Test Bank For Introductory and Intermediate Algebra, Global Edition, 6th Edition

Exam Name___________________________________

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

Provide an appropriate response.

1) Choose the expression that is equivalent to the following: 4(3a) + 4(8b) A) 8(11ab) B) 4(3a + 8b) C) 4(11ab) 2) Choose the expression that is equivalent to the following: (8x + 4y)(5y3 ) A) 8x + (4y + 5y3 ) B) (8x) + (4y)(5y3 ) C) (5y3 )(8x + 4y)

1)

D) 8(3a + 8b)

D) (8x + 5y3 )(4y)

3) Choose the expression that is equivalent to the following: 1(3y2) A) 3y3 B) 3y2 C) 4y2

D) 1

4) Choose the expression that is equivalent to the following: 0 + 6a A) 0 B) 6a C) -6a

D) 6 + a

3)

4)

5) Choose the expression that is equivalent to the following: (3x + 4y)(4y + 8x) A) (3x + 4y)(8y + 4x) B) (3x + 4y)(8x + 4y) C) 11x + 8y D) (3x + 8x)(4y + 4y) 6) Choose the expression that is equivalent to the following: 6x + 2y A) 2(3x + y) B) 8xy C) 2(3x + 2y)

5)

6)

D) 2(4x + y)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

7) Is this statement true or false? Why? (8 - 8) - 8 = 8 - (8 - 8)

7)

Use the commutative and/or associative laws to rewrite the given expression. Label each step with a reason.

8) (y + z) + 5 as (5 + z) + y 8) Provide an appropriate response.

9) Is the integer 0 positive or negative? Explain.

9)

Use the commutative and/or associative laws to rewrite the given expression. Label each step with a reason.

10) s(t9) as 9(ts) 10) 11) x(y9) as 9(xy)

11)

12) (x + 2) + 3 as 5 + x

12)

13) (4w)5 as 20w

13)

14) 2 + (a + b) as b + (2 + a)

14)

1

2)

15) (6 + y) + 4 as y + 10

15)

16) (z7)2 as 14z

16)

17) (x + 7) + y as 7 + (x + y)

17)

18) ( 7)m as 7( m)

18)

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

Simplify.

19)

2 3 3 3 + 17 34 17 34

A)

1 34

Multiply.

20) -3.4 · (-15) A) -11.6

19) B)

16 17

1 17

D)

C) -18.4

D) 51

C)

B) 18.4

2 17

Insert < or > to write a true statement.

-9.09 21) 9.06

21)

A) 9.06 < -9.09

B) 9.06 > -9.09

State the real number that corresponds to the situation.

22) This year corn production decreased 55,000 pounds from last year on Steve's farm.

A) -55,000 B) 55,000 Evaluate.

23)

p , when p = 14 and q = 2 q

A) 7

22)

23) B) 7

1 2

C) 8

D) 6

Solve the problem.

24) Wayne has $26.72 in his wallet. Janice has a debt note for $30.45 in her wallet. Find the difference between these amounts.

A) -$3.73 B) -$57.17 C) $57.17 D) $3.73 Multiply.

25) 7(3r + 5 + 9s) A) 21r + 5 + 9s

20)

B) 21r + 35 + 63s

Write an equivalent expression. Use an associative law.

26) 2 + (s + t) A) 2 + (t + s) B) 2(s + t)

2

C) 21r + 35 + 9s

D) 21r + 5 + 63s

C) (s + t) + 2

D) (2 + s) + t

24)

25)

26)

Multiply.

27) 3(3x + 5y + 2) A) 9x + 5y + 2

B) 9x + 15y + 2

C) 9x + 5y + 6

D) 9x + 15y + 6

Add. Do not use a number line except as a check.

5 4 28) - + 7 7 A)

9 7

B) -

28)

1 7

C) -

9 7

D)

1 7

Find the reciprocal, if it exists.

8x 29) 5y A)

8y 5x

29) B)

5x 8y

C)

8x 5y

D)

5y 8x

Find the absolute value.

30) 230 A) -230

B) 0

C) 230

D) 460

Multiply.

31) 3(7 + m) A) 21m

B) 21 + 7m

C) 21 + m

D) 21 + 3m

Find the absolute value.

1 32) 7 A) 0

A) 4

30)

31)

32) B) -

1 7

C)

1 7

D)

2 7

State the real number that corresponds to the situation.

33) In one state, the highest point is 4950 feet above sea level.

A) -4950 B) 4950 Find the reciprocal, if it exists.

34) -4

27)

1 B) 4

Write an equivalent expression. Use an associative law.

35) r + (3 + s) A) r + (s + 3) B) (r + 3) + s

33)

34)

1 C) 4

D) 0

C) r(3 + s)

D) (3 + s) + r

Substitute to find the value of the expression.

36) In one store, bananas cost 60 cents per pound. The cost, in dollars, of x pounds of bananas is 0.6x.

What is the cost of 2.0 pounds of bananas?

A) $3.33 B) $1.20 C) $1.40 D) $0.33

3

35)

36)

State the real number that corresponds to the situation.

37) Sales at Andrea's Formal Wear Shop were $5688 less this week than the sales last week.

A) 5688 B) -5688

37)

Find the reciprocal, if it exists.

38) 0 A) 0

38)

B) No reciprocal

Find the opposite, or additive inverse.

39) 17.7 A) -17.7

40)

C) 1

1 C) 17.7

B) 0

39) D) 17.7

11 6

A) -

40) 11 6

Simplify.

41) 12 + (-20) - 10 A) -18 Collect like terms.

42) 5q - 4 - 3p + 2q - 3p A) 5q - 6p - 6

B) -

6 11

C)

B) 42

11 6

C) 2

B) 7q - 6p - 4

C) 7q - 3p - 4

D)

6 11

D) 18

D) 7q + 6p+ 4

Substitute to find the value of the expression.

43) Mary earns three times as much per week as Maureen. If x represents the amount that Maureen earns per week, then 3x represents the amount that Mary earns per week. How much does Mary earn per week if Maureen earns $380 per week?

A) $377 B) $126.67 C) $1140 D) $383 Evaluate.

44)

x+y , when x = 13 and y = 47 10

A) 7 Subtract.

45) 9 - (-12) A) -21

42)

43)

44)

B) 5

C) 4

B) 21

C) -3

D) 6

D) 3

Insert < or > to write a true statement.

-61 46) -20

45)

46)

A) -20 > -61

B) -20 < -61

Evaluate -(-x) for the given value of x.

47) x = 137 A) -137

41)

B) 137

C) 0

4

1 D) 137

47)

Divide.

48)

1 5 ÷ 5 8

A) -

8 25

48) B) -

1 8

C) - 8

5

D) -

25 8

Answer Key Testname: C1

1) B 2) C 3) B 4) B 5) B 6) A 7) False. Answers will vary.

Using the commutative law 8) (y + z) + 5 = 5 + (y + z) Using the commutative law = 5 + (z + y) = (5 + z) + y Using the associative law 9) The integer is neither. It is not a signed integer. It is the starting point on a number line.

10) s(t9) = (t9)s Using the commutative law = (9t)s Using the commutative law = 9(ts) Using the associative law Using the associative law 11) x(y9) = (xy)9 Using the commutative law = 9(xy) Using the associative law 12) (x + 2) + 3 = x + (2 + 3) Simplifying =x+5 =5+x Using the commutative law Using the commutative law 13) (4w)5 = 5(4w) Using the associative law = (5·4)w = 20w Simplifying Using the associative law 14) 2 + (a + b) = (2 + a) + b Using the commutative law = b + (2 + a) Using the commutative law 15) (6 + y) + 4 = (y + 6) + 4 Using the associative law = y + (6 + 4) = y + 10 Simplifying Using the associative law 16) (z7)2 = z(7·2) Simplifying = z(14) = 14z Using the commutative law 17) (x + 7) + y = (7 + x) + y Using the commutative law = 7 + (x + y) Using the associative law Using the commutative law 18) ( 7)m = (7 )m Using the associative law = 7( m) 19) D 20) D 21) B 22) A 23) A 24) C 25) B 26) D 27) D 28) B 29) D 30) C 31) D 32) C 33) B

6

Answer Key Testname: C1

34) C 35) B 36) B 37) B 38) B 39) A 40) A 41) A 42) B 43) C 44) D 45) B 46) A 47) B 48) A

7

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) True or false: The solution of the equation 7y - 6 = 7y + 3 is zero.

1)

2) What value of K makes this equation equivalent to x = 3?

8x - 8 = K

2)

3) Find all values of x that make this statement true: (x + 5) + 7 = (x + 7) + 5.

3)

4) What value of K makes this equation equivalent to x = 3?

9 =3 K+x

4)

5) The solution for the equation 9(2s - 3) = 18s - 27 is given as 0. Is this correct? Explain.

5)

6) One number is twice another. If the larger number is m, how do you express the other number in terms of m?

6)

7) What value of K makes this equation equivalent to x = 2?

9x + 16x - 6 = K + 9

7)

8) Find all values of s that make this statement true: 5(5s - 6) = 25s - 30.

8)

9) Write the steps you would use to solve this equation: 2(x - 1) + 2x = -5x.

9)

10) Express three consecutive integers, all in terms of x, if x is the largest integer.

10)

1

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

Solve using the addition principle. Graph and write set-builder notation for the answer.

11) -2n - 7 > -3n - 19

11)

A) {n n < -12}

B) {n n > -12}

C) {n n -26}

D) {n n -26}

Solve the problem.

12) Jennifer's annual salary was $23,000 last year and increased 35% this year. Find Jennifer's current annual salary.

A) $39,100 B) $8050 C) $31,050 D) $26,950 Solve the problem. Round to the nearest hundredth, if necessary.

13) 77 is 90% of what number?

A) 69.3 B) 85.56 C) 8.56

D) 855.6

Solve the problem.

14) A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 20.

Find the length of a side.

A) 4 B) 9 C) 5 D) 1 Solve the equation using the addition principle.

15) -20 = b - 2 A) 22 B) -18

C) -22

D) 18

Solve. Clear fractions first.

1 1 4 16) r + 2 = r + 3 6 3 A) 3

12)

13)

14)

15)

16) B) -12

Solve the equation using the addition principle.

17) z - 22.43 = 0 A) 22.43 B) -21.43

2

C) -4

D) 4

C) -22.43

D) 21.43

17)

Solve the problem.

18) The color guard is making new triangular flags that must have a base of 18 inches to fit on their flagpoles. What is the maximum length of the triangular flags, if they want to use a maximum of 351 in.2 of cloth?

A) 78 in.

Solve. Clear decimals first.

19) 1.4x + 1.8 = -34.5 + 4.7x A) -40

B) 19.5 in.

C) 39 in.

D) 41 in.

B) 8.0

C) 7.7

D) 11

Determine whether the given number is a solution of the inequality.

20) x > -4, 14 A) Yes B) No Solve.

21) 3(2z - 3) = 5(z + 5) A) 19

B) -16

C) 34

25 4

D) 16

21)

22) B) -

4 5

C)

Solve using the multiplication principle.

23) -3b < -6 A) {b b < 2} B) {b b < -2}

15 4

C) {b b > 2}

Solve using the addition and multiplication principles.

24) 11x + 11 10x + 7 A) {x x > 11} B) {x x -4}

C) {x x < 11}

Solve using the multiplication principle.

25) 8.3x = 58.1 1 A) B) 49.8 7

D) -

5 4

D) {b b > -2}

D) {x x -4}

23)

24)

25) C) 51.1

26) -4.8m = -14.4 A) 11.4

19)

20)

Solve. Clear fractions first.

3 1 22) + x = 2 4 5 A)

18)

1 C) 3

B) 9.6

D) 7

26) D) 3

Solve the problem.

27) A high school graduating class is made up of 499 students. There are 147 more girls than boys.

How many boys are in the class?

A) 323 boys B) 176 boys C) 499 boys D) 147 boys 28) A rectangular Persian carpet has a perimeter of 220 inches. The length of the carpet is 22 inches more than the width. What are the dimensions of the carpet?

A) 66 in., 88 in.

B) 99 in., 121 in.

C) 44 in., 66 in.

D) 88 in., 110 in.

3

27)

28)

Solve the problem. Round to the nearest tenth of a percent.

29) What percent of 61 is 574?

A) 1.1% B) 94.1% Solve.

30) 9.7x - 14.8x = -96.9 A) 18

B) 19

Solve the equation using the addition principle.

31) -24.7 = 29.8 + x A) 54.5 B) -54.5 Solve.

32) -6a + 3 + 7a = 5 - 28 A) 26

B) -26

C) 941.0%

D) 0.1%

C) 20

D) 21

C) -5.1

D) 5.1

C) -36

D) 36

Solve the equation using the addition principle.

1 7 33) h - = 3 9 A)

2 3

B)

10 9

C)

4 9

D) 118.4%

C) -33.6

1 D) 4

B) -4

Solve the problem.

36) Jon has 766 points in his math class. He must have 68% of the 1400 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the term to receive credit for the class?

A) 634 points B) 521 points C) 186 points D) 952 points Solve the problem. Round to the nearest hundredth, if necessary.

37) What is 5% of 500?

A) 250 B) 25 C) 2.5

D) 0.25

Solve the equation using the addition principle.

1 3 38) h + = 2 4 1 4

B)

31)

32)

D) 4

C) 0.1%

Solve using the multiplication principle.

35) -37.6 = 9.4z

A)

30)

33)

Solve the problem. Round to the nearest tenth of a percent.

34) 934 is what percent of 789?

A) 84.5% B) 1.2%

A) -28.2

29)

34)

35)

36)

37)

38)

5 4

C)

4

2 3

D) 3

Translate the sentence to an inequality.

39) John weighs at least 124 pounds.

A) x > 124 B) x 124

C) x < 124

D) x 124

Solve using the multiplication principle.

8 8 x=40) 21 5 A) -

7 15

B) -

40) 12 35

C) -

21 5

D) -

35 12

Solve the problem.

41) One side of a rectangle is 7 inches and the other side is x inches. What values of x will make the perimeter at most 22?

A) x 4 B) 0 < x 4 C) x < 4 D) x 4

Solve.

39)

41)

42) On a biology test, a student got 25 questions correct but did not pass. On a second attempt, the student got 32 questions correct. What was the percent of increase?

A) 28% B) 72% C) 7% D) 21.9%

42)

43) 7y - 5 = 49 + y

43)

A) 9

27 B) 4

11 C) 2

22 D) 3

44) A city government budgeted $28.2 million for public transportation. This was $14.4 million more than was budgeted for parks and recreation. How much was budgeted for parks and recreation?

A) $14.8 million B) $13.8 million C) $17.8 million D) $13.3 million Solve. Clear decimals first.

45) 10.71y - 64.26 + 3.06y = 6.12y - 36.72 + 18.36 A) 6 B) -18 Solve.

46) x =

C) -6

w+y+z for y 9

D) 18

44)

45)

46)

A) y = 9x - 9w - 9z C) y = 9x + w + z

B) y = x - w - z - 9 D) y = 9x - w - z

Solve the problem.

47) Find the measures of the supplementary angles.

47)

A) 202.5° and 157.5° C) 101.25° and 78.75°

B) 50.63° and 39.38° D) 96.25° and 83.75°

5

Solve.

48) 9x + 2x = 22 A) 2

22 B) 9

C) 11

49) 5x - 2 + 7x - 6 = 7x + 5x + 8 A) 0 C) No solution

11 D) 9

49)

B) 8 D) All real numbers

Solve using the multiplication principle.

1 50) b = -3.00 9 A) -3.00

48)

50)

B) 5.00

C) 6.00

6

D) -27.00

Answer Key Testname: C2

1) False. It has no solution.

2) 16 3) x can be any value, including 0.

4) 0 5) No. The solution is all real numbers. Explanations will vary. m 1 or m 6) 2 2 7) 35 8) s can be any value, including 0.

9) Answers will vary.

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

Answer Key Testname: C2

50) D

8

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

1 1) y = x - 2; (4, 0), (-4, -4) 1) 2

Answer the question.

2) Is it possible for the x-intercept and the y-intercept of a straight line to be at the same point? Explain your answer.

2)

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

3) 3x - 3y = 12; (-2, -6), (5, 1) 3)

Answer the question.

4) Does every straight line have an x-intercept? If not, give an example of an equation whose graph does not have an x-intercept.

1

4)

Plot the ordered pairs on the rectangular coordinate system provided.

4 5) A(- , -5), B(-4, 5) 5

5)

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

6) 6x - 2y = 4; (0, -2), (3, 7) 6)

Plot the ordered pairs on the rectangular coordinate system provided.

