A) Yes

D) $0.50 per min

29)

B) No

7

Graph the equation.

30) y = x2 - 1

30)

A)

B)

C)

D)

Determine the slope, if it exists, of the graph of the given linear equation.

1 31) f(x) = - x + 6 2 A) m = -

1 2

B) m = 6

C) m = -6

8

31)

D) m =

1 2

Find the equation of the circle. Express the equation in standard form 32)

A) (x + 15)2 + (y + 15)2 = 102 C) (x - 15)2 + (y - 15)2 = 102

32)

B) (x + 15)2 + (y - 15)2 = 102 D) (x + 15)2 + (y + 15)2 = -3 2

Plot the two points given by the ordered pairs.

33) A(0, 0), B(3, 6)

33)

A)

B)

9

C)

D)

Use substitution to determine whether the given ordered pair is a solution of the given equation.

34) (-7, ); 4x + 2y2 = -20 A) Yes

B) No

Tell whether or not the relation is a function.

35) {(-1, ), (2,-6), (5, ), (9,-9), (10, )} A) Yes

B) No

Solve the problem.

36) A cross-country skier reaches the 15-km mark of a race 40 min after reaching the 5-km mark. Find the speed (average rate of change) of the skier.

45 km/hr A) B) 15 km/hr C) 10 km/hr D) 40 km/hr 2 37) The mathematical model C = 900x + 20,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $290,000?

A) 278 items B) 300 items C) 289,100 items D) 344 items Determine the domain and range of the relation.

38) {( , ), (-4, -1), ( , -8), ( , )} A) Domain: { , , -4}; Range: { , -8, -1, } C) Domain: {7, -8, -1, 5}; Range: {1, 2, -4}

B) Domain: { , , -4, };Range: { , -8, -1, } D) Domain: { , , -4, -2}; Range: { , -8, -1, }

Answer the question.

39) The points ( 3, -2) and (12 3, 3) are the points at which a particular diameter of a circle intersects the circle. What are the coordinates of the center of the circle?

15 3 -1 13 3 -1 15 3 1 13 3 1 , , , , A) B) C) D) 2 2 2 2 2 2 2 2 By graphing the function, visually estimate its domain and range.

40) t(x) = 9 - x A) Domain: [9, ); range: [9, ) B) Domain: (- , 9]; range: (- , 9] C) Domain: (- , ); range: (- , ) D) Domain: (- , 9]; range: [0, )

10

34)

35)

36)

37)

38)

39)

40)

The following table contains input-output values for a function. Is this function linear?

41) x y -6 35 8 -3 0 -1 3 8 6 35 9 80 12 143 A) Yes B) No

41)

Solve the problem.

42) On average, 13.6 % of the money consumers spend in supermarkets in England goes to the purchase of snacks and baked goods, which is four times the percent of money spent on cereals and rice. What percentage of the money spent by consumers in England's supermarkets is for the purchase of cereal and rice?

A) 1.7% B) 3.4% C) 4.4% D) 3.9% 43) A construction company builds a swimming pool with a perimeter of 58 m. The length is 11 m more than the width. Find the dimensions of the swimming pool?

A) 20 m × 9 m B) 20 m × 11 m C) 25 m × 9 m D) 15 m × 9 m Answer the question.

44) The points (-6, 1) and (-4, 5) are the points at which a particular diameter of a circle intersects the circle. What are the coordinates of the center of the circle?

A) (-4, 3) B) (-4, 4) C) (-5, 3) D) (-5, 4) Use substitution to determine whether the given ordered pair is a solution of the given equation.

5 45) 0, ; 3x + 6y = 6 6 A) Yes

Find the midpoint of the segment having the given endpoints.

47) (-3, -7) and (1, 8)

Solve the equation.

48) 9 + 13x = 0 13 A) 9

43)

44)

45)

B) No

Solve the problem.

46) To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by 1.8 and then add 32 to the result. Find F as a linear function of c, and use this function to convert 25° C to °F. A) 68°F B) 77°F C) 64.7°F D) 72.3°F

A) (-4, -15)

42)

B) (-2, 1)

15 C) - 2, 2

1 D) - 1, 2

9 B) 13

13 C) 9

9 D) 13

11

46)

47)

48)

Find the slope of the line containing the given points.

49) ( , ) and ( , -5) 1 9 A) B) 10 8

9 C) 8

Graph the equation.

50) y = x2 + 5

8 D) 9

49)

50)

A)

B)

C)

D)

12

51) 2x + y = -4

51)

A)

B)

C)

D)

13

Determine whether the graph is the graph of a function.

52)

52)

A) Yes

B) No

Determine the domain and range of the relation.

53) {(12, -2), (9, -3), (-4, -7), (-4, 9)} A) Domain: {-2, -3, -7, 9}; Range: {12, 9, -4} B) Domain: {12, 9, -4, -4}; Range: {-2, -3, -7, 9} C) Domain: {12, 9, -4, 4}; Range: {-2, -3, -7, 9} D) Domain: {12, 9, -4}; Range: {-2, -3, -7, 9}

53)

Solve and graph the solution set.

54) -4(6x - 4) < -28x + 8

54)

A) {x|x > -28} or (-28, )

B) {x|x > -2} or (-2, )

C) {x|x< -2} or (- , -2)

D) {x|x < -28} or (- , -28)

14

55)

x+1>

55)

x + 13

A) {x|x<

} or (- ,

)

B) {x|x <

} or (- ,

)

C) {x|x >

} or (

, )

D) {x|x >

} or (

, )

Determine whether the pair of lines is parallel, perpendicular, or neither.

56) y + 14 = -4x 4y = 24x - 10 A) Parallel B) Perpendicular

56) C) Neither

Solve the equation.

5 7 = + 7x 57) 7x + 11 11

57)

A) 0 C)

B) no solution

12 11

D) all real numbers

Find the domain of the function.

3x 58) f(x) = 5+x

58)

A) {x|x < 5}, or ( , 5) C) {x|x < -5}, or ( , -5)

B) {x|x > -5}, or (-5, ) D) {x|x > 5}, or (5, )

15

Find the domain and range of the function represented in the graph.

59)

59)

A) Domain: (- , 3) or (3, ); Range: (- , 3) or (3, ) B) Domain: (- , 3]; Range: (- , 3] C) Domain: (- , ); Range: (- , 3] D) Domain: (- , ); Range: (- , ) Solve the problem.

60) A computer company invested a total of $265 million in research and development in its scanners and video digitizers. If the amount the company spent on research and development on scanners was $123 million more than was spent on research and development on its video digitizers, how much in fact did the company spend on research and development on its scanners?

A) $194 million B) $132.5 million C) $265 million D) $71 million 61) If an object is dropped from a tower, then the velocity, V (in feet per second), of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Find V as a linear function of t, and use this function to evaluate V(2.7), the velocity of the object at time t = 2.7 seconds.

A) V(2.7) = 96.4 ft per sec B) V(2.7) = 95.7 ft per sec C) V(2.7) = 94.4 ft per sec D) V(2.7) = 97.7 ft per sec Find the midpoint of the segment having the given endpoints.

62) (7, 7) and (1, 4) 11 A) 4, B) ( , ) C) (8, 11) 2

11 ,4 D) 2

Solve the equation.

63) 25x - 8 = 0 8 A) 25

25 D) 8

8 B) 25

25 C) 8

Find an equation for the circle.

64) Center at (7, 0), radius 11 A) x2 + (y + 7)2 = 11

B) (x + 7)2 + y2 = 121 D) x2 + (y - 7)2 = 11

C) (x - 7)2 + y2 = 121

16

60)

61)

62)

63)

64)

Solve the problem.

65) A magazine earned $60 million in 1998 from advertising revenue and subscriptions. If the advertising revenue was 6 times the subscription revenue, how much did the magazine earn from advertising?

A) $8.6 million B) $102.9 million C) $0.9 million D) $51.4 million Solve and give interval notation for the solution set. Then graph the solution set.

1 1 66) x + 4 - or x + 4 3 3

A)

,-

13 3

-

11 , 3

B)

,-

13 3

-

11 , 3

C) -

13 11 ,3 3

D) -

13 11 ,3 3

Is the following correspondence a function?

67) 11 -16 -6 6 -13 3 A) Yes

65)

66)

67)

B) No

17

Solve the problem.

68) Find the average rate of change.

68)

Value of Car in Thousands of Dollars

Number of Years of Use

A) -$2.00 per year

B) $2.00 per year

C) $3.00 per year

D) -$3.00 per year

Find the distance between the pair of points. Give an exact answer, and where appropriate, an approximation to three decimal places.

1 1 1 69) - , 1 and - , 69) 2 2 2

A)

5 2

B)

1 2

C)

45 2

D)

The following table contains input-output values for a function. Is this function linear?

70) x y -4 -4 -2 -16 2 -20 2 -16 4 -16 4 -4 6 16 A) Yes B) No

3 2

70)

Find the distance between the pair of points. Give an exact answer, and where appropriate, an approximation to three decimal places.

71) (-2.1, ) and (-3.3, 1.8) 71) A) 5.408 B) 8.078 C) 1.697 D) 5.909

Find the domain of the function.

72) f(x) = 4 - x A) all real numbers, or (- , ) C) {x|x > 4}, or ( 4, )

72) B) {x|x 4}, or (- , 4] D) {x|x 4}, or (- , 4)

18

(4, )

Solve and write interval notation for the solution set. Then graph the solution set.

73) 4 < 1 - 4x 12

A) -

11 3 ,4 4

B) -

11 3 ,4 4

C) -

11 3 , 4 4

D) -

11 3 , 4 4

73)

Solve the problem using your calculator.

74) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). What is the correlation coefficient?

74)

Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

A) 0.246

B) 0.708

C) -0.071

Find the slope and the y-intercept of the line with the given equation.

75) x = 3 A) -3; (-3, 0) B) -3; (0, 0) C) not defined; no y-intercept D) not defined; (3, 0) Is the following correspondence a function?

76)

D) 0.235

75)

76)

A) Yes

B) No

19

Find the domain and range of the function represented in the graph.

77)

A) Domain: [0, 4]; Range: [0, 4] C) Domain: (0, 4); Range: (0, 4) Evaluate as requested.

78) Given that g(x) =

x 4 - x2

A) 1

B) Domain: (0, 4]; Range: (-4, ) D) Domain: [-4, 0]; Range: [0, 4)

, find g(0).

78)

B) does not exist

C) 0

Solve and give interval notation for the solution set. Then graph the solution set.

79) 5x < 25 or x + 2 13

A) (5, )

B) (- , -11]

(5, )

C) (- , 11]

D) (- , 5)

77)

[11, )

Plot the two points given by the ordered pairs.

20

D) 4

79)

80) A(-1, -6), B(-4, 3)

80)

A)

B)

C)

D)

21

Write equations of the horizontal and the vertical lines that pass through the given point.

81) ( , ) A) horizontal: y = ; vertical: x =

B) horizontal: y = x + 0; vertical: x = y + 0

C) horizontal: x = ; vertical; y =

D) horizontal: y = vertical: -

2 x + 0; 3

2 y=x+ 0 3

Evaluate as requested.

82) A graph of a function g is shown below. Find g(-3).

A) 2.8

B) -2.4

82)

C) 2.25

Graph the function.

1 83) f(x) = x3 - 2 3

81)

D) -4.5

83)

22

A)

B)

C)

D)

Solve and give interval notation for the solution set. Then graph the solution set.

84) 3x - 9 < -2.1 or 3x - 9 > 2.1

A) (- , -3.7]

(3.7, )

B) (- , )

C) no solution

D) (- , 2.3)

(3.7, )

23

84)

Is the following correspondence a function?

85) Domain: All students attending the University of Ohio Correspondence: Each student's teachers Range: A set of teachers A) Yes B) No

85)

Find the equation of the circle. Express the equation in standard form 86)

A) (x - 4)2 + (y + 4)2 = 32 C) (x - 4)2 + (y - 4)2 = 32

B) (x + 4)2 + (y - 4)2 = 32 D) (x + 4)2 + (y + 4)2 = 3 2

Evaluate as requested.

87) A graph of a function g is shown below. Find g(

A) -1.5

86)

87)

).

B)

C) -4.0656

Graph the function.

24

D) 2.1

88) f(x) =

88)

x+4

A)

B)

C)

D)

Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.

89) (-2, 8), (4, 10), (8, -2) 89) A) Yes B) No

25

Find the slope and the y-intercept of the line with the given equation.

7 90) f(x) = x 2 A) -

8 7 ; 0, 9 2

B)

; 0,

C)

90)

; 0, -

7 2

D) -

7 ; 0, 2

Write a slope-intercept equation for a line with the given characteristics.

9 91) m = , passes through (3, 2) 4 A) y = -

9 19 x+ 4 4

B) y =

9 19 x4 4

C) y =

Plot the two points given by the ordered pairs.

92) A(-5, 0), B(0, 5)

9 19 x+ 4 4

91) D) y =

4 19 x9 9

92)

A)

B)

26

C)

D)

93) A( , 0), B(-3, 3)

93)

A)

B)

27

C)

D)

Use substitution to determine whether the given ordered pair is a solution of the given equation.

1 5 94) , ; 6x - 4y = -5 3 4 A) Yes

B) No

Solve the equation.

1 9 x+6= 95) 12 4 A) 0

95) B) 45

C) -45

D) 99

Determine the slope, if it exists, of the graph of the given linear equation.

96) f(x) = 7 + 2x A) m = 7

94)

B) m = -2

C) m = -7

28

96) D) m = 2

Graph the equation.

97) y = -x2 + 4

97)

A)

B)

C)

D)

29

Find the coordinates of the points shown on the graph.

98)

98)

A) A: (1, 28), B: (2, -6) C) A: (6, 1), B: (-6, 2)

B) A: (6, 1), B: (2, -6) D) A: (6, 2), B: (1, 2)

Solve the problem using your calculator.

99) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Use a graphing calculator to model the data with a linear function that predicts a student's current GPA as a function of his or her entering GPA. Entering GPA 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7

99)

Current GPA 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0

A) y = 5.81 + 0.497x C) y = 4.91 + 0.0212x

B) y = 3.67 + 0.0313x D) y = 2.51 + 0.329x

Solve the problem.

100) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $2.30 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride, and use this equation to find the cost of a 5-mile taxi ride.

A) $14.45 B) $14.63 C) $15.35 D) $14.33

30

100)

Answer Key Testname: C1

1) D 2) D 3) B 4) D 5) A 6) C 7) B 8) B 9) C 10) B 11) A 12) D 13) B 14) C 15) C 16) B 17) D 18) C 19) B 20) D 21) A 22) C 23) D 24) C 25) C 26) D 27) A 28) B 29) A 30) D 31) A 32) C 33) B 34) A 35) A 36) B 37) B 38) A 39) D 40) D 41) B 42) B 43) A 44) C 45) B 46) B 47) D 48) D 49) B 50) D 31

Answer Key Testname: C1

51) C 52) A 53) D 54) C 55) D 56) C 57) B 58) B 59) C 60) A 61) A 62) A 63) B 64) C 65) D 66) B 67) B 68) A 69) B 70) B 71) C 72) B 73) A 74) B 75) C 76) A 77) A 78) C 79) D 80) C 81) A 82) C 83) D 84) D 85) B 86) D 87) B 88) C 89) A 90) C 91) B 92) B 93) B 94) B 95) B 96) D 97) B 98) C 99) B 100) A 32

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

The graph of the function f is shown below. Match the function g with the correct graph.

1) g(x) = -f(-x) + 3

A)

B)

C)

D)

1

1)

2) g(x) = f(x - 1)

2)

A)

B)

C)

D)

2

3) g(x) = f(-x) + 4

3)

A)

B)

C)

D)

3

4) g(x) = f(x) + 2

4)

A)

B)

C)

D)

4

5) g(x) = 2f(x)

5)

A)

B)

C)

D)

5

6) g(x) = f(x) - 3

6)

A)

B)

C)

D)

6

7) g(x) = -f(-x) - 4

7)

A)

B)

C)

D)

7

8) g(x) = f(x + 3)

8)

A)

B)

C)

D)

8

9) g(x) = -

1 f(x) 2

9)

A)

B)

C)

D)

10) g(x) = - 4f(x + 5)2 + 3

10)

9

A)

B)

C)

D)

10

11) g(x) = -f(x) - 1

11)

A)

B)

C)

D)

Solve the problem.

12) The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 16 inches?

A) 806.24 in2 B) 100.48 in2 C) 50.24 in2 D) 803.84 in2 Determine algebraically whether the function is even, odd, or neither even nor odd.

13) f(x) = -7x4 - 5x - 5 A) Even

B) Odd

C) Neither

11

12)

13)

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.

14)

A) origin

B) y-axis

C) x-axis

14)

D) no symmetry

Using the graph, determine any relative maxima or minima of the function and the intervals on which the function is increasing or decreasing. Round to three decimal places when necessary.

1 1 15) f(x) = x3 + x2 - x + 1 15) 2 2

A) relative maximum: 0.684 at x = 0.549; relative minimum: 2.056 at x = -1.215; increasing (-1.215, 0.549); decreasing ( , -1.215), (0.549, ) B) no relative maxima or minima; increasing ( , -1.215), (0.549, ); decreasing (-1.215, 0.549) C) relative maximum: 2.056 at x = -1.215; relative minima: 0.684 at x = 0.549 and 1 at x = 0; increasing (-1.215, 0.549); decreasing ( , -1.215), (0.549, ) D) relative maximum: 2.056 at x = -1.215; relative minimum: 0.684 at x = 0.549; increasing ( , -1.215), (0.549, ); decreasing (-1.215, 0.549)

12

16) f(x) = x2 - 6x + 7

16)

A) relative minimum: -2 at x = 3; increasing (3, ); decreasing ( , 3) B) relative maximum: 3 at y = -2; increasing ( , 3); decreasing (3, ) C) relative minimum: 3 at y = -2; increasing ( , 3); decreasing (3, ) D) relative maximum: -2 at x = 3; increasing (3, ); decreasing ( , 3) For the pair of functions, find the indicated domain.

1 17) For f(x) = x - 3 and g(x) = x-9 Find the domain of fg.

A) [0, 9) (9, )

17)

B) [3, )

C) (3, 9)

(9, )

D) [3, 9)

(9, )

Write an equation for a function that has a graph with the given characteristics.

18) The shape of y = x is reflected across the y-axis. This graph is then vertically stretched by a factor of 6.7. Finally, the graph is shifted 3 units downward.

A) f(x) = 3 -x - 6.7 B) f(x) = 6.7 -x - 3 C) f(x) = 6.7 -x + 3 D) f(x) = -6.7 x - 3 Determine the domain and range of the function.

19)

18)

19)

A) domain: [-2, 2]; range: [-2, ) C) domain: (-2, ); range: (-2, )

B) domain: [-2, ); range: [-2, 2] D) domain: [-2, ); range: [-2, )

13

Solve the problem.

20) Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of 60 mph with a surface area of 35 ft2 experiences a drag of 357 N (Newtons), how fast must a car with 49 ft2 of surface area travel in order to experience a drag force of 449.82 N? A) 59 mph B) 51 mph C) 54 mph

Find f(x) and g(x) such that h(x) = (f g)(x).

21) h(x) = (5x - 13)2 A) f(x) = (5x)2 , g(x) = -13

Answer the question.

22) How can the graph of f(x) =

D) 56 mph

21)

B) f(x) = 5x - 13, g(x) = x2

C) f(x) = 5x2 , g(x) = x - 13

20)

D) f(x) = x2 , g(x) = 5x - 13

1 1 - 12 be obtained from the graph of y = ? x+3 x

22)

A) Shift it horizontally 3 units to the left. Shift it 12 units up.

1 B) Shrink it horizontally by a factor of . Shift it 12 units down.

2 C) Shift it horizontally 3 units to the left. Shift it 12 units down.

D) Shift it horizontally 3 units to the right. Stretch it vertically by a factor of 12.

Find an equation of variation for the given situation.

23) y varies directly as x, and y = 0.7 when x = 0.1 .

A) y = 0.6 x

B) y = 7x

C) y = 0.8 x

For the function f, construct and simplify the difference quotient

24) f(x) = A)

1 D) y = x 7

f(x + h) - f(x) . h

x 6-x

24)

x (6 - x + h)(6 - x)

C) -

23)

6 (6 - x + h)(6 - x)

B)

hx (6 - x - h)(6 + x)

D)

6 (6 - x - h)(6 - x)

Write an equation for a function that has a graph with the given characteristics.

25) The shape of y = x is shifted 6 units to the left. Then the graph is shifted 8 units upward.

A) f(x) = x + 8 + 6 B) f(x) = 8 x + 6 = + + f(x) x 6 8 C) D) f(x) = x - 6 + 8 For the pair of functions, find the indicated composition.

26) f(x) = x + 5, g(x) = 8x - 9 Find (f g)(x).

A) 8 x - 4 B) 8 x + 5 - 9

25)

26) C) 2 2x - 1

14

D) 2 2x + 1

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x).

27) g(x) = f(x - 1); (8, 20) A) (9, 20) B) (8, 19) C) (8, 21) For the pair of functions, find the indicated sum, difference, product, or quotient.

28) f(x) = 3x + 3, g(x) = 25x - 16 Find (fg)(x).

A) (3x + 3)(25x - 16) B) (3x + 3)(5x - 4) C) ( 3x + 3)( 25x - 16) D) (5x - 4)( 3x + 3) Graph the function.

29) f(x) = x + 4

D) (7, 20)

27)

28)

29)

A)

B)

C)

D)

15

Determine the intervals on which the function is increasing, decreasing, and constant.

30)

A) Increasing on (-3, 1); Decreasing on (-5, -3) and (0, 5); Constant on (1, 2) B) Increasing on (-3, -1); Decreasing on (-5, -2) and (2, 4); Constant on (-1, 2) C) Increasing on (-5, -3) and (2, 5); Decreasing on (-3, 0); Constant on (0, 2) D) Increasing on (-3, 0); Decreasing on (-5, -3) and (2, 5); Constant on (0, 2)

16

30)

Graph the function.

31) g(x) = (x + 5)3

31)

A)

B)

C)

D)

17

Given the graph of the function f(x) = -x 3 + 3x; find a formula for g(x) . f(x) = -x3 + 3x g(x) = 32)

A) g(x) = -x3 + 3x + 3 C) g(x) = -(x + 3)3 + 3(x + 3)

32)

B) g(x) = -(x - 3)3 + 3(x - 3) D) g(x) = -x3 + 3x - 3

Find the requested function value. x-2 , g(x) = 4x + 1 33) f(x) = 2 Find (g f)(-6).

25 A) 2

33)

B) -15

C) -20

Find an equation of variation for the given situation.

34) y varies jointly as x and w and inversely as z, and y = A) y =

39xw z

B) y =

36xw z2

D)

39 when x = 2, w = 3, and z = 30.

5

C) y = 34xwz

D) y =

34) 26z xw

Solve the problem.

35) The time it takes to complete a certain job varies inversely as the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 30 carpenters to do the same job?

A) 19.5 hr B) 8.7 hr C) 30 hr D) 40 hr Find an equation of variation for the given situation.

36) y varies inversely as x and y = 0.75 when x = 24 21 A) y = 18x B) y = x

18 C) y = x

19 D) y = x

Find f(x) and g(x) such that h(x) = (f g)(x).

10 37) h(x) = 10x + 7

C) f(x) =

36)

37)

10x + 7

B) f(x) =

10 , g(x) = 10x + 7 x

10x + 7, g(x) = 10

D) f(x) =

10 , g(x) = 10x + 7 x

A) f(x) = 10, g(x) =

35)

18

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

38) x2 + y2 = 9 38) A) Origin only C) y-axis only

B) x-axis only D) x-axis, y-axis, origin

For the pair of functions, find the indicated composition.

2 3 , g(x) = 39) f(x) = x-7 2x Find (f g)(x).

4x A) 3 - 14x

B)

39)

2x 3 - 14x

C)

4x 3 + 14x

Find an equation of variation for the given situation.

40) y varies inversely as the square of x, and y = 8 when x = 4 126 128 A) y = B) y = 32x2 C) y = 2 x x2

D)

3x - 21 4x

40) D) y = 32x

Answer the question.

3 3 41) How can the graph of f(x) = - x + 4 be obtained from the graph of y = x?

A) Shift it horizontally 4 units to the right. Reflect it across the x-axis.

B) Shift it horizontally 4 units to the left. Reflect it across the y-axis.

C) Shift it horizontally 4 units to the left. Reflect it across the x-axis.

D) Shift it vertically 4 units upward. Reflect it across the x-axis.

Graph the function. Use the graph to find any relative maxima or minima.

42) f(x) = -x2 + 4

A) No relative extrema B) Relative minimum of 4 at x = 0 C) Relative maximum of 4 at x = 0 and relative minimum at x = 3 D) Relative maximum of 4 at x = 0

19

41)

42)

For the pair of functions, find the indicated domain.

1 , g(x) = x + 5 43) f(x) = x+1

43)

Find the domain of g f.

A) ( , ) C) (- , -1) (-1, )

44) f(x) =

B) (- , -6) D) (- , -1]

(-6, ) [-1, )

2x 5 , g(x) = x-3 x+8

44)

Find the domain of f + g.

A) (- , -5) (-5, -2) (-2, ) C) (- , )

B) (- , -8) D) (- , -3)

(-8, 3) (-3, 8)

(3, ) (8, )

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

45) y = 3x2 - 4 45) A) x-axis only C) x-axis, y-axis, origin

B) Origin only D) y-axis only

For the pair of functions, find the indicated domain.

46) f(x) = 5 - x; g(x) = x - 2 Find the domain of fg.

A) ( , 2) (5, ) B) [2, 5]

46) C) (2, 5)

For the pair of functions, find the indicated sum, difference, product, or quotient.

47) f(x) = 2x - 5, g(x) = 5x + 2 Find (fg)(x).

A) 10x2 - 23x - 10 B) 10x2 - 10 C) 10x2 - 21x - 10 Answer the question.

48) How can the graph of f(x) = -

1 1 + 4 be obtained from the graph of y = ? x x

D) ( , 10)

(10, )

47) D) 7x2 - 21x - 3

48)

A) Reflect it across the y-axis. Shift it 4 units down.

B) Reflect it across the y-axis. Shift it 4 units up.

C) Reflect it across the x-axis. Shift it 4 units down.

D) Reflect it across the x-axis. Shift it 4 units up.

A graph of y = f(x) follows. No formula for f is given. Graph the given equation.

1 49) y = - f(x) 2

20

49)

A)

B)

C)

D)

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.

50)

A) y-axis

B) Origin

C) x-axis, origin

50)

D) x-axis

Find an equation of variation for the given situation.

51) y varies jointly as x and the square of z and inversely as w , and y = 30 when x = 3, z = 4, and w = 8.

20xz 2 5xz 2 20xz 5xz A) y = B) y = C) y = D) y = w w w w

21

51)

For the pair of functions, find the indicated domain.

3 52) f(x) = 4x + 6, g(x) = x+8

52)

Find the domain of f + g.

A) (0, ) C) (- , -3) or (-3, )

B) (- , ) D) (- , -8) or (-8, )

For the pair of functions, find the indicated composition.

7 8 53) f(x) = x, g(x) = - x 8 7 Find (f g)(x).

A) x

53)

B) 1

C) 0

D) -x

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.

54)

A) y-axis

B) x-axis

C) x-axis, origin

54)

D) Origin

Solve the problem.

55) The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 45 miles per hour in 40 minutes, how fast must it travel to cover the same distance in 30 minutes?

80 135 4 mph mph mph A) 60 mph B) C) D) 3 4 135 Solve.

56) AAA Technology finds that the total revenue function associated with producing a new type of computer chip is R(x) = 52 - 0.3x2 , and the total cost function is C(x) = 5x + 17, where x represents the number of units of chips produced. Find the total profit function, P(x) .

A) P(x) = -0.3x2 + 5x - 35 B) P(x) = -0.3x2 + 5x + 69

C) P(x) = -0.3x2 - 5x + 35

D) P(x) = 0.3x2 + 5x + 37

Graph the function.

22

55)

56)

57) f(x) = -1 - x, for x 2, 1 - 3x, for x > 2

57)

A)

B)

C)

D)

23

58) f(x) =

x2 + 6x + 8 , for x -2, x+2 -4,

58)

for x = -2

A)

B)

C)

D)

24

Find an equation of variation for the given situation.

59) y varies jointly as x and p and inversely as the square of s, and y = A) y =

32x2 p s2

B) y = 9xps2

C) y =

7 when x = 1, p = 7, and s = 4.

2

12xp2 s

D) y =

8xp s2

Given the graph of the function f(x) = -x 3 + 3x; find a formula for g(x) . f(x) = -x3 + 3x g(x) = 60)

A) g(x) = -(x + 3)3 + 3(x + 3) C) g(x) =

60)

B) g(x) = 3(-x3 + 3x)

1 (-x3 + 3x) 3

D) g(x) = -x3 + 3x + 3

Consider the functions F and G as shown in the graph. Provide an appropriate response.

61) Find the domain of FG.

A) [-1,3]

59)

B) [-3,4]

C) [-1,4]

61)

D) [-3,3]

Answer the question.

3 3 62) How can the graph of h(x) = 0.3 -x be obtained from the graph of y = x?

A) Reflect it across the y-axis. Stretch it vertically by a factor of 3.

B) Reflect it across the y-axis. Shrink it vertically by a factor of 0.3.

C) Reflect it across the x-axis. Shrink it vertically by a factor of 0.3.

D) Reflect it across the x-axis. Stretch it vertically by a factor of 3.

25

62)

For the function f, construct and simplify the difference quotient

63) f(x) = 5x + 9 10(x + 9) A) 5 + h

f(x + h) - f(x) . h

63)

18 C) 5 + h

B) 5

D) 0

For the pair of functions, find the indicated domain.

64) f(x) = x2 - 1, g(x) = 2x + 3

64)

Find the domain of g f.

A) ( , )

B) - , -

C) [1, )

D) (-1, 1)

3 2

-

3 , 2

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.

65)

A) y-axis

B) x-axis

C) x-axis, y-axis

65)

D) no symmetry

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

66) y = (x - 4)(x + 4) 66) A) y-axis only B) x-axis, y-axis, origin C) Origin only D) x-axis only For the pair of functions, find the indicated domain.

67) f(x) = x2 - 64, g(x) = 2x + 3 Find the domain of f g.

A) (-8, 8)

67)

B) [0, )

C) ( , )

D) [8, )

For the pair of functions, find the indicated sum, difference, product, or quotient.

6 1 , g(x) = 68) f(x) = x-6 9+x Find (ff)(x).

6 A) (x - 6)2

B)

36

C)

(x - 6)2

36 (x - 6)(9 + x)

A graph of y = f(x) follows. No formula for f is given. Graph the given equation.

26

68)

D)

36

x - 62

69) y = -2f(x + 1) - 3

69)

A)

B)

C)

D)

Find an equation of variation for the given situation.

70) s varies directly as the square of t, and s = 512 when t = 8 .

1 2 t A) s = 8t2 B) s = C) s = 64t2 64

27

1 D) s = t2 8

70)

Solve.

71) Acme Communication finds that the total revenue function associated with producing a new type of cellular phone is R(x) = 211x - x2 , and the total cost function is C(x) = 5,000 + 9x, where x

71)

represents the number of units of cellular phones produced. Find the total profit function, P(x) .

A) P(x) = -x2 + 202x - 5,000 B) P(x) = x4 - 202x2 + 5,000

C) P(x) = -2x2 + 226x - 6,000

D) P(x) = -x2 + 220x + 5,000

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

72) y = |13x| 72) A) x-axis only B) y-axis only C) Origin only D) x-axis, y-axis, origin Solve the problem.

73) The intensity of light from a light source varies inversely as the square of the distance from the source. Suppose the the intensity is 40 foot-candles at a distance of 10 feet. What will the intensity be at a distance of 11 feet? Round your answer to the tenths place.

A) 33.3 foot-candles B) 32.8 foot-candles C) 32.5 foot-candles D) 33.1 foot-candles Solve.

74) The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 168 seconds are required to make a 3 -by- 7 enlargement, find the time required for a 7 -by- 8 enlargement.

A) 504 sec B) 560 sec C) 392 sec D) 448 sec

Find an equation of variation for the given situation.

75) y varies inversely as x and y = 18 when x = A) y =

2 x

B) y =

1 9

73)

74)

75)

11 x

C) y =

-7 x

D) y =

9 x

Graph the function. Use the graph to find any relative maxima or minima.

76) f(x) = |x + 4| - 4

A) Relative minimum of 3.7 at x = -4 C) Relative minimum of 4.2 at x = -4

B) Relative minimum of -4 at x = -4 D) Relative maximum of 4 at x = -4

28

76)

Answer the question.

77) How can the graph of f(x) = -7x3 + 10 be obtained from the graph of y = x3 ?

A) Stretch it horizontally by a factor of -7. Reflect it across the x-axis. Shift it vertically 10 units downward.

B) Stretch it horizontally by a factor of 10. Reflect it across the x-axis. Shift it vertically 7 units upward.

C) Stretch it vertically by a factor of 7. Reflect it across the y-axis. Shift it vertically 10 units upward.

D) Stretch it vertically by a factor of 7. Reflect it across the x-axis. Shift it vertically 10 units upward.

77)

For the piecewise function, find the specified function value. for x -1, 78) f(x) = 8x, x - 5, for x > -1 f(-2) A) -7

78) B) -16

C) 16

D) -3

Find f(x) and g(x) such that h(x) = (f g)(x).

79) h(x) = -13x2 + 40 A) f(x) = -13x2 + 40, g(x) = C) f(x) =

-13x2, g(x) =

79)

x

40

For the pair of functions, find the indicated composition.

80) f(x) = -2x + 2, g(x) = 6x + 9 Find (g f)(x).

A) -12x - 3 B) -12x + 20

B) f(x) =

-13x, g(x) = x2 + 40

D) f(x) =

x, g(x) = -13x2 + 40

80) C) 12x + 21

D) -12x + 21

For the pair of functions, find the indicated domain.

81) f(x) = x2 - 16, g(x) = 2x + 3 Find the domain of f - g.

A) (-4, 4)

81)

B) [4, )

C) [0, )

For the piecewise function, find the specified function value.

5x + 1, for x < 1, 82) f(x) = 9x, for 9 x 14, 9 - 9x, for x > 14 f(9) A) -72 B) 6 C) 81

29

D) ( , )

82)

D) 127

Use the given graph to find the x-intercept and the zero of the function.

83)

A) (-5, -4); -5

B) (-4, 0); -4

C) (0, 0); 0

Graph the equation.

84) y = 2 x

83)

D) (-5, 0); -5

84)

A)

B)

30

C)

D)

A graph of y = f(x) follows. No formula for f is given. Graph the given equation.

85) y = f(2x)

A)

B)

31

85)

C)

D)

Find an equation of variation for the given situation.

86) y varies inversely as x and y = 4.75 when x = 0.44 2.49 10.8 A) y = B) y = x x

C) y = 10.8x

2.09 D) y = x

Determine algebraically whether the function is even, odd, or neither even nor odd.

87) f(x) = -9 A) Even B) Odd C) Neither Find the point that is symmetric to the given point with respect to the requested axis.

88) Symmetric with respect to the y-axis (1.5, -1.75) A) (-1.5, 1.75) B) (1.5, -1.5) C) (-1.75, 1.5)

86)

87)

88) D) (-1.5, -1.75)

Graph the function.

89) f(x) = (x + 1)3 - 1

89)

32

A)

B)

C)

D)

Solve the problem.

90) The distance it takes to stop a car varies directly as as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 51 miles per hour?

A) 182.07 ft B) 194.37 ft C) 156.06 ft D) 182.41 ft Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.

91)

A) x-axis, y-axis, origin C) x-axis, origin

B) x-axis D) Origin

33

90)

91)

Determine whether the given function is even, odd, or neither even nor odd.

92)

A) Odd

B) Even

92)

C) Neither

Solve the problem.

93) The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 24 feet tall having a measurement of 5 feet around the trunk?

A) 57 ft3 B) 48 ft3 C) 40 ft3 D) 52 ft3 Find f(x) and g(x) such that h(x) = (f g)(x).

94) h(x) = 5x + 4 A) f(x) = x, g(x) = 5x + 4 C) f(x) = - x , g(x) = 5x + 4 Answer the question.

95) How can the graph of f(x) =

B) f(x) = -x , g(x) = 5x - 4 D) f(x) = x , g(x) = 5x + 4

1 (x + 10)2 - 11 be obtained from the graph of y = x2 ?

2

A) Shift it horizontally 10 units to the left. Shrink it vertically by a factor of 2. Shift it 11 units down.

1 B) Shift it horizontally 10 units to the left. Shrink it vertically by a factor of . Shift it 11 units 2 down.

C) Shift it horizontally 10 units to the right. Shrink it vertically by a factor of

1 . Shift it 11 units 2

down.

D) Shift it horizontally 10 units to the right. Stretch it vertically by a factor of 2. Shift it 11 units up.

34

93)

94)

95)

Consider the functions F and G as shown in the graph. Provide an appropriate response.

96) Find the domain of F/G.

A) [-3,-1)

(-1,4)

B) [-1,2) (2,3]

C) [-1,3]

96)

D) [-3,4]

Find an equation of variation for the given situation.

1 .

97) p varies directly as q, and p = 1 when q = 12 A) p = 11 q

97) C) p =

B) p = 12q

1 q 12

D) p = 13q

Answer the question.

98) How can the graph of f(x) = - x + 8 be obtained from the graph of y = x?

A) Shift it horizontally -8 units to the left. Reflect it across the x-axis.

B) Shift it horizontally 8 units to the right. Reflect it across the x-axis.

C) Shift it horizontally 8 units to the left. Reflect it across the x-axis.

D) Shift it horizontally 8 units to the left. Reflect it across the y-axis.

Determine algebraically whether the function is even, odd, or neither even nor odd.

3 99) f(x) = 20 x A) Even B) Odd C) Neither

35

98)

99)

Determine whether the given function is even, odd, or neither even nor odd.

100)

A) Neither

B) Odd

100)

C) Even

Consider the functions F and G as shown in the graph. Provide an appropriate response.

101) Graph F + G.

A)

B)

36

101)

C)

D)

Find an equation of variation for the given situation.

102) y varies directly as z, and y = 33 when z = 165 .

1 A) y = z B) y = -2z 5

1 C) y = - z 2

37

102) D) y = 5 z

Graph the function.

103) g(x) = -4 x

103)

A)

B)

C)

D)

Determine algebraically whether the function is even, odd, or neither even nor odd.

104) f(x) = x2 + 2 A) Even

B) Odd

C) Neither

38

104)

Determine whether the given function is even, odd, or neither even nor odd.

105)

A) Even

B) Neither

105)

C) Odd

Use the given graph to find the x-intercept and the zero of the function.

106)

A) (-5, 0); -5

B) (0, 0); 0

C) (-2, 0); -2

Graph the function.

1 107) f(x) = - 2 x

106)

D) (-5, -2); -5

107)

39

A)

B)

C)

D)

Graph the function. Use the graph to find any relative maxima or minima.

108) f(x) = x2 + 6x + 8

A) Relative maximum of -1.2 at x = -3.1 C) Relative maximum of -1 at x = -3

B) Relative minimum of -1.2 at x = -3.1 D) Relative minimum of -1 at x = -3

Write an equation for a function that has a graph with the given characteristics.

109) The shape of y = x2 , but upside-down and vertically stretched by a factor of 7.

A) f(x) = 7(x - 7)x2

108)

B) f(x) = (x - 7)2

C) f(x) = -7x2

40

D) f(x) = 7x2

109)

Determine whether the given function is even, odd, or neither even nor odd.

110)

A) Even

B) Odd

110)

C) Neither

Graph the function.

1 111) f(x) = x-5

111)

A)

B)

41

C)

D)

42

Answer Key Testname: C2

1) D 2) C 3) B 4) A 5) A 6) B 7) A 8) D 9) C 10) A 11) C 12) D 13) C 14) A 15) D 16) A 17) D 18) B 19) D 20) C 21) D 22) C 23) B 24) D 25) C 26) C 27) A 28) C 29) C 30) D 31) D 32) B 33) B 34) A 35) B 36) C 37) B 38) D 39) A 40) C 41) C 42) D 43) C 44) B 45) D 46) B 47) C 48) D 49) C 50) D 43

Answer Key Testname: C2

51) D 52) D 53) D 54) A 55) A 56) C 57) B 58) A 59) D 60) B 61) A 62) B 63) B 64) A 65) B 66) A 67) C 68) B 69) C 70) A 71) A 72) B 73) D 74) D 75) A 76) B 77) D 78) B 79) D 80) D 81) D 82) C 83) D 84) D 85) C 86) D 87) A 88) D 89) C 90) A 91) A 92) B 93) B 94) D 95) B 96) B 97) B 98) C 99) B 100) B 44

Answer Key Testname: C2

101) A 102) A 103) B 104) A 105) B 106) A 107) A 108) D 109) C 110) C 111) D

45

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Match the equation to the correct graph.

1 1) y = - (x + 5)2 - 3 2

1)

A)

B)

C)

D)

1

2) y = 2(x + 2)2 - 3 A)

B)

C)

2)

D)

3) y = 2(x - 1)2 - 6 A)

B)

C)

D)

2

3)

4) y = -(x + 3)2 + 2 A)

B)

C)

D)

5) y = (x - 6)2 A)

B)

C)

D)

3

4)

5)

6) y = -(x + 5)2 + 7 A)

B)

C)

D)

7) y = (x + 6)2 A)

B)

C)

D)

4

6)

7)

8) y = x2 - 6 A)

B)

C)

D)

9) y =

1 (x - 4)2 + 1 2

8)

9)

A)

B)

C)

D)

5

Use the quadratic formula to find the exact solutions.

10) x2 + 11x = -28 A) -4, -7

B) -7, 4

C) 4, 7

D) -4, 7

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.

11) f(x) = x2 - 3x + 8 3 3 A) Increasing on - , ; decreasing on , 2 2

B) Increasing on C) Increasing on

3 , 2

3 , 2

D) Increasing on - , -

Solve.

; decreasing on - , ; decreasing on - ,

10)

11)

3 2

3 2

3 3 ; decreasing on - , 2 2

12) m 2/3 + 2m1/3 - 24 = 0 A) 64, -216

B) 64

C) -64, 216

D) 4,096, 46,656

Solve the inequality and graph the solution set.

13) x < 3

12)

13)

A)

B)

C)

D)

Find the range of the given function.

14) f(x) = x2 - 3x + 10 31 , A) 4

67 , B) 4

31 C) - , 4

6

67 D) - , 4

14)

Determine whether there is a maximum or minimum value for the given function, and find that value.

1 2 13 15) f(x) = x - 4x 2 2 A) Minimum:

35 2

B) Maximum: - 32

29 2

D) Maximum: 0

C) Minimum: -

Solve.

16) f(x) = -x2 - 10x - 30 A) Maximum: 5

B) Maximum: -5

C) Minimum: 0

D) Minimum: 5

17) x1/3 = -5 A) -243

B) -15

C) -125

D) No solution

B) 0

11 C) 2

18)

10 + x +

11 - 5x = -1

A) 1

A) (-5, 0), (-1, 0); -5, -1 C) (5, 0), (1, 0); 5, 1

16)

17)

18) D) No solution

19) John owns a hotdog stand. His profit is represented by P(x) = -x 2 + 12x + 43, with P(x) being profit and x the number of hotdogs sold. What is the most he can earn?

A) $36 B) $91 C) $79 D) $73 Use the given graph to find the x-intercepts and zeros of the function.

20)

15)

19)

20)

B) (-5, 0), (1, 0); -5, 1 D) (-1, 0), (5, 0); -1, 5

Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.

21) 3x2 = 3x - 2 21)

A) Two different real-number solutions B) One real solution C) Two different imaginary-number solutions

7

Solve.

22) x = 3 A) -3, 3

B) 3

23) 15x 3 - 20x2 - 6x + 8 = 0 5 5 3 , , A) 2 2 4

C) 9

22)

D) -3

23) B) -

2 2 4 , , 5 5 3

C) -

2 , 5

2 4 ,5 3

D) -

2 , 5

2 4 , 5 3

Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.

24) x2 + 8x + 16 = 0 24)

A) Two different imaginary-number solutions B) Two different real-number solutions C) One real solution

Solve by completing the square to obtain exact solutions.

25) x2 + 2x - 15 = 0 A) -3,

25) C) -i 15, i 15

D) -10, -5

5 B) x = 2

5 C) x = 2

5 D) x = 4

B) - 3, - 1

9 C) - , 1 7

5 11 D) - , 3 3

C) -5 ± 3 5

-5 ± 3 5 D) 2

B) 3, -5

Find the axis of symmetry of the given function.

26) f(x) = -2x2 + 5x + 7 5 A) x = 4

Solve.

27) (3p + 7)2 = -2(3p + 7) + 8 5 11 A) , 3 3

Solve by completing the square to obtain exact solutions.

28) x2 + 5x - 5 = 0 5+3 5 A) 2

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.

1 29) f(x) = - x2 + 5x - 3 3 15 15 ; decreasing on , 11 11

B) Increasing on - ,

15 15 ; decreasing on , 4 4

C) Increasing on - ,

15 15 ; decreasing on , 13 13

D) Increasing on - ,

15 15 ; decreasing on , 2 2

27)

28)

-5 - 3 5 B) 2

A) Increasing on - ,

26)

8

29)

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. i 30) 4+i A)

Solve.

1 4 i + 17 17

31) 16 - x - 9 = 7 A) -32, 14

B)

4 i 17

C)

B) -18, 0

1 4 i 17 17

C) -14, 32

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

32) (8 + 3i)2 A) 73 - 48i

33) (8 - 8i)(2 + 5i) A) 56 + 24i

B) 55 - 48i

C) 55 + 48i

30) D)

1 17

D) 0, 18

D) 73 + 48i

31)

32)

33)

B) -40i2 + 24i - 16

C) 56 - 24i

D) -24 - 56i

Graph.

34) f(x) = -2x2 - 2x - 1

34)

A)

B)

9

C)

D)

Find the axis of symmetry of the given function.

35) f(x) = x2 - 20x + 106 A) x = 10

Solve.

B) x = 6

C) x = -10

D) x = 0

C) - 4, - 5

2 D) - , 3

36) (2m + 6)2 + 6(2m + 6) + 8 = 0 A) - 2, - 1

B) 4, 5

Solve the inequality and graph the solution set.

37) |3x + 5| > -6

35)

36)

37)

A) ( , )

B)

C)

D)

Solve and write interval notation for the solution set.

38) |x - 6| > 0.5 A) (5.5, 6.5) C) (- , 5.5) (6.5, )

B) (- , 5.5] D) (- , )

10

[6.5, )

38)

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

7 + 8i 39) 2 - 3i

39)

A)

-24 + 2 7 16 + 3 7 i + 13 13

B)

-24 + 2 7 13

C)

16 + 3 7 i 13

D)

-24 + 2 7 16 + 3 7 i 13 13

Express the number in terms of i.

40) -64 A) -8i

40) B) 8i

C)

8i

D) - 8 i

Solve.

41)

2x + 15 = x + 2 A) -1 + 2 3

41) B) -1 - 2 3

C) -1 ± 2 3

D) 0

Use the quadratic formula to find the exact solutions.

42) 4t2 - 7t = 1 A)

7±

8

65

B) -

42)

7 65 i ± 8 8

C)

-7 ± 65 8

D)

7 65 i ± 8 8

Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.

43) x2 + 7x - 8 = 0 43)

A) One real solution B) Two different imaginary-number solutions C) Two different real-number solutions

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

44) (3 + 7i)(3 + 4i) A) 37 + 9i B) -19 - 33i C) 28i2 + 33i + 9 Find the axis of symmetry of the given function.

45) f(x) = -2x2 + 5x + 7 5 A) x = 8

Solve.

46) x + 2 - 4 = A)

Express the number in terms of i.

47) -28 A) 7 2 i

44) D) -19 + 33i

5 B) x = 8

5 C) x = 2

5 D) x = 4

B) No solution

C) -5, 9

D) -9,

45)

46)

47) B) 2 7 i

C) -2 7 i

11

D) 14i

Solve and write interval notation for the solution set.

48) |7x + 7| > -6

48)

A) (- , ) C) - ,

B) No solution ,

D) - , -

1 7

-

13 , 7

Use the given graph to find the x-intercepts and zeros of the function.

49)

A) (4, 0), (2, 0); 4, 2 C) (-4, 0), (-2, 0); -4, -2

49)

B) (-4, 0), (2, 0); -4, 2 D) (-2, 0), (4, 0); -2, 4

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.

50) f(x) = -x2 + 2x + 8

50)

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

51) 9i(2 - 8i)

51)

A) Increasing on (1, ); decreasing on (- , 1) B) Increasing on (- 1, ); decreasing on (- , - 1) C) Increasing on (- , 1); decreasing on (1, ) D) Increasing on (- , - 1); decreasing on (- 1, )

A) 72 + 18i

B) 72 - 18i

C) -72 + 18i

D) 18i - 72i2

Simplify. Write your answer in the form a + bi, where a and b are real numbers.

52) (13 + 8i) - (2 + 4i) A) 15 + 12i B) 11 + 4i C) -15 - 12i

D) 15 - 4i

Express the number in terms of i.

53) - -5 A) - 5 i

D) -5i

52)

53) B)

5i

C)

5i

Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.

54) x2 + 5x + 8 = 0 54)

A) Two different real-number solutions B) One real solution C) Two different imaginary-number solutions

12

Find the vertex of the parabola.

55) f(x) = x2 - 18x + 82 A) (1, 9)

B) (0, 9)

C) (1, 0)

D) (9, 1)

55)

Use the graph to find the vertex, the axis of symmetry, and the maximum or minimum value of the function.

56) 56)

A) (-2, 4); x = -2; maximum: 4 C) ( , ); x = ; maximum: -2 Solve.

57)

B) ( , -2); x = ; maximum: -2 D) ( , -4); x = -2; maximum:

1 1 1 + + =9 t 5t 7t

A)

47 45

57) B)

47 63

C)

47 315

Solve graphically. Round solutions to three decimal places, where appropriate.

58) 5x2 - 32x + 11 = 0 A) 0.365, 6.035

D)

43 315

B) -7.169, -1.498

C) -8.669, -2.998

D) 0.865, 6.535

B) i

C) -1

D) -i

58)

Simplify.

59) i17 A) 1

Graph.

13

59)

60) f(x) =

Solve.

1 2 x - 2x + 4 2

60)

A)

B)

C)

D)

61) 4x2 + 28 = 0 A) ±7i

61) C) ± 7 i

B) 14

Solve and write interval notation for the solution set.

62) |x| 6.3 A) (- , -6.3) (6.3, ) C) (- , -6) (6, )

B) [-6.3, 6.3] D) (- , -6.3] [6.3, )

14

D) 8

62)

Find the zeros of the function. Give exact answers.

63) f(x) = 2x2 + 11x + 3 -11 ± 97 A) 2

63)

-11 ± 115 B) 2

C)

11 ±

4

115

-11 ± 97 D) 4

Simplify.

64) (-i)38 A) -i

B) 1

C) i

64)

D) -1

Determine whether there is a maximum or minimum value for the given function, and find that value.

65) f(x) = x2 + 6x + 0 A) Maximum: -9

B) Minimum: 0

C) Maximum: 9

D) Minimum: -9

Solve the problem.

66) A grasshopper is perched on a reed 5 inches above the ground. It hops off the reed and lands on the ground about 6.7 inches away. During its hop, its height is given by the equation h = -0.3x2 + 1.25x + 5, where x is the distance in inches from the base of the reed, and h is in inches.

65)

66)

How far was the grasshopper from the base of the reed when it was 3.75 inches above the ground?

Round to the nearest tenth.

A) 5.0 in.

B) 1.7 in.

C) 6.7 in.

D) 0.8 in.

Solve.

67)

1 1 1 = + , for t A m t

A) t =

mA m-A

67) B) t = 1 -

mA m-A

C) t =

Use the quadratic formula to find the exact solutions.

68) x2 + 6x = 16 A) -2, 8

69) x2 + 35 = 5x 5 115 i A) ± 2 2 Solve.