7) A(1, -3), B(-5, 1)

2

7)

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

8) y = x + 5; (0, 5), (-3, 2) 8)

Answer the question.

9) What is the y-intercept of the line y = b?

9)

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

1 10) y = x + 2; (2, 3), (-2, 1) 10) 2

Answer the question.

11) What can you say about a line if every point on the line has the same x coordinate?

3

11)

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

12) x + 2y = 8; (2, 3), (-2, 5) 12)

13) 2x + y = 6; (1, 4), (5, -4)

13)

Answer the question.

14) Explain how you would find the x intercept of a line with an equation of the form Ax + By = C. Plot the ordered pairs on the rectangular coordinate system provided.

15) A(0, 2), B (0, -4)

4

14)

15)

16) A(4, 0), B (-5, 0)

16)

17) A(4, 3), B(-2, -4)

17)

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

18)

5

19) A(-5, -3), B(-1, 5)

19)

Answer the question.

20) What can you say about the graph of Ax + By = C if B is equal to zero?

20)

Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary.

21) y = x - 3; (7, 4), (-2, -5) 21)

Plot the ordered pairs on the rectangular coordinate system provided.

22) A(6, 2), B(4, -4)

22)

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

List the quadrant(s) in which the given point is located.

23) (14, -12) A) IV B) II

C) III

6

D) I

23)

Find the coordinates of the y-intercept and the x-intercept, in that order.

24) 3x + y = 3 A) (-1, 0) (6, 0) B) (3, 6) (-1, 3) C) (0, -1) (0, 6)

D) (1, 0) (0, 3)

Find the x- and y-intercepts for the equation. Then graph the equation.

25) 2x - 5 = y

A)

5 , 0 , 0, -5 2

B) -5, 0 , 0,

24)

25)

5 2

Determine whether the given ordered pair is a solution of the equation.

26) 3x + y = 18; (5, 3) A) No B) Yes

26)

List the quadrant(s) in which the given point is located.

27) The first coordinate is positive.

A) I, II B) III, IV

27)

C) II, III

7

D) I, IV

Solve the problem.

28)

28)

Let x = 24 and y = 6. Find the pitch of the roof.

1 1 A) B) 6 4

C)

1 2

Graph the line containing the given pair of points and find the slope.

29) (-9, 0) (-12, -1)

A) -3

B) 3

8

D)

1 3

29)

C) -

1 3

D)

1 3

Solve the problem.

30) Over one particular stretch of road, the Whitepoint Highway rises 513 ft over a horizontal distance of 3700 ft. Find the grade of the road.

A) 6.9% B) 3.5% C) 13.9% D) 0.07% Find the x- and y-intercepts for the equation. Then graph the equation.

31) -6x - 30y = 30

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

30)

31)

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

Find the slope of the line going through the pair of points.

32) (3, -6.8), (2.9, 0.3) A) 71 B) -0.1

C) -71

9

D) 7.1

32)

33) (-8, -8), (-5, -8) A) 0

B) 2

C) -5

Find the coordinates of the labeled points.

34)

33)

34)

A) A(-6, 6); B(4, -4) C) A(-6, 0); B(-4, -4)

B) A(6, 0); B(4, -4) D) A(-6, 0); B(4, -4)

Graph the line containing the given pair of points and find the slope.

35) (1, 5) (0, 0)

A)

D) 1

1 5

B) -

10

1 5

35)

C) 5

D) -5

11

Graph.

36) 4y = 10

36)

A)

B)

C)

D)

Find the slope of the line going through the pair of points.

37) (-2, 1), (-4, 5) 1 A) - 2 B) 2

C) 3

12

1 D) 3

37)

Solve the problem.

38) The value of a particular car is represented in the following graph. Find the rate of change of the value of the car with respect to time, in dollars per year.

A) -$500 per year

B) -$750 per year

C) -$700 per year

Graph the line containing the given pair of points and find the slope.

39) (2, -4) (-1, 2)

A) -

1 2

B) 2

13

38)

D) -$600 per year

39)

C) - 2

D)

1 2

Solve the problem.

40) The value V, in dollars, of a shopkeeper's inventory software program is given by V = -20t + 450, where t is the number of years since the shopkeeper first bought the program. Find the value of the software after 0 years, 6 years, and 10 years.

A) $450, $330, and $210 B) $450, $570, and $250 C) $430, $330, and $250 D) $450, $330, and $250

14

40)

Graph the linear equation.

41) 4x - y = 8

41)

A)

B)

C)

D)

List the quadrant(s) in which the given point is located.

42) (-4, 6) A) III B) II Find the slope of the line.

43) 3x + 4y = 21 4 A) 3

B) -

C) I

3 4

C)

15

3 4

D) IV

D)

4 3

42)

43)

Graph.

44) -4x = -6

44)

A)

B)

C)

D)

16

Graph the linear equation.

45) x + 8y = 5

45)

A)

B)

C)

D)

17

Find the slope of the line.

46)

A) -

1 3

46)

B) -3

C)

1 3

D) 3

Determine whether the given ordered pair is a solution of the equation.

47) 5x - 4y = 32; (4, 3) A) Yes B) No Find the coordinates of the y-intercept for the given equation.

48) y = 8x - 9 A) (0, 9) B) (-9, 0) C) (8, -9)

47)

D) (0, -9)

Find the slope of the line.

49)

A) 1

48)

49)

B) 6

C) -6

D) -1

Solve the problem.

50) The value V, in dollars, of a shopkeeper's inventory software program is given by V = -40t + 250, where t is the number of years since the shopkeeper first bought the program. After how many years is the value of the software $10?

A) 8 yr B) 5 yr C) 6 yr D) 7 yr

18

50)

Graph the linear equation.

51) 2y + 6x = 14

51)

A)

B)

C)

D)

19

Find the coordinates of the labeled points.

52)

52)

A) A(-5, 2); B(0, 4) C) A(5, -2); B(1, -4)

B) A(5, 2); B(0, 4) D) A(5, 2); B(0, -4)

20

Answer Key Testname: C3

1) Show that (4, 0) is a solution: 1 y= x- 2 2 0 =?

1 (4) - 2 2

0 =? 2 - 2 0 =? 0 TRUE Show that (-4, -4) is a solution: 1 y= x- 2 2 -4 =?

1 (-4) - 2 2

-4 =? -2 - 2 -4 =? -4

TRUE

Coordinates of the additional solution may vary but should satisfy y =

1 x - 2.

2

2) Yes. If the line passes through the origin, then both the x-intercept and the y-intercept are at (0, 0).

3) Show that (-2, -6) is a solution: 3x - 3y = 12 3(-2) - 3(-6) =? 12 -6 - (-18) =? 12 12 =? 12 TRUE Show that (5, 1) is a solution: = 12 3x - 3y =? 12 3(5) - 3(1) =? 12 15 - (3) 12 =? 12 TRUE Coordinates of the additional solution may vary but should satisfy 3x - 3y = 12.

4) The x-intercept is the point where the line crosses the x-axis. Lines parallel to the x-axis do not intercept the x-axis.

Thus the graph of any equation of the form y = b where b 0 has no x-intercept.

5)

21

Answer Key Testname: C3

6) Show that (0, -2) is a solution: 6x - 2y =4 6(0) - 2(-2) =? 4 0 - (-4) =? 4 4 TRUE =? 4 Show that (3, 7) is a solution: =4 6x - 2y =? 4 6(3) - 2(7) =? 4 18 - 14 4 TRUE =? 4 Coordinates of the additional solution may vary but should satisfy 6x - 2y = 4.

7)

8) Show that (0, 5) is a solution: y=x+ 5 5 =? 0 + 5 5 =? 5 TRUE Show that (-3, 2) is a solution: y=x+ 5 2 =? -3 + 5 2 =? 2 TRUE Coordinates of the additional solution may vary but should satisfy y = x + 5.

9) (0, b) 10) Show that (2, 3) is a solution: 1 y= x+ 2 2 3 =?

1 (2) + 2 2

3 =? 1 + 2 3 =? 3 TRUE Show that (-2, 1) is a solution: 1 y= x+ 2 2 1 =?

1 (-2) + 2 2

1 =? -1 + 2 1 =? 1

TRUE

Coordinates of the additional solution may vary but should satisfy y =

22

1 x + 2.

2

Answer Key Testname: C3

11) The line is vertical.

12) Show that (2, 3) is a solution: x + 2y =8 2 + 2(3) =? 8 2+6 =? 8 8 TRUE =? 8 Show that (-2, 5) is a solution: x + 2y = 8 -2 + 2(5) =? 8 -2 + 10 =? 8 8 TRUE =? 8 Coordinates of the additional solution may vary but should satisfy x + 2y = 8.

13) Show that (1, 4) is a solution: 2x + y =6 2(1) + 4 =? 6 2+4 =? 6 6 TRUE =? 6 Show that (5, -4) is a solution: =6 2x + y =? 6 2(5) + (-4) =? 6 10 + (-4) 6 TRUE =? 6 Coordinates of the additional solution may vary but should satisfy 2x + y = 6.

14) Let y = 0 and solve for x.

15)

16)

23

Answer Key Testname: C3

17)

18)

19)

20) The graph is a vertical line.

21) Show that (7, 4) is a solution: y=x- 3 4 =? 7 - 3 4 =? 4 TRUE Show that (-2, -5) is a solution: y=x- 3 -5 =? -2 - 3 -5 =? -5 TRUE Coordinates of the additional solution may vary but should satisfy y = x - 3.

24

Answer Key Testname: C3

22)

23) A 24) D 25) A 26) B 27) D 28) B 29) D 30) C 31) B 32) C 33) A 34) D 35) C 36) C 37) A 38) C 39) C 40) D 41) D 42) B 43) B 44) A 45) B 46) C 47) B 48) D 49) A 50) C 51) C 52) D

25

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) Simplify the expressions (2x)0 and (2x0 ) and explain how you arrived at your answers.

1)

2) When is the square of the sum the sum of a square; i.e., when is (A + B)2 = A2 + B2 ?

2)

3) What must be done to the dividend before beginning the "long division" process for (8b3 + 5b2 + 9b4 + 9b + 4) ÷ (3b + 7)?

3)

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

Multiply and simplify.

4) y-7 · y-3 1 A) y4

1 C) y10

B) y10

1 D) -10 y

4)

Simplify.

5) -(-4x4 - 4x3 - x2 + 7.1) A) -4x4 - 4x3 - x2 + 7.1 C) 4x4 - 4x3 - x2 + 7.1

Subtract.

6) -

5)

B) 4x4 + 4x3 + x2 - 7.1

D) 4x4 - 4x3 + x2 - 7.1

7x6 + 19x3 - 14 ( 3x6 + 12x3 - 12)

A) 4x6 + 22x3 - 26

6)

B) 4x6 + 7x3 - 26

C) 9x9

D) 4x6 + 7x3 - 2

B) 1

C) 0

D) -1

Evaluate.

7) (-9)0 A) -9

Convert to decimal notation.

8) 1.87 × 106 A) 18,700,000

8) B) 112.2

Evaluate the polynomial.

9) x2 + y2 - z 2 for x = 1, y= 3, and z = 3 A) 9

Convert to decimal notation.

10) 105 A) 1,000,000

7)

B) 10

B) 10,000,000

C) 1,870,000

D) 187,000

C) 19

D) 1

C) 100,000 1

D) 10,000

9)

10)

Simplify.

11)

5a 2 3

A)

11) 5a 2 9

B)

25a 9

C)

25a 2 3

D)

25a 2 9

Express using positive exponents. Then simplify.

1 -2 12) 2 A) -

1 4

B)

12)

1 4

C) - 4

D) 4

C) -0.08x28

D) 0.08x11

Multiply.

13) (0.4x7 )(0.2x4 ) A) 0.08x28

B) -0.08x11

Collect like terms.

14) 5q8 + 8q8 + 8q8 A) 21q24

13)

14) B) 320q8

C) 320q24

D) 21q8

Solve the problem.

15) During the first seconds, the height h in feet of a baseball after t seconds is given by h = -16t2 + 87t + 3.6. Use the graph below to estimate the height of the ball after 3 seconds.

A) 121 feet

B) 157 feet

C) -144 feet

2

D) 103 feet

15)

Evaluate the polynomial.

16) -32 + 4x2 - 5x3 , when x = -2 A) 24

B) 12

C) 14

D) 0

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.

17) -18x2 A) Binomial, degree 0 C) Monomial, degree 2

B) Monomial, degree -18 D) Binomial, degree -18

Solve the problem.

18) The average weight W (in ounces) of a fish caught in a certain lake is given by W = 0.001x3 + 0.03x2 + 1.3, where x is the length in inches. Use the graph below to estimate the

16)

17)

18)

weight of a fish from the lake that is 14 inches long.

A) 13 ounces

B) 9 ounces

C) 11 ounces

D) 7 ounces

B) 50.41 + x10

C) 50.41 - x25

D) x10 - 50.41

Multiply.

19) (7.1 - x5 )(7.1 + x5 ) A) 50.41 - x10

Solve the problem.

20) The polynomial 0.041h - 0.018A - 2.69 can be used to estimate the lung capacity, in liters, of a female with height h cm and age A years. Find the lung capacity of a 60-year-old woman who is 166 cm tall. Round to the nearest liter.

A) 55 liters B) 11 liters C) -3 liters D) 3 liters

3

19)

20)

Find the degree of the polynomial.

21) x4 yz - x6 y2 - 3x3 y2 z 3 A) 4

B) 8

C) 3

D) 6

Compute each expression and compare.

22) 1 2 + 4 2 ; (1 + 4)2

22)

A) 17; 25; square of sum is greater than sum of squares B) 10; 10; both are equal C) 10; 25; square of sum is greater than sum of squares D) 17; 10; sum of squares is greater than square of sum

Perform the division. x4 - 256 23) x2 - 16 A) x2 - 16x + 4

21)

23) B) x2 + 16

C) x2 + 4x + 4

D) x2 - 16

B) 0

C) 20

D) 5

Evaluate.

24) p5 , when p = 0 A) 1

Divide and simplify. t-3 25) t-7 A) t4

24)

25) B) t10

C) t-10

D) t-4

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.

26) It has been estimated that the average American watches 58,240 hours of television in a lifetime.

26) 3 4 A) 58.24 × 10 hours B) 5.824 × 10 hours

C) 5.824 × 103 hours

D) 5.824 × 105 hours

4

Write an algebraic expression that represents the total area of the four smaller rectangles.

27) x

27)

4

x

5

A) x2 + 9x + 20

B) x2 + 10x + 25

C) x2 + 8x + 16

D) x2 - 8x + 16

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.

28) The earth is approximately 92,900,000 miles from the sun. If 1 mile = 1.61 × 103 m, what is the distance to the sun in meters?

A) 5.7 × 1010 m B) 5.7 × 10-10 m

Add.

C) 1.50 × 1011 m

29) (4x8 - 5x4 + 3x 2 + 4) + (5x7 + 3x4 - 2x) A) 4x8 + 5x7 + 2x4 + 3x2 - 2x + 4

Evaluate the polynomial.

30) -4x3 - 5x2 - 44, when x = -3 A) 79

32) (9s + 15t) + (11t - 2s) A) 7s + 26t

29)

D) 9x8 - 2x4 + 3x2 - 2x + 4

B) 7

Write the number in scientific notation.

31) 878,835 A) 8.78835 × 105 B) 8.78835 × 10-5 Add.

D) 1.50 × 1010 m

B) 4x8 + 5x7 - 2x4 + 3x2 - 2x + 4

C) 9x8 - 8x4 + 3x2 - 2x + 4

28)

B) 33st

Identify the like terms in the polynomial.

33) 3x3 + 3x2 - 7x3 A) x3

C) 19

D) 9

C) 8.78835 × 101

D) 8.78835 × 106

C) 11s + 26t

D) 20s + 13

B) 3x3 and -7x3

C) 3x3 and 7x3

D) None of the terms are like.

5

30)

31)

32)

33)

Express the following using negative exponents.

1 34) 63 A) 6 3

34)

B) 3 -6

C) 6 -4

D) 6 -3

Multiply.

35) (a - b)(a 2 - ab - 8b2 ) A) a 3 - 2a 2 b - 8ab2 + 8b3

B) a 3 - 2a 2 b - 9ab2 - 8b3

C) a 3 - 7a 2 b + 8b3

35)

D) a 3 - 2a 2 b - 7ab2 + 8b3

Write an algebraic expression that represents the total area of the four smaller rectangles.