70) 16t3 + 3t = -16t2 A) 0,

,

m-A mA

D) t = 1 +

mA m-A

B) -8, 2

C) 8, 2

D) -8, -2

B) 0, 5

5 5 C) ± i 2 2

D) -5, 5

1 3 B) - , 4 4

3 C) - , 8

1 3 D) 0, - , 4 4

69)

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

1 - 4i 71) (1 + 4i)2 A) -

47 76 i + 289 289

68)

B) -

47 52 i + 289 289

C)

15

1 12 i + 289 289

70)

71) D) -

47 52 i 289 289

Solve and write interval notation for the solution set.

72) 9x + 7 < 6

13 B) - , 9

A) (- , 9) C) -

13 1 ,9 9

D) - , -

State whether the function is linear or quadratic.

73) f(x) = - 5x2 A) Linear

Express the number in terms of i.

74) - -28 A) -14i

13 9

73)

B) Quadratic

74) B) 2 7 i

Solve by completing the square to obtain exact solutions.

75) 12x 2 + 28x + 15 = 0 6 2 A) , 5 3

72)

1 - , 9

5 3 B) , 6 2

C) -7 2 i

D) -2 7 i

6 3 C) - , 5 2

5 3 D) - , 6 2

Solve the problem.

76) A stuntman jumps from a rooftop 335 ft off the ground. How long will it take him, falling freely, to reach the ground? (Use the formula s = 16t2 .)

A) About 4.6 sec

B) About 20.9 sec

C) About 73.2 sec

D) About 10.5 sec

C) x = -2

2 D) x = 3

Find the axis of symmetry of the given function.

77) f(x) = -3x2 + 4x 1 A) x = 3

B) x = - 1

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

78) (8 + 7i)(3 - 3i) A) -21i2 - 3i + 24 B) 45 + 3i C) 45 - 3i

16

75)

76)

77)

78) D) 3 + 45i

Use the given graph to find the x-intercepts and zeros of the function.

79)

A) (-3, 0), (3, 0); -3, 3 C) (-3, 0); -3

79)

B) (3, 0); 3 D) (0, 0); 0

Simplify. Write your answer in the form a + bi, where a and b are real numbers.

80) (8 + -9) + (4 + -49) A) 12 + 9i B) 12 + 10i C) 12 + 4i

D) 12 + 58i

80)

Solve.

81)

6q + 7 = 7

A) 7

B)

28 3

C) 49

D)

81)

49 6

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.

82) f(x) = x2 - 4x + 3

82)

Determine whether there is a maximum or minimum value for the given function, and find that value.

83) f(x) = x2 - 3x + 16

83)

A) Increasing on (- 2, ); decreasing on (- , -2) B) Increasing on (2, ); decreasing on (- , 2) C) Increasing on (- , - 2); decreasing on (-2, ) D) Increasing on (- , 2); decreasing on (2, )

91 A) Minimum: 4

91 B) Maximum: 4

Solve and write interval notation for the solution set.

84) x > 5 A) (-5, 5) B) (-5, )

C) Minimum:

143 D) Minimum: 8

C) (- , -5)

D) (5, )

(5, )

Find the vertex of the parabola.

1 3 85) h(x) = x2 - 4x 2 2 A) 4,

17 2

84)

85) B) 2, -

15 2

C) -4,

17

45 2

D) 4, -

19 2

Express the number in terms of i.

86) -7 A) -7i

86) B)

7i

C) - 7 i

D)

7i

Solve.

8q - 7 = 7 49 A) 8

87)

87)

21 B) 4

C) 49

D) 7

Use the given graph to find the x-intercepts and zeros of the function.

88)

A) (3, 0), (8, 0); 3, 8 C) (-8, 0), (3, 0); -8, 3

88)

B) (-3, 0), (8, 0); -3, 8 D) (-3, 0), (-8, 0); -3, -8

Solve.

89)

5

2x + 7 = 3

A) 243

B) 118

C)

Solve the inequality and graph the solution set.

90) x > 2

243 2

89) D) 236

90)

A)

B)

C)

D)

18

Solve.

91) 4x3 + x2 - 64x - 16 = 0 1 A) 4, 4

1 B) -16, 16, 4

C) -4, 4 , -4

Simplify. Write your answer in the form a + bi, where a and b are real numbers.

92) (-5 - 6i) - (7 - i) A) -12 + 5i B) -12 - 5i C) 12 + 5i Solve.

93) 7x = 5 5 A) 7

5 5 B) - , 7 7

5 C) 7

Simplify. Write your answer in the form a + bi, where a and b are real numbers.

94) (-9 + 13i) - (6 - 4i) A) 3 - 17i B) -15 - 17i C) -3 - 17i Use the quadratic formula to find the exact solutions.

95) 3x2 - 14x - 5 = 0 A) -3, 5

1 B) - , 3 5

1 C) - , 5 3

1 D) -4, 4, 4

D) -12 - 6i

7 7 D) - , 5 5

D) -15 + 17i

1 D) - , -3 5

Use the given graph to find the x-intercepts and zeros of the function.

96)

A) (-1, 0), (4, 0); -1, 4 C) (-4, 0), (1, 0); -4, 1

91)

92)

93)

94)

95)

96)

B) (-4, 0), (-1, 0); -4, -1 D) (1, 0), (4, 0); 1, 4

Simplify. Write your answer in the form a + bi, where a and b are real numbers.

97) (-6 - 7i) + (12 + 5i) A) 12 - 2i B) 6 + 2i C) 6 - 2i State whether the function is linear or quadratic.

98) f(x) = 6 + 6x2 A) Linear

B) Quadratic

19

D) 12 + 2i

97)

98)

Solve the problem.

99) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6 ft more than its distance from the wall.

A) 18 ft B) 30 ft C) 36 ft D) 24 ft Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

1 + 5i 100) (1 - 5i)2 A)

1 15 i + 676 676

B) -

37 55 i 338 338

C) -

37 35 i + 338 169

100) D) -

37 61 i 338 338

Solve the problem.

101) A rectangular garden has dimensions of 13 feet by 10 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 420 square feet?

A) 8 ft B) 8.5 ft C) 6 ft D) 7 ft Find the range of the given function.

1 19 102) f(x) = x2 - 2x 2 2 A) -

7 , 2

Solve.

103) x + 5 - 4 = 12 A) -3, 11

101)

102) 23 , 2

C) - , 0

D) - , - 11

B) -11, 11

C) -21, 11

D) 13, 11

B) -

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.

104) (-8 + 3i)2 A) 73 + 48i

99)

B) 55 - 48i

C) 73 - 48i

D) 55 + 48i

103)

104)

Use the graph to find the vertex, the axis of symmetry, and the maximum or minimum value of the function.

105) 105)

A) ( , -3); x = ; minimum: -3 C) (-3, -3); x = -3; minimum: 3

B) (-3, 3); x = -3; minimum: 3 D) (-3, 3); x = 3; minimum: -3

20

Solve.

106)

2 6 4 = y + 4 y - 4 y2 - 16

106)

A) 36

B) -9

C)

D)

24

Use a graphing calculator to find the zeros of the function. Round to three decimal places.

107) f(x) = 1.29x2 - 14.56x - 1.79

107)

Use the given graph to find the x-intercepts and zeros of the function.

108)

108)

A) -11.408, 0.122

B) 0.124, 11.163

C) -0.243, 22.817

A) (-5, 0), (-2, 0); -5, -2 C) (-2, 0), (5, 0); -2, 5

D) -0.122, 11.408

B) (-5, 0), (2, 0); -5, 2 D) (5, 0), (2, 0); 5, 2

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.

109) f(x) = -x2 + 3x - 9 3 A) Increasing on , 2

3 ; decreasing on - , 2

B) Increasing on - ,

3 3 ; decreasing on , 4 4

C) Increasing on - ,

3 3 ; decreasing on , 2 2

D) Increasing on - ,

3 3 ; decreasing on , 8 8

21

109)

Answer Key Testname: C3

1) B 2) A 3) C 4) D 5) C 6) D 7) D 8) A 9) B 10) A 11) C 12) A 13) B 14) A 15) C 16) B 17) C 18) D 19) C 20) B 21) C 22) A 23) D 24) C 25) B 26) D 27) D 28) D 29) D 30) A 31) D 32) C 33) A 34) B 35) A 36) C 37) A 38) C 39) A 40) B 41) A 42) A 43) C 44) D 45) D 46) D 47) B 48) A 49) D 50) C 22

Answer Key Testname: C3

51) A 52) B 53) A 54) C 55) D 56) A 57) C 58) A 59) B 60) C 61) C 62) B 63) D 64) D 65) D 66) A 67) A 68) B 69) A 70) D 71) B 72) C 73) B 74) D 75) D 76) A 77) D 78) C 79) A 80) B 81) A 82) B 83) C 84) C 85) D 86) B 87) D 88) D 89) B 90) D 91) D 92) B 93) B 94) D 95) C 96) C 97) C 98) B 99) B 100) B 23

Answer Key Testname: C3

101) C 102) B 103) C 104) B 105) A 106) B 107) D 108) C 109) C

24

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Match the equation with the appropriate graph.

18x 1) f(x) = x2 - 9

1)

A)

B)

C)

D)

1

Use the leading-term test to match the function with the correct graph.

2) f(x) = 4x + 2x2 - 7x3 A)

B)

C)

D)

2

2)

Match the equation with the appropriate graph.

3x2 3) f(x) = x2 - 9

3)

A)

B)

C)

D)

3

Use the leading-term test to match the function with the correct graph.

4) f(x) = x4 - 3x3 + 13x2 + x - 30 A)

B)

C)

D)

4

4)

Match the equation with the appropriate graph.

6 5) f(x) = 2 x -1

5)

A)

B)

C)

D)

5

Use the leading-term test to match the function with the correct graph.

1 6) f(x) = - x3 - 6x2 + 8x + 45 5 A)

B)

C)

D)

6

6)

7) f(x) =

1 2 x -4 3

7)

A)

B)

C)

D)

7

8) f(x) = x5 - x4 + x3 + 3 A)

B)

C)

D)

8

8)

9) f(x) = 3x2 + 6 A)

B)

C)

D)

9

9)

10) f(x) = -0.7x6 - x5 + 6x4 - 5x3 - 5x2 + x - 3 A)

B)

C)

D)

10

10)

11) f(x) = -0.3x7 + 0.16x6 - 0.18x5 + x4 + x3 - 8x - 5 A)

B)

C)

D)

11

11)

Match the equation with the appropriate graph.

6 12) f(x) = 2 x +1

12)

A)

B)

C)

D)

12

13) f(x) =

x3 x2 + 4

13)

A)

B)

C)

D)

13

14) f(x) =

x3 x2 - 9

14)

A)

B)

C)

D)

Solve the problem.

15) If there are x teams in a sports league and all the teams play each other twice, a total of N(x) games are played, where N(x) = x2 - x. A soccer league has 8 teams, each of which plays the others twice.

15)

If the league pays $49 per game for the field and officials, how much will it cost to play the entire schedule?

A) $3,136 B) $3,528 C) $2,744 D) $2,842

Using synthetic division, determine whether the numbers are zeros of the polynomial.

16) i, -i, 6; f(x) = x3 - 6x2 + x - 6 A) No; no; no

B) Yes; yes; no

C) No; no; yes

D) Yes; yes; yes

16)

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts.

14

17) f(x) =

x+3

17)

x-4 3

A) x-intercept: (3, 0) , y-intercept: 0,

3 ; 64

B) x-intercept: (0, 0) , y-intercept: (0, 0) ;

C) x-intercept: (3, 0) , y-intercept: 0, -

3 ; 64

15

D) x-intercept: (-3, 0) , y-intercept: 0, -

3 ; 64

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and factor f(x) into linear factors.

18) f(x) = x3 - 64 18)

A) 4, -2 + 2 3 , -2 - 2 3 ; f(x) = (x - 4) (x + 2 - 2 3 )(x + 2 + 2 3 ) B) 4, 2 + 2 3 i, 2 - 2 3 i ; f(x) = (x - 4) (x - 2 - 2 3 i)(x - 2 + 2 3 i) C) 4, -2 + 2 3 i, -2 - 2 3 i ; f(x) = (x - 4) (x + 2 - 2 3 i)(x + 2 + 2 3 i) D) 4, -2 + 3 i, -2 - 3 i ; f(x) = (x - 4) (x + 2 - 3 i)(x + 2 + 3 i) Solve.

19) The function h(t) = -16t2 + 192t - 560 gives the height h, in feet, of a flare fired from the bottom of a gorge 560 feet deep with an initial velocity of 192 ft/sec. The flare fired is visible only when it is above the rim (h = 0). During what interval can the flare be seen?

A) (10, 12) B) (15, 17) C) (5, 7) D) (0, 5)

Provide the requested response.

20) Suppose that a polynomial function of degree 4 with rational coefficients has -2 + 2i, 2 zeros. Find the other zeros.

A) -2 - 2i , 2 + 6 B) -2 - 2i , -2 - 6 C) 2 - 2i , -2 - 6 D) 2 - 2i , 2 + 6 Given that the polynomial function has the given zero, find the other zeros.

3i 21) f(x) = x4 - 9; A) C) -

3i 3 i, 3, -3

B) - 3 i, D) 3

20)

21) 3,-

Find the zeros of the polynomial function and state the multiplicity of each.

22) f(x) = x4 - 19x2 + 48

3

A) 16, multiplicity 1; 3, multiplicity 1 B) -4, multiplicity 1; 4, multiplicity 1; - 3, multiplicity 1; 3, multiplicity 1 C) 16, multiplicity 1; - 3, multiplicity 1; 3, multiplicity 1 D) -4, multiplicity 1; 4, multiplicity 1; - 3, multiplicity 1

16

6 as

19)

22)

Find the correct end behavior diagram for the given polynomial function.

23) f(x) = 1.95x4 + 5x2 + x - 3 A)

B)

C)

Give all possible rational zeros for the polynomial.

24) f(x) = 2x3 - 5x2 + 7x - 11 1 11 A) ±1, ±11, ± , ± 2 2

11 B) ±1, ±2, ±11, ± 2

C) ±1, ±2, ±11

D) ±1, ±

Factor the polynomial f(x). Then solve the equation f(x) = 0.

25) f(x) = x3 - 3x2 - 18x + 40 A) (x - 2)(x + 4)(x - 5) ; 2, -4, 5 C) (x + 2)(x - 4)(x + 5) ; -2, 4, -5

D)

24)

1 2 , ±2, ± 11 11

B) (x - 2)(x + 4)(x - 6) ; 2, -4, 6 D) (x - 2)(x + 4)(x - 5) ; -2, 4, -5

17

23)

25)

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. x+4 26) f(x) = 26) 2 2x - 7x - 4

A) No x-intercepts , y-intercept: (0, -1) ;

B) x-intercept: (-4, 0) , y-intercept: (0, 1) ;

C) x-intercept: (-4, 0) , y-intercept: (0, -1) ;

D) No x-intercepts , y-intercept: (0, -1) ;

Find only the rational zeros.

27) f(x) = x4 + 4x3 + 4x2 - 8x - 64 A) -4, 2 C) 4, -1

B) -4, -3 D) No rational zeros

Provide the requested response.

28) Suppose that a polynomial function of degree 5 with rational coefficients has -4, 3, -4, 5 - i as zeros. Find the other zero(s).

A) 5 + i B) -5 - i C) 4, -3, 4, 5 + i D) -5 + i

18

27)

28)

Graph the polynomial function. Use synthetic division and the remainder theorem to find the zeros.

29) f(x) = x4 + 2x3 - 3x2 - 4x + 4

A) 1 (multiplicity 2), -2, 2;

B) -1, 1, -2 (multiplicity 2);

C) -1 (multiplicity 2), -2 (multiplicity 2);

D) 1 (multiplicity 2), -2 (multiplicity 2);

29)

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial.

30) f(x) = 16x4 - 8 + 0.11x2 - 8x 30)

A) Quartic; 16x4 ; 16; 4 C) Quadratic; x4 ; 16; 4

B) Constant; -8; -8; 0 D) Quadratic; 0.11x2 ; 0.11; 2

19

Find the requested polynomial.

31) Find a polynomial function of degree 3 with -5 , 0 ,

Solve.

1 as zeros.

2

31)

A) f(x) = x3 +

11 2 5 x - x 2 2

B) f(x) = x3 -

9 2 5 x - x 2 2

C) f(x) = x3 +

9 2 5 x - x 2 2

D) f(x) = x3 -

9 2 5 x + x 2 2

32) x2 + 8x + 16 0 A) {4} C) {-4}

B) [4, ) D) (- , -4] [-4, )

32)

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

33) -6i, 8 33) A) f(x) = x4 + 28x2 - 288 B) f(x) = x4 + 56x2 + 288 C) f(x) = x4 - 56x2 + 288

D) f(x) = x4 - 28x2 - 288

A polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x), and express P(x) in the form d(x)· Q(x) + R(x).

34) P(x) = x3 - 3 34) d(x) = x + 3

A) (x + 3)(x2 - 3x + 9) C) (x + 3)(x2 + 3x + 9) + 0

B) (x + 3)(x2 - 3x + 9) - 30 D) (x + 3)(x2 + 3x + 9) + 6

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts.

1 35) f(x) = 35) x-5 2

20

A) x-intercept:

1 , 0 , no y-intercepts ; 5

C) No x-intercepts, y-intercept: 0,

B) No x-intercepts, y-intercept: 0,

1 ; 25

D) No x-intercepts, y-intercept: 0, -

Find the vertical asymptote(s) of the graph of the given function. x+4 36) g(x) = x-5 A) x = 5

B) x = -4

1 2 , ±2, ± , ±11, ±22 A) ±1, ± 11 11

D) y = 5

1 2 1 ,± B) ±1, ± , ±11, ± 2 11 22

1 2

D) ±1, ±

Graph the function.

21

1 ; 25

36)

C) x = -5

Give all possible rational zeros for the polynomial.

37) f(x) = 22x7 + 88x3 + 2x - 11

C) ±1, ±11, ±

1 ; 25

1 11 1 1 , ±11, ± ,± ,± 2 2 11 22

37)

38) f(x) = 4x3 - 4x2 - 12x + 12

38)

A)

B)

C)

D)

Find the requested polynomial.

39) Find a polynomial of degree 3 having the following zeros: 1 + 3 , 1 - 3 , and 4 A) f(x) = x3 - 7x2 + 7x - 8 B) f(x) = x3 - 6x2 + 6x - 8 C) f(x) = x3 + 6x2 - 6x + 8

D) f(x) = x3 - 6x2 + 6x + 8

22

39)

Use long division to determine whether the binomial is a factor of f(x).

40) f(x) = x3 - 4x2 - 31x + 70; x + 5 A) Yes

40)

B) No

Find only the rational zeros.

41) f(x) = x3 - 9x2 + 6x + 56 A) 5, 8, -2

B) -5, -8, 2

C) 4, 7, -2

D) -4, -7, 2

Find the zeros of the polynomial function and state the multiplicity of each.

42) f(x) = 4x3 + x2 - 64x - 16 A) 4, multiplicity 2;

42)

1 , multiplicity 1 4

B) -4, multiplicity 1; 4, multiplicity 1; C) -4, multiplicity 2; -

1 , multiplicity 1 4

1 , multiplicity 1 4

D) -4, multiplicity 1; 4, multiplicity 1; -

1 , multiplicity 1 4

List the critical values of the related function. Then solve the inequality.

4x x > 43) 7x - 2 x + 1 A) -1,

2 ; (- , -1) 7

2 , 7

43)

B) No critical values; (- , ) D) -1, 0,

C) No critical values;

Use synthetic division to find the quotient and the remainder.

44) (2x4 - x3 - 15x2 + 3x) ÷ (x + 3) A) Q(x) = (2x3 - 7x2 + 6x - 15); R(x) = - 45 C) Q(x) = (2x3 - 5x2 + 3); R(x) = 9

2 , 2; (-1, 0) 7

2 ,2 7

B) Q(x) = (2x3 + 5x2 + 3); R(x) = 9

46) f(x) =

9 4

B) y =

5 9

45) C) y = 0

D) None

(x - 5)(x + 6) x2 - 9

A) x = 3, x = -3

44)

D) Q(x) = (2x3 - 7x2 + 6x - 15); R(x) = 45

Find the horizontal asymptote, if any, of the rational function.

9x3 - 5x - 6 45) f(x) = 4x3 - 9x + 3 A) y =

41)

46) B) y = 5, y = -6

C) y = 1

23

D) None

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and factor f(x) into linear factors.

47) f(x) = x3 + 8x2 - 2x - 16 47)

A) -8, -2, 2; f(x) = (x + 8)(x + 2)(x - 2)

B) - 8, multiplicity 2; - 2, multiplicity 2; f(x) = (x + C) - 8, multiplicity 2; -2; f(x) = (x + 8) 2 (x + 2) D) -8, - 2,

2; f(x) = (x + 8)(x +

2)(x -

8) 2 (x +

2)2

2)

Use substitution to determine whether the given number is a zero of the given polynomial.

48) -2; f(x) = -x4 - 8x2 - x - 4

48)

Find the correct end behavior diagram for the given polynomial function.

49) f(x) = 5x6 - x 5 + 5x2 - 2

49)

A) Yes

A)

B) No

B)

C)

D)

A polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x), and express P(x) in the form d(x)· Q(x) + R(x).

50) P(x) = 3x4 - 2x3 - 10x2 + 15 50) d(x) = x - 2

A) (x - 2)(3x3 + 4x2 - 2x - 4) + 7 C) (x - 2)(3x3 + 4x2 + 2x + 4) + 22

B) (x - 2)(3x3 + 4x2 - 2x + 11) + 22 D) (x - 2)(3x3 - 4x2 - 2x - 4) + 7

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. x2 - 9 51) f(x) = 51) x+2

A) x-intercept: (0, 0) , y-intercept: (0, 0) ;

24

B) x-intercepts: (-3, 0) and (3, 0) , y-intercept: 0,

9 2

C) x-intercepts: (-3, 0) and (3, 0) , y-intercept: 0, -

D) x-intercept: (0, 0) , y-intercept: (0, 0) ;

25

9 2

Solve the given inequality (a related function is graphed).

52) x3 - 5x2 9x - 45

x-intercepts: (-3, 0), (3, 0), (5, 0) A) (- , -3) (3, ) B) (- , -3]

52)

[3, )

C) (- , -3]

[3, 5]

D) (- , -3)

State the domain of the rational function. x-3 53) f(x) = x2 + 5x

53)

A) (- , 3) (3, ) C) (- , 5) (5, ) Solve.

(3, 5)

B) (- , -5) (-5, ) D) (- , -5) (-5, 0) (0, )

54) x3 - 7x 60 - 6x2 A) [-5, -4] [3, ) C) (- , -5] [-4, 3]

B) [-3, 3] D) [-3, )

54)

A polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x), and express P(x) in the form d(x)· Q(x) + R(x).

55) P(x) = x3 + 8 55) d(x) = x - 4

A) (x - 4)(x2 + 4x + 16) C) (x - 4)(x2 - 4x + 16) - 56

B) (x - 4)(x2 - 4x + 16) + 72 D) (x - 4)(x2 + 4x + 16) + 72

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. x3 + x2 - 2x 56) f(x) = 56) x2 - 36

26

A) x-intercepts: (-2, 0) and (1, 0) 1 y-intercept: 0, 3

B) x-intercepts: (-2, 0), (0, 0), and (1, 0) y-intercept: (0, 0)

C) x-intercepts: (-2, 0), (0, 0), and (1, 0) y-intercept: (0, 0)

D) x-intercepts: (-2, 0), (0, 0), and (1, 0) y-intercept: (0, 0)

Find the oblique asymptote, if any, of the rational function. x2 - 3x + 7 57) f(x) = x+5 A) y = x + 10 Solve.

57)

B) None

C) x = y + 3

D) y = x - 8

58) If a rocket is propelled upward from ground level at 98 m/sec, its height in meters after t seconds is given by h = -4.9t2 + 98t. During what interval of time will the rocket be higher than 445.9 m?

A) (8, 12)

B) (6, 13)

C) (7, 13)

58)

D) (7, 12)

Solve the problem.

59) The polynomial 0.0057x3 - 0.004x2 + 0.187x + 1.38 gives the approximate total earnings of a company, in millions of dollars, where x represents the number of years since 1996. This model is valid for the years from 1996 to 2000. Determine the earnings for 1997. Round your answer to two decimals, if necessary.

A) $1.38 million B) $1.78 million C) $1.57 million D) $1.58 million

27

59)

Provide the requested response.

60) Suppose that a polynomial function of degree 6 with rational coefficients has 3i, -2 + 5i, 5 zeros. Find the other zeros.

A) -3i, 2 - 5i , -5 + 2 B) 2 - 5i , -5 + 2 C) -3i, -2 - 5i , 5 + 2 D) -2 - 5i , 5 + 2 Using synthetic division, determine whether the numbers are zeros of the polynomial.

61) -5, 0; f(x) = 4x4 + 16x3 - 16x2 + 19x - 5 A) Yes; yes

Solve.

B) No; yes

C) No; no

2 as

D) Yes; no

62) The function h = -16t2 + 32t + 320 gives the height h, in feet, of a coin tossed upward from a balcony 320 feet high with an initial velocity of 32 ft/sec. During what interval of time will the coin be at a height of at least 80 feet?

A) [5, 10] B) [4, 5] C) [0, 5] D) [0, 1]

28

60)

61)

62)

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts.

2x 63) f(x) = 63) 2 x + 5x + 4

A) x-intercept: (0, 0) , y-intercept: (0, 0) ;

B) x-intercept: (0, 0) , y-intercept: (0, 0) ;

C) x-intercept: (0, 0) , y-intercept: (0, 0) ;

D) x-intercept: (0, 0) , y-intercept: (0, 0) ;

Find the requested polynomial.

64) Find a polynomial function of degree 3 with 5, 2i, -2i as zeros.

A) f(x) = x3 - 5x2 - 4x + 20 B) f(x) = x3 + 5x2 + 4ix + 20i C) f(x) = x3 - 5ix2 + 4x + 20

D) f(x) = x3 - 5x2 + 4x - 20

Use synthetic division to find the function value.

65) f(x) = x2 + 2x - 5; find f(-4 - 2i) A) -1 + 4i

B)

64)

+ 4i

C)

29

D) -1 + 12i

65)

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

66) 2, -10, 4 + 5i 66) 4 2 4 3 2 A) f(x) = x - 43x + 488x - 820 B) f(x) = x - 6x + 10x - 244x + 820 C) f(x) = x4 - 122x2 + 488x - 820

D) f(x) = x4 - 6x3 - 10x2 + 244x - 820

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function.

67) P(x) = 9x20 - 5x14 - 6x11 + 3x2 - 7x 67)

A) 3 positive; 2 negative C) 1 or 3 positive; 0 or 2 negative

B) 0 or 2 positive; 0 or 2 negative D) 1 or 3 positive; 1 or 3 negative

Find the vertical asymptote(s) of the graph of the given function. x2 + 3x - 18 68) f(x) = x2 - 2x - 15 A) x = 3, x = -5

B) y = -3, y = 5

68)

C) x = -3, x = 5

D) x = 5

Solve the given inequality (a related function is graphed).

69) -x3 + 2x2 + 9x - 18 < 0

x-intercepts: (-3, 0), (2, 0), (3, 0) A) (3, ) B) (- , -3)

69)

(2, 3)

C) (-3, 2)

Factor the polynomial f(x). Then solve the equation f(x) = 0.

70) f(x) = x3 + 10x2 + 29x + 20 A) (x - 2)(x - 5)(x - 6) ; 2, 5, 6 C) (x + 2)(x + 5)(x + 6) ; 2, 5, 6

D) [-3, 2]

B) (x + 1)(x + 4)(x + 5) ; -1, -4, -5 D) (x + 1)(x + 4)(x + 5) ; 1, 4, 5

Use synthetic division to find the function value.

71) f(x) = x3 - 2x2 + 4x - 1; find f(-4) A) -111

(3, )

B) 15

C) -113

30

D) 16

[3, )

70)

71)

Solve.

72) The population P, in thousands, of Marysburg is given by P(t) =

72)

300t , 2t2 + 8

where t is the time, in months.

Find the population at t = 0, 2, 4, and 9 months.

A) 0; 37,500; 27,000; 14,294 C) 0; 30,000; 24,000; 12,706

B) 0; 18,750; 15,000; 7,941 D) 0; 37,500; 30,000; 15,882

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and factor f(x) into linear factors.

73) f(x) = x3 - 12x - 16 73)

A) -2, multiplicity 2; 4; f(x) = (x + 2)2 (x - 4)

B) -2, multiplicity 2; -4; f(x) = (x + 2)2 (x + 4)

C) -4, -2, 2; f(x) = (x + 4)(x + 2)(x - 2)

D) -2, 2, 4; f(x) = (x + 2)(x - 2)(x - 4)

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

74) - 6 , -2i 74) 4 2 4 2 A) f(x) = x + 2x - 24 B) f(x) = x + 2x + 12 C) f(x) = x4 - 32x2 - 24

D) f(x) = x4 - 2x2 - 24

List the critical values of the related function. Then solve the inequality. x+3 x-5 + <0 75) x-4 x-3 A) 3, 4; (- , 3) (4, ) C) 3, 4; (3, 4)

75)

B) -4, -3; (- , -4) (-3, ) D) -4, -3; (-4, -3)

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible.

7 76) Vertical asymptotes x = -7, x = -2; horizontal asymptote y = - ; x-intercept (1, 0) 76) 2

A) f(x) =

-7x2 - 7x 2x2 + 18x + 28

B) f(x) =

7x2 + 7x 2x2 + 18x + 28

C) f(x) =

-7x2 + 7x 2x2 + 18x + 28

D) f(x) =

-7x2 + 7x 2x2 + 9x + 14

Graph the piecewise function.

31

-x - 6, 77) f(x) = 9, x2 - 5,

for x < -2, for -2 x < 0,

77)

for x 0

A)

B)

C)

D)

Use long division to determine whether the binomial is a factor of f(x).

78) f(x) = 4x3 - 31x2 + 27x + 90; x - 6 A) No

B) Yes

32

78)

State the domain of the rational function.

4 79) f(x) = 8-x A) (- , 8) (8, ) C) (- , - 4) (- 4, 4) Solve.

79) B) (- , 4) (4, ) D) (- , - 8) (- 8, 8)

(4, )

80) x2 + 16x + 47 0 A) (- , -8 - 17 ) (-8 + C) [-8 - 17 , -8 + 17 ]

(8, )

80) 17, )

B) (- , - 17] [ 17, ) D) (- , -8 - 17] [-8 +

17, )

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and factor f(x) into linear factors.

81) f(x) = x3 - 5x2 + 11x - 15 81)

A) -3, 1 + 2i, 1 - 2i; f(x) = (x + 3)(x - 1 - 2i)(x - 1 + 2i) B) 3, 1 +

5, 1 -

5 ; f(x) = (x - 3)(x - 1 -

5)(x - 1 + 5)

C) 3, -1 + 2i, -1 - 2i; f(x) = (x - 3)(x + 1 - 2i)(x + 1 + 2i) D) 3, 1 + 2i, 1 - 2i; f(x) = (x - 3)(x - 1 - 2i)(x - 1 + 2i) Find the horizontal asymptote, if any, of the rational function.

5 82) f(x) = 2 x +6 A) y = 5

B) y = 0

Use synthetic division to find the function value.

83) f(x) = 2x4 + 4x3 + 7x2 - 7x - 2; find f(2) A) 104

B) 120

82) C) x = 0

D) None

C) -12

D) 76

83)

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and factor f(x) into linear factors.

84) f(x) = x3 - 9x2 + 12x + 14 84)

A) 7, -1 + 3 , -1 - 3 ; f(x) = (x - 7)(x + 1 - 3)(x + 1 + 3) B) -7, 1 + 3 , 1 - 3 ; f(x) = (x + 7)(x - 1 - 3)(x - 1 + 3) C) 7, 1 + 3 , 1 - 3 ; f(x) = (x - 7)(x - 1 - 3)(x - 1 + 3) D) 7, 1 + 3 , 1 - 3 ; f(x) = (x - 7)(x + 1 - 3)(x + 1 + 3) Find only the rational zeros.

85) f(x) = x5 - 9x4 + 21x3 + 11x2 - 100x + 100 A) 5, 2, 3 C) 5, 2, -2

Find the correct end behavior diagram for the given polynomial function.

86) f(x) = -x6 + 6x5 - x2 - 6x + 3 A)

85)

B) -5, 2, -2 D) No rational zeros

B)

C)

33

D)

86)

Find the horizontal asymptote, if any, of the rational function. x+9 87) f(x) = 2 2x + 5x - 9 A) y = 1

B) y =

1 2

87) C) y = 0

D) None

Graph the polynomial function. Use synthetic division and the remainder theorem to find the zeros.

88) f(x) = 3x3 + 5x2 - 16x - 12

A) 2, -

2 , -3; 3

B) 2,

2 , -3; 3

C) 2, -

2 , 3; 3

D) 2,

2 , 3; 3

34

88)

List the critical values of the related function. Then solve the inequality.

5 3 < 89) 2 3x +1 x + 7x A) -7,

-3 -2 6 -3 + 2 6 -3 - 2 6 1 , - , 0, ; -7, 3 3 3 3

B) No critical values; (- , ) -3 -2 6 -3 + 2 6 -3 - 2 6 1 1 , - , 0, ; ,C) 3 3 3 3 3 D) -

1 1 , 0; - , 3 3

-

0,

1 ,0 3

89) -3 + 2 6 , 3

-3 + 2 6 3

(0, )

Solve the inequality.

90) For the function f(x) = x2 - 3x - 28, solve f(x) 0.

A) [7, ) B) [-4, 7]

C) (- , -4]

91) For the function h(x) =

2x , solve h(x) < 0. (x - 3)(x - 4)

A) (- , 2] [6, )

B) (- , 2) (6, )

[7, )

90)

91) C) (- , 0) (2, 6)

35

D) (- , -4]

D) [2, 6]

Solve.

92) The population P, in thousands, of Jonesburg is given by P(t) =

92)

500t , 2t2 + 7

where t is the time, in months.

Graph the function on the interval [0, ) and complete the following: P(t) as t .

A)

C)

B)

P(t)

45 as t

P(t)

1 as t

.

D)

.

P(t)

50 as t

P(t)

0 as t

.

.

Find the vertical asymptote(s) of the graph of the given function. x2 + 6x 93) f(x) = x2 - 2x - 48 A) x = 8, x = -6

B) x = -8, x = 6

C) x = 8

36

93) D) None

Solve.

94) The average cost per tape, in dollars, for a company to produce x sports videotapes is given by the function 15x + 50 A(x) = for x > 0 x

94)

Graph the function on the interval (0, ) and complete the following: A(x) as x .

A)

C)

B)

A(x)

20 as x

A(x)

0 as x

.

D)

.

A(x)

1 as x

A(x)

15 as x

.

.

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts.

3x2 - 4x - 4 95) f(x) = 95) x-2

37

A) x-intercept: 2, 0 , y-intercept: (0, 2) ;

C) x-intercept: -

B) x-intercept: -2, 0 , y-intercept: (0, 2) ;

2 , 0 , y-intercept: (0, 2) ; 3

D) x-intercept:

2 , 0 , y-intercept: (0, 2) ; 3

List the critical values of the related function. Then solve the inequality.

-7 >0 96) -7x - 4 A)

4 4 ; - , 7 7

B) -

4 4 ; - , 7 7

C) 0; (0, )

96) D) -

7 7 ; - ,4 4

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

97) 3 - 3 , 1 + i 97) A) f(x) = x4 - 8x3 + 20x2 - 24x + 12 B) f(x) = x4 + 8x3 - 20x2 + 24x + 10 C) f(x) = x4 - 3x3 + 20x2 - 12x + 12

D) f(x) = x4 + 10x3 + 20x2 - 24x + 12

Find the zeros of the polynomial function and state the multiplicity of each.

98) f(x) = -5x2 (x - 9)(x + 2)3

98)

A) -2, multiplicity 3; 9, multiplicity 1 B) -2, multiplicity 3; 0, multiplicity 2; 9, multiplicity 1 C) -2, multiplicity 1; 2, multiplicity 1; 9, multiplicity 1 D) -2, multiplicity 3; 0, multiplicity 2; 2, multiplicity 1; 9, multiplicity 1

Find the vertical asymptote(s) of the graph of the given function. x-4 99) f(x) = x2 + 6 A) x = 2, x = -2

B) x = -6

C) x = 6

38

99) D) None

Solve.

100) Suppose that the temperature T, in degrees Fahrenheit, of a person during an illness is given by the 5t function T(t) = + 98.6 , where t is the time, in hours. Find the interval on which the 2 t +1 temperature is over 100 .

A)

B) (0.564, 6.008)

C) (0.306, 3.265)

D) (0, 1)

Find the horizontal asymptote, if any, of the rational function.

8x2 + 4 101) f(x) = x2 - 4 A) y = 8

B) y = 0

101) C) y = 4

D) None

Find the zeros of the polynomial function and state the multiplicity of each.

1 102) f(x) = 4x(x - 4)(x + 11) x 2 A) -11, multiplicity 1;

1 , multiplicity 1; 4, multiplicity 1 2

B) -4, multiplicity 1; -

1 , multiplicity 1; 0, multiplicity 1; 11, multiplicity 1 2

C) -4, multiplicity 1; -

1 , multiplicity 1; 11, multiplicity 1 2

D) -11, multiplicity 1; 0, multiplicity 1;

100)

102)

1 , multiplicity 1; 4, multiplicity 1 2

List the critical values of the related function. Then solve the inequality.

3 4 103) 2 2 x - 9 x + 8x + 15 A) -5, -3, 3, 27; (-5, -3) (3, 27] C) 27; [27, )

103)

B) -5, -3, 3, 27; (- , -5) (-3, 3) [27, ) D) -3, 3, 27; (- , -3) (3, 27]

Solve.

104) 10 - x2 0 A) [ 10, )

104) B) [- 10,

10]

C) (- , - 10]

39

D) (-10, 10)

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts.

1 105) f(x) = 105) 4x2

A) No x-intercepts, no y-intercepts ;

B) No x-intercepts, no y-intercepts ;

C) No x-intercepts, no y-intercepts ;

D) No x-intercepts, no y-intercepts ;

For the function find the maximum number of real zeros that the function can have, the maximum number of x-intercepts that the function can have, and the maximum number of turning points that the graph of the function can have.

106) f(x) = 8x3 + 2x2 - 3x + 6 106)

A) 3; 3; 2

B) 3; 3; 3

C) 2; 2; 1

D) 3; 2; 1

Find the oblique asymptote, if any, of the rational function. x+9 107) f(x) = 2 5x + 7x - 9 A) y = x + 5

107)

B) x = y + 5

C) y = x + 9

40

D) None

Solve.

108) 3x3 - 2x2 8x 4 A) - , 3 C) -

108) [2, )

B) [0, 2]

4 ,2 3

D) - , -

4 3

[0, 2]

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

109) 1 - 3 , 1 + i 109) 4 3 2 4 3 2 A) f(x) = x + 3x + 4x - 1 B) f(x) = x - 6x + 8x - 4 C) f(x) = x4 + 6x3 + 4x2 - 4

D) f(x) = x4 - 4x3 + 4x2 - 4

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. x-1 110) f(x) = 110) 2 x - 5x - 6

A) x-intercept: (-1, 0) , y-intercept: 0, -

1 ; 12

41

B) x-intercept: (1, 0) , y-intercept: 0,

1 ; 6

C) x-intercept: (-1, 0) , y-intercept: 0,

1 ; 12

D) x-intercept: (1, 0) , y-intercept: 0, -

1 ; 6

Find the vertical asymptote(s) of the graph of the given function.

7 111) g(x) = x+5 A) x = -5

B) x = 7

C) y = -5

Use synthetic division to find the quotient and the remainder.

112) (x5 + 8x4 + 9x3 - 15x2 + 21x + 19) ÷ (x + 6) A) Q(x) = x4 + 2x3 - 3x2 + 3x - 3 ; R(x) = 3 C) Q(x) = x4 + 2x3 - 3x2 + 3x + 1; R(x) = 0

42

111) D) y = 7

B) Q(x) = x3 + 2x2 - 3x + 3 ; R(x) = 1 D) Q(x) = x4 + 2x3 - 3x2 + 3x + 3 ; R(x) = 1

112)

Find only the rational zeros.

113) f(x) = x6 + 1

113)

1 1 ,A) 1, -1, 6 6

C) 1, -1,

1 1 ,, 2 2

B) 1, -1 1, -

1

D) No rational zeros

List the critical values of the related function. Then solve the inequality. x2 - 4x - 5 <0 114) x2 + 11x + 30 A) -1, 5; (-1, 5) C) -6, -5, -1, 5; (-6, -5) (-1, 5)

B) -5, 1, 5, 6; (- , -5) (1, 5) (6, ) D) -6, -5, -1, 5; (- , -6) (-5, -1) (5, )

43

114)

Answer Key Testname: C4

1) D 2) D 3) D 4) B 5) A 6) B 7) D 8) A 9) D 10) A 11) A 12) C 13) B 14) B 15) C 16) D 17) D 18) C 19) C 20) A 21) B 22) B 23) A 24) A 25) A 26) C 27) D 28) A 29) D 30) A 31) C 32) C 33) A 34) B 35) C 36) A 37) D 38) B 39) D 40) A 41) C 42) D 43) D 44) D 45) A 46) C 47) D 48) B 49) A 50) A 44

Answer Key Testname: C4

51) C 52) C 53) D 54) C 55) D 56) C 57) D 58) C 59) C 60) C 61) D 62) C 63) A 64) D 65) D 66) A 67) C 68) C 69) C 70) B 71) C 72) D 73) A 74) D 75) C 76) C 77) D 78) B 79) A 80) D 81) D 82) B 83) D 84) C 85) C 86) C 87) C 88) A 89) A 90) B 91) C 92) D 93) C 94) D 95) C 96) B 97) A 98) B 99) D 100) C 45

Answer Key Testname: C4

101) A 102) D 103) B 104) B 105) C 106) A 107) D 108) D 109) D 110) B 111) A 112) D 113) D 114) C

46

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Choose the function that might be used as a model for the data in the scatter plot.

1)

1)

A) Exponential, f(x) = abx or f(x) = P0 ekx, k > 0 B) Logarithmic, f(x) = a + b ln x C) Exponential, f(x) = ab-x or f(x) = P0 e-kx, k > 0 D) Polynomial, not quadratic 2)

2)

A) Quadratic, f(x) = ax2 + bx + c a B) Logistic, f(x) = 1 + be-kx C) Exponential, f(x) = ab-x or f(x) = P0 e-kx, k > 0 D) Polynomial, not quadratic

1

Match the function with one of the graphs.

3) f(x) = 4 x + 2 A)

B)

C)

D)

2

3)

4) f(x) = ex - 3 A)

B)

C)

D)

3

4)

5) f(x) = 2e-x A)

B)

C)

D)

4

5)

6) f(x) = 3 + ex A)

B)

C)

D)

5

6)

Choose the function that might be used as a model for the data in the scatter plot.

7)

A) Logarithmic, f(x) = a + b ln x B) Exponential, f(x) = abx or f(x) = P0 ekx, k > 0 C) Polynomial, not quadratic a D) Logistic, f(x) = 1 + be-kx

6

7)

Match the function with one of the graphs.

3 x 8) f(x) = 4

8)

A)

B)

C)

D)

7

Choose the function that might be used as a model for the data in the scatter plot.

9)

9)

A) Exponential, f(x) = abx or f(x) = P0 ekx, k > 0 B) Logarithmic, f(x) = a + b ln x C) Exponential, f(x) = ab-x or f(x) = P0 e-kx, k > 0 D) Quadratic, f(x) = ax2 + bx + c 10)

10)

A) Exponential, f(x) = ab-x or f(x) = P0 e-kx, k > 0 B) Logarithmic, f(x) = a + b ln x C) Polynomial, not quadratic a D) Logistic, f(x) = 1 + be-kx

8

11)

11)

A) Logarithmic, f(x) = a + b ln x B) Quadratic, f(x) = ax2 + bx + c

C) Polynomial, not quadratic D) Exponential, f(x) = abx or f(x) = P0 ekx, k > 0 Match the function with one of the graphs.

12) f(x) = ex - 7 A)

B)

C)

D)

9

12)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

13) Explain how the graph of f(x) = ln x could be used to graph the function g(x) = ex - 1.

14) The product, power, and quotient rules enable us to simplify expressions like log

rs . a pv

13) 14)

Explain why such expressions can always be simplified without using the quotient rule.

For the function f, use composition of functions to show that f-1 is as given.

3 15) f(x) = x3 - 6, f-1 (x) = x + 6

15)

Provide an appropriate response.

16) Explain why log 13 is between 3 and 4.

2

16)

17) Explain how the equation log x = 1 could be solved using the graph of f(x) = log x.

17)

18) Prove that the function f is not one-to-one. f(x) = x2 + 2

18)

19) Explain why 1 is excluded from being a logarithmic base.

19)

20) Without using a calculator, determine which of these numbers is larger:

8 3 or 8 3 .

20)

21) Explain the error in the following: log 2 + log M = log (2 + M).

3 3 3

21)

22) Prove that the function f is not one-to-one.

2 f(x) = x6

22)

For the function f, use composition of functions to show that f-1 is as given. x + 5 -1 , f (x) = 4x - 5 23) f(x) = 4

23)

8 + x -1 8 , f (x) = x x-1

24)

Provide an appropriate response.

25) Prove that the function f is not one-to-one. f(x) = x - 2

25)

24) f(x) =

26) Explain the error in the following: log 8 - log N = log (8 - N).

6 6 6

10

26)

For the function f, use composition of functions to show that f-1 is as given.

3 27) f(x) = x + 2, f-1 (x) = x3 - 2

27)

Provide an appropriate response.

5 9x - 1 .

28) Find f(f-1 (1,536)) given that f(x) = 8x - 7

28)

29) Without using a calculator, determine which of these numbers is larger: 1.3 or 2.4.

29)

30) Suppose that $1000 is invested for 5 years at 4% interest, compounded annually. In what year will the most interest be earned? Why?

30)

31) Explain why f(x) = 2 x is an exponential function but f(x) = x2 is not.

31)

For the function f, use composition of functions to show that f-1 is as given.

4 3 32) f(x) = - x, f-1 (x) = - x 3 4

33) f(x) =

x + 8 -1 , f = 5x - 8 5

32)

33)

Provide an appropriate response.

34) Explain how the graph of f(x) = ex could be used to graph the function g(x) = 1 + ln x.

34)

35) Prove that the function f is one-to-one.

1 f(x) = 6 - x 2

35)

36) Prove that the function f is one-to-one. f(x) = 3x - 1

36)

37) Explain why negative numbers do not have logarithms.

37)

For the function f, use composition of functions to show that f-1 is as given. x - 4 -1 , f (x) = 7x + 4 38) f(x) = 7

Provide an appropriate response.

39) Explain the error in the following: log 3y = log 3 · log y.

4 4 4 40) Prove that the function f is one-to-one.

3 f(x) = x + 5

38)

39) 40)

11

41) Prove that the function f is one-to-one. f(x) = x3 - 4

41)

42) Without using a calculator, explain why 2 must be greater than 8 but less than 16.

42)

43) Prove that the function f is not one-to-one. f(x) = 2 - x4

43)

For the function f, use composition of functions to show that f-1 is as given.

5 7 44) f(x) = x, f-1 (x) = x 7 5

44)

Provide an appropriate response.

45) Explain why a

log a 5

= 5.

45)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve.

46) In 1998, the population of Country C was 21 million, and the exponential growth rate was 1% per year. Find the exponential growth function.

A) P(t) = 210.01t , where P(t) is in millions and t is the number of years after 1998.

46)

B) P(t) = 21e0.01t, where P(t) is in millions and t is the number of years after 1998.

C) P(t) = 21e0.01, where P(t) is in millions and t is the number of years after 1998.

D) P(t) = 21e1t, where P(t) is in millions and t is the number of years after 1998.

Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function.

47) f(x) = 2 x + 4 47)

12

A) Shift y = 2 x up 4 unit(s)

B) Shift y = 2 x up 4 unit(s)

C) Shift y = 2 x down 4 unit(s)

D) Shift y = 2 x down 4 unit(s)

Use the compound-interest formula to find the account balance with the given conditions: P = principal, r = interest rate, t = time, in years.

48) P = $1000, t = 8, r = 12% compounded annually A) $1,475.96 B) $2,475.96 C) $2,210.68 D) $2,773.08

Graph the one-to-one function as a solid curve and its inverse as a dashed curve on the same axes.

49) y = x - 4

13

48)

49)

A)

B)

C)

D)

Find the domain and range of the inverse of the given function.

50) f(x) = 2x - 3 A) Domain: (- , 3) (3, ); range: all real numbers B) Domain: [0, ) ; range: all real numbers C) Domain: all real numbers; range: (- , -3) (-3, ) D) Domain and range: all real numbers

50)

Find the domain and the vertical asymptote of the function.

51) f(x) = ln( - x) A) Domain: (- , -9); vertical asymptote: x = -9 B) Domain: (- , ); vertical asymptote: x = C) Domain: ( , ); vertical asymptote: x = D) Domain: (-9, ); vertical asymptote: x = -9

51)

Find the value of the expression.

52) log 10 0.00001 A) 0.00001

52) B) -0.00005

C) -5

14

D)

Graph the function.

53) f(x) = 2 (x + 1)

53)

A)

B)

C)

D)

Find the following using a calculator. Round to four decimal places.

54) log 97 A) 4.5747 B) 1.4868 C) 5.0747 Convert to a logarithmic equation.

55) e-t = 25 A) log 25 (- t) = e

B) ln 25 = -t

C) ln t = - 25

15

D) 1.9868

D) log t 25 = e

54)

55)

Find the inverse of the relation.

56) {( , ), ( , ), (-7, -12)} A) {(7, 2), (-16, 17), (-12, -7)} C) {( , -16), ( , ), (-12, -7)}

B) {(7, 2), (-7, 17), (-12, -16)} D) {(7, 2), (7, 17), (-12, -7)}

Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse.

7x + 6 57) f(x) = -7x - 2 A) f-1 (x) =

2x + 6 -7x - 7

B) Not one-to-one

C) f-1 (x) =

7x + 6 -7x - 2

D) f-1 (x) =

56)

57)

-7x - 7 2x + 6

Express as a sum of logarithms.

58) log 8 xy

58)

A) log 4 x + log 4 y

B) log 4 x - log 4 y

C) log 8 x - log 8 y

D) log 8 x + log 8 y

Graph the piecewise function.

59) for x -2, -5, 2 f(x) = x + 4, for -2 < x 0, ex, for x > 0

59)

16

A)

B)

C)

D)

Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse.

60) f(x) = (x + 1)3 A) f-1 (x) = C) f-1 (x) =

3 3

3

x+1

B) f-1 (x) = 1 -

x-1

D) Not one-to-one

x

Find the value of the expression.

61) log5 5 3 A) 1

60)

61) B) 5 3

C) 3log5 5

D) 3

Graph the function. Describe its position relative to the graph of the indicated basic function.

17

62) f(x) = e4x - 4; relative to f(x) = ex

62)

A) Shrunk horizontally; moved down 4 unit(s)

B) Shrunk horizontally; moved up 4 unit(s)

C) Stretched horizontally; moved up 4 unit(s)

D) Stretched horizontally; moved down 4 unit(s)

Convert to a logarithmic equation.

63) 15,6251/6 = 5 1 A) = log 5 15,625 6

1 B) 5 = log 15,625 6

C) 5 = log 1/6 15,625

D)

18

1 = log 15,625 5 6

63)

Find the logarithm using the change-of-base formula.

64) log8.3 6.6 A) 0.8195

64)

B) 0.8917

C) 0.7952

D) 1.1215

Solve the problem.

65) An artifact is discovered at a certain site. If it has 66 % of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.012% annually.)

A) 5,500 yr B) 1,504 yr C) 2,833 yr D) 3,463 yr

65)

Graph the equation as a solid line. Graph the inverse relation as a dashed line on the same axes by reflecting across the line y = x.

66) y = x2 + 3 66)

A)

B)

C)

D)

19

Graph the function.

67) f(x) = e3x - 3

67)

A)

B)

C)

D)

Convert to a logarithmic equation.

68) yz = 3 A) z = log y 3

B) y = log 9 z

C) z = log 9 y

D) y = log z 3

Find the logarithm using the change-of-base formula.

69) log 100 A) 4.023

68)

69)

B) 4.6052

C) 0.2486

20

D) 1.1447

Find the inverse of the relation.