36) x

36)

7

x

8

A) x2 + 15x + 56

B) x2 + 14x + 49

C) x2 + 16x + 64

D) x2 - 15x + 56

Express using positive exponents. Then simplify.

37) - 3 -2 A)

1 6

B) -

37)

1 9

C) 9

D) - 9

Simplify.

38) (-5p3 q3 r3 )5

Divide.

39)

38)

A) -25p8 q8 r8

B) (-5)5 p8 q8 r8

C) (-5)15p15q15r15

D) (-5)5 p15q15r15

3x8 - 3x5 + x2

39)

x

A) 3x7 - 3x5 + x2

B) 3x7 - 3x4 + x

C) 0

6

D) 3x8 - 3x5 + x

Multiply.

40) 5(-7x + 9) A) -35x + 9

B) 10x

C) -7x + 45

D) -35x + 45

Simplify.

41) -(7x - 9) A) 7x - 9

B) 7x + 9

C) -7x - 9

D) -7x + 9

Solve the problem.

42) Find a polynomial for the the shaded areas of the figure.

40)

41)

42)

6

x

x

x

x

x

x

6

x

A) 4x2 - 24x

x

B) 4x2 - 24x + 36

C) 4x2

D) 8x2 - 24x + 36

B) 22x3 - 6

C) 22x10 - 6x7

D) 16x7

Multiply.

43) 2x7 (11x3 - 3) A) 22x10 - 3 44) (x + y - 2)(x + y + 2) A) x2 + y2 + 2xy + 4

B) x2 + y2 - 4 D) x2 + y2 + 2xy - 4

C) x2 + y2 + 2(xy - 2)

Subtract.

45) -

7x7 - 4x6 - 3x5 + 6 (2x7 + 6x6 - 6x5 + 2)

43)

44)

45)

A) 9x7 + 2x6 - 9x5 + 4 C) 9x7 + 2x6 - 9x5 + 8

B) 5x7 + 2x6 - 9x5 + 8 D) 5x7 - 10x6 + 3x5 + 4 7

Identify the missing terms in the polynomial.

46) -3x3

46)

A) x2 -term, x-term

B) x-term

C) x2 -term, x-term, 0-degree term

D) none

Multiply.

47) (2a - 7)2 A) 2a 2 + 49

Add.

B) 2a 2 - 28a + 49

C) 4a 2 + 49

D) 4a 2 - 28a + 49

48) 3x7 + 9x6 - 7x5 + 1 5x7 + 5x6 - 8x5 + 3

47)

48)

A) 8x14 + 14x 12 - 15x10 + 4 C) 6x7 + 6x6 + 6x5 + 14

B) 7x36 + 4 D) 8x7 + 14x6 - 15x5 + 4

Multiply.

49) (x2 - x + 8)(x + 5) A) x3 + 40

B) x3 + 6x2 + 13x + 40 D) x3 + 4x2 + 40

C) x3 + 4x2 + 3x + 40

Divide.

50)

49)

40x4 + 30x 5

50)

A) 8x4 + 6x

B) 8x3 + 6

C) 8x4 + 30x

D) 40x4 + 6x

Multiply.

51) (x - 12)(x + 12) A) x2 - 144

B) x2 - 24

C) x2 - 24x - 144

D) x2 + 24x - 144

Identify the degree of each term and the degree of the polynomial.

52) 9x2 - 3x + 6 A) 9, -3, 6; 9

Add.

B) 2, 1, 0; 2

C) 2, 0, 0; 2

53) (-6 + 9x5 + 3x3 ) + (3x5 + 2x3 + 8) A) 12 + 5x5 + 2x3

B) 19x 8

C) -3x5 + 11x3 + 11

D) 12x 5 + 5x3 + 2

8

D) 2, 1, 0; 9

51)

52)

53)

Answer Key Testname: C4

1) (2x)0 = 1, because the exponent is applied to the entire quantity in the parentheses. (2x0 ) = 2 because the exponent is applied only to the x.

2) Now (A + B)2 = A2 + 2AB + B2 , so that (A + B)2 = A2 + B2 just in case 2AB = 0, that is A = 0 or B = 0. The square of the sum is the sum of the squares in the case (at least) one of the numbers is 0.

3) The dividend must be written with descending powers. That is, 9b4 + 8b3 + 5b2 + 9b + 4.

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

Answer Key Testname: C4

48) D 49) C 50) A 51) A 52) B 53) D

10

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) Why is the answer (x2 - 36)(x2 + 36) not the correct answer to the instruction "Factor (x4 - 1296) completely"?

1)

2) Explain the error in the following: x2 + 2x - 15 = (x - 5)(x + 3)

2)

3) A student is trying to solve the equation (x + 5)(x - 6) = 8. The student has set x + 5 = 8 and x - 6 = 8 and found that two solutions x = 3, x = 14. The student checks his or her results by plugging in his or her solutions into the original equation and finds that they do not work.

How would you advise him or her?

3)

4) Assuming you have factored out the largest common factor at the outset, why can you reject a possible factor such as (2x + 2) or (3x - 6) when you are factoring a trinomial?

4)

5) In factoring a trinomial in x as (x + a)(x + b), what must be true of a and b, if the coefficient of the last term of the trinomial is positive?

5)

6) How could you solve the equation (6x + 4)(10x - 7)(7x - 3) = 0? How many equations do you need to solve? What are their solutions?

6)

7) Use the FOIL method to show that (8x + 16)(x - 4) is 8x2 - 16x - 64. If you were asked to completely factor 8x2 - 16x - 64, why would it be incorrect to give (8x + 16)(x - 4) as your

7)

8) Explain the difference between a factor and a multiple of a number.

8)

9) Explain the error in the following: x2 - y2 = (x - y)2

9)

10) A student was trying to solve the problem 4x(4x - 9) = 0. The student knew that he or she should set 4x - 9 = 0 but was confused about whether or not he or she should set 4x = 0, or 4 = 0 and x = 0. How would you advise this student?

10)

answer?

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

Factor.

11) x2 + 2xy - 8y2 A) (x - 4y)(x + 2y)

B) (x + 4y)(x - 2y)

C) (x - 4y)(x + y)

1

D) (x - y)(x + 2y)

11)

Solve the problem.

12) In a sports league of n teams in which each team plays every other team twice, the total number N of games to be played is given by N = n 2 - n. How many teams are in a softball league if the total number of games played is 90?

A) 11 B) 10

C) 8

D) 9

13) Within a group of n people, the number of possible handshakes, N, is given by 1 N = (n 2 - n). At a party, everybody shakes hands with every other person. If the total number of 2 handshakes is 210, how many people are at the party?

A) 23 B) 21 C) 20

B) (9, 0), (-2, 0)

C) (-9, 0), (2, 0)

D) (9, 0), (1, 0)

C) 0

9 D) 2

Solve by factoring and using the principle of zero products.

15) 8n 2 + 36n = 0 9 A) - , 36 2

9 B) - , 0 2

13)

D) 22

Find the x-intercepts of the graph of the equation. (The grids are intentionally not included.)

14) y = x2 + 7x - 18

A) (11, 0)

12)

14)

15)

Factor.

16) 64s3 + 1

A) (4s - 1)(16s2 + 4s + 1) C) (4s + 1)(16s2 - 4s + 1)

16)

B) (4s + 1)(16s2 + 1) D) (64s + 1)(s2 - 4s + 1)

Determine whether the following is a difference of squares.

17) -64x2 + 64y2 A) Yes

17)

B) No

Factor.

18) x2 - x - 30 A) (x + 1)(x - 30)

B) (x + 6)(x - 5)

C) (x + 5)(x - 6)

2

D) Prime

18)

Factor completely.

19) 175x2 - 28y2

19)

A) 7(5x - 2y)2

B) 7(5x + 2y)(5x - 2y)

C) (35x + 14y)(5x - 2y)

D) (5x + 2y)(35x - 14y)

Factor.

20) x3 - 27

A) (x - 3)(x2 + 9) C) (x + 27)(x2 - 1)

Factor by grouping.

21) x3 - 7x2 - 8x + 56

A) (x + 7)(x2 + 8)

Factor.

22) x2 +

20)

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

B) (x - 7)(x2 - 8)

C) (x + 7)(x3 - 8)

D) (x - 7)(x2 + 8x)

2 1 x+ 3 9

A) Prime

22) B) x +

2 2 3

C) x x +

2 3

D) x +

1 2 3

Solve the problem.

23) In a sports league of n teams in which each team plays every other team twice, the total number N of games to be played is given by N = n 2 - n. What is the total number of games to be played in a football league having 25 teams?

A) 625 B) 650

C) 600

23)

D) 50

24) Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 12 miles, the distance between the cars was 4 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?

A) 20 miles B) 24 miles C) 16 miles D) 12 miles Factor completely.

25) x4 - 256

24)

25)

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

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

C) (x + 4)2 (x - 4)2

Solve by factoring and using the principle of zero products.

26) x2 + 4x - 45 = 0 A) -9, 1

21)

B) -9, 5

C) 9, -5

D) 9, 5

Solve the problem.

27) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 feet. Find the length of the ladder if the length is 2 feet more than its distance from the wall.

A) 10 feet B) 12 feet C) 6 feet D) 8 feet

3

26)

27)

Factor.

28) 40x 8y9 + 64x6 y5 + 80x 4y2

28)

A) 8x4 (5x4 y9 + 8x2 y5 + 10y2 )

B) No common factor

C) 8x4 y2 (5x4 y7 + 8x2 y3 + 10)

D) 8(5x8 y9 + 8x6 y5 + 10x4 y2 )

29) 15z 2 + 4z - 4 A) Prime

B) (15z + 2)(z - 2)

C) (3z - 2)(5z + 2)

30) 375k3 m - 192m 4

A) 3m(5k + 4m 2 )(25k2 - 20km + 16km2 ) C) 3m(5k - 4m)(25k2 + 20km + 16m 2 )

D) (3z + 2)(5z - 2)

B) (15km - 12m 2 )(25k2 + 16m 2 ) D) 3m(125k - 4m)(k2 + 20km + 16m 2 )

Solve using the principle of zero products.

5 1 =0 31) z z 8 5 A) -

5 1 , 8 5

B)

29)

30)

31)

5 1 , 8 5

C) -

Determine whether the following is a trinomial square.

32) x2 - 8x + 64 A) No

1 ,0 5

D)

1 ,0 5

32)

B) Yes

Factor.

33) u2 - 2uv - 24v2 A) (u - v)(u + 6v)

B) (u - 4v)(u + v)

C) (u + 4v)(u - 6v)

34) 16x 2 - 24xt + 9t2 A) (4x + 3t)(4x + 3t) C) (4x - 3t)(4x - 3t)

D) (u - 4v)(u + 6v)

34)

B) Prime D) (16x - 3t)(x - 3t)

Solve the problem.

35) The height of a triangle is 4 cm more than the length of the base. If the area of the triangle is 198 cm2 , find the height and length of the base.

A) height: 18 cm; base: 14 cm C) height: 21 cm; base: 17 cm

35)

B) height: 22 cm; base: 18 cm D) height: 23 cm; base: 17 cm

Factor completely.

36) x10 + 12x 5 + 36 A) (x5 + 6)2

33)

C) (x5 - 6)2

B) Prime

D) (x5 + 6)(x5 - 6)

36)

Factor.

37) 12x 2 - 25xy + 12y2 A) (12x + 4y)(x + 3y) C) (3x - 4y)(4x - 3y)

B) (3x + 4y)(4x + 3y) D) (3x + 4y)(4x - 3y)

4

37)

38) p6 - 64y6

38)

A) (p + 2y)(p - 2y)(p2 + 2py + 4y2 )(p2 - 2py + 4y2 ) B) (p + 2y)(p - 2y)(p4 + 4p2 y2 + 16y4 ) C) (p3 + 8y3 )(p3 - 8y3 ) D) (p2 - 4y2 )(p4 + 4p2 y2 + 16y4 )

39) x3 - x2 - 72x A) Prime

B) x(x + 8)(x - 9)

C) x(x + 9)(x - 8)

40) 9x4 - 18x3 + 8x2 A) x2 (3x - 2)(3x - 4)

D) x(3x + 2)(3x + 4)

B) (20z - 3)(z + 3)

C) (4z - 3)(5z + 3)

42) 245x2 + 350xy + 125y2

D) Prime

D) 5(49x2 + 70xy + 25y)

C) (35x + 25y)(7x + 5y) 43) x2 + 7xy - 120y2 A) (x - 15y)(x + y) C) (x - y)(x + 8y)

43)

B) (x - 15y)(x + 8y) D) (x + 15y)(x - 8y)

Factor completely.

44) 3x3 + 6x2 y - 24xy2

44)

A) (x - 2y)(3x2 + 12xy)

B) 3x(x - 2y)(x + 4y) D) (3x2 + 6xy)(x - 4y)

C) 3x(x + 2y)(x - 4y)

A) prime

41)

42)

B) 5(7x + 5y)2

A) 5(7x - 5y)(7x + 5y)

Factor using the ac-method.

45) 27x 2 - 117x - 90

39)

40)

B) (9x2 + 2)(x2 + 4)

C) x2 (9x - 1)(x - 8)

41) 20z 2 - 3z - 9 A) (4z + 3)(5z - 3)

D) (x2 + 1)(x - 72)

B) 9(3x - 2)(x + 5)

Solve using the principle of zero products.

46) (x - 6)(x + 2) = 0 A) 6, 2 B) 6, -6, 2, -2

C) 9(3x + 2)(x - 5)

D) (27x + 18)(x - 5)

C) 6, -2

D) -6, 2

45)

46)

Factor.

47) 84x 2 + 49xy + 7y2 A) (21x + 7y)(4x + y) C) (3x + y)(7x + 3y)

B) 7(3x + y)(4x + y) D) 7(3x - y)(4x - y)

5

47)

Factor completely.

48) 49y4 - 25

2 A) (7y2 - 5)

2 B) (7y2 + 5)

C) Prime

D) (7y2 + 5)(7y2 - 5)

48)

Find the x-intercepts of the graph of the equation. (The grids are intentionally not included.)

49) y = x2 - 5x - 14

A) (-2, 0) (7, 0)

B) (2, 0), (-7, 0)

C) (9, 0)

D) (2, 0), (1, 0)

B) -7, -8

C) 7, 8

D) -7, 8

B) x3 y3

C) x y

Solve by factoring and using the principle of zero products.

50) x2 - x = 56 A) 1, 56

Find the GCF. 51) x5 y5 , x4 y3 , x4 y4 , -x y A) x4 y3

49)

50)

51)

Factor completely.

52) 98x 2 - 128

D) -xy

52)

A) 2(7x + 8)(7x - 8) C) 2(7x - 8)2

B) (7x + 8)(14x - 16) D) (14x + 16)(7x - 8)

6

Find the x-intercepts of the graph of the equation. (The grids are intentionally not included.)

53) y = x2 - x - 42

A) (42, 0)

B) (7, 0), (6, 0)

C) (1, 0), (-42, 0)

D) (-6, 0), (7, 0)

54) x2 + 5xy - 14y2 A) (x - 7y)(x + 2y)

B) (x - 7y)(x + y)

C) (x - y)(x + 2y)

D) (x + 7y)(x - 2y)

53)

Factor.

55) 6x3 - 26x2 - 20x A) 2(3x - 2)(x + 5)

B) (x2 - 5)(6x + 4)

C) x(3x + 2)(2x - 10)

D) 2x(3x + 2)(x - 5)

56) 80z 8 + 108z5 + 36z2 A) (4z 4 + 4)(5z 4 + 3)

55)

56)

B) 4z 2 (5z3 - 3)(4z 3 - 3)

C) 4(4z 6 + 3)(5z 2 + 3)

54)

D) 4z 2 (4z3 + 3)(5z 3 + 3)

57) 3a 3 + 6a 2 - 45a A) 3a(a + 5)(a - 3)

B) 3a(a + 5)(a + 3)

C) 3a(a - 5)(a + 3)

D) 3a(a - 5)(a - 3)

58) 12x 2 + 13xt + 3t2 A) Prime

B) (3x - t)(4x - 3t)

C) (12x + t)(x + 3t)

D) (3x + t)(4x + 3t)

59) 125y9 - z 9 A) (25y3 - z 3 )(5y6 + y3 z 3 + z 6 )

B) (25y3 + z 3 )(5y6 + y3 z 3 + z 6 ) D) (5y3 - z 3 )(25y6 - 5y3 z 3 + z 6 )

C) (5y3 - z 3 )(25y6 + 5y3 z 3 + z 6 )

Solve the problem.

60) The product of two consecutive integers is 29 more than their sum. Find the integers.

A) 6, 7 or -5, -4 B) -5, -4 C) 5, 6 or -5, -4 D) 6, 7

7

57)

58)

59)

60)

Answer Key Testname: C5

1) The term x2 - 36 can still be factored as (x - 6)(x + 6).

2) The factorization yields a middle term of -2x rather than 2x: x2 + 2x - 15 = (x + 5)(x - 3)

3) The equation needs to be set to zero in order to use the zero-factor theorem.

4) Factors such as (2x + 2) or (3x - 6) contain a common factor and, since the largest common factor has already been removed, such factors are not possible.

5) The numbers a and b must have the same sign (both positive or both negative).

2 7 3 , 6) Set each factor equal to 0 in turn, and solve. There would thus be three equations to solve. - , 3 10 7 7) The factor of 8 should be factored out.

8) A factor is a number in a product while a multiple of a number is a product of it and some natural number. For example, 6 = 2 x 3, so 2 and 3 are FACTORS of 6; 18 = 3 x 6, so 18 is a MULTIPLE of 6.

9) x2 - y2 is a difference of squares, not a binomial square. x2 - y2 = (x + y)(x - y)

10) Setting 4x = 0 is not a problem because x =

0 = 0.

4

11) B 12) B 13) B 14) C 15) B 16) C 17) A 18) C 19) B 20) B 21) B 22) D 23) C 24) C 25) D 26) B 27) A 28) C 29) D 30) C 31) D 32) A 33) C 34) C 35) B 36) A 37) C 38) A 39) B 40) A 41) C 42) B 8

Answer Key Testname: C5

43) D 44) B 45) C 46) C 47) B 48) D 49) A 50) D 51) C 52) A 53) D 54) D 55) D 56) D 57) A 58) D 59) C 60) A

9

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Answer the question.

1) Explain why, when one number is a factor of another, the least common denominator of the numbers is the larger number.

2) For x

1 , the rational expression

1)

9 (x - 1 ) is equal to 9 . Can the same be said for x- 1

2)

9x - 1 ? Explain why or why not. x- 1

3) Explain why the least common denominator of two (different) prime numbers is the product of the two numbers.

4) If 4 is substituted for x in the rational expression

3)

x- 4 0 , the result is . Mathematicians 0 x2 - 16

4)

have been known to say "Any number divided by itself is 1." Does this mean that this expression is equal to 1 for x = 4 ? Explain why or why not.

5) Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

5)

6) Without multiplying by the least common denominator and solving, explain why the x 3 rational equation has no solution. (Hint: Examine both numerators and = x-3 x-3

6)

denominators carefully.)

7) Describe two ways in which multiplying by 1 is used in adding or subtracting using fractional notation.

7)

8) Explain in your own words how to divide rational expressions. (How would you explain this to a student in this class who was absent from class?).

8)

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

Find an equation of variation in which the following are true.

9) x varies inversely as y2 , and x = 7 when y = 15.

A) x = 1575y2

1575 B) x = y2

C) x =

1

1575y2

D) x =

1

-8y2

Subtract. Simplify, if possible.

5(y - 1) y- 5 6y 10) 3y - 7 7 - 3y 3y - 7 A)

-10 3y - 7

9)

10) B)

-2y 3y - 7

C)

1

-10 (3y - 7)(7 - 3y)

D)

10 3y - 7

Solve the equation. x+9 10 = 11) x-3 3-x A) 19 12)

11) B) 1

C) -19

D) -1

9 x = x-9 x-9

A) No solution Find the LCM. 13) 54, 12 A) 36

12) B) 0

C) 9

D) -9

B) 54

C) 108

D) 18

Subtract. Simplify, if possible.

9 7 14) 2 3x 3x2 A)

2

3x2

14) B)

3

C) 2

2x2

D)

2 6x4

Solve the problem.

15) A loaded moving truck is traveling 15 mph faster than a freight train. In the time it takes the train to travel 80 miles, the truck travels 110 miles. Find the speed of the truck.

A) 11 mph B) 55 mph C) 15 mph D) 110 mph Simplify.

4 +

16)

2 x

16 x

B) 1

C)

x 16

D) 16

Subtract. Simplify, if possible.

13 8 17) 13x 13x A)

Simplify.

18)

5 13x

17) B)

13x 5

C) 5

D)

5 26x

12m 3 p2

18)

6m 8 p

A) 2m 5 p2

15)

16)

x 1 + 4 8

A)

13)

B)

2m 5

C) 2mp

p

2

D)

2p m5

Perform the indicated operation. Simplify, if possible.

49 x 1 4 + 19) 9 (7x + 1) 9 x( 7 x + 1) x A) C)

19)

49 x2 + 252x + 35 63 x2 + 9x

7(x + 5 )

63 x2 + 9x

B)

49x2 + 252x + 35 9x

D)

7(x + 5 ) 9x

Solve the equation.

7 1 =4 20) x x A)

7 4

20) B) 1

C)

2 3

D) 2

Multiply and, if possible, simplify.

2z 3 8 · 21) 4 z2 A)

4 z

21) B) 4z

C)

4z 2 z3

D)

z 4

Solve the equation.

4 1 = 22) x+2 x-8 A)

34 3

22) B) - 10

C)

34 5

D)

10 3

Divide and simplify.

-18 + 6x 9 - 3x ÷ 23) 18 9 A)

x-3 x+3

23) B) 1

C)

x-3 3-x

Find an equation of variation in which the following are true.

24) y varies directly as x and inversely as z, and y = 18 when x = 2 and z = 9.

85 x 81x A) y = 84xz B) y = C) y = z z

D) -1

80z D) y = x

Find all numbers for which the rational expression is not defined. x2 - 25 25) x2 - 2x - 35 A) x = -5 and x = 7

B) x = 5 and x = -5

C) x = 5 and x = -7

3

24)

25) D) x = 0

Simplify.

26)

y2 + 5y

26)

y2 + 6y

A)

7y + 10 8y + 12

B)

y+ 5 y+ 6

C)

y+ 5 y2 + 6y

D)

y2 + 5y y+ 6

Find the LCM.

27) 8a - 48 , a 2 - 6a A) 8 a(a - 6 )

B) 8 a 2 - 6

C) 8 a 2 - 48

27) D) 8 a - 6

Multiply and, if possible, simplify. k2 + 7k + 12 k2 + 6k · 28) k2 + 10k + 24 k2 - 3k - 18 A)

k2 + 6k k- 6

28) B)

1 k- 6

C)

k k- 6

Solve the problem.

29) Sven can type 39 words per minute. How many words would he type in A) 10 words

B) 585 words

C) 156 words

D)

k k2 + 10k + 24

1 hour (15 minutes)?

4

D) 146 words

Divide and simplify.

4 7 30) ÷ 9 2 A)

8 63

30) B)

9 14

C)

14 9

D)

63 8

Perform the indicated operation. Simplify, if possible.

8x 4x - 3 3x 31) x- 5 5 -x x- 5 A)

15x + 3 x- 5

B)

31)

9x - 3 3x + 15

C)

9x - 3 x- 5

D)

15x - 3 x+ 5

Find all numbers for which the rational expression is not defined.

9 32) b+8 A) b = -8

B) b = 8

32)

C) b = 0

D) None

Subtract. Simplify, if possible.

20 10 33) q- 4 q- 4 A)

10 q

29)

33) B)

10 q- 4

C)

4

20(q - 4) 10(q - 4)

D)

30 q- 4

Simplify.

34)

15x + 3 9

A)

5x 3

34) B) 5x + 1

C)

5x + 1 3

D)

5x + 1 9

Add. Simplify, if possible.

2 5 + 35) 15x 15x A) 1

35) B)

15x 7

C)

7 15x

D)

7 30x

Solve the problem.

36) The Epson Stylus 850 can print Helen's class project in 24 minutes. The Epson Stylus 500 can print the project in 30 minutes. If the two printers work together, how long would they take to print out the project?

3 1 of a minute A) B) 13 minutes C) 9 minutes D) 120 minutes 40 3 Multiply. Do not simplify. x - 4 -1 · 37) 8 - x -1 A)

(8 - x)(-1) (x - 4)(-1)

37) B)

(x - 4)(-1) 8-x

C)

x-4 (8 - x)(-1)

D)

(x - 4)(-1) (8 - x)(-1)

Subtract. Simplify, if possible.

3x + 16 x+6 38) 2 2 x + 3x - 10 x + 3x - 10 A) 2x + 10

36)

38) B)

1 x-1

C)

2x + 22 2 x + 3x - 10

D)

2 x-2

For the pair of similar triangles, find the length of the indicated side.

39)

In the left triangle, the hypotenuse has length 10, and the longer leg has length 8. In the right triangle, the hypotenuse has length 5, the longer leg has length 4, and the shorter leg has length 3.

Find the length, x, of the shorter leg of the left triangle.

A) x = 3 B) x = 9 C) x = 4 D) x = 6

5

39)

Simplify.

40)

x 2 4y 8y3 2

8y3

-

40)

x 4y

A) -1

C)

B) 1 - (9y2 + 8y)

9y2 C) 8y

Find the reciprocal.

41) 9y2 + 8y A)

1 9y2 + 8y

2xy2 - 2 2 - 2xy2

B) 1

D)

2xy2 - 2 2xy2 + 2

41) D) 8y2 + 9y

Divide and simplify. z 2 + 8z + 15 z 2 + 3z ÷ 42) 2 2 z + 12z + 35 z + 3z - 28 A)

z 2 z + 12z + 35

42) B)

z-4 z

C) z - 4

D)

z-4 z 2 + 7z

Find an equation of variation in which y varies inversely as x and the following is true.

43) y = 50, when x = 26 1300 1.92 A) y = B) y = 1300x C) y = 1.92x D) y = x x Subtract. Simplify, if possible.

3 9 44) 14x 10x2 A)

-6

14x + 10x2

44) B) -

6

C)

140x2

18 70x2

D)

3(5x - 21) 70x2

Divide and simplify.

4 2 ÷ 45) y-x x-y A) 2

45) B) -2

C) -4

D)

2(x - y) y-x

Solve the equation.

3 y = 46) y 9 y - 60 A) - 12 ,- 15 Find the LCM. 47) 30, 18, 15 A) 30

43)

46) B) 12 ,- 15

C) 12 , 15

D) - 12 , 15

B) 45

C) 18

D) 90

6

47)

Find the equation of variation if the following is true.

48) Suppose r varies directly as s and r = 0.3333 when s = 1.

A) r = 2s B) r = 3s C) r = 4s

D) r = 0.3333s

Add. Simplify, if possible.

7 4 + 49) x5 y xy3 A)

Solve.

4x4 + 7y2 x5 y3

49) B)

4x5 + 7y3 x5 y3

C)

11 x5 y3

D)

11 xy

50) The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 9 foot length with diameter 4 inches cost?

A) $170.40 B) $178.10 C) $178.37 D) $172.80

Add. Simplify, if possible. x + 5 x - 3 9(x + 1) + + 51) x-8 8-x x-8 A)

Simplify.

52)

9x + 17 (x - 8)3

3 5

B)

11x + 11 x-8

C)

9x + 17 x-8

D)

9x + 9 x-8

52) B) 3

C)

x-5 5x - 25

D)

5 3

Add. Simplify, if possible.

7 9 + 53) r r- 5 A)

Simplify.

54)

35 r - 16 r( 5 - r)

53) B)

16 r - 35 r(r - 5 )

C)

35 r - 16 r(r - 5 )

D)

16 r - 35 r( 5 - r)

1 +1 a

54)

1 -1 a

A)

50)

51)

9x2 - 45x 15x2 - 75x

A)

48)

1+a 1-a

Find the LCM. 55) r2 + 16 r + 64 , r2 + 8 r A) (r + 8 )2

B) 1 - a2

C) 1

D)

a

1 - a2

55)

B) r(r + 8 )2

C) r(r + 1)(r + 8 )

7

D) r(r + 8 )

Solve.

56) The number of miles per gallon of gasoline that a car averages varies inversely as the average speed the car travels. A car gets 26 miles per gallon at 39 mph. How many miles per gallon will it get at 67 mph?

A) 44.7 miles per gallon B) 0.07 miles per gallon C) 15.1 miles per gallon D) 0.02 miles per gallon

Simplify.

57)

4x + 2 2 20x + 18x + 4

A)

4x + 2 2 20x + 18x + 4

57) B)

4x 5x + 2

Find the equation of variation if the following is true.

58) Suppose p varies directly as q and p = 1 when q = A) p = 8q

56)

C)

1 5x + 2

D)

4x + 5 5x + 18

1 .

9

58) C) p =

B) p = 10q

8

1 q 9

D) p = 9q

Answer Key Testname: C6

1) Every prime factor of the smaller number is contained in the prime factorization of the larger number. Then the least common denominator will contain each prime factor exactly the number of times it appears in the larger number, and hence, is the larger number.

2) Answers will vary.

3) The numbers have no common factors, so the least common denominator must contain all the factors of both numbers and, hence, is their product.

4) Answers will vary.

5) Answers will vary.

6) Since the denominators are the same, the numerators must be the same. Then x = 3; but this value of x makes the denominators 0, so the equation has no solution.

7) Multiplying by 1 is used to write each fraction with the least common denominator as its denominator and to simplify the sum or difference.

8) Answers will vary.

9) B 10) A 11) C 12) A 13) C 14) A 15) B 16) A 17) A 18) D 19) D 20) D 21) B 22) A 23) D 24) C 25) A 26) B 27) A 28) C 29) B 30) A 31) C 32) A 33) B 34) C 35) C 36) B 37) D 38) D 39) D 40) A 41) A 42) B 43) A 44) D 45) B 9

Answer Key Testname: C6

46) C 47) D 48) D 49) A 50) D 51) C 52) A 53) B 54) A 55) B 56) C 57) C 58) D

10

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) Can the point-slope equation be used to write an equation of a vertical line? Why or why not?

1)

2) Describe a situation in which point-slope form would be more useful.

2)

3) Can an equation of a vertical line be written in slope-intercept form?

3)

4) Why is the slope of a vertical line undefined?

4)

5) Explain why the order in which coordinates are subtracted to find slope does not matter as long as x-coordinates are subtracted in the same order as y-coordinates.

5)

6) Why is the slope of a horizontal line zero?

6)

7) Explain in your own words why equations of the form y = b have graphs that are horizontal lines.

7)

8) The total number of reported cases of AIDS in the United States has risen from 372 in 1981 to 100,000 in 1989 and 200,000 in 1992. Does a linear equation fit this data? Why or why not?

8)

9) Without making a drawing, explain why the graph of the equation y = x - 5 passes through three quadrants.

9)

10) If one line has a slope of -3 and another line has a slope of -6, which line is steeper? Why?

10)

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

Write an equation of the line described.

11) Through (3, -6), perpendicular to -3x - 5y = 36 3 33 5 A) y = x B) y = x - 11 5 5 3

5 C) y = - x + 11 3

Graph.

1

5 D) y = - x - 12 3

11)

12) 14x = -28

12)

A)

B)

C)

D)

2

Find the intercepts and then graph the line.

13) 6x - 30y = 0

13)

A) (0, 0); (0, 0)

B) (0, 0); (0, 0)

C) (0, 0); (0, 0)

D) (0, 0); (0, 0)

Find the slope of the line containing the two given points.

14) (4, -9) and (-4, -18) 27 9 A) B) 0 8

8 C) 9

Find an equation of the line containing the given pair of points 15) (7, -53) and (1, -5) 1 431 1 417 A) y = x B) y = - x C) y = 8x - 109 8 8 8 8

3

9 D) 8

14)

15) D) y = -8x + 3

Graph using the slope and the y-intercept.

16) 5x + 3y = 15

16)

A)

B)

C)

D)

4

Graph the function.

17) f(x) = 7 - x2

17)

A)

B)

C)

D)

5

Find the intercepts and then graph the line.

18) 2.6y - 2.1x = 10.92

18)

A) (0, -4.2); (-5.2, 0)

B) (0, 4.2); (-5.2, 0)

C) (0, -5.2); (4.2, 0)

D) (0, 5.2); (4.2, 0)

Solve the problem.

19) Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 793. Find a linear function S(t), which fits this data, and which expresses score as a function of time.

A) S(t) = 3.8925t + 494.25 B) S(t) = -4.325t + 490.25 C) S(t) = 3.8925t - 494.25 D) S(t) = 4.325t + 490.25 Find an equation of the line containing the given pair of points 20) (0, 0) and (2, -5) 5 2 5 A) y = - x - 5 B) y = - x C) y = - x 2 5 2 6

5 D) y = x 2

19)

20)

Graph using the slope and the y-intercept.