70) {( , ), (-6, -1), ( , ), (-2, -1)} A) {( , ), ( , -6), ( , ), (-1, -2)} C) {( , ), (-1, -6), ( , ), (-1, -2)}

B) {(-1, 6), (-9, -6), (-6, 2), (-1, 2)} D) {( , ), (-1, -6), ( , -6), (-1, -2)}

Graph the function.

1 x 71) f(x) = 5

70)

71)

A)

B)

C)

D)

The graph of a one-to-one function f is given. Sketch the graph of the inverse function f-1 , on the same set of axes. Use a dashed line for the inverse.

21

72)

72)

A)

B)

C)

D)

Evaluate to four decimal places using a calculator.

73) e1.643 A) 2.6994

B) 7.3891

C) 5.1707

22

D) 4.4661

73)

Find the domain and range of the inverse of the given function.

6 74) f(x) = x-2 A) Domain: (- , 2) (2, ) Range: (- , ) C) Domain: (- , ) Range: (- , 2) (2, )

74)

B) Domain: (- , 2) (2, ) Range: (- , 0) (0, ) D) Domain: (- , 0) (0, ) Range: (- , 2) (2, )

Find a formula for the inverse of the function described below.

75) A size 58 dress in Country C is size 9 in Country D. A function that converts dress sizes in Country x C to those in Country D is f(x) = - 20.

2 A) f-1 (x) = 2(x + 20) C) f-1 (x) = x + 20

75)

B) f-1 (x) = 2x + 20 D) f-1 (x) = 2(x - 20)

Solve the problem.

76) An initial investment of $1000 is appreciated for 4 years in an account that earns 13% interest, compounded semiannually. Find the amount of money in the account at the end of the period.

A) $1,630.47 B) $1,553.99 C) $655 D) $1,655.00

76)

Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function.

77) f(x) = 5 - 3 -x 77)

A) Shift y = 3 x up 5 unit(s), reflect across the y-axis, and reflect across the x-axis

B) Shift y = 3 x up 5 unit(s), reflect across the y-axis, and reflect across the x-axis

23

C) Reflect y = 3 x across the y-axis, reflect across the x-axis and down 5 unit(s)

D) Reflect y = 3 x across the y-axis, reflect across the x-axis and shift up 5 unit(s)

24

The graph of a one-to-one function f is given. Sketch the graph of the inverse function f-1 , on the same set of axes. Use a dashed line for the inverse.

78) 78)

A)

B)

C)

D)

25

Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function.

79) f(x) = ln x - 6 79)

A) Shift y = ln x up 6 units

B) Shift y = ln x down 6 units

C) Shift y = ln x right 6 units

D) Shift y = ln x down 6 units

Evaluate to four decimal places using a calculator.

80) e0.52 A) 1.6820

B) 1.4135

Find an equation of the inverse relation.

81) y = -4x - 8 A) y = -4 - 8x B) y = -4x + 8

26

C) 1.8589

D) -0.6539

C) x = -4y + 8

D) x = -4y - 8

80)

81)

Express as a single logarithm and, if possible, simplify.

1 82) logax + 4 loga y - 4 loga x 2 A) loga

y4 x7/2

B) loga

82)

x y4

C) loga x6 y4

Solve the logarithmic equation.

83) log ( 2 + x) - log (x - 2 ) = log 5 A) 3

5 C) 2

B)

Convert to a logarithmic equation.

84) 100.9031 = 8 A) 0.9031 = log 9 10

B) 10 = log 9 0.9031

C) 8 = log 10 0.9031

D) 0.9031 = log 10 8

27

D) loga x4 y4

83) D) - 3

84)

Answer Key Testname: C5

1) C 2) D 3) D 4) C 5) A 6) B 7) D 8) C 9) A 10) B 11) B 12) C 13) Reflect the graph of f(x) = ln x across the line y = x and then translate it to the right one unit. rs can be written as the product rs(p-1 )(v-1 ) 14) The quotient pv 15) Answers may vary. One possible solution is: 3 3 1. (f-1 f)(x) = f-1 (f(x)) = f-1 x3 - 6 = x3 - 6 + 6 = x3 = x; 3 3 3 2. (f f-1 )(x) = f(f-1 (x)) = f x + 6 = x+6 -6=x+6-6= x 16) log 2 8 = 3 and log 2 16 = 4. Since 8 < 13 < 16, then 3 < log 2 13 < 4. This is true because log 2 x is an increasing function.

17) Graph f(x) = log x and g(x) = 1 on the same set of axes. The solution is the first coordinate of the point of intersection of the two graphs.

18) Answers may vary. Possible answer: Find two numbers a and b for which a b and f(a) = f(b). Two such numbers are -1 and 1 because f(-1) = f(1) = 3.

Thus, f is not one-to-one.

19) It excludes x = 1 y which is not a function.

20) 8 3 = 8 3/2 and 3/2 < 3, so 8 3 is larger.

21) A sum of logarithms is not equal to a logarithm of a sum. log 2 + log M = log 2M 3 3 3 22) Answers may vary. Possible answer: Find two numbers a and b for which a b and f(a) = f(b). Two such numbers are -1 and 1 because f(-1) = f(1) = 2.

Thus, f is not one-to-one.

23) Answers may vary. One possible solution is: 1. (f-1 f)(x) = f-1 (f(x)) = f-1 x + 5 /4 = 4 x + 5 /4 - 5 = x + 5 - 5 = x; 2. (f f-1 )(x) = f(f-1 (x)) = f 4x - 5 = 4x - 5 + 5 /4 = 4x/4 = x 24) Answers may vary. One possible solution is: 8 8 8 1. (f-1 f)(x) = f-1 (f(x)) = f-1 8 + x /x = = = = x; 8+x 8+x-x 8 -1 x x x

2. (f f-1 )(x) = f(f-1 (x)) = f

8 = x-1

8+

8 x-1

8 x-1

=

8 x-1 +8 x-1 8 x-1

28

=

8x = x 8

Answer Key Testname: C5

25) Answers may vary. Possible answer: Find two numbers a and b for which a b and f(a) = f(b). Two such numbers are -3 and 3 because f(-3) = f(3) = 1.

Thus, f is not one-to-one.

26) A difference of logarithms is not equal to the logarithm of the difference.

8 log 6 8 - log 6 N = log 6 N 3 3 3 27) 1. (f-1 f)(x) = f-1 (f(x)) = f-1 ( x + 2) = ( x + 2) - 2 = x; 3 2. (f f-1 )(x) = f(f-1 (x)) = f(x3 - 2) = (x3 - 2) + 2= x 28) 1,536

29) Since the bases are the same, the base with the larger exponent is the larger number. Thus, 2.4 is larger.

30) The most interest will be earned in the fifth year, because the amount on which the interest is paid is greatest at the end of the fourth year.

31) 2 x is an exponential function because the variable is in the exponent. In f(x) = x2 , the variable is not in the exponent; this is a polynomial function.

32) Answers may vary. One possible solution is: 4 3 4 1. (f-1 f)(x) = f-1 (f(x)) = f-1 - x = - - x = x; 3 4 3 3 4 3 2. (f f-1 )(x) = f(f-1 (x)) = f - x = - - x = x 4 3 4

x+8 x+8 =5 - 8 = x; 33) 1. (f-1 f)(x) = f-1 (f(x)) = f-1 5 5 5x - 8 + 8 2. (f f-1 )(x) = f(f-1 (x)) = f(5x - 8) = =x 5

34) Reflect the graph of f(x) = ex across the line y = x and then translate it up one unit.

35) Assume that f(a) = f(b) for any numbers a and b in the domain of f.

1 1 Since f(a) = 6 - a and f(b) = 6 - b, we have 2 2 6-

1 1 a=6- b 2 2

1 1 a=- b 2 2

a=b Thus if f(a) = f(b) then a = b and f is one-to-one.

36) Assume that f(a) = f(b) for any numbers a and b in the domain of f.

Since f(a) = 3a - 1 and f(b) = 3b - 1, we have 3a - 1 = 3b - 1 3a = 3b a=b Thus if f(a) = f(b) then a = b and f is one-to-one.

37) Consider f(x) = log

a

x, or y = log

a

x, where a is a positive constant other than 1. Then a y = x, and since a is positive, x

must be positive.

38) Answers may vary. One possible solution is: 1. (f-1 f)(x) = f-1 (f(x)) = f-1 x - 4 /7 = 7 x - 4 /7 + 4 = x - 4 + 4 = x; 2. (f f-1 )(x) = f(f-1 (x)) = f 7x + 4 = 7x + 4 - 4 /7 = 7x/7 = x

29

Answer Key Testname: C5

39) A logarithm of a product is not equal to a product of logarithms. log

4

3y = log

4

3 + log y 4

40) Assume that f(a) = f(b) for any numbers a and b in the domain of f.

3 3 Since f(a) = a + 5 and f(b) = b + 5, we have 3 3 a+5 = b+ 5 3 3 a = b a=b Thus if f(a) = f(b) then a = b and f is one-to-one.

41) Assume that f(a) = f(b) for any numbers a and b in the domain of f.

Since f(a) = a 3 - 4 and f(b) = b3 - 4, we have a 3 - 4 = b3 - 4 a 3 = b3

a=b Thus if f(a) = f(b) then a = b and f is one-to-one.

42) Since 3 < < 4, 2 3 < 2 < 2 4 ; that is 2 is greater than 2 3 (or 8), but less than 2 4 (or 16). This is true because 2 x is an

increasing function.

43) Answers may vary. Possible answer: Find two numbers a and b for which a b and f(a) = f(b). Two such numbers are -2 and 2 because f(-2) = f(2) = -14.

Thus, f is not one-to-one.

5 7 5 x = x; 44) 1. (f-1 f)(x) = f-1 (f(x)) = f-1 x = 7 5 7 7 5 7 2. (f f-1 )(x) = f(f-1 (x)) = f x = x =x 5 7 5

45) Let log

a

5 = x. Then a x = 5. Replacing x with log

a

5, we have a

46) B 47) A 48) B 49) B 50) D 51) B 52) C 53) C 54) D 55) B 56) D 57) A 58) D 59) B 60) C 61) D 62) A 63) D 64) B 65) D 66) D 30

log a 5

= 5.

Answer Key Testname: C5

67) A 68) A 69) A 70) C 71) C 72) A 73) C 74) D 75) A 76) D 77) D 78) D 79) D 80) A 81) D 82) A 83) A 84) D

31

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) You are graphing 2x2 + 3y2 > 5. You have drawn the graph of 2x2 + 3y2 = 5. What single point will allow you to determine the correct region?

A) The origin B) (2, 5)

C) (2, 3)

2) You are finding the partial fraction decomposition of the expression

1)

D) (3, 5) x2 - 6x + 9

(x2 - 8x + 15)(x + 5)

.

2)

You should ...

A) Solve the equation x2 - 6x + 9 = A(x + 5) + B(x - 3) + C(x + 5) B) Solve the equation x2 - 6x + 9 = A(x - 5) + B(x - 3) + C(x + 5)

C) Solve the equation x2 - 6x + 9 = (Ax + B)(x2 - 8x + 15) + C(x + 5) D) Use long division to divide the numerator by the denominator 3) You are finding the partial fraction decomposition of the expression You should ...

A) Solve the equation x3 - 8x + 16 = (Ax + B)(x2 - 7x + 12) B) Use long division to divide the numerator by the denominator C) Solve the equation x3 - 8x + 16 = A(x - 4) + B(x - 3) D) Solve the equation x2 - 7x + 12 = (Ax + B)(x3 - 8x + 16)

1

x3 - 8x + 16 . x2 - 7x + 12

3)

Find the graph that matches the given system of equations.

4) 2x + y = 1 x + y = -7 A)

4) B)

C)

D)

2

Match the inequality with a graph.

5) 6x - 7y -5

5)

A)

B)

C)

D)

3

6) -x > y

6)

A)

B)

C)

D)

Provide an appropriate response.

7) Which one of the following is a description of the graph of the inequality? (x - 2)2 + (y - 1)2 > 64 A) the region inside the circle with center (-2, -1) and radius 8 B) the region outside a circle with center (2, 1) and radius 8 C) the region outside a circle with center (-2, -1) and radius 8 D) the region inside a circle with center (2, 1) and radius 8

4

7)

Find the graph that matches the given system of equations.

8) 2x + y = 13 2x - 3y = 1 A)

8) B)

C)

D)

5

Match the system of inequalities with a graph.

9) y 2x - 3, y -x

9)

A)

B)

C)

D)

Match the inequality with a graph.

6

10) 3 - 3x > y

10)

A)

B)

C)

D)

7

Find the graph that matches the given system of equations.

11) x = -3y x - y = -4 A)

11) B)

C)

D)

8

Match the system of inequalities with a graph.

12) 3y - x 3, y + 2x 5, y -x

12)

A)

B)

C)

D)

9

13) 2y - x < 4, y + 2x < 6

13)

A)

B)

C)

D)

10

14) 2y - x 4, y + 3x 6, y 0

14)

A)

B)

C)

D)

11

Match the inequality with a graph.

15) 6x - 5y > -1

15)

A)

B)

C)

D)

12

Find the graph that matches the given system of equations.

16) 3x + 4y = -4 5x - 2y = -24 A)

16) B)

C)

D)

13

Match the inequality with a graph.

17) 6x + 7y > -4

17)

A)

B)

C)

D)

14

Match the system of inequalities with a graph.

18) 3y - x -3, y + 3x 5, -y x - 2

18)

A)

B)

C)

D)

15

Find the graph that matches the given system of equations.

19) 2x - y = 0 -4x + 2y = 0 A)

19) B)

C)

D)

16

20) 2x - y = 1 -6x + 2y = -3 A)

20) B)

C)

D)

Provide an appropriate response.

21) Equating the numerators in the process of partial fraction decomposition, your friend has obtained the algebraic expression 7x - 7 = A(3x - 3) + B(x + 7) + C(x + 7). From this equation, what can you say about the original expression?

A) The original expression has a repeating linear factor in the denominator.

B) The original expression has a non-reducible quadratic factor in the denominator.

C) The original expression has the factor (x2 + 7) in the denominator.

D) The original expression has a numerator of (7x - 7)(3x - 3)(x + 7)(x + 7).

17

21)

Find the graph that matches the given system of equations.

22) 3x + y = 10 y = 3x - 2 A)

22) B)

C)

D)

18

Match the system of inequalities with a graph.

23) 4y - x > -28, y + 6x < 39, 4x > y, y< 0

23)

A)

B)

C)

D)

19

Find the graph that matches the given system of equations.

24) x + y = 8 y=x+ 2 A)

24) B)

C)

D)

20

Match the system of inequalities with a graph.

25) 3y - x > -19, y + 5x < 31, x > 0, y< 0

25)

A)

B)

C)

D)

Provide an appropriate response.

26) Equating the numerators in the process of partial fraction decomposition, your friend has obtained the algebraic expression 3x - 3 = A(3x - 5) + B(x + 4). From this equation, what can you say about the original expression?

A) The denominator of the original expression is 3x2 + 7x - 20.

B) The original expression has repeated linear factors in the denominator.

C) The original expression has a non-reducible quadratic factor in the denominator.

D) The numerator of the original expression is 3x2 + 7x - 20.

21

26)

Find the graph that matches the given system of equations.

27) 3x + y = -10 y = 3x + 2 A)

27) B)

C)

D)

Provide an appropriate response.

28) Which one of the following is a description of the graph of the inequality? (x - 5)2 + (y + 2)2 < 1 A) the region outside a circle with center (-5, ) and radius 1 B) the region outside a circle with center (5, -2) and radius 1 C) the region inside a circle with center (5, -2) and radius 1 D) the region inside the circle with center (-5, ) and radius 1

22

28)

Match the system of inequalities with a graph.

29) x - y < 2, x+y<5

29)

A)

B)

C)

D)

Match the inequality with a graph.

23

30) -3x < 7 - 2y

30)

A)

B)

C)

D)

Provide an appropriate response.

31) The partial fraction decomposition of an expression is 3x +

6 8 . From this 2x - 3 2x2 - 3

decomposition, what can you say about the original expression?

A) The denominator of the original expression contained repeated linear factors.

B) The numerator of the original expression was 3x2 + 6x - 8.

C) The denominator of the original expression contained a nonreducible quadratic factor.

D) The numerator of the original expression was of a degree greater than the denominator of the original expression.

24

31)

Match the system of inequalities with a graph.

32) y x - 8, y x

32)

A)

B)

C)

D)

25

Find the graph that matches the given system of equations.

33) 3x + 4y = 2x - 3y = -23 A)

33) B)

C)

D)

26

Match the inequality with a graph.

34) 8y -7x

34)

A)

B)

C)

D)

27

35) -3y x

35)

A)

B)

C)

D)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

36) Evaluate A by expanding down the second column. Show all your work.

2 -3 -4 A = 2 0 -2 4 1 -3 Rewrite the expression using a determinant. Show all your work. a+b 37) c

28

36)

37)

Solve the problem.

38) Evaluate A by expanding down the third column. Show all your work.

-3 0 0 2 A= 3 1 0 0 5 5 6 4 -2 2 -1 0 Rewrite the expression using a determinant. Show all your work.

39) ax2 + bx Provide an appropriate answer.

1 and B = 3 -5 . Show that AB BA. Show all your work.

40) Let A = -1 1 -1 2 3 Provide an appropriate response.

41) When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Provide an appropriate answer.

42) Let A = 1 -1 and B = 5 4 . Show that A(A + B) = A2 + AB. Show all your work.

5 4 -2 -3 Provide an appropriate response.

43) When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 7. What does this indicate to you about the system of equations?

Solve the problem.

44) Evaluate A by expanding down the third column. Show all your work.

4 -4 -2 A = -4 -1 -5 -5 -3 3 45) Evaluate A by expanding across the second row. Show all your work.

1 -5 -4 A = 0 2 -1 4 1 -3 Provide an appropriate response.

46) Consider the linear equation in three variables x - y + z = 3. Find a pair of linear equations that, when considered together with the given equation, will form a system having infinitely many solutions.

Solve the problem.

47) Evaluate A by expanding across the third row. Show all your work.

5 4 0 -1 -3 -1 -1 5 A= 0 -2 0 5 1 -1 5 0 29

38)

39)

40)

41)

42)

43)

44)

45)

46)

47)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find a system of inequalities with the given graph.

48)

A) y -x + 9 y 4 y x

48)

B) y -x + 9 y 4 y x

C) y y x y

-x + 9 4 0 0

D) y -x + 9 y 4 y x

Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination.

49) 9w + 7x - 5y - 4z = 14 8w + 5x - 8y - 4z = -7 9w - 7x + 6y + 5z = -30 -5w - 4x + 7y + 9z = -5 A) (1, 5, 4, 2) B) (-1, 4, -5, 2) C) (-1, 5, 4, -2) D) No solution Solve the problem.

50) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $60 and on an SST ring is $20?

A) 20 VIP and 0 SST B) 20 VIP and 4 SST C) 24 VIP and 0 SST D) 24 VIP and 4 SST

30

49)

50)

Graph the linear inequality.

51) x - y < -2

51)

A)

B)

C)

D)

Graph the system of inequalities, and find the coordinates of the vertices.

31

52) 6y - x 8, -y + 3x 6, x 0

52)

A)

B)

C)

D)

Given matrix A, find the indicated cofactor.

53) Find A34.

2 0 A= 2 2 0 1 -3 2 A) 10

1 -1 0 1 4 -2 0 0

53)

B) 20

C) 0

32

D) -10

Solve.

54) A canoeist paddled 6 miles upstream in 6 hours and returned to his starting point downstream in 45 minutes. What was the speed of the current?

A) 5 mph B) 4.5 mph C) 4 mph D) 3.5 mph

54)

55) An airplane travels 400 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the speed of the wind.

A) 200 mph B) 100 mph C) 150 mph D) 50 mph

55)

Find the product, if possible.

6 8 -4 56) 7 1 5 -9 -9 1 -7 -6 8 A) -2 17 13

56) B)

C) -2 17 13

33

7 1 5 6 8 -4 -9 -9 1 -7 -6 8

D)

42 8 -20 -63 -9 5 -49 -49 40

Graph.

57) y < x

A)

B)

C)

D)

Let u represent

58)

57)

1 1 1 , v represent , and w represent . Solve first for u, v, and w. Then solve the system of equations. x y z

5 6 1 5 - + =x y z 9

58)

6 1 1 1 + + = x y z 2 1 1 5 91 + + = x y z 18

A) -

1 1 , ,- 1 9 6

B) (-9, 6, -1)

C) (-9, 6, 1)

34

D) -

1 1 , ,1 9 6

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.

59) x + 3y = -8 -14x - 4y = -2 A) (1, -3) B) (-3, 1) C) (3, -1) D) (-1, 3) Decompose into partial fractions.

3x4 - 3x3 + 5x2 + 12x + 13 60) (x + 2) (x - 1)4 A)

1 2 3 5 10 + + + + x + 2 x - 1 (x - 1)2 (x - 1)3 (x - 1)4

B)

5 7 2 4 3 + + + x + 2 x - 1 (x - 1)2 (x - 1)3 (x - 1)4

C)

5 2 17 12 -1 + + + + x + 2 x - 1 (x - 1)2 (x - 1)3 (x - 1)4

D)

3 1 6 2 1 + + + + x + 2 x - 1 (x - 1)2 (x - 1)3 (x - 1)4

59)

60)

Perform the matrix operation.

61) Given A = 0 -1 and B = -2 0 , find AB. 2 3 -1 1 A) B) 1 -1 -4 -6 -7 3 2 4

61) C)

35

-1 1 -1 -7

D)

0 2 -2 3

Find the maximum and minimum values of the function and the values of x and y for which they occur.

62) Q = 2x + 5y, subject to 3x + 2y 6, -2x + 4y 8, x 0, y 0.

A) Maximum: 12

1 1 9 when x = and y = ; minimum: 0 when x = 0 and y = 0 4 2 4

B) Maximum: 13

1 1 5 when x = and y = ; minimum: 0 when x = 0 and y = 0 2 2 2

62)

C) Maximum: 10 when x = 0 and y = 2; minimum: 0 when x = 0 and y = 0 1 1 9 D) Maximum: 12 when x = and y = ; minimum: 4 when x = 2 and y = 0 4 2 4 Write the augmented matrix for the system.

63) 5x + 2y = 9 9x + 8y = 47 A) 5 2 9 B) 5 9 9 9 8 47 2 8 47

63) C) 5 2 47 8 9 9

Decompose into partial fractions.

4x3 + 8x2 + 5x - 7 64) 2x2 - x - 1

D)

9 25 47 9 8

64)

A) 2x + 5 +

16/3 10/3 + 2x + 1 x - 1

B) 2x - 5 +

13 7 + 2x + 1 x - 1

C) 2x + 5 -

7/3 13/3 + 2x + 1 x - 1

D) 2x - 5 -

5/3 1/3 + 2x + 1 x - 1

36

Graph the linear inequality.

65) -3x - 5y -15

A)

B)

C)

D)

Let u represent

66)

65)

1 1 1 , v represent , and w represent . Solve first for u, v, and w. Then solve the system of equations. x y z

1 1 1 + + =1 x y z

66)

1 1 3 1 - - = x y z 3 1 1 1 + + =1 x y z

A) ( , -3, )

B) (-1, 3, 3)

C) ( , -3, -3)

37

D) 1, -

1 1 , 3 3

Solve the problem.

67) A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100.

The camp can accommodate up to 35 staff members and needs at least 20 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost?

A) 13 counselors and 17 aides B) 19 counselors and 23 aides C) 8 counselors and 12 aides D) 13 counselors and 16 aides Find the product, if possible.

3 68) -6 2 3 0 -3 A) -18 0 -9

67)

68) B)

C) -18 0 -9

D) -27

Use the Gauss-Jordan method to find A-1 , if it exists.

108 69) A = 1 2 3 253 A) B) 112 9 -40 16 -3 13 -5 025 -1 833 5 -2

48

69) C)

38

-1 0 -8 -1 -2 -3 -2 -5 -3

D) Does not exist

Graph the linear inequality.

70) y -4

70)

A)

B)

C)

D)

Solve using Cramer's rule.

71) -3x + 5y - z = -15 x - 5y + 9z = x+ y+ z= A) (8, 3, 6)

71)

B) (9, 1, 6)

C) (3, 6, 3)

39

D) (8, -3, -6)

Solve the system.

- 6y + z = -3 72) 5w -w + 5x + y - 5z = 4 + 6z = 20 6w - x + x - 5y - z = -24 A) (5, 0, -5, 0)

72)

B) (-2, 6, 7, -4)

C) (6, -2, 5, -3)

D) (1, -2, -7, -3)

Provide an appropriate response.

73) Suppose that you are solving a system of three linear equations and three variables by the Gaussian elimination method and you obtain the augmented matrix.

73)

1 -11 -15 3 0 10 -6 26 0 -12 1 -18 What row operation would you perform next?

1 .

A) Multiply row 2 by 10

B) Add row 1 to row 2.

C) Multiply row 1 by -

1 .

11

D) Add 12 times row 1 to -11 times row 3 to obtain a zero in the third row, second column position.

Decompose into partial fractions.

560x2 + 320x 74) (x2 + 4)(x + 6)

74)

A)

104x - 304 456 x+6 x2 + 4

B)

104x - 304 456 + x+6 x2 + 4

C)

104x + 456 304 2 x +6 x +4

D)

104x 152 + x+6 x2 + 4

Solve the problem.

75) Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.

The total income from all 3 investments is $1600. The combined income from the 5% and 6% investments is the same as the income from the 8% investment. Find the amount invested at each rate.

A) $8000 at 5%; $10,000 at 6%; $7000 at 8% B) $10,000 at 5%; $10,000 at 6%; $5000 at 8% C) $10,000 at 5%; $5000 at 6%; $10,000 at 8% D) $5000 at 5%; $10,000 at 6%; $10,000 at 8% Decompose into partial fractions.

11x2 - 13x + 6 76) (x - 2)(x2 + 2)

75)

76)

A)

7x + 1 4 + x2 + 2 x - 2

B) -

C)

7x - 1 4 2 x -2 x +2

D)

40

7x + 1 4 + x2 + 2 x - 2

7x + 4 1 + 2 x -2 x +2

Determine the order of the matrix.