3 21) y = x + 1 4

21)

A)

B)

C)

D)

7

Find the slope of the line.

22)

A) -2

22)

B)

1 2

1 2

C) 2

D) -

C) 3a 2 + 12a

D) 6a 2 + 12a

Find the function value.

23) Find f(2a) when f(x) = 3x2 + 6x.

A) 12a 2 + 6a B) 12a 2 + 12a

Solve the problem.

24) In 1995 the United States recovered 23% of its municipal solid wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Find a linear function P(t) that fits this data.

A) P(t) = -1.2t + 7 B) P(t) = 1.2t + 17 C) P(t) = 1.2t + 24 D) P(t) = 0.6t - 17

23)

24)

Find the function value.

25) Find f(-3) when f(x) = x4 + -3.

A) 24 B) -84

C) 78

Find the slope of the line containing the two given points.

26) (-8.5, -18.4) and (16.9, 9.7) 281 281 A) B) 254 254

C) -

8

254 281

D) 9

D)

254 281

25)

26)

Solve.

27) Cars sold

27)

Year Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 1993?

A) 700 cars B) 600 cars C) 750 cars D) 150 cars

Find a linear function whose graph has the given slope and y-intercept.

9 62 28) Slope - , y-intercept 0, 7 7 A) f(x) = C) f(x) =

9 62 x7 7

28)

B) f(x) = -

9 62 x+ 7 7

D) f(x) =

Write an equation of the line described.

29) Through (-9, -7), perpendicular to x = 8 A) y = -7 B) y = -9

9 62 x+ 7 7

9 62 x7 7

C) y = 7

Determine whether the graph is the graph of a function.

30)

D) y = -9x - 7

29)

30)

A) Not a function

B) Function

9

The graph of a function f is provided. Determine the requested function value.

31) f(4)

A) -5

B) 5

Find the domain.

32) f(x) = 5x - 6 A) {x x is a real number and x C) All real numbers

C) 3

}

31)

D) -3

B) {x x is a real number and x } D) {x x is a real number and x -8}

Is the following correspondence a function?

33) Name Test Score Bob L. 93 Susan H. 83 Jim H. 76 Bruce B. 96 A) Yes

32)

33)

B) No

34)

34)

A) No

B) Yes

10

Find the intercepts and then graph the line.

35) 8y = -24 + 3x

35)

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

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

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

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

Find the domain.

36) f(x) =

-2 4-x

36)

A) {x x is a real number and x -4} C) {x x is a real number and x }

B) {x x is a real number and x -2} D) {x x is a real number and x }

11

Find the function value.

37) f(-2)

A) 6

37)

B) 3

C) 7

Graph the function.

1 38) f(x) = x + 4 4

D) 5

38)

A)

B)

12

C)

D)

Find a linear function whose graph has the given slope and y-intercept.

39) Slope 2, y-intercept (0, -8) A) f(x) = 2x - 8 B) f(x) = -8x - 2 C) f(x) = 2x + 8

D) f(x) = 2x + 2

The graph of a function f is provided. Determine the requested function value.

40) f(-1)

A) 6

B) 4

Find the slope of the line containing the two given points.

41) (6, -2) and (4, 7) 1 9 A) B) 2 2

13

40)

C) -2

D) 0

2 C) 9

9 D) 2

Tell whether the lines are "parallel", "perpendicular", or "neither."

42) 9x + 3y = 12 12x + 4y = 18 A) Parallel B) Neither

39)

41)

42) C) Perpendicular

Find a linear function whose graph has the given slope and y-intercept.

1 43) Slope , y-intercept (0, 4) 2 A) f(x) = -

Solve.

1 x-4 2

B) f(x) = -

1 x+4 2

C) f(x) =

43) 1 x+4 2

D) f(x) =

1 x-4 2

44) Cars sold

44)

Year Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 1995?

A) 600 cars B) 250 cars C) 800 cars D) 850 cars

14

Graph using the slope and the y-intercept.

45) 9 · f(x) = 6x - 27

45)

A)

B)

C)

D)

15

The graph of a function f is provided. Determine the requested function value.

46) f(-1)

A) -2

B) 2

C) -1

Find an equation of the line containing the given pair of points 47) (-5, 0) and (2, -6) 5 30 5 30 6 30 A) y = x B) y = - x C) y = - x 7 7 7 7 7 7 Graph using the slope and the y-intercept.

1 48) f(x) = - x + 4 2

46)

D) 0

6 30 D) y = x 7 7

47)

48)

A)

B)

16

C)

D)

Find a linear function whose graph has the given slope and y-intercept.

2 11 49) Slope - , y-intercept 5 5

49)

A) f(x) =

2 11 x+ 5 5

B) f(x) = -

2 11 x+ 5 5

C) f(x) =

2 11 x5 5

D) f(x) = -

2 11 x5 5

Determine the slope and the y-intercept.

50) 12y + 4x + 2 = 9 + 4x

7 ) A) Slope 0, y-intercept (0, 12

C) Slope 0, y-intercept (0,

1 7 ) B) Slope , y-intercept (0, 3 12

7 ) 12

D) Slope -

50)

1 7 , y-intercept (0, ) 3 3

Find the domain.

51) f(x) = x3 - 3 A) {x x is a real number and x

51) 3

B) {x x is a real number and x 3}

-3}

C) {x x is a real number and x -3}

D) All real numbers

Find the function value.

52) Find f(2) when f(x) = -x + 5.

A) 2 B) 6

C) -3

17

D) 3

52)

Find the slope of the line.

53)

A) -3

53)

B) 3

C)

1 3

D) -

1 3

Is the following correspondence a function?

54)

54)

A) Yes

B) No

Find an equation of the line containing the given pair of points 17 9 and 9, 55) 1, 72 8 A) y = 9x -

631 72

B) y = 9x -

9 8

55) C) y =

1 1 x+ 9 8

Determine whether the graph is the graph of a function.

56)

D) y =

1 631 x+ 9 648

56)

A) Not a function

B) Function

18

Solve the problem.

57) It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t) = .28t + 1, for t > 10. Find the approximate number of fish that can be caught if you fish for 32 minutes.

A) About 36 fish B) About 9 fish C) About 21 fish D) About 34 fish Graph the function.

58) f(x) = 6 - x

57)

58)

A)

B)

C)

D)

19

Graph.

59) y + 4 = 0

59)

A)

B)

C)

D)

20

The graph of a function f is provided. Determine the requested function value.

60) f(1)

A) -3

B) -1

C) 1

21

60)

D) -27

Answer Key Testname: C7

1) No; the slope of a vertical line is undefined.

2) Point-slope form would be more useful if you wanted to find an equation of a line with a specified slope passing through a specified point that is not the y-intercept.

3) No, the slope of a vertical line is undefined. y1 - y2 y1 - y2 = .

4) For any two points on the line (a, y1 ) and (a, y2 ), y1 y2 , m = a-a 0 5) m =

y2 - y1 -1 · (y2 - y1 ) y1 - y2 = = . x2 - x1 -1 · (x2 - x1 ) x1 - x2

6) For any two points on the line (x1 , b) and (x2 , b), x1 x2 , m =

b-b 0 = = 0. x1 - x 2 x 1 - x 2

7) The second coordinate of any point on the graph is b, regardless of the first coordinate, so the graph is a line parallel to the x-axis and b units above or below it. Thus, the graph is a horizontal line.

8) No; the rate of increase is not constant. The slope of the segment from (0, 372) to (8, 100,000) is 12,453.5 while the slope of the segment from (8, 100,000) to (11, 200,000) is 33,333.3.

9) When x < 0, then y < 0 and the graph contains points in quadrant III. When 0 < x < 5, then y < 0 and the graph contains points in quadrant IV. When x > 5, then y > 0 and then graph contains points in quadrant I. 10) The line with a slope of -6 is steeper, because the larger the absolute value of the slope, the steeper the line.

11) B 12) D 13) D 14) B 15) D 16) D 17) B 18) B 19) D 20) C 21) C 22) C 23) B 24) B 25) C 26) B 27) C 28) B 29) A 30) B 31) A 32) C 33) A 34) A 35) C 36) D 37) D 38) B 39) A 40) B 41) D

22

Answer Key Testname: C7

42) A 43) C 44) D 45) A 46) A 47) C 48) B 49) B 50) C 51) D 52) D 53) C 54) A 55) C 56) A 57) B 58) B 59) B 60) A

23

Exam Name___________________________________

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

Solve.

1) In triangle ABC, the measure of angle B is 5° more than three times the measure of angle A. The measure of angle C is 15° more than the measure of angle A. Which one of the following is true?

A) Angle C is 47° B) Angle A is 35° C) Angle B is 102° D) None of these

1)

2) Some people must eat a low-sodium diet with no more than 2000 mg of sodium per day. By eating 1 cracker, 1 pretzel, and 1 cookie, a person would ingest 149 mg of sodium. If a person ate 8 pretzels and 8 cookies, he or she would ingest 936 mg of sodium. By eating 6 crackers and 7 pretzels, the person would take in 535 mg of sodium. Find the amount of sodium in each. Which of the following is true?

A) A cracker has 30 mg of sodium.

B) A pretzel has 49 mg of sodium.

C) A cookie has 71 mg of sodium.

D) None of these

2)

Solve the problem.

3) A merchant has coffee worth $20 a pound that she wishes to mix with 90 pounds of coffee worth $ 90 a pound to get a mixture that can be sold for $80 a pound. How many pounds of the $20 coffee should be used?

A) 15 lb B) 52.5 lb C) 7.5 lb D) 105 lb Solve.

4) x - y + 5z = -23 5x + z = -5 x + 2y + z = -9 A) (0, -2, -5)

3)

4)

B) (-5, 0, -2)

C) No solution

D) (-5, -2, 0)

Classify the system as consistent or inconsistent, and dependent or independent.

5) x + y = -11 x - y = -5 A) Inconsistent and dependent B) Inconsistent and independent C) Consistent and dependent D) Consistent and independent

1

5)

Solve graphically.

6) 2x + y = 6 4x + 2y = 12

6)

A) Infinite number of solutions C) No solution

B) (0, 6) D) (5, -4)

Classify the system as consistent or inconsistent, and dependent or independent.

7) x - 8 = y y+ 2=x A) Consistent and dependent B) Consistent and independent C) Inconsistent and dependent D) Inconsistent and independent Solve the problem using the elimination method.

8) Two angles are supplementary, and one is 40° more than three times the other. Find the smaller angle.

A) 35° B) 105° C) 145° D) 75° Solve the problem.

9) In a chemistry class, 6 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) 6.0 L B) 2.0 L C) 3.0 L D) 4.0 L Solve the problem using the elimination method.

10) There were 38,000 people at a ball game in Los Angeles. The day's receipts were $229,000. How many people paid $11 for reserved seats and how many paid $4 for general admission?

A) 27,000 paid $11 and 11,000 paid $4 B) 18,750 paid $11 and 19,250 paid $4 C) 11,000 paid $11 and 27,000 paid $4 D) 19,250 paid $11 and 18,750 paid $4

7)

8)

9)

10)

11) In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

A) two-point shots: 11; three-point shots: 6 B) two-point shots: 10; three-point shots: 7 C) two-point shots: 12; three-point shots: 5 D) two-point shots: 6; three-point shots: 11

11)

12) In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

A) 28° and 62° B) 12° and 78° C) 21° and 69° D) 37° and 53°

12)

2

Solve the problem.

13) The perimeter of a rectangle is 78 m. If the width were doubled and the length were increased by 12 m, the perimeter would be 132 m. What are the length and width of the rectangle?

A) width 14 m, length 19 m B) width 24 m, length 15 m C) width 15 m, length 24 m D) width 19 m, length 19 m Solve the problem using the elimination method.

14) A salesman sold $200 more than the rest of the sales staff. If the sales total for the day was $2050, how much did the rest of the sales staff sell?

A) $925 B) $1025 C) $1850 D) $1125 Solve by the substitution method.

15) x + y = 7 5x + 5y = 35 A) (0, 0) C) (7, 5) Solve.

13)

14)

15) B) (8, -1) D) Infinite number of solutions

16) Mike, Joe, and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours or if Mike and Joe work together for 2 hours and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works alone for 2 hours, and Bill works alone for 1 hour. How much time does it take for each man working alone to complete the painting?

A) Mike 12 hr, Joe 10 hr, Bill 10 hr B) Mike 8 hr, Joe 16 hr, Bill 8 hr C) Mike 16 hr, Joe 8 hr, Bill 8 hr D) Mike 8 hr, Joe 8 hr, Bill 16 hr

Classify the system as consistent or inconsistent, and dependent or independent.

17) x + 6y = 17 2x + 12y = 34 A) Inconsistent and independent B) Inconsistent and dependent C) Consistent and independent D) Consistent and dependent Solve the problem using the elimination method.

18) Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.

A) 110° B) 70° C) 25° D) 155° Solve the system of equations by the elimination method.

19) 5x - 6y = -5 15x - 18y = 15 A) (-25, 30) C) (25, -30)

16)

17)

18)

19) B) infinitely many solutions D) no solution

3

Solve graphically.

20) 3x - 2y = 4 -6x + 4y = 7

20)

A) Infinite number of solutions C) (1, 2)

B) (2, 1) D) No solution

Solve the problem.

21) Ellen wishes to mix candy worth $1.79 per pound with candy worth $3.75 per pound to form 22 pounds of a mixture worth $2.95 per pound. How many pounds of the more expensive candy should she use?

A) 9 pounds B) 18 pounds C) 11 pounds D) 13 pounds Solve.

22) The sum of three numbers is 5. The first, minus the second, plus 2 times the third, is 0. The third, plus 4 times the first, plus the second, is -10. What are the numbers?

A) -5, 5, 5 B) 5, -5, -5 C) No solution D) -5, -5, 5

Solve graphically.

23) 3x + 2y = 5 -6x - 4y = 5

A) (-1.5, -1)

21)

22)

23)

B) (1, 1)

C) No solution

D) (1.5, -1)

Solve the problem.

24) Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $5.00, how many of the coins are nickels?

A) 18 nickels B) 12 nickels C) 10 nickels D) 23 nickels

4

24)

Classify the system as consistent or inconsistent, and dependent or independent.

25) x + 5y = 19 5x - 6y = 2 A) Consistent and independent B) Consistent and dependent C) Inconsistent and dependent D) Inconsistent and independent Solve.

26) x + y + z = 6 x - z = -2 y + 3z = 11 A) (1, 2, 3) =0 27) 2x + y x - 3y + z = 0 3x + y - z = 0 A) (0, 1, 0)

26)

B) (-1, 2, -3)

C) (0, 1, 2)

D) no solution 27)

B) (1, 0, 0)

C) (0, 0, 0)

D) no solution

Solve graphically.

28) x = -2 y=1

28)

A) (1, -2) C) (-2, 1)

B) No solution D) Infinitely many solutions

Classify the system as consistent or inconsistent, and dependent or independent.

29) 3x = y + 3 6x - 2y = 3 A) Consistent and dependent B) Consistent and independent C) Inconsistent and dependent D) Inconsistent and independent Solve.

30) x - y + 2z = -3 4x + z = 0 x + 5y + z = 15 A) (0, 0, 3)

25)

29)

30)

B) No solution

C) (0, 3, 0)

5

D) (0, 3, -3)

Classify the system as consistent or inconsistent, and dependent or independent.

31) 4x + 4y = 1 8x + 8y = 2 A) Consistent and independent B) Inconsistent and independent C) Inconsistent and dependent D) Consistent and dependent Solve the problem.

32) The sum of two numbers is 34 and their difference is 12. Find the numbers.

A) 23 and 11 B) 25 and 37 C) 11 and 23 Solve by the substitution method.

33) x + 6y = -1 7x + 7y = -7 A) (1, -1) 34) x + 3y = 18 7x + 4y = 24 A) (1, 5)

B) No solution

C) (0, -1)

B) No solution

C) (0, 6)

D) (-6, 0)

35) C) (-5, 2)

D) (2, -5)

36) C) (6, 5)

D) No solution

37) B) No solution

C) (7, 8)

Solve using the elimination method.

38) x + y = 11 x-y=7 A) (-9, 3) B) No solution

39) x - y + z = 8 x+y+z=6 x + y - z = -12 A) (-2, -1, 9)

D) (-1, 0) 34)

Solve using the elimination method.

36) 4 x - y = 19 5x + y = 35 A) (5, 6) B) (6, 6)

Solve.

32)

33)

Solve the system of equations by the elimination method.

35) -0.8x + 0.4y = 4.8 0.1x - 0.1y = -0.7 A) (-0.5, 0.2) B) (-50, 20)

Solve by the substitution method.

37) x - 5y = -27 -6x - 6y = -90 A) (-8, 8)

D) 9 and 25

31)

D) (8, 7)

38) C) (9, 2)

D) (8, 3)

39)

B) (-2, -1, -9)

C) (2, -1, -9)

6

D) (2, -1, 9)

40) A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 100 black, 110 white and 85 red wires. How many of each cable were made?

A) 15 cable A B) 15 cable A C) 15 cable A D) 15 cable A 15 cable B 25 cable B 98 cable B 25 cable B 25 cable C 88 cable C 15 cable C 15 cable C

40)

41) An airplane travels 800 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

A) 300 mph B) 200 mph C) 400 mph D) 100 mph

41)

42) Jane wants to buy a photocopier. The salesperson has the following information on 3 models. If all 3 are used, a specific job can be done in 50 minutes. If copier A operates for 20 minutes and copier B for 50 minutes, one-half the job is finished. If copier B operates for 30 minutes and copier C for 80 minutes, three-fifths of the job is done. Which is the fastest copier, and how long does it take for this copier to finish the whole job?

A) A is fastest; 120 minutes B) C is fastest; 100 minutes C) B is fastest; 100 minutes D) C is fastest; 120 minutes

42)

Solve the problem using the elimination method.

43) A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $5.00. Another customer buys 4 hot dogs and 3 bags of potato chips for $9.00. Find the cost of each item.

A) $1.75 for a hot dog; $1.25 for a bag of potato chips B) $1.50 for a hot dog; $1.25 for a bag of potato chips C) $1.50 for a hot dog; $1.00 for a bag of potato chips D) $1.00 for a hot dog; $1.50 for a bag of potato chips Solve.

43)

44) Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 7 miles per hour, and Delvis is traveling at the speed of 4 miles per hour. In 2 hours what is the distance between them?

A) 7 miles B) 15 miles C) 6 miles D) 3 miles

44)

45) The sum of a student's three scores is 225. If the first is 20 points more than the second, and the sum of the first two is 24 more than twice the third, what was the first score?

A) 47 B) 67 C) 89 D) 69

45)

46) x - y + z = -8 x + y + z = -10 x+y-z= 0 A) No solution

46)

B) (-4, -1, -5)

C) (-5, -4, -1)

D) (-4, -5, -1)

Solve the problem.

47) A sum of money amounting to $3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

A) 7 quarters B) 9 quarters C) 11 quarters D) 16 quarters

7

47)

48) A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A) 37 one-dollars B) 44 one-dollars C) 42 one-dollars D) 47 one-dollars

48)

49) Mardi received an inheritance of $60,000. She invested part at 8% and deposited the remainder in tax-free bonds at 11%. Her total annual income from the investments was $5700. Find the amount invested at 8%.

A) $30,000 B) $54,300 C) $29,000 D) $15,000

49)

Solve using the elimination method.

50) x + 6y = 26 2x + 6y = 22 A) (-3, -4) B) No solution Solve.

50) C) (4, 4)

D) (-4, 5)

51) Michael's bank contains only nickels, dimes, and quarters. There are 56 coins in all, valued at $4.90.

The number of nickels is 4 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

A) 41 B) 11 C) 6 D) 9

Solve the system of equations by the elimination method.

3 1 52) x - y = -18 2 3

52)

3 2 x + y = -9 4 9

A) (0, 12)

51)

B) (12, 0)

C) (-12, 0)

8

D) (0, -12)

Answer Key Testname: C8

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

Answer Key Testname: C8

51) C 52) C

10

Exam Name___________________________________

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

Choose the ordered pair which is a solution of the inequality.

1) x + y > 0 A) (0, 0) B) (1, -1) C) (-1, 1) 2) 2x + 4y 8 A) (0, 0) 3) 2x + 3y 0 A) (1, -1)

B) (3, 2)

C) (1, 1)

D) (1, 0)

D) (1, 0)

1)

2)

3)

1 1 B) , 2 3

C) (1, 1)

1

D) (-1, 1)

Match the inequality with a graph.

4) 8x + 3y > -2

4)

A)

B)

C)

D)

Choose the number that is a solution of the inequality.

5) f - 12 < -4 A) 10 B) 8

C) 11

2

D) 7

5)

Match the inequality with a graph.

6) 8y -5x

6)

A)

B)

C)

D)

Choose the ordered pair which is a solution of the inequality.

7) 2x - 4y 6 A) (3, -1) B) (2, -2) C) (1, -1)

3

D) (0, -2)

7)

Match the inequality with a graph.

8) 2x - 5y > -5

8)

A)

B)

C)

D)

Choose the ordered pair which is a solution of the inequality.

9) 2x + 3y 5 A) (0, 2) B) (1, 2) C) (3, 2)

4

D) (1, 1)

9)

Match the inequality with a graph.

10) -x > y

10)

A)

B)

C)

D)

Choose the ordered pair which is a solution of the inequality.

11) 2x - 4y < 6 A) (0, -2) B) (2, -2) C) (3, -1) Match the inequality with a graph.

5

D) (-1, 1)

11)

12) 7 - 5x > y

12)

A)

B)

C)

D)

Choose the ordered pair which is a solution of the inequality.

13) 2x + 4y > 8 A) (2, 2) B) (0, 0) C) (0, 1)

D) (2, 1)

Choose the number that is a solution of the inequality.

14) a - 5 < -8 A) -1 B) -4

D) 1

C) 4

6

13)

14)

15) 5t + 9 4t - 2 A) -14

B) -13

C) -11

D) -12

Choose the ordered pair which is a solution of the inequality.

16) x + y 0 A) (-1, 0) B) (-2, 1) C) (0, -1)

D) (1, -1)

Choose the number that is a solution of the inequality.

17) -3n - 3 -4n + 2 A) 6 B) 7

D) 8

C) 5

Match the inequality with a graph.

18) -4y x

15)

16)

17)

18)

A)

B)

C)

D)

7

19) 6x - 7y -5

19)

A)

B)

C)

D)

20) -9x < 1 - 4y

20)

8

A)

B)

C)

D)

Choose the ordered pair which is a solution of the inequality.

21) 2x + 3y < 5 1 1 A) (3, 2) B) , C) (2, 2) 2 2 22) 2x + 4y 8 A) (2, 1)

B) (0, 0)

C) (0, 1)

Choose the number that is a solution of the inequality.

23) 8n + 4 > 7n + 7 A) 0 B) 2 Solve.

24)

7x - 1 1 7x - 1 < - or 15 3 15

A)

,-

4 7

6 , 7

C) 4

21) D) (1, 1)

22)

D) (1, 1)

23)

D) 1

1 3

24) B) -

4 6 , 7 7

25) -3c + 2 -19 or -3c + 2 > -4 A) (2, 7] B) ( , -7]

(-2, )

9

2 16 , 3 21

C) (- , )

D) -

C) (- , )

D) ( , 2)

[7, )

25)

Write interval notation.

26) {x x < 2} A) (2, )

B) (- , 2)

C) (- , 2]

D) [2, )

Solve and graph.

27) x < 1 or x < 5

26)

27)

A) (1, 5)

B) (- , 5)

C) (- , 1)

(5, )

D) (1, )

Solve.

28) x + 2 = 6 A) {4} 29) 2 2t - 2 or 12 2t - 2 A) (- , )

Simplify.

30) 5.3z A) -5.3 z 31)

B)

C) {4, -8}

B) [-7, -2]

C) ( , 2]

B) -5.3z

C) 5.3z

D) {-4, 8}

[7, )

D) [2, 7]

D) 5.3 z

-10 x

A)

28)

29)

30)

31) 10 x

B)

-10 x

C)

-10 x

Graph the system of inequalities, and find the coordinates of the vertices.

10

D)

10 x

32) y 3x - 1, y -3x - 1, x 3

Solve.

32)

A)

B)

C)

D)

33) |a - 2| = |a - 6| A)

B) 4

C) {8}

11

D) -

1 4

33)

Solve and graph. Write the result in interval notation.

34) f - 12 -4

34)

A) (- , 8]

B) [8, )

C) (- , 8)

D) (8, )

Solve.

35) Body mass index is given by the formula I =

704.5W . Mary's height is 62 in. What weights W will H2

35)

allow Mary to keep her body mass index I between 18.5 and 25?

A) {W|119.2 lb < W < 142.2 lb} B) {W|1.6 lb < W < 2.2 lb} C) {W|92.3 lb < W < 123 lb} D) {W|100.9 lb < W < 136.4 lb}

36) 1.1x + 2.9 > 0.3x + 1.22 A) (- , -2.1) 37) -5(k - 5) < -7 + (-6k + 9) A) ( , 9) Simplify.

38)

B) (- , -2.2)

C) (-2.1, )

B) ( , - 7)

C) ( , - 23)

D) (-2.2, )

D) ( , 23)

x4 -y

A)

36)

37)

38) x4 -y

B)

x4 y

C)

12

x4 y

D)

x4 -y

Solve and graph. Write the result in interval notation.

39) 0.25a > 2

39)

A) (- , 8)

B) [8, )

C) (- , 8]

D) (8, )

Solve the compound inequality. Express the solution using interval notation. Graph the solution set.

40) x 3 or x 6

40)

A) (3, 6)

B) (-3, 6)

C) [-6, -3]

D) (- , 3]

Solve.

[6, )

41) The equation y = 0.005x + 0.30 can be used to determine the profit y, in dollars, of producing x items. How many items x must be produced so the profit will be at least $1273?

A) {x 0 < x 254,539} B) {x x 253,540} C) {x x 254,540} D) {x x 254,660}

Simplify.

42) -3x A) 3 x

B) 3x

C) 3 x

13

D) -3x

41)

42)

Solve the compound inequality. Express the solution using interval notation. Graph the solution set.

43) x < 2 or x < 8

43)

A) (2, 8)

B) (- , 8)

C) (2, )

D) (- , 2)

(8, )

Write interval notation for the graph.

44)

Solve.

A) [1, )

B) (- , 1]

C) (1, - )

45) 7x + 6 = 9 1 5 ,A) 2 2

3 15 B) - , 7 7

C)

46) 3 x + 8 - 9 = 3 A) - 4, - 12

B) - 4, 10

C) - 4

3 15 ,7 7

D) (- , 1)

45) D)

D) - 12

Find the distance between the points on a number line.

1 2 47) - , 2 3 A) 6

Solve.

48)

B)

11 19

46)

47)

1 6

C)

6 7

D)

7 6

2 - 3x 5x - 6 = 7 8

A)

44)

48) B)

58 26 , 59 11

C)

14

11 , 13 19

D)

58 59

49) -

4 10 x 5 11

A) - ,

8 11

49) B)

8 , 11

C)

Find the indicated intersection or union.

50) {q, s, u, v, w, x} A) {q} B) {q, s, u, v, w, x} Solve.

51) 3(3x + 1) < 5 - 5(3x - 3) 17 A) , 24

B)

5 , 24

25 , 22

D) - ,

25 22

C) {q, s, u, v, w}

D)

17 , C) 24

5 , D) 24

Solve and graph. Write the result in interval notation.

52) f - 4 < 8

50)

51)

52)

A) (12, )

B) (- , 12)

C) (- , 12]

D) [12, )

Solve.

53) Assume that the mathematical model C(x) = 18x + 170 represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between between $665,000 and $989,000?

A) {x 570 < x < 760} B) {x 360 < x < 540} C) {x 540 < x < 720} D) {x 380 < x < 570}

53)

54) -20 -3z + 4 -2 A) (-8, -2)

54)

55)

B) [-8, -2]

C) (2, 8)

D) [2, 8]

1 1 (x + 2) > (5x + 4) 2 6

A) - , - 1

55) B) - , 1

C) 1,

15

D) - 1,

Solve and graph. Write the result in interval notation.

56) x - 10 < -6

56)

A) [4, )

B) (- , 4]

C) (- , 4)

D) (4, )

Solve the absolute value inequality. Write the solution set using interval notation.

57) x 19 A) (- , -19] B) (- , -19] [19, ) C) [-19, 19] D) (- , 19]

16

57)

Graph the system of inequalities, and find the coordinates of the vertices.

58) 3x - 2y 6 x-1 0

A)

B)

C)

D)

17

58)

Solve and graph. Write the result in interval notation.

5 59) x < -9 7

A) - ,

C)

Solve.

60)

7 45

B)

,-

5 63

D) -

45 , 7

,-

5x - 32 5x - 32 < -9 or 4 4

A)

59)

,-

4 5

60)

-3

44 , 5

C) (- , )

Find the distance between the points on a number line.

61) 18.4, -17.0 A) 35.4 B) 1.4 Solve.

63 5

B) -

4 ,4 5

D)

,-

4 5

4,

C) 0.7

D) 17.7

62) 3x + 9 < 24 A) [5, )

B) ( , 5]

C) (5, )

D) ( , 5)

63) -6 < x + 9 < 5 A) (-15, 14)

B) (-15, -4)

C) (-14, -3)

D) (3, 14)

C) 6

D) -6

C) [-2, 2)

D) (-2, 2]

Find the distance between the points on a number line.

64) 1, -5 A) 4 B) -4

61)

62)

63)

64)

Write interval notation for the graph.

65)

A) [-2, 2]

B) (-2, 2)

18

65)

Solve.

66) Company A rents copiers for a monthly charge of $160 plus 8 cents per copy. Company B rents copiers for a monthly charge of $320 plus 4 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

A) 4000 copies B) 2000 copies C) 4100 copies D) 8000 copies 67)

3x + 5 =4 3

A)

66)

67) B) -

7 3

C)

17 3

Graph the system of inequalities, and find the coordinates of the vertices.

68) 3y - x 1, y - x 4, 2 x 5

A)

B)

19

D)

7 17 ,3 3

68)

C)

Write interval notation.

69) {x < x < } A) [3, 7]

D)

B) [3, 7)

C) (3, 7]

20

D) (3, 7)

69)

Graph the inequality on a plane.

70) x + y < -4

70)

A)

B)

C)

D)

21

Graph the system of inequalities, and find the coordinates of the vertices.

71) 2x + y 4 y-1 0

Solve.

A)

B)

C)

D)

72) |2x - 5| = -4 A)

73)

1 9 , B) 2 2

2 6 C) - , 5 5

71)

9 1 D) - , 2 2

5 (5x - 3) > 35 3

A)

24 , 5

72)

73) B)

,

24 5

C)

22

18 , 5

D)

,

18 5

Answer Key Testname: C9

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

Answer Key Testname: C9

51) A 52) B 53) B 54) D 55) B 56) C 57) C 58) D 59) B 60) D 61) A 62) D 63) B 64) C 65) D 66) A 67) D 68) B 69) D 70) D 71) A 72) A 73) A

24

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) Explain in your own words why

a 2 a when a is negative.

1)

2) Explain in your own words why possible solutions of radical equations must be checked.

2)

3) Explain why no assumptions need to be made regarding the numbers represented by x and

3)

y when you are simplifying the expression

3

x4 y9 .

4) Use what you know about factoring a difference of cubes to devise a method for 3 3 rationalizing a denominator of the form a - b.

5) Explain why it is easier to approximate

2 1 compared to using 2 2

4)

2 = 1.414213562

5)

when a calculator is not available.

6) In an equilateral triangle, all sides have the same length. Can a right triangle be equilateral? Why or why not?

6)

7) Explain a method that could be used to solve

7)

8) Explain the error in the following.

x2 - 25 =

x-1+

x-

2x + 3 -

x2 -

25 = x - 5

4 + x = 0.

8)

9) Why is it important to know how to multiply radical expressions before learning to divide them?

9)

10) What is the difference between real numbers and complex numbers?

10)

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

Solve the problem. If necessary, round to the nearest tenth.

11) A car dealer advertised a big sale by stretching a string of banners from the top of the building to the edge of the driveway. If the building is 17 m high and the driveway is 49 m from the building, how long is the string of banners?

A) 46.0 m B) 8.1 m C) 51.9 m D) 24.0 m Find the following. Assume that the letter can represent any real number.

12) x2 A) x2

B) - x

C) x

Graph.

1

11)

12) D) x

13) f(x) =

x+3

13)

A)

B)

C)

D)

Rewrite without rational exponents, and simplify, if possible.

14) 165/4 A) 1024

B) 35

14) C) 32

Add or subtract. Then simplify by collecting like radical terms, if possible.

15) -5 11 - 14 11 A) -8 11 B) 9 11 C) 18 11

2

D)

5

8

15) D) -19 11

Multiply. Assume that no radicands were formed by raising negative numbers to even powers.