2 77) -1 4 A) 1 Evaluate the determinant. x -1 -3 78) x 4 x 3 0 x2

A) 5x3 - 3x + 36

77) B) 3

C) 1 × 3

78) B) 5x3 + 3x + 36

C) 3x3 + 3x - 36

Find the product, if possible.

6 8 -1 -9 2 -5 79) -7 -1 -7 -7 -9 7 -2 5 -5 2 3 5 A) -54 16 5 49 9 -49 -4 15 -25

B)

D) -78 -105 -2 -49 -68 -35 -57 -76 12

A)

Solve.

41 -5 4 88 26 -1 88

D) 3x3 + 3x + 36

79)

C)

80) 5 6

D) 3 × 1

-9 2 -5 -7 -1 -7 -2 5 -5 6 8 -1 -7 -9 7 2 3 5

-78 -49 -57 -105 -105 -76 -2 -35 12

80) B)

C)

16 16 27

D) Not defined 26 -1 88

81) A mother is choosing which baby foods to serve her infant. A jar of meat has 4 g of protein and 32 calories. A jar of vegetables has 2 g of protein and 16 calories. How much of each will she need to serve to get 3 g of protein and 117 calories?

A) There are infinitely many such combinations.

B) 2 jars of meat and 1.5 jars of vegetables C) There is no such combination.

D) 1.5 jars of meat and 2 jars of vegetables

41

81)

Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.

82) 4x + 7y = 102 82) 8x + 14y = 204 A) Consistent; independent B) Inconsistent; dependent C) Consistent; dependent D) Inconsistent; independent Decompose into partial fractions.

4x2 + 2x + 42 83) (x2 - 49)(x - 1) A) C)

83)

2 3 1 + + x-7 x+7 x-1 5

x2 - 49

-

1 x-1

Solve the system.

84) x + y + z = 1 x - y + 2z = 1 4x + y + z = 13 A) (-2, -1, 4)

B)

3 2 1 + x-7 x+7 x-1

D)

5 3 2 + x-7 x+7 x-1

84)

B) (-2, 4, -1)

C) ( , -1, -2)

D) No solution

Write the system of equations that corresponds to the augmented matrix.

5 1 0 17 85) 1 0 8 -17 - 5 10 2 17 A) B) 5x + y 5x + y = 17 = -17 x x + 8z = -17 + 8z = 17 -5x + 10y + 2z = 17 -5x + 10y + 2z = -17 C)

D)

5x + z = 17 x + 8y + 8z = -17 -5x + 10y + 2z = 17

5x + y + z = 17 x + y + 8z = -17 -5x + 10y + 2z = 17

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.

86) -5x + 3y = 8 -2x + 4y = A) (-6, -2) B) (6, 2) C) (2, 6) D) (-2, -6)

42

85)

86)

Solve the problem.

87) Suppose an animal feed to be mixed from soybean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 9 lb of mineral ash. Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein, 10 lb of fat, and 8 lb of mineral ash. Each 100-lb sack of oats costs $10 and contains 20 lb of protein, 5 lb of fat, and 1 lb of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost?

3 9 sacks of soybeans and 1 sacks of oats A) 1 11 11

87)

B) 2 sacks of soybeans and 0 sacks of oats C) 0 sacks of soybeans and 2 sacks of oats 7 5 D) sacks of soybeans and sacks of oats 3 6 Solve using the substitution method. Use a graphing calculator to check your answer.

88) x + y = -11 x-y= A) ( , -5) B) (-5, -6) C) (-6, -5) Solve using Cramer's rule.

89) 8x + 8y = 64 -2x + 5y = 40 A) (0, 9)

D) No solution

89) B) (-1, )

C) (0, 8)

Solve using the elimination method. Use a graphing calculator to check your answer.

90) 9x + 8y = 16 -3x - 6y = 18 A) (8, -6) B) (8, -7) C) (7, -6) Write the augmented matrix for the system.

91) 8x + 7y + 2z = 97 3x + 7y + 6z = 81 5x + 2y + 3z = 41 8 7 2 8 5 5 97 A) 3 7 6 B) 7 7 2 81 5 2 3 2 6 3 41

D) No solution

90) D) No solution

91)

97 2 7 8 C) 81 6 7 3 41 3 2 5

Perform the matrix operation.

92) Given A = 8 -9 and I = 1 0 , find IA. 8 3 01 A) B) 0 -1 -9 8 0 11 3 8 Solve the system.

93) x - y + 5z = -23 -4x + 4y - 20z = -5 x + 4y + z = 3 A) (-5, 0, )

88)

8 7 2 97 D) 3 7 6 81 5 2 3 41

92) C)

8 -9 8 3

D)

8 3 8 -9

93)

B) (-5, , 0)

C) (0, 2, -5)

43

D) No solution

Solve the problem.

94) A croissant, a cup of coffee, and a fruit bowl from Kelley's Coffee Cart cost a total of $5.50, and a croissant costs twice as much as a cup of coffee. Kelley posts a notice announcing that, effective next week, the price of a croissant will go up 20% and the price of coffee will go up 15%. After the increase, the total price of the purchase will be $5.91. Find the cost of each item before the increase.

A) A fruit bowl costs $3.25, a croissant costs $1.50, and a cup of coffee costs $0.75.

B) A fruit bowl costs $3.25, a croissant costs $0.86, and a cup of coffee costs $1.80.

C) A fruit bowl costs $3.25, a croissant costs $1.80, and a cup of coffee costs $0.86.

D) The prices cannot be determined from the given information.

Solve using Cramer's rule.

95) x + 4y = 41 -6x + 3y = -3 A) ( , ) Solve.

96) x 3 = 6 21 A) -4

94)

95) B) (-5, 10)

C) ( , )

D) No solution

96) B) 12

C) 6

44

D) 2

Graph the system of inequalities, and find the coordinates of the vertices.

97) 2y + x -2, y + 3x 9, y 0, x 0

A)

B)

C)

D)

Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination.

98) 5w + 5x - 5y - 5z = -4 -w - 2x - 2y - z = -2 4w + 5x + 5y + 4z = -5 4w + 6x + 6y + 4z = 6 5 2 A) , - , 5, -1 B) (-z, z, -z, z) 2 5 C) -

5 2 z, z, - 5z, z 2 5

D) No solution

45

97)

98)

Perform the matrix operation.

99) Given A = -3 4 , find 3A. 0 2 A) B) 0 7 -9 4 0 2 3 5 Find the product, if possible.

-6 100) 4 -7 7 3 -5 -6 9 3 A) 39 -24

99) C)

D)

-9 12 0 2

-9 12 0 6

100) B)

C) -24 39

4 -7 7 -5 -6 9 -6 3 3

D) -24 39

Solve.

101) x 1 = -1 2x A) -1

101) B) 1

C) -1, 1

D) - -1,

-1

102) Tickets for the school play cost $7 for students and $10 for adults. On opening night, all 360 seats were filled, and the box office revenues were $2,580. How many student and how many adult tickets were sold?

A) 340 student and 20 adult B) 340 adult and 20 student C) 360 student and 0 adult D) 320 adult and 40 student Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.

103) -5x - y - 3z = -71 5x + 4z = 73 6y + z = 37 A) (-9, 5, 18) B) (9, 5, 7) C) (9, 7, 5) D) No solution Use the Gauss-Jordan method to find A-1 , if it exists.

104) A = 5 -4 -1 2 A) B) 1 2 5 2 3 3 6 3 -

105) A = A)

1 5 6 6

4 -1 -2 1 -2 1-

102)

103)

104) C)

1 1 6 3

D)

1 2 3 3 1 5 6 6

1 2 3 3 -

1 6

5 6

105) 1 2 1 2

B)

C)

1 1 - 2 2 -1 -2

1 1 2 2 -1

46

2

D)

1 1 2 2 1 2

Let u represent

106)

1 1 1 , v represent , and w represent . Solve first for u, v, and w. Then solve the system of equations. x y z

3 1 5 37 - - = x y z 24 -

106)

1 5 6 37 - + =x y z 8

4 1 1 1 - - = x y z 3

A) ( , , -3)

B) ( , , )

C)

1 1 1 , , 8 2 3

D)

1 1 1 , ,8 2 3

Decompose into partial fractions.

3x3 - 6x2 - 6x + 14 107) (x - 1)3 (x + 4)

107)

A)

1 2 1 2 + + + x - 1 (x - 1)2 (x - 1)3 x + 4

B)

1 2 1 2 + + x - 1 (x - 1)2 (x - 1)3 x + 4

C)

2 1 2 1 + x - 1 (x - 1)2 (x - 1)3 x + 4

D)

1 1 2 1 + x - 1 (x - 1)2 (x - 1)3 x + 4

Solve the problem.

108) The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the 3 years considered.

Year, x 1990, 0 1996, 6 2008, 18

Number of dog collars (in thousands) 20.0 14.0 23.6

Fit a quadratic function f(x) = ax2 + bx + c to the data. What is the value of b?

A) -1.2 B) -1.6 C) 2.3

Evaluate the determinant.

2 -2 109) x x 6 A) -6x2 + 2x

108)

D) 1.9

109) B) 6x2 - 2x

C) -6x2 - 2x

47

D) 6x2 + 2x

Solve the problem.

110) The following table shows the number of resistors, in thousands, produced by Allied Electronics in 3 recent years.

Year, x 2003, 0 2006, 3 2008, 5

110)

Number of resistors (in thousands) 12 69 137

Fit a quadratic function f(x) = ax2 + bx + c to the data. Using this function, what would you predict the resistor production of Allied Electronics to be in 2020?

A) 1,109,500 resistors B) 1,044,500 resistors C) 1,056,000 resistors D) 1,049,000 resistors

Use the Gauss-Jordan method to find A-1 , if it exists.

111) A = -1 5 5 -20 A) B) 4 1 -20 -5 1 -4 -1 1 5

111) C)

1 4 5 20

D) Does not exist

Solve.

112) A student takes out two loans totaling $16,000 to help pay for college expenses. One loan is at 7% simple interest, and the other is at 10% simple interest. The first-year interest is $1,300. Find the amount of the loan at 10%.

A) $10,000 B) $600 C) $700 D) $6,000 Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.

113) 3x - y + 5z = 25 2x + 2y - 3z = 9 -3x - 2y + z = -22 A) (-3, 9, 6) B) (3, 5, 9) C) (3, 9, 5) D) No solution

48

112)

113)

Find the maximum and minimum values of the function and the values of x and y for which they occur.

114) F = 8x + 12y, subject to 40x + 80y 560, 6x + 8y 72, x 0, y 0.

114)

A) Maximum: 100 when x = 8 and y = 3; minimum: 0 when x = 0 and y = 0 B) Maximum: 100 when x = 8 and y = 3; minimum: 84 when x = 0 and y = 7 C) Maximum: 96 when x = 12 and y = 0; minimum: 0 when x = 0 and y = 0 D) Maximum: 96 when x = 12 and y = 0; minimum: 84 when x = 0 and y = 7 Find x and y.

115) x+3 y+4 = 9 6 -3 7 7 -3 A) x = 6, y = 2

115)

B) x = -6, y = -2

C) x = 6, y = -3

Use the Gauss-Jordan method to find A-1 , if it exists.

116) A = 0 -3 0 7 A) B) -3 3 -3 0 7 -7 7 0

D) x = 9, y = 6

116) C)

0 3 0 -7

D) Does not exist

Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination.

117) x - y + 5z = -9 4x + z = -1 x + 5y + z = A) (-1, 4, 0) B) (-1, 0, 4) C) (0, 4, -1) D) No solution

49

117)

Graph.

118) y

118)

x

A)

B)

C)

D)

Determine the order of the matrix.

119) 3 -3 9 7 A) 1

119) B) 4 × 1

C) 4

D) 1 × 4

Solve.

120) A lumber yard has fixed costs of $4,300.00 per day and variable costs of $0.19 per board-foot produced. Lumber sells for $2.19 per board-foot. How many board-feet must be produced and sold daily to break even?

A) 1,433 board-feet B) 1,806 board-feet C) 2,150 board-feet D) 22,631 board-feet

50

120)

121) In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A) 1.5 L B) 3.0 L C) 2.5 L D) 0.5 L Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination.

122) 9w + 7x - 6y - 4z = -23 8w + 5x - 9y - 4z = -31 9w + 7x + 7y + 5z = 20 -6w - 4x + 7y + 9z = 19 A) (2, 3, -4, -2) B) (-1, 4, -5, 2) C) (2, -3, 4, -1) D) No solution Use the Gauss-Jordan method to find A-1 , if it exists.

0 3 0 -3 123) A = 6 9 -2 -6 12 6 -4 -3 18 0 -4 0

A)

C)

1 3

1 3

1

-

2 3

1 3

3 2

-

3 2

2 3

-

B)

1 1 3 3

1 6

0

-1

2 1 3 3

0

3 2

1 2

-

3 2

3 3 2 2

1 2

2 3

1 3

0

-

4 3

2 1 3 3

0

1 3

-1

3 2

4 3

1 3

2 3

3 2

1 3

-

-

1 1 3 3 1 6

-

0

-

3 2 1 2

-

1 6

-

D) Does not exist

1 3 0

Decompose into partial fractions.

3x - 21 124) (x + 5)(x - 4) A)

1 4 x-4 x+5

122)

123)

1 3

-

1 3

121)

124) B)

3 21 x+5 x-4

C)

51

4 1 x+5 x-4

D)

4 1 + x+5 x-4

Solve the problem.

125) The following table shows the market prices per pound that a trucker can get for his load of fruit in three cities: San Francisco (S.F.), Las Vegas (L.V.), and Los Angeles (L.A).

125)

S.F. L.V. L.A. Peaches $0.50 $0.60 $0.40 Apples $0.40 $0.80 $0.50 The trucker has a load of 1,000 pounds of peaches and 3000 pounds of apples. Write the information from the table as a 2 x 3 matrix B. Write a row matrix A for which the entries represent the number of pounds of each type of fruit in the truck. If C = AB, find c12. What does this entry of C represent?

A) c12 = 3,000. c12 represents the total value of the load in San Francisco.

B) c12 = 1,600. c12 represents the total value of the load in Las Vegas.

C) c12 = 3,000. c12 represents the total value of the load in Las Vegas.

D) c12 = 1,250. c12 represents the total value of the load in Las Vegas.

Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.

126) 6 = 4x + 6y 126) -18y - 12x = -18 A) Consistent; dependent B) Inconsistent; independent C) Consistent; independent D) Inconsistent; dependent Write a matrix equation equivalent to the system of equations.

127) x + y + z = -5 2x - 2y + 4z = -5 -5x + 2y + 4z = 3 A) B) x 11 1 11 1 -5 -2 4 -5 y -2 4 -5 = 2 -5 2 4 -5 2 4 z 3 C) D) 0 00 x 1 11 -5 = -5 2 -2 4 y 2 -2 4 -5 2 4 -5 2 4 z 3

127)

x y z

=

x y z

-5 = -5 3

-5 2 3

Solve the problem.

128) Softee Blankets charges $6 for shipping orders of $20 or less, $10 for orders from $20.01 to $70, and $15 for orders over $70. One week shipping charges for 540 orders totaled $5,320. There were 50 more orders for $20 or less shipped than there were orders for over $70. Find the number of orders shipped at each rate.

A) $20 or less: 290; $20.01 to $70: 130; over $70: 120 B) $20 or less: 250; $20.01 to $70: 170; over $70: 120 C) $20 or less: 170; $20.01 to $70: 250; over $70: 120 D) The numbers cannot be determined from the given information.

52

128)

Solve.

129) 3 x = -13 x4 13 A) 3

129) B) 25

C) -5, 5

D) No solution

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.

130) 2x + 8y + 6z = 20 4x + 2y - 2z = -2 3x - y + z = 11 A) (2, 1, 6) B) (2, -1, 4) C) (-1, 2, 1) D) No solution Solve the problem.

131) The matrices give points and rebounds for five starting players in two games. Find the matrix that gives the totals.

Points Rebounds 22 3 16 5 F= 8 12 6 11 10 2

S=

A)

Points Rebounds 18 4 17 3 12 9 4 10 10 3 62 5

B)

7 33 21 21 5

C)

40 8 20 10 20

Use the Gauss-Jordan method to find A-1 , if it exists.

132) A = 4 1 1 -5 A) B) 4 1 5 1 21 21 21 21 1 5 21 21

1 21

D) 5 62

130)

131)

40 7 33 8 20 21 10 21 20 5

132) C)

4 21

5 21

1 21

1 4 21 21

53

D) -

5 1 21 21

-

1 21

4 21

Decompose into partial fractions.

4x3 + 8x2 - 6x + 2 133) 2x2 - x - 1

133)

A) 2x + 5 -

7/3 13/3 + 2x + 1 x - 1

B) 2x + 5 -

13/3 8/3 + 2x + 1 x - 1

C) 2x - 5 -

5/3 1/3 + 2x + 1 x - 1

D) 2x - 5 -

13 7 + 2x + 1 x - 1

Graph the system of inequalities, and find the coordinates of the vertices.

134) 3x - 2y 6 x-1 0

A)

B)

C)

D)

54

134)

Write a matrix equation equivalent to the system of equations.

135) 5x - 8y = 4 -6x + 7y = -1 A) B) 5 -8 x = 4 x 5 -8 = 4 -6 7 y -1 -1 y -6 7 C) D) 4 -8 x = 5 5 -8 4 = x -6 7 y -6 -6 7 -1 y Solve using the elimination method. Use a graphing calculator to check your answer.

136) -5x + 0 = y -3x + 2y = A) (-3, 3) B) (-3, 4) C) (-4, 4)

135)

136) D) No solution

Solve the problem.

137) A computer manufacturer has three outlet stores that sell its four computer systems. The following table shows the numbers of systems sold by the three stores in July.

System 1 System 2 System 3 System 4

137)

Store 1 Store 2 Store 3 20 10 20 40 20 20 10 50 10 30 30 30

The prices of the systems are: $1200 for System 1, $1500 for System 2, $1600 for System 3, and $ 2,000 for System 4. Write the information from the table as a 4 x 3 matrix B. Write a row matrix A for which the entries represent the prices for the systems. If C = AB, find c12. What does this entry of C represent?

A) c12 = 182,000. c12 represents the total sales at Store 2 in July.

B) c12 = 170,000. c12 represents the total sales at Store 3 in July.

C) c12 = 160,000. c12 represents the total sales at Store 1 in July.

D) c12 = 150,000. c12 represents the sales of System 2 at all stores in July.

Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination.

138) x + 4y - 3z = 4 -8x - 8y + 6z = -8 6x + 16y - 9z = 3 6 1 1 3 6 9 1 z- ,- z- ,z z+ , z- ,z A) B) 10 5 5 5 10 5 20 5 C)

6 1 ,- ,0 5 5

D) No solution

55

138)

Find a system of inequalities with the given graph.

139)

A) y y x x y

-x + 3 0 0 9 7

139)

B) y -x + 3 x 9 y 7

C) y y x y

-x + 3 0 0 7

D) y y x x

-x + 3 0 0 9

Solve the problem.

140) A $112,000 trust is to be invested in bonds paying 6%, CDs paying 5%, and mortgages paying 8%.

The bond and CD investment must equal the mortgage investment. To earn a $7,610 annual income from the investments, how much should the bank invest in bonds?

A) $31,000 B) $56,000 C) $23,000 D) $33,000

56

140)

Graph the linear inequality.

141) x + y < -6

141)

A)

B)

C)

D)

Graph the inequality.

57

142) x + y

142)

3

A)

B)

C)

D)

Decompose into partial fractions.

43x - 144 143) 6x2 - 43x + 72 A)

9 8 + 2x - 9 3x - 8

143) B)

9 8 2x - 9 3x - 8

C)

58

9 8 + 2x + 9 3x + 8

D)

8 9 3x - 8 2x - 9

Write the system of equations that corresponds to the augmented matrix.

144) 1 7 -2 18 1 8 A) B) C) 7x + y = -2 7x + 7y = -2 x + 7y = -2 x + 18y = 8 18x + 18y = 8 18x + y = 8

144) D)

x + y = -2 x+y= 8

Given matrix A, find the indicated minor.

145) Find M42.

-6 A = -3 0 -3 A) 6

0 2 5 2

5 -1 0 1 4 -2 0 0

Solve the system.

146) 5w + x - 3y + z = 20 -w + 5x + y - 5z = 10 2w - x + 5y + 3z = 4 w + x - 5y - z = 4 A) (-2, 5, 2, 1)

145)

B) 3

C) -6

D) 0

146)

B) (-6, -1, 2, 5)

C) (6, -4, 0, 5)

D) (6, -2, 1, -5)

Solve the problem.

147) A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F1 and F2 . For one year, species A requires 1.5 units of F1 and 1.25 units of F2 . Species B requires 2.0 units of F1 and 1.8 units of F2 . The forest can normally supply at most 947 units of F1 and 487 units of F2 per year. What is the maximum total number of these animals that the forest can support?

A) 324 animals B) 389 animals C) 956 animals D) 177 animals

59

147)

Answer Key Testname: C6

1) A 2) B 3) B 4) B 5) B 6) D 7) B 8) D 9) A 10) A 11) B 12) A 13) A 14) A 15) A 16) C 17) B 18) B 19) B 20) D 21) A 22) B 23) D 24) B 25) A 26) A 27) C 28) C 29) B 30) D 31) D 32) D 33) D 34) A 35) A 36) Answers may vary. One possible solution follows.

A = 3 2 -2 + 0 2 -4 - 1 2 -4 4 -3 4 -3 2 -2 = 3(-6 + 8) + 0(-6 + 16) - 1(-4 + 8) = 3(2) + 0(10) - 1(4) = 2 37) Answers will vary. One possible solution follows. a -b a+b 1 1 1 1 1 = a + b = (a) + (b) = (a) - (-b) = 1 1 c c c c c c c c

60

Answer Key Testname: C6

38) Answers may vary. One possible solution follows.

31 0 -3 0 2 -3 0 2 -3 0 2 A =0 55 4 +0 554 +6 310 +1 3 10 5 54 -2 2 0 -2 2 0 -2 2 0 = 6 2 3 1 + 0 -3 0 + 0 -3 0 + 1 2 3 1 + 0 -3 0 + 4 -3 0 3 1 5 5 5 5 3 1 -2 2 -2 2 = 6 2(6 + 2) + 0(-6 + 0) + 0(-3 - 0) + 1 2(15 - 5) + 0(-15 - 0) + 4(-3 - 0) = 6 2(8) + 0(-6) + 0(-3) + 1 2(10) + 0(-15) + 4(-3) = 6(2)(8) + 1(20 - 12) = 96 + 8 = 104 39) Answers will vary. One possible solution follows. a -b ax2 + bx = (a)(x2 ) + (b)(x) = (a)(x2 ) - (-b)(x) = x x2 40) Answers may vary. One possible solution follows.

Left-hand side: 1 3 -5 = -8 8 AB = -1 1 -1 2 3 1 -1 Right-hand side: 1 = -8 8 BA = 3 -5 -1 2 3 1 -1 1 -1 41) The system has dependent equations.

42) Answers may vary. One possible solution follows.

Left-hand side: 1 -1 + 5 4 = 1 -1 A(A + B) 5 4 -2 -3 -2 -3 -1 1 6 3 3 2 = = 3 1 -2 -3 -21 -9 Right-hand side: = A2 + AB

1 -1 1 -1 + 1 -1 5 4 -2 -3 -2 -3 -2 -3 5 4 3 2 0 0 = + -25 -20 4 11 3 2 = -21 -9

43) The system is inconsistent.

44) Answers may vary. One possible solution follows.

A = -2 -4 -1 + 5 4 -4 + 3 4 -4 -5 -3 -5 -3 -4 -1 = -2(12 - 5) + 5(-12 - 20) + 3(-4 - 16) = -2(7) + 5(-32) + 3(-20) = -234 45) Answers may vary. One possible solution follows.

A = 0 -5 -4 + 2 1 -4 + 1 1 -5 1 -3 4 -3 4 1 = 0(15 + 4) + 2(-3 + 16) + 1(1 + 20) = 0(19) + 2(13) + 1(21) = 47 46) Answers will vary. One example: 3x - 3y + 3z = 9 and 3x + 2y - 3z = 5 61

Answer Key Testname: C6

47) Answers may vary. One possible solution follows.

4 0 -1 5 0 -1 5 4 -1 5 4 0 A = 0 -1 -1 5 + 2 -3 -1 5 + 0 -3 -1 5 - 5 -3 -1 -1 1 5 0 1 -1 0 1 -1 5 -1 5 0 = 2 5 -1 5 - 0 -3 5 - 1 -3 -1 - 5 5 -1 -1 - 4 -3 -1 + 0 -3 -1 5 0 1 0 1 5 1 5 1 -1 -1 5 = 2 5(-25) - 0 - 1(-14) - 5 5(-6) - 4(-14) + 0 = 2 -111 - 5 26 = -352 48) D 49) C 50) A 51) B 52) C 53) D 54) D 55) D 56) B 57) D 58) C 59) A 60) A 61) B 62) A 63) A 64) A 65) B 66) A 67) C 68) C 69) B 70) D 71) A 72) C 73) A 74) B 75) C 76) A 77) D 78) A 79) C 80) D 81) C 82) C 83) B 84) C 85) A 86) C 87) B 88) B 89) C 62

Answer Key Testname: C6

90) B 91) D 92) C 93) D 94) A 95) C 96) B 97) A 98) D 99) D 100) D 101) C 102) A 103) B 104) C 105) D 106) A 107) B 108) B 109) D 110) D 111) B 112) D 113) C 114) A 115) A 116) D 117) C 118) B 119) D 120) C 121) A 122) C 123) B 124) C 125) C 126) A 127) D 128) C 129) C 130) B 131) D 132) C 133) B 134) B 135) A 136) A 137) A 138) B 139) A 63

Answer Key Testname: C6

140) D 141) D 142) C 143) A 144) C 145) A 146) D 147) B

64

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Match the given equation with one of the graphs.

1) x2 + y2 = 4 A)

B)

C)

D)

1

1)

2) x2 = 4y A)

B)

C)

D)

2

2)

3) 36x 2 + 4y2 = 144 A)

B)

C)

D)

3

3)

4) x2 + y2 - 4x - 6y = -4 A)

B)

C)

D)

4

4)

5) 36x 2 + 36y2 = 1,296 A)

B)

C)

D)

5

5)

6) y2 - x2 = 81 A)

B)

C)

D)

6

6)

Match the system of equations with one of the graphs.