16) ( 7 + 10)( 7 - 10) A) -3 B) 7 - 2 70 C) 7 + 2 70 D) 17

16)

Use the laws of exponents to simplify. Write the answer with positive exponents.

2 17) (r1/3 · s1/3 ) A) r1/6 s1/6 B) r2 s2 C) r1/9 s1/9

17)

D) r2/3 s2/3

Identify the radicand.

18) 8ab b2 - 6 A) Simplify.

19) -

b2 - 6

18) C) b2

B) 8ab

256 A) 16 C) does not exist as a real number

D) b2 - 6

19)

B) -128 D) -16

Solve.

20)

6q - 5 = 5

A) 25

Rewrite with rational exponents.

21) ( 7mn)5 A) (7mn)5/2

Express in terms of i.

22) 3 - -18 A) -3 + 3i

25 B) 6

20)

10 C) 3

D) 5

C) (7mn)2/5

5(7mn) D) 2

21)

7mn 5 B) 2

22) B) 3 + 3 2

C) 3 + 3i 2

D) 3 - 3i 2

A) 1 - i

B) -1 + i

C) -1 - i

D) 1 + i

2x + 5 - x - 2 = 3 A) 2, 38

B) -2

C) 3, 8

D) 2

Simplify to the form a + bi.

23) i632 + i467

23)

Solve.

24)

Add or subtract. Then simplify by collecting like radical terms, if possible.

25) 26 11 - 11 11 A) 37 11 B) 165 C) 15

3

24)

25) D) 15 11

Rationalize the denominator. Assume that no radicands were formed by raising negative numbers to even powers.

1- 6 26) 26) 1+ 6 A)

7-2 6 -5

B) 1

C)

Use rational exponents to write a single radical expression.

4 4 27) 14p 20q 4 4 A) 34pq B) 280pq

3/2 29) (9y4 ) A) 2711

D)

-5 - 2 6 7

27) C)

Rewrite without rational exponents, and simplify, if possible.

28) 1251/3 A) 50

7+2 6 -5

4

34(p + q)

D)

4

280(p + q)

B) 5

C) 25

D) 15

B) 27y6

C) 9y12

D) 27y3/2

Multiply. Assume that no radicands were formed by raising negative numbers to even powers.

3 3 30) 36( 6 - 4) 3 3 3 3 3 A) 6 6 - 24 B) 6 - 4 36 C) 6 6 - 4 D) 216 - 4 36

28)

29)

30)

Add or subtract. Then simplify by collecting like radical terms, if possible. Assume that no radicands were formed by raising negative numbers to even powers.

31) 2 - 7 72 - 7 98 31) A) -14 2 B) -14 172 C) -90 172 D) -90 2

Solve the problem.

32) A manufacturer's cost is given by C = 400

3

n + 200, where C is the cost and n is the number of

parts produced. How many parts are produced when the cost is $6200?

A) 27,000 B) 3375 C) 225

Use the laws of exponents to simplify. Write the answer with positive exponents.

2 33) (9a 1/7 · b5/7) 10/7 10/7 A) 9a 2/7b B) 81(ab) C) 18a 2/7b5/7 Express in terms of i.

34) -162 A) 9i 2

32)

D) 6000

10/7 D) 81a 2/7b

33)

34) B) -9 2

C) 9 2

4

D) -9i 2

Simplify.

35)

37 x4

35) 37 x2

A)

B)

37x4 x4

C)

For the given function, find the indicated function value.

3 36) For f(x) = 2x - 1, find f(-62).

A) 5 C) 4

37 x

D)

37 x4

B) -5 D) Does not exist as a real number

Divide and simplify to the form a + bi.

9 - 5i 37) 5 - 2i A)

55 7 i 29 29

B)

36)

37) 35 43 i + 29 29

C)

55 1 + i 21 3

D)

5 1 + i 3 3

Simplify.

38)

10 r4

38) 10 r2

A)

B)

Express in terms of i.

39) -275 A) 5i 11

10 r

C)

10r4 r4

D)

10 r4

39) B) -5i 11

C) 5 11

D) -5 11

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.

40) a = 3, b = 4 A) c = 5 B) c = 12 C) c = 3.742 D) c = 7 Simplify.

41)

5 w18 x20

A)

40)

41)

w5

5

x4

w

B)

w3

5

x3

w4

C)

w3

5

x4

w3

D)

w3 w x4

Multiply. Assume that no radicands were formed by raising negative numbers to even powers.

42) 4 5( 11 + 5) A) 4 55 + 5 B) 4 55 + 20 C) 20 11 + 20 D) 4 11 + 5

42)

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.

43) a = 15, c = 25 A) b = 24 B) b = 20 C) b = 25 D) b = 18

43)

5

Simplify.

44)

3 y19 125

3 A) 5y6 y

44) 3 y6 y B) 5

3 y6 + y C) 5

3 D) y6 - 5 y

Divide and simplify. Assume that all expressions under radicals represent positive numbers.

112 42 45) 14 6 B) 8 6

C) 14 7

Find the domain of f.

46) f(x) = 11 - 4x 11 A) x x 4

11 B) x x < 4

11 C) x x 4

D) x x

Add or subtract and simplify.

47) (5 - 4i) + (8 + 2i) A) 13 + 2i

B) 13 - 2i

C) -13 + 2i

D) -3 + 6i

A) 56

45)

D) 8 7

11 4

Solve the problem. If necessary, round to the nearest tenth.

48) Find all ordered pairs on the y-axis of a Cartesian coordinate system that are 10 units from the point (6, 0) A) (64, 0) B) (0, -64), (0, 64) C) (0, 8) D) (0, -8), (0, 8)

46)

47)

48)

Add or subtract. Then simplify by collecting like radical terms, if possible. Assume that no radicands were formed by raising negative numbers to even powers.

49) -6 27 - 2 243 - 2 75 49) A) -146 3 B) -46 3 C) 146 3 D) -6 3

Solve the problem. If necessary, round to the nearest tenth.

50) On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 33 m long and the shadow is 23 m, how tall is the building?

A) 23.7 m B) 40.2 m C) 22.3 m D) 10.0 m

6

50)

Answer Key Testname: C10

1) a 2 denotes the principal, or positive, square root of a 2 . Thus, when a is negative, a 2 a.

2) The square of a number is equal to the square of its opposite. Thus, while squaring both sides of a radical equation allows us to find the solutions of the original equation, this procedure can also introduce numbers that are not solutions of the original equation.

3) Odd roots exist for all real numbers.

3 3 3 3 3 3 3 3 3 3 3 a b = ( a - b)( a 2 + ab + b2 ). To rationalize the denominator of the form a - b we 4) a - b = 3 3 3 a 2 + ab + b2 multiply by 1 using 3 3 3 a 2 + ab + b2 5) The calculation 1.414213562/2 is easier to perform than 1/1.414213562 when a calculator is not available.

6) No; consider an equilateral triangle with side s. If this were a right triangle, then it would hold that s2 + s2 = s2 , or

2s2 = s2 . This is true only for s = 0, so a right triangle cannot be equilateral.

7) Use the addition principle to get two radical terms on each side of the equation. Square both sides. The resulting equation will have one radical term on each side. Isolate the two radical terms on one side of the equation, and square both sides a second time. Now one radical term remains. Isolate it, and square both sides again. This eliminates the final radical term, and you can proceed with the solution. a 2 - b2 . In this case, let x = 13. Then x2 - 25 = 132 - 25 = 169 - 25 = 144 = 12, but x2 8) In general, a 2 - b2 - 25 = 132 - 25 = 13 - 5 = 8.

9) If division requires rationalizing the denominator, it is necessary to know how to multiply radical expressions.

10) A complex number is any that can be written a + bi, where a and b are real numbers. Real numbers are complex numbers a + bi, where b = 0. In the real number system, negative numbers do not have square roots. In the complex number system, they do.

11) C 12) C 13) A 14) C 15) D 16) A 17) D 18) D 19) D 20) D 21) A 22) D 23) A 24) A 25) D 26) A 27) B 28) B 29) B 30) B 31) D 32) B 33) D 34) A 35) A 7

Answer Key Testname: C10

36) B 37) A 38) A 39) A 40) A 41) C 42) B 43) B 44) B 45) D 46) A 47) B 48) D 49) B 50) A

8

Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) When using the quadratic formula, why is it necessary only to examine the discriminant to determine if the equation has real-number solutions?

1)

2) Explain without plotting points, why the graph of y = (x + 3)2 looks like the graph of y = x2 translated three units to the left.

2)

3) Suppose the graph of a quadratic equation has two x-intercepts. How could you use the intercepts to find the vertex of the graph?

3)

4) Explain in your own words a sequence of steps that can be used to solve any quadratic equation in the most efficient way.

4)

5) Given the solutions of a quadratic equation, is it possible to reconstruct the original equation? Why or why not?

5)

6) Write a quadratic equation that is most easily solved using the principle of square roots.

Explain why the principle of zero products would not work as easily on the equation you wrote.

6)

7) Explain how a quadratic inequality can be solved by examining a parabola that opens upward.

7)

8) Explain why y = ax2 + bx + c and y = -ax2 - bx - c have the same x-intercepts.

8)

9) Compare the graphs of y = a(x - h)2 + k and y = -a(x - h)2 + k. What restrictions, if any, must be placed on a, h, and k if both graphs are to have the same x-intercepts?

9)

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

Solve. Provide answers in interval notation.

1 10) 2 x A) - , 0

1 , 2

10)

B) 0, 2

C) - , 0

2,

D) 0,

1 2

Solve.

11) 5y-2 - 4y-1 - 1 = 0 1 A) , -1 5

11)

1 B) - , 1 5

C) - 5, 1

1

D) 5, - 1

Determine which of the following four functions might be used as a model for the data: linear: f(x) = mx + b; quadratic: f(x) = ax 2 + bx + c, a > 0; quadratic: f(x) = ax 2 + bx + c, a < 0; polynomial, not quadratic or linear.

12)

12)

Unidentified Flying Object

Altitude in thousands of feet

Linear distance in miles 2 A) f(x) = ax + bx + c, a < 0

B) Polynomial, not quadratic or linear D) f(x) = ax2 + bx + c, a > 0

C) f(x) = mx + b Solve. Give exact solutions.

13) y2 = 6

13) B) ± 6

A) 3

C)

D) 36

6

Find the vertex.

14) f(x) = 2x2 + 12x + 23 A) (5, -3)

B) (3, -5)

C) (-5, 3)

14)

D) (-3, 5)

Solve by completing the square.

15) y2 + 4y - 3 = 0 A) 2 +

7

15) B) -2 ± 2 7

C) -1 ±

Find the quadratic function that fits the set of data points.

16) (-3, -1), (2, -76), (5, -193) A) f(x) = -3x2 + 3x - 1

7

B) f(x) = 2x2 + 18x + 28 D) f(x) = -3x2 - 18x - 28

C) f(x) = 3x2 + 18x - 1

2

D) -2 ±

7

16)

Determine which of the following four functions might be used as a model for the data: linear: f(x) = mx + b; quadratic: f(x) = ax 2 + bx + c, a > 0; quadratic: f(x) = ax 2 + bx + c, a < 0; polynomial, not quadratic or linear.

17)

17)

Acme Computer Products

Marginal revenue in $/connector

Number of connectors produced

A) f(x) = ax2 + bx + c, a < 0

B) f(x) = mx + b D) f(x) = ax2 + bx + c, a > 0

C) Polynomial, not quadratic or linear Solve the problem. Give the answer to the nearest tenth.

18) The position of an object moving in a straight line is given by s = t2 - 8t, where s is in feet and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 16 feet?

A) 9.7 sec B) 17.0 sec C) 12.8 sec D) 9.5 sec

Solve.

19) 3 = A)

8 1 x x2 -4 ± 13 3

19) B)

-8 ± 13 3

C)

-4 ± 19 3

Determine the nature of the solutions of the equation.

20) s2 - 7s - 8 = 0 A) One real

Solve.

21) 9x2 = -20x - 3 -20 ± 73 A) 9

B) Two nonreal

D)

-4 ± 13 6

C) Two real

20)

21) -10 ± 127 B) 9

-10 ± 73 C) 18

-10 ± 73 D) 9

Without graphing, find the line of symmetry.

15 (x + 3)2 - 3 22) f(x) = 2 A) x = -3

18)

22)

B) x = -2

C) x = 3

3

D) x = -4

Solve.

23) 6 + x 2 - 12 6 + A) 15

Find the line of symmetry.

24) f(x) = 4x2 - 40x + 98 A) x = -2

Solve.

x + 21 = 0 B) 15

23) C) -

B) x = 2

15

C) x = 5

25) What is the minimum product of two numbers whose difference is 90?

A) -4050 B) -22.5 C) -45

D) No solution

D) x = -5

D) -2025

24)

25)

Determine which of the following four functions might be used as a model for the data: linear: f(x) = mx + b; quadratic: f(x) = ax 2 + bx + c, a > 0; quadratic: f(x) = ax 2 + bx + c, a < 0; polynomial, not quadratic or linear.

26)

26)

IA Robotics

Growth of revenue in millions

Year

A) Polynomial, not quadratic or linear C) f(x) = ax2 + bx + c, a < 0

B) f(x) = mx + b D) f(x) = ax2 + bx + c, a > 0

Determine the nature of the solutions of the equation.

27) 3y2 = -6y - 8 A) One real

B) Two real

C) Two nonreal

Solve. Provide answers in interval notation. x-7 0 28) x+8 A) [-8, 7]

28)

B) (-7, 8]

C) [-7, 8]

Without graphing, find the maximum value or minimum value.

29) f(x) = 7(x - 5)2 - 9 A) 9

27)

B) -9

C) 7

4

D) (-8, 7]

D) 5

29)

Solve. Provide answers in interval notation.

2x + 3 0 30) x-3 A) (- , -3) C) - , -

3 2

30)

3 , 2

B) -3,

[3, )

D) -

Find the x-intercepts.

31) f(x) = 64x2 - 32x + 4

3 ,3 2

31)

1 B) - , 0 4

A) No x-intercepts C)

3 2

1 ,0 4

D)

1 1 , 0 and - , 0 4 4

Determine the nature of the solutions of the equation.

32) 2x2 - 5 5 - 3 = 0 A) Two real

B) One real

C) Two nonreal

Solve the equation by completing the square.

33) x2 + x + 6 = 0 1 23 i A) - ± 2 2

32)

33)

1 23 B) ± 2 2

1 23 C) - ± 2 2

1 23 i D) ± 2 2

B) 4

C) No solution

D) 2, 7

Solve.

34) x - 9 x + 14 = 0 A) 4, 49 35) x4 - 33x2 + 32 = 0 A) ±1, ±4 2

35) B) ±1, ±4 3

C) ±2, ±4

D) ±1, ± 2

Solve the equation by completing the square.

36) p2 + 5p - 5 = 0 5 3 5 A) - ± 2 2

36)

5 3 5 B) - + 2 2

Solve. Round results to the nearest thousandth.

37) 5x2 = 10 + 14x A) -1.200, -1.600

Solve.

38) 4x2 - 3x = -4 3 55 i A) ± 8 8

34)

B) 3.390, -0.590

5 3 5 C) ± 2 2

D) -5 ± 3 5

C) 0.590, -3.390

D) 1.600, 1.200

37)

38) B) -

3 55 ± 8 8

C) -

5

3 55 i ± 8 8

D)

3 55 ± 8 8

Solve. Provide answers in interval notation.

39) x2 - 2x - 24 0 A) [6, )

B) (- , -4]

C) [-4, 6]

D) (- , -4]

[6, )

Find the x-intercepts.

40) 25x 2 + 4 = 0

40)

A) x-intercepts (0, - i

2 2 ), (0, i ) 5 5

C) No x-intercepts

41) f(x) = 2x2 - 13x - 45

B) x-intercepts (- i

2 2 , 0), (i , 0) 5 5

D) x-intercepts (-

2 2 , 0), ( , 0) 5 5

5 B) x-intercepts (9, 0) and ( , 0) 2

A) No x-intercepts C) x-intercepts (9, 0) and (-

5 , 0) 2

B) (- , -7) D) (- , -9)

42) (-7, -4)

Determine the nature of the solutions of the equation.

43) w2 - 5w + 8 = 0 A) Two nonreal

B) One real

C) Two real

Solve. Provide answers in interval notation.

-4x + 3 >0 44) 7x2 + 6 4 3

B) -

43)

44)

3 , 4

C) - ,

Find the x-intercepts of the function.