7) x2 + y2 + 13y = 0

7)

x2 + y2 = 2x

A)

B)

C)

D)

7

Match the given equation with one of the graphs.

8) y2 = 3x A)

B)

C)

D)

8

8)

9) 100x2 + 4y2 = 400 A)

B)

C)

D)

9

9)

10) y2 = 25 - x2 A)

B)

C)

D)

10

10)

11)

(x + 4)2 (y - 5)2 =1 64 16

11)

A)

B)

C)

D)

11

12) y2 - 4x2 = 36 A)

B)

C)

D)

12

12)

13) 2y2 - 32x - 16 = 0 A)

B)

C)

D)

13

13)

14) x2 = -3y A)

B)

C)

D)

14

14)

Match the system of equations with one of the graphs.

15) x2 + 9y2 = 9

15)

x2 + y2 = 49

A)

B)

C)

D)

15

Match the system of inequalities with one of the graphs.

16) y -x2

16)

x + y -2 A)

B)

C)

D)

16

17) x2 + y2 49 y 5x A)

B)

C)

D)

17)

17

Match the given equation with one of the graphs.

18) 9x2 + 49y2 = 441 A)

B)

C)

D)

18

18)

Match the system of inequalities with one of the graphs.

19) x2 + y2 49

19)

x+y> 3 A)

B)

C)

D)

19

Match the given equation with one of the graphs.

20) 64x 2 + y2 - 512x + 960 = 0

20)

A)

B)

C)

D)

20

21) x2 - y2 = 100 A)

B)

C)

D)

21

21)

22) (x + 4)2 = 6(y - 4) A)

B)

C)

D)

22

22)

Match the system of equations with one of the graphs.

23) y2 - 2y = x - 6

23)

xy = 5 A)

B)

C)

D)

23

Match the given equation with one of the graphs.

24) 4x2 + 49y2 = 196 A)

B)

C)

D)

24

24)

25) 64x 2 - 36y2 = 2,304 A)

B)

C)

D)

25

25)

26)

x2 y2 =1 9 64

26)

A)

B)

C)

D)

26

Match the system of equations with one of the graphs.

27) x2 - y2 = 81

27)

x2 + y2 = 36

A)

B)

C)

D)

27

Match the system of inequalities with one of the graphs.

28) x2 + y2 < 16

28)

y 1 A)

B)

C)

D)

28

Match the given equation with one of the graphs.

29) (y + 1)2 = 8(x + 6) A)

B)

C)

D)

29

29)

Match the system of equations with one of the graphs.

30) xy = 9 x+y=6 A)

30) B)

C)

D)

30

Match the given equation with one of the graphs. y2 x2 =1 31) 25 9

31)

A)

B)

C)

D)

31

32) x2 + y2 - 4x + 8y = -16 A)

B)

C)

D)

32

32)

33) (x + 4)2 = 2(y + 3) A)

B)

C)

D)

33

33)

34)

x2 y2 =1 81 16

34)

A)

B)

C)

D)

34

Match the system of inequalities with one of the graphs.

2 35) y > x - 9 2y - x < -12 A)

35) B)

C)

D)

35

Match the given equation with one of the graphs.

36) x2 + y2 + 8x + 4y = -11 A)

B)

C)

D)

36

36)

37)

(y - 3)2 (x + 2)2 =1 49 25

37)

A)

B)

C)

D)

37

Match the system of equations with one of the graphs.

38) x2 - y2 = 64

38)

x2 + y2 = 81

A)

B)

C)

D)

38

Match the given equation with one of the graphs.

39) x2 + y2 + 4x + 4y = 0 A)

B)

C)

D)

39

39)

40) 2x2 + 3y2 - 20x + 30y + 119 = 0

40)

A)

B)

C)

D)

40

Match the system of equations with one of the graphs.

41) 25x 2 + 9y2 = 225

41)

x+y=6 A)

B)

C)

D)

41

42) y= x2 - 2x - 6 4y - x = 3 A)

B)

C)

D)

42)

42

Match the given equation with one of the graphs.

43) 2x2 + 16y = 8 A)

B)

C)

D)

43

43)

Match the system of equations with one of the graphs.

44) x2 - y2 = 16

44)

x - 4 = 7y A)

B)

C)

D)

44

Match the given equation with one of the graphs.

45) 16x 2 - 64y2 = 1,024 A)

B)

C)

D)

45

45)

46) y2 = -3x A)

B)

C)

D)

46

46)

47) 64x2 + 16y2 = 1,024 A)

B)

C)

D)

47

47)

Match the system of equations with one of the graphs.

48) 16x 2 + 49y2 = 784

48)

y- x=4 A)

B)

C)

D)

48

Match the given equation with one of the graphs.

49) (y - 3)2 = -2(x + 4) A)

B)

C)

D)

49)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide the proper response.

Solve.

50) Describe the graph of the equation (x - 6)2 + (y - 4)2 = 0.

50)

51) Is the graph of a parabola with vertical axis the graph of a function? Explain your answer.

51)

52) Which hyperbola is wider? Explain. x2 y2 x2 y2 I) II) =1 =1 9 36 9 144

52)

Provide the proper response.

53) Is the graph of a circle the graph of a function? Explain your answer.

Solve.

54) Find an equation for the hyperbola with vertices (4, 2) and (4, 6) and e = 14.

49

53)

54)

Provide the proper response.

55) Describe the graph of the equation (x - 4)2 + (y - 3)2 = -25.

55)

56) Indicate whether the following equation is an ellipse or a hyperbola.

196x2 + 9y2 = 1,764

56)

57) Explain why the graph of a hyperbola does not satisfy the conditions for the graph of a function.

57)

58) Without graphing, justify why x2 + 9 - 6x - 16y + 48 = 0 is the equation of a parabola.

58)

Solve.

59) Find an equation of an ellipse with vertices (-5,0) and (5, 0) and eccentricity equal to

60) Find an equation for the hyperbola with vertices (4, -2) and (4, 6) and e =

4 .

8

59)

7 .

4

61) Find an equation of an ellipse with vertices (0, -11) and (0, 11) and eccentricity equal to

60)

2 .

7

Provide the proper response.

62) Explain in your own words how you can tell from the equation whether the graph is an ellipse or a hyperbola.

Solve.

63) Find the eccentricity of an ellipse whose vertices are (-21, 0) and (21, 0) and whose foci are (-15, 0) and (15, 0).

Provide the proper response.

64) Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up and down or left and right.

65) Discuss the graph of the equation

x2 y2 + = 1 if a = b. a 2 b2

50

61)

62)

63)

64)

65)

66) To graph

x2 y2 = 1 on a graphics calculator, we must consider the union of the graphs 16 36

of the two functions. y1 = 6

x2 - 1 and y2 = -6 16

explain (a) how the solution set of

66)

x2 x2 - 1. Using the graph of y = - 1, 16 16

x2 - 1 0 can be determined graphically and (b) how it 16

relates to the domain of the hyperbola.

Solve.

67) Find the eccentricity of an ellipse whose vertices are (0, -54) and (0, 54) and whose foci are (0, -34) and (0, 34).

67)

68) Which hyperbola has larger eccentricity?

I)

68)

II)

69) Find the eccentricity of the hyperbola given by

x2 y2 =1 9 36

51

69)

Provide the proper response.

70) Solve the given system of equations x2 + y2 = 5

70)

xy = 2

71) Discuss the symmetries exhibited by an ellipse centered at the origin.

71)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Graph the system of inequalities. Shade the region that represents the solution set.

72) x2 + y 3 x2 - y 1

A)

B)

C)

D)

52

72)

Find the vertex, the focus, and the directrix of the parabola.

73) y = -2x2 - 4x + 2 = 0 1 A) V: -1, ; F: (-1, 2); D: x = 6 2

C) V: -1, -

23 33 31 ; F: -1, ; D: x = B) V: -1, 25 8 8

5 ; F: (-1, -4); D: x = -12 2

D) V: (-1, ); F: -1,

; D: y =

Find the equation of the hyperbola satisfying the given conditions.

2 2 74) Vertices at (0, 4) and (0, -4); asymptotes y = x and y = - x 9 9 A)

y2 x2 =1 16 81

B)

y2 x2 =1 16 324

C)

53

y2 x2 =1 324 16

73)

74) D)

y2 x2 =1 81 4

Graph the parabola and its vertex, focus, and directrix.

75) y2 = -8x

75)

A)

B)

C)

D)

Find the vertex, the focus, and the directrix of the parabola.

76) (y - 8)2 = -8(x + 2) A) V: (-2,8); F: (-4, 8); D: x = C) V: (-2,8); F: (-4, 8); D: x = -2

B) V: (0,8); F: (-4, 8); D: x = 0 D) V: (-2,8); F: (-4, 6); D: x =

Find the foci of the given hyperbola. y2 x2 =1 77) 9 4

76)

77) B) (0, - 13) , (0, D) (0, -3), (0, 3)

A) (-2, 0), (2, 0) C) (- 13, 0) , ( 13, 0) 54

13)

Solve.

78) 5x2 - 2y2 = 13 3x2 + 2y2 = 59

78)

A) (3, 4), (4, 3), (-3, -4), (-4, -3) C) (3, 4), (-3, 4), (3, -4), (-3, -4)

B) (-3, -4), (-4, -3) D) (3, -4), (3, 4)

Graph the circle.

79) x2 + y2 - 6x - 10y + 25 = 0

79)

A)

B)

C)

D)

Graph the parabola.

55

80) y =

Solve.

1 2 x 16

80)

A)

B)

C)

D)

81) x2 + y2 = 23 y2 = 2x + 15 A) (2, C) (2,

19), (-4, 19), (-3,

81) 7), (2, - 19), (-4, - 7) 7), (2, - 19), (-3, - 7)

B) (2, 2 5), (-4, 2 5), (2, -2 5), (-4, -2 5) D) (3, 19), (-4, 7), (3, - 19), (-4, - 7)

Graph.

56

82) x2 - y2 = 32

Solve.

82)

A)

B)

C)

D)

83) x2 + y2 + 9y = 0 x2 + y2 = 5x

83)

A) (0,1)

405 225 ,106 106

B) (1, -1)

405 225 ,106 106

C) (0,0)

405 225 ,106 106

D) (1,0)

405 225 ,106 106

57

84) 2x2 + y2 = 17 3x2 - 2y2 = -6

84)

A) (1, 3) and (-1, -3) C) (2, -3) and (-2, 3)

B) (1, 3), (1, -3), (-1, 3), (-1, -3) D) (2, 3), (2, -3), (-2, 3), (-2, -3)

Graph.

1 85) y2 - x2 = 16

85)

A)

B)

C)

D)

Find an equation of a parabola satisfying the given conditions.

86) Focus (0, 2 ), directrix y = -2 A) y2 = 4 x B) x2 = 8 y C) y2 = 8 x Graph.

58

D) x2 = 2 y

86)

87) 9x2 - y2 = 36

87)

A)

B)

C)

D)

Find the equation of the hyperbola satisfying the given conditions.

88) Vertices at (0, 2) and (0, -2); foci at (0, 4) and (0, -4) y2 x2 y2 x2 y2 x2 =1 =1 =1 A) B) C) 4 16 4 12 12 4

59

y2 x2 =1 D) 16 4

88)

Find the focus and directrix of the parabola.

89) x2 + 20y = 0 A) F: (-5, 0); D: y = 5 C) F: (0, -5); D: y = 5

B) F: (0, -5); D: x = 5 D) F: (0, -5); D: y = -5

Draw the graph of the equation.

90) (y - 4)2 = 2(x - 2)

89)

90)

A)

B)

C)

D)

60

Find the vertices and the foci of the given ellipse. x2 y2 + =1 91) 100 36

91)

A) V: (0, -10), (0, 10); F: (0, -6), (0, 6) C) V: (-10, 0), (10, 0); F: (-8, 0), (8, 0) Solve.

B) V: (-10, 0), (10, 0); F: (-6, 0), (6, 0) D) V: (0, -10), (0, 10); F: (0, -8), (0, 8)

92) Find the dimensions of a rectangular enclosure with perimeter 32 yd and area 55 yd2 .

A) 6 yd by 10 yd B) 5 yd by 10 yd C) 6 yd by 11 yd D) 5 yd by 11 yd

61

92)

Graph the circle.

93) x2 + y2 + 12x + 10y + 52 = 0

93)

A)

B)

C)

D)

Find the center of the hyperbola.

94) 6x2 - y2 - 36x + 12y - 132 = 0 A) (-2, 6);

Solve.

B) (3, 1);

C) (-3, -6)

95) 5x2 - 5y2 = 5 2x 2 + y2 = 2

D) (3, 6)

94)

95)

A) (0, -1), (0, 1) C) (-1, -2), (-1, 2), (1, -2), (1, 2)

B) (-1, 2), (1, 2) D) (-1, 0), (1, 0)

62

96) 64x 2 + 25y2 = 1,600 5y - 8x = 40 A) (0, 8), (-5,0)

96) B) (0, -5), (8, 0)

C) (0, 5), (0, -8)

D) (0, -8), (5, 0)

Find the vertices and the foci of the given ellipse. x2 y2 + =1 97) 256 400

97)

A) V: (0, -20), (0, 20); F: (0, -12), (0, 12) C) V: (-20, 0), (20, 0); F: (-12, 0), (12, 0)

B) V: (-20, 0), (20, 0); F: (0, -16), (0, 16) D) V: (0, -20), (0, 20); F: (-16, 0), (16, 0)

Find the foci of the ellipse.

98) 36(x - 3)2 + 25(y + 2)2 = 900

98)

A) ( - 11, -2), ( + 11, -2) C) ( , -2 - 11), ( , -2 + 11)

B) (-2, 3 - 11), (-2, 3 + D) ( , 4), ( , -8)

Find an equation of an ellipse satisfying the given conditions.

99) Foci: (0,-2) and (0, 2) ; length of major axis: 10 x2 y2 x2 y2 x2 y2 + =1 + =1 + =1 A) B) C) 25 10 21 25 10 25 Find the focus and directrix of the parabola.

100) y2 = 24x A) F: (6, 0); D: x = -6 C) F: (6, 0); D: x = 6

11)

D)

x2 y2 + =1 25 21

99)

100)

B) F: (6, 6); D: x = 6 D) F: (0, 6); D: y = -6

Solve.

101) x2 + xy + y2 = 39 x+y=2 A) (-5, 7) C) (7, -5)

101) B) (6, -4), (-6, 8) D) (7, -5) , (-5, 7)

102) The roof of a building is in the shape of the hyperbola y2 - 10x2 = 64, where x and y are in meters.

Refer to the figure and determine the height, h, of the outside walls.

A=4 m

A) 26 m

B) 15 m

C) 224 m

63

D) 5.1 m

102)

Graph the system of inequalities. Shade the region that represents the solution set. y x2 103) x+y> 3

A)

B)

C)

D)

64

103)

Solve.

104) An electronics manufacturer's revenue R for selling x mobile phones is given by R = 0.25x2 - 140x.

A competing electronics manufacturer's revenue for selling a similar mobile phone is R = 60x.

Under what circumstances will both manufacturers make the same revenue?

A) They will make the same revenue if they sell 0 or 200 phones.

B) They will make the same revenue if they sell 0 or 800 phones.

C) They will make the same revenue if they sell 800 phones.

D) They will never make the same revenue.

Find the asymptotes of the hyperbola.

105) x2 - y2 = 98

105)

A) y = 98x, y = - 98x

B) y = x, y = - x

C) y =2x, y = - 2x

D) y =

x x ,y=98 98

Find the vertices of the hyperbola. y2 x2 =1 106) 9 4 A) (-3, 0), (3, 0)

104)

106) B) (0, 3), (0, -3)

C) (0, 2), (0, -2)

D) (-2, 0), (2, 0)

Solve the problem.

107) A satellite dish has a parabolic cross section and is 8 feet deep. The focus is 9 feet from the vertex.

Find the width of the satellite dish at the opening. Round your answer to the nearest foot.

A) 34 ft B) 42 ft C) 38 ft D) 36 ft

65

107)

Draw the graph of the equation.

108) (y - 1)2 = -5(x + 2)

108)

A)

B)

C)

D)

Solve the problem.

109) A cross-section of an irrigation canal is a parabola. If the surface of the water is 20 feet wide and the canal is 24 feet deep at the center, how deep is it 5 feet from the edge?

A) 18 ft B) 10.5 ft C) 6 ft D) 13.5 ft Graph the ellipse.

66

109)

110)

(x + 4)2 (y + 2)2 + =1 4 9

110)

A)

B)

C)

D)

67

Solve.

111) Beaufort Canal has a semi-elliptical cross section with a width W = 70 feet and a depth D = 11 feet (see figure). The keel on Sasha's yacht rides 4 feet below the water line at the keel's deepest point. If the yacht travels parallel to the canal, and assuming the canal is completely full of water, how close can Sasha bring the yacht's centerline to the edge of the canal without running aground? (The keel is the very bottom of a boat hull and runs directly below the boat's centerline from front to back.)

A) 4 ft

B) 11 ft

C) 3 ft

Draw the graph of the equation.

112) x2 - 9y - 6x = 0

111)

D) 24 ft

112)

A)

B)

68

C)

D)

Find the focus and directrix of the parabola.

113) x = 10y2 1 1 , 0 ; D: x = A) F: 40 40

C) F:

113)

1 1 ; D: x = B) F: 0, 40 40

1 1 , 0 ; D: x = 10 10

D) F: 0,

1 1 ; D: y = 40 40

Find the foci of the given hyperbola.

114) y2 - 9x2 = 9

114)

A) (0, 10), (0, - 10) C) (3, 0), (-3, 0)

B) (0, 3), (0, -3) D) ( 10, 0), (- 10, 0)

Solve.

115) 25x 2 + 16y2 = 400 4y + 5x = 20 A) (0, 4), (5, 0)

115) B) (0, 5), (4,0)

C) (0, -5), (-4, 0)

D) (0, -4), (0, -5)

116) Four squares with sides 3 in. long are cut from the corners of a rectangular metal sheet that has an area of 198 in.2 . The edges are bent up to form an open box with a volume of 180 in.3 . Find the dimensions of the box.

A) Height: 18 in.; length: 3 in.; width: 11 in.

C) Height: 3 in.; length: 21 in.; width: 11 in.

B) Height: 3 in.; length: 15 in.; width: 14 in.

D) Height: 3 in.; length: 12 in.; width: 5 in.

Graph the parabola.

69

116)

117) y2 = 9x

117)

A)

B)

C)

D)

Solve.

118) A certain amount of money saved for 1 year at a certain annual interest rate (simple interest) yielded $25.80 in interest. If we had added $43 to the principal and reduced the interest rate by 2 percentage point(s), the interest would have been the same. Find the principal and the rate.

A) $215.00, 12% B) $2,570.00, 10% C) $2,570.00, 12% D) $4.34, 59.49% Find the foci of the ellipse.

119) 16x 2 - 96x + 25y2 + 150y - 31 = 0 A) (-1, -3), (7, -3)

B) (0, -3), (6, -3)

C) (-3, -1), (-3, 7) 70

D) (-2, -3), (8, -3)

118)

119)

Provide the proper response.

120) In the ellipse

(y + 3)2 (x - 7)2 + = 1, what is the equation of the horizontal axis of symmetry? The 36 16

vertical axis of symmetry?

A) Horizontal: y = 3; Vertical: x = 7 C) Horizontal: y = 7; Vertical: x = -3

B) Horizontal: y = 3; Vertical: x = -7 D) Horizontal: y = -3; Vertical: x = 7

71

120)

Answer Key Testname: C7

1) D 2) A 3) D 4) C 5) A 6) C 7) D 8) D 9) D 10) B 11) C 12) C 13) B 14) B 15) B 16) B 17) D 18) B 19) C 20) B 21) A 22) D 23) C 24) B 25) A 26) A 27) B 28) A 29) D 30) C 31) A 32) C 33) D 34) A 35) D 36) A 37) D 38) B 39) D 40) C 41) D 42) C 43) B 44) D 45) C 46) C 47) A 48) C 49) C 50) It is the single point (6, 4).

72

Answer Key Testname: C7

51) The graph of a parabola with vertical axis opens up or down. It is the graph of a function since it passes the vertical line test.

52) Hyperbola II is wider because it will have larger eccentricity (e = c/a and c2 = a 2 + b2 ). a is the same for both equations but c is greater for the second equation.

53) It is not a function since it does not pass the vertical line test. (y - 4)2 (x - 4)2 =1 54) 4 45

55) This equation has no graph.

56) Ellipse 57) The graph of a hyperbola does not satisfy the vertical line test.

58) The coefficients of x2 and y are not zero but the coefficient of y2 is zero.

59)

x2 y2 + =1 25 18.75

60)

(y - 2)2 (x - 4)2 =1 16 33

61)

x2 y2 + =1 111.122449 121

62) In the equation of an ellipse, the x2 - and y2 -terms both have positive coefficients. In the equation of a hyperbola, one squared term has a negative coefficient (either x2 or y2 but not both).

63) 0.71428571

64) The branches open left and right if x2 has a positive coefficient and y2 has a negative coefficient. They open up and down if y2 has a positive coefficient and x2 has a negative coefficient.

65) If a = b, the graph of the equation is a circle, a special case of an ellipse. x2 - 1 lies above or on the x-axis in (- , -4] [4, ). This set is the same as the domain of the given 66) The graph of y = 16 hyperbola.

67) 0.62962963 68) II 69) 2.24 70) (2, 1), (1, 2), (-2, -1), (-1, -2) 71) An ellipse centered at the origin is symmetric with respect to the x-axis, the y-axis, and the origin.

72) D 73) D 74) B 75) B 76) A 77) B 78) C 79) B 80) D 81) A 82) C 83) C 84) D 85) C 86) B

73

Answer Key Testname: C7

87) D 88) B 89) C 90) D 91) C 92) D 93) D 94) D 95) D 96) A 97) A 98) C 99) B 100) A 101) D 102) B 103) A 104) B 105) B 106) B 107) A 108) B 109) A 110) C 111) B 112) C 113) A 114) A 115) B 116) D 117) D 118) A 119) B 120) D

74

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use mathematical induction to prove the following. n 1) (9 7 ) = 9 7n

1)

2) If a is a constant and 0 < a < 1, then a n < a n-1 .

2)

3) If a is a constant and 0 < a < 1, then a n < 1.

3)

4) 4 n > 4 n-1

4)

5) 9 n > n

5)

6) 0.85n < 0.85n-1

6)

7) 6 + 12 + 18 + . . . + 6n = 3n(n + 1)

7)

8) 1 · 2 + 2 · 3 + 3 · 4 + . . . + n(n + 1) =

n(n + 1)(n + 2) 3

8)

9) 1 · 3 + 2 · 4 + 3 · 5 + . . . + n(n + 2) =

n(n + 1)(2n + 7) 6

9)

10) 1 2 + 4 2 + 7 2 + . . . + (3n - 2)2 =

11) 1 -

12)

n

1 2

1-

n(6n 2 - 3n - 1) 2

10)

1 1 1 ... 1= 3 n+1 n+1

(7i + 8) =

i=1

11)

n(7n + 23) 2

12)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Evaluate the sum.

6 (k2 - 2) 13) 2 k=3 A) 78

13) B) 39

C) 40

1

D) 21

Find the first 4 terms of the recursively defined sequence.

14) a 1 = 3, a n + 1 = (an )2 A) 3, 4, 9, 16 B) 3, 9, 27, 81 Solve.

14) C) 3, 6, 12, 24

15) When a single card is drawn from an ordinary 52-card deck, find the probability of getting a red card.

1 1 1 A) 2 B) C) D) 4 52 2

Expand.

16) (1 - 5)4 + (1 + A) 44 5

5)4

C) 55

D) 112

17) D) 486 3

C) 486

18) A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

13 2 6 A) 6 B) C) D) 6 13 13

Evaluate the sum.

5 (3i - 2) 19) i=1 A)

15)

16) B) 48 5

Find the indicated term.

17) 6, 6 3, 18, . . . ; the 9th term.

A) 162 3 B) 1,458 Solve.

D) 3, 9, 81, 6,561

18)

19) B)

C) 5

D)

Evaluate.

20) 56C5

A) 458,377,920

20) B) 91,675,584

C) 3,819,816

D) 7,639,632

What term of the arithmetic sequence is the given number?

4 5 28 21) , , 2, . . . ; 3 3 3 A) 22 Write sigma notation.

22) 9 + 27 + 81 + 243 + 729 6 3i A) i=1

21)

B) 26

C) 24

D) 25

5

5

6

B)

3i

C)

i=2

i=1

2

3i

D)

i=2

22) 3i

Solve the problem.

23) A town has a population of 1,000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

A) 1,720 people B) 2,172 people C) 1,993 people D) 1,828 people Evaluate.

24)

6!

4!

24) A) 30

Solve.

23)

B) 6

C) 2!

D)

3 2

25) When a single card is drawn from an ordinary 52-card deck, find the probability of getting a black 7.

1 1 3 1 A) B) C) D) 26 52 52 13

Find the nth, or general, term.

1 1 1 26) , , , . . .

3 9 27 A) 3 n-1

25)

26) B)

1 3n

C)

1 3 + 6(n - 1)

D)

1 n-1 3 +2

Evaluate.

27) 46P10

A) 1.479 x 1017

Solve.

B) 1.479 x 1015

C) 2.958 x 1016

28) How many different three-number "combinations" are possible on a combination lock having 27 numbers on its dial?

A) 16,848 B) 17,550 C) 33,696 D) 8,775

Find the indicated term of the binomial expansion.

29) 4th term; (3x + 2y)9

Evaluate.

30) 6!

A) 244,944x6 y3

B) 489,888x6 y3

C) 163,296x3 y6

D) 244,944x6 y4

A) 1,440

B) 720

C) 360

D) 120

Find the indicated sum.

31) Find the sum of the first 7 terms in the geometric series 3 + 9 + 27 + . . .

A) 1092 B) 9840 C) 3279 Solve.

D) 1.479 x 1016

32) Find the sum of the first 27 terms of the series 7 + 16 + 25 + 34 + . . . .

A) 6,939 B) 3,348 C) 13,014

3

D) 1122

D) 6,696

27)

28)

29)

30)

31)

32)

Find the sum, if it exists.

33) k=1

2 k 7

A) -

2 5

33) B)

2 5

C)

7 5

Find the first term and the common difference.

34) -10, -14, -18, -22, . . .

A) a 1 = -10, d = -4

B) a 1 = -10, d = -8

C) a 1 = -10, d = -12

D) a 1 = -10, d = 4

D) Does not exist

34)

Expand.

35) (a - b)6 A) a 6 + 6a 5 b + 15a 4 b2 + 20a 3 b3 + 15a 2 b4 + 6ab5 + b6

35)

B) a 6 - 6a 5 b + 15a 4 b2 - 20a 3 b3 + 15a 2 b4 - 6ab5 + b6 C) a 6 - 6a 5 b - 15a 4 b2 - 20a 3 b3 - 15a 2 b4 - 6ab5 - b6

D) -a 6 + 6a 5 b - 15a 4 b2 + 20a 3 b3 - 15a 2 b4 + 6ab5 - b6 Solve.

36) A sequence of yearly payments of $5,000 is invested at the end of each of 12 years at an interest rate of 4.8%%, compounded annually. What is the total amount of the annuity after 12 years?

A) $78,170.36 B) $78,670.36 C) $79,670.36 D) $77,670.36

36)

37) In how many distinguishable ways can the letters of the word WINDOW be arranged?

A) 120 B) 360 C) 36 D) 720

37)

What term of the arithmetic sequence is the given number?

38) 4, 8, 12, . . . ; 188 A) 49 B) 45 Evaluate.

39)

C) 46

D) 47

11 5

39)

A) 210

B) 2310

Determine the number of subsets of the set.

40) A set of 8 elements A) 128 B) 16

C) 462

D) 42

C) 256

D) 17

Find the nth, or general, term.

1 41) , 1, 5, . . .

5 A)

38)

1 4 + (n - 1) 5 5

40)

41) B)

1 n-1 4 + 5 5

C)

4

1 + 5(n - 1) 5

D)

1 n-1 (5) 5

Solve.

42) A lottery game contains 22 balls numbered 1 through 22. What is the probability of choosing a ball numbered 23?

1 A) B) 0 C) 22 D) 1 22

42)

Evaluate.

43) 7 C0 A) 1

B) 2,520

Find the sum.

4 (4k - 5) 44) k=1 A) 21 Evaluate.

45)

C) 1,260

D) 5,040

43)

44) B) 15

C) 20

D) 11

6!

8!

45) A)

1 2!

B) 2!

Evaluate the sum.

10 (-1)k 46) k=0 A) 0

C) 56

D)

1 56

46) B) 11

C) 1

D) 10

Find the first term and the common difference.

11 7 1 1 , , ,,...

47) 12 12 4 12

47)

A) a 1 =

11 11 ,d= 12 12

B) a 1 =

11 , d =- 1 12

C) a 1 =

11 1 ,d= 12 3

D) a 1 =

11 1 ,d=12 3

Find the indicated term of the arithmetic sequence.

4 3 2 , , , . . . ;20th term 48) 11 11 11 A) -

14 11

Evaluate the sum.

4 i 3 49) i=1 A) 120

B) -

48)

12 11

C) -

13 11

D) -

15 11

49) B) 81

C) 12

5

D) 243

Evaluate.

50) 8 P3 A) 6,720

B) 336

C) 240

50)

D) 168

Find the nth, or general, term.

8 8 51) 8, , , . . .

5 25 A) 8

1 n-1 5

51) B) 8 n-1 -

32 5

C) 8 +

1 (n - 1) 5

D) 8 -

32 (n - 1) 5

Solve the problem.

52) A deposit of $9,000 is made in an account that earns 9% interest compounded quarterly. The balance in the account after n quarters is given by the sequence 0.09 n a n = 9,000 1 + n = 1, 2, 3, ...

4 Find the balance in the account after 7 years.

A) $16,832.90 B) $16,874.90

C) $16,780.90

D) $16,634.90

Find the indicated term of the arithmetic sequence.

1 3 53) , 1, , . . . ;16th term 2 2 A) 8

53)

B) 7

C)

54) $807, $782 ,$757, . . . ;19th term A) $332 B) $357

15 2

D)

13 2

C) $382

D) $407

Find the indicated term.

55) $1000, $1010, $1,020.10, . . . ; the 9th term A) $1,082.86 B) $9,090

C) $1,072.14

D) $1,093.69

Find the common ratio.

56) 4, -4, 4, -4, 4, . . .

A) 1

C) -1

D) -4

Evaluate.

57)

B) 4

16 1

A) 2.092 × 1013

52)

54)

55)

56)

57) B) 16

C) 240

Solve the problem.

58) In a science experiment, Stephen collected data which formed the sequence: 0.0432, 0.0462, 0.0492, 0.0522, 0.0552, 0.0582, 0.0612, 0.0642, 0.0672, 0.0702 Is this sequence arithmetic? If so, what is the common difference?

A) No B) Yes; 0.0032 C) Yes; 0.004

6

D) 32

58)

D) Yes; 0.003

Solve.

59) In a class of 14 students, 4 students got an A, 3 students got a B, 2 students got a C, and 5 students got a D on a test. How many ways can the grades be assigned?

A) 84,084 B) 2,522,520 C) 420,420 D) 1,681,680

59)

60) In how many different ways can the letters in the word PAYMENT be arranged if the letters are taken 4 at a time?

A) 28 B) 420 C) 840 D) 210

60)

Find the nth, or general, term. m2 m3 , ,...

61) m, 10 100 A)

Solve.

mn 101-n

61) B)

mn 10(1 - n)

C)

mn 10n-1

62) In how many different ways can 7 people line up for play tickets?

A) 7 B) 5,040 C) 1

Find the sum.

4 9 k+ 2 (4k - 1.4) 63) 4 k=1 k=5 A) 34.35 B) 28.15

D)

m n+1 10n

D) 823,543

63) C) 26.85

D) 23.15

Determine how many of the first 5 statements in the sequence obtainable from the given statement are true.

360 . (n 3) 64) The measure of each exterior angle of a regular polygon with n sides is n A) 5 Evaluate the sum.

7 (-1)2k+1 4k 65) k=4 A) -8

B) 2

C) 3

Find fraction notation.

67) 1.81818 . . .

20 A) 11

64)

D) 4

65) B) 8

C) 88

D) -88

Find the first 4 terms of the recursively defined sequence.

66) a 1 = 4, a 2 = 2, a n + 1 = a n - a n - 1 A) 4, 2, 6, 8

62)

66)

B) 4, 2, 0, -2

C) 4, 2, -2, -4

18,180 B) 9999

180 C) 100

7

D) 4, 2, 2, -2

67) D) 10

Evaluate the sum.

5 1 68) 2k(k + 1) k=2 1 A) 10

68) B)

1 4

C)

Find the common ratio.

69) 4, -12, 36, -108, 324, . . .

A) 3

D)

1 6

69)

1 C) 3

B) -16

Evaluate the sum.

3 (k2 - 4k + 8) 70) k=1 A) 62

1 8

D) -3

70) B) -34

C) -10

D) 14

Expand.

71) (3x + 5)3 A) 9x6 + 15x3 + 15,625

71)

B) 27x 3 + 135x2 + 135x + 125

C) 9x2 + 30x + 25

D) 27x 3 + 135x2 + 225x + 125

Find the indicated quantity.

72) a 8 , when a 1 = -2 and d = 4 A) 26

72) B) -30

C) -34

D) 30

73) a 1 , when a 10 = 100 and a 16 = 76 A) -2 Solve.

73)

B) -8

C) 6

D) -14

74) A 6-sided die is rolled. What is the probability of rolling a number less than 3?

1 2 1 1 A) B) C) D) 6 3 3 2

74)

Predict the general, or nth term, a n, of the sequence.

75) -3, 12, -48, 192, . . .

A) -3(-4)n-1

B) -3 + (-4)n

C) -3(-4)n

D) -12n-1

Write sigma notation.

1 1 1 1 + -...

76) 1 - + 4 9 16 25 A)

5 i=1

1 i2

75)

76) B) i=1

(-1)i+1 i2

C) i=1

8

(-1)i i2

D)

5 i=1

(-1)i i2

What is the degree of the expression?

6 77) (7x2 + 6x + 5) A) 12 B) 18

C) 8

D) 9

77)

Predict the general, or nth term, a n, of the sequence.

78) 4 , 20 , 36 , 52 , 68 , . . .

A) a n = 4(16)n - 1

78) B) a n = 16n - 3

C) 16n - 12

Find the indicated term of the binomial expansion.

79) 5th term; (5x + 4)5 A) 6,400x

C) 8,000x2

B) 1,600x

D) a n = 12n - 16

79) D) 5,120

Predict the general, or nth term, a n, of the sequence.

80) 4, 8, 12, 16, 20, . . .

A) 5n

B) n + 4

C) 4n

D) n 4

Determine how many of the first 5 statements in the sequence obtainable from the given statement are true.

81) n 2 - n + 17 is prime.

A) 5

82) n 2 + n + 1 is prime.

A) 3 Evaluate.

83)

B) 4

C) 3

D) 2

B) 4

C) 2

D) 5

s p

81)

82)

83) A)

s! p!(s - p)!

B)

s! (s - p)!

C)

s! p!

D)

1 p!(s - p)!

Find the nth, or general, term.

1 84) x, 1, , . . . x A) x2-n

84) B) xn

C)

1 2-n x

D) xn-1

Find the first 4 terms of the recursively defined sequence.

85) a 1 = 6, a 2 = 7, a n + 1 = a n + a n - 1 A) 6, 7, 12, 18 Solve.

80)

85)

B) 6, 7, 42, 294

C) 6, 7, 13, 14

D) 6, 7, 13, 20

86) Suppose 5 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 kings with any other card?

1 1 1 1 A) B) C) D) 5,997,600 676 10,829 54,145

9

86)

Find the sum.

572 i 87) i=1 A) 571

87) B) 163,306

C) 573

Find the indicated term of the sequence.

88) a n = (4n - 5)2; a 9 A) 729 B) 961

88)

Find the indicated term of the binomial expansion.

89) 6th term; (x + 3y)12 A) 192,456x7 y5

Evaluate.

90)

D) 163,878

B) 192,456x5 y7

C) 1225

D) 1681

C) 64,152x7 y5

D) 64,152x7 y6

45 3

A) 85,140

89)

90) B) 3,575,880

C) 1,980

Find the indicated term of the sequence.

91) a n = ln en ; a 110 A) 1 B) ln 110

D) 14,190

91) C) 110

D) 111

Evaluate.

92) 11C8

A) 165

92) B) 831,600

C) 6.653 × 106

D) 330

Solve the problem.

93) If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so on, how much money will be in the bank after 30 days?

A) $9.30 B) $4.65 C) $2.33 D) $0.30 Determine how many of the first 5 statements in the sequence obtainable from the given statement are true. n(n + 1) .

94) The sum of the first n numbers is 2 A) 5

B) 3

C) 2

D) 4

Find fraction notation.

95) 1.1010101 . . .

109 A) 9

109 B) 90

109 C) 99

109 D) 100

96) 0.131313 13 A) 90

13 B) 99

11 C) 100

13 D) 100

10

93)

94)

95)

96)

Solve the problem.

97) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). (i) Use a graphing calculator to fit a linear sequence regression function a n = an + b

97)

to the data, where n is the cost of advertising (in thousands of dollars) and a n is number of products sold (in thousands). (ii) Use this function to estimate the number of products sold if the cost of advertising is $10,000.

Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

A) (i) a n = 2.79n + 55.8;

B) (i) a n = 5.79n + 94.3;

(ii) 83.7 thousand products C) (i) a n = 2.73n + 34.8;

(ii) 27,955.8 products D) (i) a n = 3.02n + 55.8;

(ii) 80.7 thousand products

(ii) 90.4 thousand products

Find the indicated term of the sequence.

1,000 ; a 171 98) a n = 15 n A) 0

B)

98) 3565 171

C)

1565 171

D) -985

Find the indicated quantity.

99) a 1 , when d = 5 and a 46 = 214 A) -11

99)

B) 5

C) -1

D) -6

Solve.

100) In a class there are 23 girls and 34 boys. In how many ways can you pick 2 boys and 2 girls to form a committee?

A) 1,122 B) 141,933 C) 567,732 D) 506 Evaluate the sum.

7 4 k 101) k=3 A) 25

101) B) 48

C) 100

D) 100

Find the first 4 terms of the recursively defined sequence.

1 102) a 1 = 2, a n+1 = an A) 2,

1 1 1 1 , , , 2 2 2 2

100)

B) 2,

102)

1 1 1 , , 4 8 16

C) 2,

11

1 1 , 2, 2 2

D)

1 1 , 4, , 8 2 4

Evaluate.

103)

s 10

A)

103) s! (s - 10)!

B)

s!

10!(s - 10)!

C) s!

D)

s!

10!

Solve.

104) A credit company allocates 8-digit account numbers such as 1122-3421 where the digits 1 through 9 are used. How many different account numbers can there be?

A) 220,345 B) 13,440 C) 40,320 D) 43,046,721 What term of the arithmetic sequence is the given number?

5 1 1 109 , ,,...;105) 14 7 14 14 A) 37 Evaluate.

106)

105)

B) 40

C) 42

106) 7 6

C) 1

B) 6

1 C) 2

B)

Find the common ratio.

107) 3, 6, 12, 24, 48, . . .

A) 2

108)

D) 39

7!

6!

A) 7!

Evaluate.

104)

D) 7

107) D) -2

42 5

A) 850,668

108) B) 1,722

C) 2,686,320

D) 68,880

Solve.

109) A pendulum bob swings 5.0 cm on its first oscillation. On each subsequent oscillation the bob 2 travels of the previous distance. Find the total distance the bob travels before coming to rest.

5 A) 12.4 cm

B) 3.3 cm

C) 11.7 cm

109)

D) 4.1 cm

Solve the problem.

110) A stack of poles has 39 poles in the bottom row, 38 poles in the next row, and so on, with 7 poles in the top row. How many poles are there in the stack?

A) 759 poles B) 684 poles C) 752 poles D) 766 poles

110)

Evaluate.

111) 10P10 A) 1,814,400

B) 1

C) 2

12

D) 3,628,800

111)

112) 9 C5 A) 3,024

B) 126

C) 7,560

13

D) 48

112)

Answer Key Testname: C8

1) Answers may vary. One possibility: n Sn : (9 7 ) = 9 7n 1 S1 : (9 7 ) = 9 7·1 k Sk: (9 7 ) = 9 7k Sk+1 : (9 7 )k+1 = 9 7(k+1) 1 1. Basis step: Since 9 7·1 = 9 7 = (9 7 ) , S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 . k (9 7 ) = 9 7k k (9 7 ) (9 7 ) = 9 7k(9 7 ) k+1 (9 7 ) = 9 7k+6 k+1 (9 7 ) = 9 7(k+1) 2) Answers may vary. One possibility:

Sn : If a is a constant and 0 < a < 1, then a n < a n-1 .

S1 : If a is a constant and 0 < a < 1, then a 1 < a 1-1 .

Sk: If a is a constant and 0 < a < 1, then a k < a k-1 .

Sk+1 : If a is a constant and 0 < a < 1, then a k+1 < a k.

1. Basis step: Since a 1-1 = a 0 = 1 and it is given that a < 1 (which implies a 1 < 1), S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

If a is a constant and 0 < a < 1, then a k < ak-1 .

If a is a constant and 0 < a < 1, then a k · a < a k-1 · a.

If a is a constant and 0 < a < 1, then a k+1 < a (k-1)+1 .

Multiplying by a, a > 0

If a is a constant and 0 < a < 1, then a k+1 < a k.

3) Answers may vary. One possibility: Sn : If a is a constant and 0 < a < 1, then a n < 1.

S1 : If a is a constant and 0 < a < 1, then a 1 < 1.

Sk: If a is a constant and 0 < a < 1, then a k < 1.

Sk+1 : If a is a constant and 0 < a < 1, then a k+1 < 1.

1. Basis step: Since it is given that a < 1, then a 1 < 1. Therefore, S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

If a is a constant and 0 < a < 1, then a k < 1.

If a is a constant and 0 < a < 1, then a k · a < 1 · a.

If a is a constant and 0 < a < 1, then a k+1 < a.

If a is a constant and 0 < a < 1, then a k+1 < a < 1.

If a is a constant and 0 < a < 1, then a k+1 < 1.

Multiplying by a, a > 0 Given a < 1

14

Answer Key Testname: C8

4) Answers may vary. One possibility: Sn : 4 n > 4 n-1 S1 : 4 1 > 4 1-1 Sk: 4 k > 4 k-1 Sk+1 : 4 k+1 > 4 k 1. Basis step: Since 4 1-1 = 4 0 = 1 and 4 1 > 1, S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

4 k > 4 k-1 4 k · 4 > 4 k-1 · 4

4 k+1 > 4 (k-1)+1

Multiplying by 4, 4 > 0

4 k+1 > 4 k 5) Answers may vary. One possibility: Sn : 9 n > n S1 : 9 1 > 1 Sk: 9 k > k Sk+1 : 9 k+1 > k + 1 1. Basis step: Since 9 1 > 1, S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

9k > k 9k · 9 > k · 9

9 k+1 > k(1 + 8) 9 k+1 > k + 8k 8k 1 9 k+1 > k + 1

Multiplying by 9, 9 > 0

8 1 and k 1

6) Answers may vary. One possibility: Sn : 0.85n < 0.85n-1 S1 : 0.851 < 0.851-1 Sk: 0.85k < 0.85k-1 Sk+1 : 0.85k+1 < 0.85k 1. Basis step: Since 0.851-1 = 0.850 = 1 and 0.851 < 1, S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

0.85k < 0.85k-1 0.85k · 0.85 < 0.85k-1 · 0.85 0.85k+1 < 0.85(k-1)+1

Multiplying by 0.85, 0.85 > 0

0.85k+1 < 0.85k.

15

Answer Key Testname: C8

7) Answers may vary. One possibility: Sn : 6 + 12 + 18 + . . . + 6n = 3n(n + 1) S1 : 6 = 3 · 1 · (1 + 1) Sk: 6 + 12 + 18 + . . . + 6k = 3k(k + 1) Sk+1 : 6 + 12 + 18 + . . . + 6k + 6(k + 1) = 3(k + 1)(k + 2) 1. Basis step: Since 3 · 1 · (1 + 1) = 3 · 2 = 6, S1 is true.

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

6 + 12 + 18 + . . . + 6k = 3k(k + 1)

By Sk

6 + 12 + 18 + . . . + 6k + 6(k + 1) = 3k(k + 1) + 6(k + 1) Adding 6(k + 1) 6 + 12 + 18 + . . . + 6k + 6(k + 1) = (3k + 6)(k + 1) Distributive law 6 + 12 + 18 + . . . + 6k + 6(k + 1) = 3(k + 2)(k + 1) 6 + 12 + 18 + . . . + 6k + 6(k + 1) = 3(k + 1)(k + 2).

8) Answers may vary. One possibility: n(n + 1)(n + 2) Sn : 1 · 2 + 2 · 3 + 3 · 4 + . . . + n(n + 1) = 3 S1 : 1 · 2 =

1 · (1 + 1) · (1 + 2) 3

Sk: 1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) =

k(k + 1)(k + 2) 3

Sk+1 : 1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) + (k + 1)(k + 2) = 1. Basis step: Since

(k + 1)(k + 2)(k + 3) 3

1 · (1 + 1) · (1 + 2) 1 · 2 · 3 = = 1 · 2, S1 is true.

3 3

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) =

k(k + 1)(k + 2) 3

1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) + (k + 1)(k + 2) = =

k(k + 1)(k + 2) 3(k + 1)(k + 2) + 3 3

=

(k + 3)(k + 1)(k + 2) 3

=

(k + 1)(k + 2)(k + 3) .

3

k(k + 1)(k + 2) + (k + 1)(k + 2) 3

16

Answer Key Testname: C8

9) Answers may vary. One possibility: Sn : 1 · 3 + 2 · 4 + 3 · 5 + . . . + n(n + 2) = S1 : 1 · 3 =

n(n + 1)(2n + 7) 6

1(1 + 1)(2 · 1 + 7) 6

Sk: 1 · 3 + 2 · 4 + 3 · 5 + . . . + k(k + 2) =

k(k + 1)(2k + 7) 6

Sk+1 : 1 · 3 + 2 · 4 + 3 · 5 + . . . + k(k + 2) + (k + 1)(k + 3) = 1. Basis step: Since

(k + 1)(k + 2)[2(k + 1) + 7] 6

1(1 + 1)(2 · 1 + 7) 1 · 2 · 9 = = 1 · 3, S1 is true.

6 6

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

1 · 3 + 2 · 4 + 3 · 5 + . . . + k(k + 2) =

k(k + 1)(2k + 7) 6

1 · 3 + 2 · 4 + 3 · 5 + . . . + k(k + 2) + (k + 1)(k + 3) = =

k(k + 1)(2k + 7) 6(k + 1)(k + 3) + 6 6

=

(k + 1)(k[2k + 7]) (k + 1)(6[k + 3]) + 6 6

=

(k + 1)(k[2k + 7] + 6[k + 3]) 6

=

(k + 1)[(2k2 + 7k) + (6k + 18)] 6

=

(k + 1)(2k2 + 13k + 18) 6

=

(k + 1)(k + 2)(2k + 9) 6

=

(k + 1)(k + 2)[2(k + 1) + 7] .

6

k(k + 1)(2k + 7) + (k + 1)(k + 3) 6

17

Answer Key Testname: C8

10) Answers may vary. One possibility: Sn : 1 2 + 4 2 + 7 2 + . . . + (3n - 2)2 = S1 : 1 2 =

n(6n 2 - 3n - 1) 2

1 · (6 · 1 2 - 3 · 1 - 1) 2

Sk: 1 2 + 4 2 + 7 2 + . . . + (3k - 2)2 =

k(6k2 - 3k - 1) 2

Sk+1 : 1 2 + 4 2 + 7 2 + . . . + (3k - 2)2 + [3(k + 1) - 2]2 = 1. Basis step: Since

(k + 1)[6(k + 1)2 - 3(k + 1) - 1] 2

1 · (6 · 1 2 - 3 · 1 - 1) 1 · (6 - 3 - 1) 1 · 2 = = = 1 = 1 2 , S1 is true.

2 2 2

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

1 2 + 4 2 + 7 2 + . . . + (3k - 2)2 =

k(6k2 - 3k - 1) 2

1 2 + 4 2 + 7 2 + . . . + (3k - 2)2 + [3(k + 1) - 2]2 = =

6k3 - 3k2 - k + (3k - 2)2 2

=

6k3 - 3k2 - k + (9k2 + 6k + 1) 2

=

6k3 - 3k2 - k 18k2 + 12k + 2 + 2 2

=

6k3 + 15k2 + 11k + 2 2

=

(k + 1)(6k2 + 9k + 2) 2

=

(k + 1)[(6k2 + 12k + 6) - (3k + 4)] 2

=

(k + 1)[6(k2 + 2k + 1) - (3k + 4)] 2

=

(k + 1)[6(k + 1)2 - 3(k + 1) - 1] .

2

k(6k2 - 3k - 1) + [3(k + 1) - 2]2 2

18

Answer Key Testname: C8

11) Answers may vary. One possibility: 1 1 1 1 Sn : 1 1... 1= 2 3 n+1 n+1 S1 : 1 -

1 1 = 2 1+1

Sk: 1 -

1 2

Sk+1 : 1 -

11 2

1 1 1 ... 1= 3 k+ 1 k+ 1

1-

1 1 ... 13 k+ 1

1. Basis step: Since

1-

1 1 = k+ 2 k+ 2

1 1 1 = = 1 - , S1 is true.

1+1 2 2

2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 .

1-

1 2

1-

1 1 1 = ... 13 k+ 1 k+ 1

1-

1 2

1-

1 1 ... 13 k+ 1

=

1 k+ 2 1 k+ 1 k+ 2 k+ 2

=

1 (k + 2) - 1 k+ 1 k+ 2

=

1 k+ 1 k+ 1 k+ 2

=

1 . k+ 2

1-

1 1 1 = 1k+ 2 k+ 1 k+ 2

19

Answer Key Testname: C8

12) Answers may vary. One possibility: n n(7n + 23) Sn : (7i + 8) = 2 i=1 1 · (7 · 1 + 23) S1 : 7 + 8 = 2 Sk:

k

(7i + 8) =

k(7k + 23) 2

i=1 k+1 (k + 1)[7(k + 1) + 23] Sk+1 : [7i + 8] = 2 i=1 1 · (7 · 1 + 23) 7 + 23 = = 15 = 7 + 8, S1 is true.

1. Basis step: Since 2 2 2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1 . k

(7i + 8) =

i=1

k(7k + 23) 2

[7(k + 1) + 8] + k+1

k

(7i + 8) = [7(k + 1) + 8] +

i=1 (7i + 8) = [7(k + 1) + 8] +

i=1 2[7(k + 1) + 8] k(7k + 23) = + 2 2

k(7k + 23) 2

k(7k + 23) 2

=

(14k + 14 + 16) + (7k2 + 23k) 2

=

(7k2 + 14k + 7) + (7 + 16 + 23k) 2

=

7(k2 + 2k + 1) + (23 + 23k) 2

=

7(k + 1)2 + 23(1 + k) 2

=

(k + 1)[7(k + 1) + 23) .

2

13) B 14) D 15) D 16) D 17) C 18) D 19) D 20) C 21) D 22) D 23) C 20

Answer Key Testname: C8

24) A 25) A 26) B 27) D 28) B 29) B 30) B 31) C 32) B 33) B 34) A 35) B 36) B 37) B 38) D 39) C 40) C 41) D 42) B 43) A 44) C 45) D 46) C 47) D 48) D 49) A 50) B 51) A 52) C 53) A 54) B 55) A 56) C 57) B 58) D 59) B 60) C 61) C 62) B 63) D 64) A 65) D 66) C 67) A 68) D 69) D 70) D 71) D 72) A 73) D 21

Answer Key Testname: C8

74) C 75) A 76) B 77) A 78) C 79) A 80) C 81) A 82) B 83) A 84) A 85) D 86) D 87) D 88) B 89) A 90) D 91) C 92) A 93) B 94) A 95) C 96) B 97) A 98) C 99) A 100) B 101) C 102) C 103) B 104) D 105) D 106) D 107) A 108) A 109) B 110) A 111) D 112) B

22