45) f(x) = (x2 - 5x)2 + 74 (x2 - 5x) - 480 A) (-1, 0), (6, 0) C) (-6, 0), (80, 0)

Solve.

41)

9 D) x-intercepts (-5, 0) and ( , 0) 2

Solve. Provide answers in interval notation.

42) (b + 9)(b + 7)(b + 4) < 0 A) (-4, ) C) (-9, -7) (-4, )

A) - , -

39)

3 4

D) (- , 0)

B) (1, 0), (-6, 0), (8, 0), (10, 0) D) (6, 0), (-80, 0)

45)

46) A projectile is thrown upward so that its distance above the ground after t seconds is h = -10t2 + 380t. After how many seconds does it reach its maximum height?

A) 38 sec B) 19 sec C) 9 sec D) 28.5 sec

46)

47) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c = 2x2 - 196x + 67, where c is the cost in dollars, and x is the number of watches repaired. How

47)

many watches must he repair to have the lowest cost?

A) 33 watches B) 67 watches C) 49 watches

6

D) 20 watches

Solve. Give exact solutions.

48) 4x2 = 44 A) ± 11

48) B) 12

C) 22

D) ±11

Solve. Provide answers in interval notation.

4x 8 49) -5x + 1 A) 0,

49)

1 5

C) - ,

B) - , 0 2 11

2 , 11

D)

1 , 5

2 1 , 11 5

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

50) f(x) = -8x2 + 48x - 67 A) maximum: 5

Solve.

51)

B) minimum: -5

C) minimum: 0

D) maximum: -5

x-2 2 x-2 -2=0 x+2 x+2

A) 1, -2

51) B) -1, 2

C) 0, - 6

Find the quadratic function that fits the set of data points.

52) (5, 5), (7, 9), (-1, 41) A) f(x) = x2 - 10x + 30

D) 0, - 3

52)

B) f(x) = - x2 - 10x + 5 D) f(x) = 7x2 - 10x - 30

C) f(x) = x2 - 5x + 5

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

53) f(x) = -x2 - 16x - 66 A) maximum: 2

Solve.

54)

B) minimum: 0

C) maximum: -2

D) minimum: 2

1 3 + = -1 x x2

A)

1 11 i ± 2 2

53)

54) B) -

1 11 ± 2 2

C) -

1 11 i ± 2 2

D)

1 11 ± 2 2

Solve. Give exact solutions.

55) (x + 4)2 - 2 = 0

55)

A) -2 + 2, -2 - 2 C) -4 + i 2, -4 - i 2

B) -4 + 2, -4 D) -2, 6

Solve. Round results to the nearest thousandth.

56) 9x2 - 2x - 8 = 0 A) 0.537, -0.759

50)

B) 0.838, -1.060

C) 0.759, -0.537

7

2

D) 1.060, -0.838

56)

Determine which of the following four functions might be used as a model for the data: linear: f(x) = mx + b; quadratic: f(x) = ax 2 + bx + c, a > 0; quadratic: f(x) = ax 2 + bx + c, a < 0; polynomial, not quadratic or linear.

57)

57)

IA Robotics

Growth of revenue in millions

Year

B) f(x) = ax2 + bx + c, a > 0

A) Polynomial, not quadratic or linear C) f(x) = ax2 + bx + c, a < 0

D) f(x) = mx + b

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.

1 58) S = gt2 for t 2 A) t =

g 2S

Find the line of symmetry.

59) f(x) = x2 - 18x + 81 A) x = -9

C) t =

B) x = 9

C) x = -2

Solve the equation by completing the square.

60) 5x2 - 4x - 9 = 0 A)

5 ,1 9

2S g

B) t = 2 gs

B)

9 , -1 5

C)

5 ,0 9

D) t = 2gS

D) x = 2

D)

5 , -1 9

Without graphing, find the line of symmetry.

9 61) f(x) = - (x + 5)2 - 7 4 A) x = 6 Solve.

58)

59)

60)

61)

B) x = 4

C) x = -7

D) x = -5

62) Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than the rate going, and if the distance each way was 7 miles, find her rate going.

A) 1.5 mph B) 5.9 mph C) 3.7 mph D) 5.5 mph

8

62)

Solve the problem.

63) Use a quadratic function to estimate the number of daytime accidents that occur at 70 km/h.

TRAVEL SPEED (in kilometers per hour) 60 80 100

NUMBER OF DAYTIME ACCIDENTS (for every 200 million kilometers driven) 80 130 210

A) 363.75 per 200,000,000 kilometers driven C) -8.75 per 200,000,000 kilometers driven Without graphing, find the vertex.

64) f(x) = - 5(x - 15)2 + 3 A) (3, 0)

B) -79.875 per 200,000,000 kilometers driven D) 101.25 per 200,000,000 kilometers driven

B) (0, 3)

C) (15, 3)

Solve. Provide answers in interval notation.

65) (a - 5)(a - 6)(a - 9) > 0 A) (5, 6) (9, ) B) (9, )

C) (- , 5)

D) (15, -15)

(6, 9)

D) (- , 6)

Write a quadratic equation having the given numbers as solutions.

66) 5, 10 5 A) x2 + 11 5x + 50 = 0 B) x2 + 50 5x - 11 = 0 2 C) x - 11 5x + 50 = 0 D) x2 + 50 5x + 11 = 0

B) minimum: 0

C) maximum: 4

9

64)

65)

66)

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

67) f(x) = x2 - 8x + 17 A) minimum: 1

63)

D) maximum: -1

67)

Graph.

68) f(x) = 3(x - 4)2 + 3

68)

A)

B)

C)

D)

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

69) f(x) = -9x2 - 90x - 235

69)

Find the x-intercepts.

70) f(x) = x2 + 10x

70)

A) minimum: 10

B) maximum: 10

C) minimum: 0

A) No x-intercept C) x-intercepts (0, -10) and (-10, 0)

D) maximum: -10

B) x-intercepts (0, 0) and (10, 0) D) x-intercepts (0, 0) and (-10, 0)

10

Solve.

2 71) (x2 - 2) - 8(x2 - 2) + 16 = 0 A) 6 , 6 B) ± 6

Without graphing, find the vertex.

72) f(x) = -(x + 7)2 - 2 A) (-7, -2)

71)

B) (7, 2)

C) ± 6 , ± 6

D) ± 6 , ± 10

C) (-7, 2)

D) (7, -2)

Determine the nature of the solutions of the equation.

73) 1 + 4z 2 = -2z A) Two real

Solve. Give exact solutions.

74) 64x 2 + 36 = 0 3 A) ± 4

Find the x-intercepts of the function.

75) f(x) = x1/2 + 4x1/4 - 5 A) (1, 0)

B) Two nonreal

C) One real

3 B) ± i 4

3 C) ± + i 4

3 D) ± i 4

B) (1, 0), (625, 0)

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

D) (5, 0)

Write a quadratic equation having the given numbers as solutions.

3 2 76) , 2 5 A) 10x 2 + 19x + 6 = 0 C) 5x2 + 4x + 3 = 0 77) 12i, -12i A) x2 - 24x + 144

72)

73)

74)

75)

76)

B) 10x 2 - 19x + 6 = 0 D) 5x2 + 3x + 4 = 0

B) x2 + 144

C) x2 - 144

11

D) x2 + 24x + 144

77)

Determine which of the following four functions might be used as a model for the data: linear: f(x) = mx + b; quadratic: f(x) = ax 2 + bx + c, a > 0; quadratic: f(x) = ax 2 + bx + c, a < 0; polynomial, not quadratic or linear.

78)

78)

Unidentified Flying Object

Altitude in thousands of feet

A) f(x) = ax2 + bx + c, a > 0

Linear distance in miles

B) f(x) = mx + b D) f(x) = ax2 + bx + c, a < 0

C) Polynomial, not quadratic or linear

12

Answer Key Testname: C11

1) If b2 - 4ac < 0, then the radicand in the quadratic formula is negative and the equation has only nonreal solutions. If b2 - 4ac 0, the radicand is nonnegative and the solutions are real numbers.

2) Observe that y = ((a - 3) + 3)2 = a2 . That is, for any y-value on the graph of y = x2 , the same y-value occurs on the graph of y = (x + 3)2 at an x-value three units less than (or 3 units to the left of) the corresponding x-value of y = x2 .

3) Find the average of the values of the x-coordinates of the x-intercepts to find the x-coordinate of the vertex. Then substitute this value for x in the quadratic equation to find the y-coordinate of the vertex.

4) 1) If the quadratic equation is of the type x2 = k, use the principle of square roots.

2) If the quadratic equation is of the type ax2 + bx + c = 0, b 0, use the principle of zero products, if possible.

3) If the quadratic equation is of the type ax2 + bx + c = 0, b 0, and factoring is difficult or impossible, use the quadratic formula.

5) No. Given the solutions of a quadratic equation, it is possible to find an equation equivalent to the original equation but not necessarily expressed in the same form as the original equation. For example, we can find a quadratic equation with solutions -2 and 4. (x - (-2)) (x - 4) = 0 (x + 2)(x - 4) = 0 x2 - 2x - 8 = 0 Now x2 - 2x - 8 = 0 has solutions -2 and 4. However, the original equation might have been in another form, such as 2x(x - 3) -x(x - 4) = 0.

6) Answers may vary. One such equation is x2 + 2x + 1 = 5. In order to solve this equation using the principle of zero products, it would be necessary to factor x2 + 2x - 4 as (x + 1 - 5)(x + 1 + 5).

7) Consider ax2 + bx + c. If a > 0, then the graph of y = ax2 + bx + c is a parabola that opens up. We can examine the

parabola to determine the intervals on which the polynomial has positive values and the interval on which it has negative values. If a < 0, we can multiply both sides of the inequality by -1, reversing the inequality symbol. Then the graph of y = -ax2 - bx - c is a parabola that opens up and we can proceed as above.

8) Since ax2 + bx + c = 0 and -ax2 - bx - c = 0 are equivalent equations, they have the same solutions.

9) The graphs are reflections of each other across the line y = k. If the graphs are to have the same x-intercepts, k must be 0. (No restrictions on a or h are necessary.)

10) A 11) C 12) C 13) B 14) D 15) D 16) D 17) D 18) A 19) A 20) C 21) D 22) A 23) B 24) C 25) D 26) D 27) C 28) D 29) B 13

Answer Key Testname: C11

30) D 31) C 32) A 33) A 34) A 35) A 36) A 37) B 38) A 39) C 40) C 41) C 42) D 43) A 44) C 45) A 46) B 47) C 48) A 49) D 50) A 51) C 52) A 53) C 54) C 55) B 56) D 57) A 58) C 59) B 60) B 61) D 62) B 63) D 64) C 65) A 66) C 67) A 68) D 69) D 70) D 71) C 72) A 73) B 74) D 75) A 76) B 77) B 78) D 14

Exam Name___________________________________

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

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

1) h(x) = 6(8x + 7)2 - 9 A) f(x) = 8x + 7, g(x) = 6x2 - 9

C) f(x) = 6x2 - 9, g(x) = (8x + 7)2

2) h(x) =

1)

B) f(x) = (6x - 9)2 , g(x) = 8x + 7 D) f(x) = 6x2 - 9, g(x) = 8x + 7

x5 - 4 x5 + 2

2)

A) f(x) =

1 , g(x) = x5 - 4 5 x +2

B) f(x) = x5 + 2, g(x) = x5 - 4

C) f(x) =

x-4 , g(x) = x5 x+2

D) f(x) = x5 , g(x) =

3) h(x) = ( x - 5)5

x-4 x+2

3)

x5 , g(x) = x - 5

A) f(x) =

x - 5, g(x) = x5

B) f(x) =

C) f(x) =

x, g(x) = (x - 5)5

D) f(x) = x5 , g(x) =

x-5

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

4) Explain why f(x) = 2 x is an exponential function but f(x) = x2 is not.

4)

5) Explain how the equation log x = 1 could be solved using the graph of f(x) = log x.

5)

6) Explain the error in the following: log 2 + log M = log (2 + M).

3 3 3

6)

7) Without using a calculator, explain why 2 must be greater than 8 but less than 16.

7)

8) Explain why negative numbers do not have logarithms.

8)

9) Explain why 1 is excluded from being a logarithmic base.

9)

10) Explain the error in the following: log 3y = log 3 · log y.

4 4 4

10)

11) Explain how the graph of f(x) = ex could be used to graph the function g(x) = 1 + ln x.

11)

12) Explain the error in the following: log 8 - log N = log (8 - N).

6 6 6

12)

1

13) Explain why a

log a 5

= 5.

13)

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

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

4 14) f(x) = x+5 A) f-1 (x) =

5 + 4x x

B) Not a one-to-one function

C) f-1 (x) =

-5x + 4 x

D) f-1 (x) =

Find the common logarithm to four decimal places.

15) log 36.05 A) 3.5849 B) 4.0849 Using a calculator, find to the nearest ten-thousandth.

16) 101.0455 A) 11.1045

B) 0.0193

14)

x 5 + 4x

C) 1.0569

D) 1.5569

C) 0.0445

D) 2.8445

15)

16)

Convert to a logarithmic equation.

1 17) 2 -2 = 4 A) -2 = log 2

1 4

17) B) -2 = log1/ 4 2

C)

2

1 = log 2 -2 4

D) 2 = log -2

1 4

Graph the relation using solid circles and the inverse using open circles.

18) {(-9, 3), (9, -3), (-7, -1), (7, 1)}

A)

B)

C)

D)

Solve the problem.

19) Use the formula L = 10 · log

I , where the loudness of a sound in decibels is determined by I, the I0

number of watt/m2 produced by the soundwave, and I0 = 10-12 watt/m2 . What is the intensity in watt/m2 of a noise measured at 35 decibels? Round to the nearest tenth.

A) 3.5 × 10-10 watt/m2 B) 3.2 × 10-8 watt/m2

C) 3.2 × 10-9 watt/m2

D) 3.3 × 1013 watt/m2

3

18)

19)

Graph the function.

20) f(x) = ln(x - 2)

20)

A)

B)

C)

D)

Use composition to verify whether or not the inverse is correct.

1 21) f(x) = 7x - 7, f-1 (x) = x + 1 7 A) No

21) B) Yes

Find the inverse of the relation.

22) {(-5, -4), (5, 4), (-3, 6), (3, -6)} A) {(-4, -5), (-5, 5), (6, -3), (-6, 3)} B) {(-4, -5), (4, 5), (6, 5), (-6, 3)} C) {(-4, -5), (4, 5), (6, -3), (-6, 3)}

22)

4

Using a calculator, find to the nearest ten-thousandth.

23) eln 2 A) 2.718

B) 5.437

C) 7.389

D) 2

23)

Graph.

24) f(x) = 3 2x - 1

24)

A)

B)

C)

D)

Solve the problem. When appropriate, round the solution to the nearest tenth. As needed, use the formula pH = -log H3 O+ .

25) Find the [H3 O+ ] if the pH = 9 .

A) 10 -9

B) .1

C) 2.2

5

D) 10 9

25)

Solve the problem.

26) A size 6 dress in Country C is size 26 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x + 20. Find a formula for the inverse of the function described. Use the inverse function to find dress sizes in the Country C that correspond to the size of 28 in France.

1 1 A) B) 4 C) 8 D) 8 4 Express as a single logarithm.

27) log 2 12 + log 2 13 A) log 4 25

27) B) log 2 156

C) log 2 25

D) log 4 156

Find the requested composition of functions.

6 and g(x) = x - 3, find g f(x).

28) Given f(x) = x2 A)

3 x2

B)

28)

6 2 x -3

C)

Determine whether the function is one-to-one.

29) f(x) = 64 - x2 A) Yes

6 -3 x2

D)

6

(x - 3)2

29)

B) No

Find the requested composition of functions.

30) Given f(x) = 7x + 8 and g(x) = 5x - 1, find f g(x).

A) 35x + 1 B) 35x + 15 Solve.

26)

C) 35x + 39

D) 35x + 7

31) How long will it take for $7600 to grow to $23,400 at an interest rate of 2.1% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

A) 54.11 yr B) 214.77 yr C) 147 yr D) 53.69 yr

Solve the problem.

32) The half-life of a certain radioactive substance is 8 years. Suppose that at time t = 0, there are 29 g of the substance. Then after t years, the number of grams of the substance remaining will be: 1 t/16 N(t) = 29 2

30)

31)

32)

How many grams of the substance will remain after 56 years? Round to the nearest hundredth when necessary.

A) 0.32 g B) 0.64 g C) 1.28 g D) 2.56 g

Express as a single logarithm.

33) log 4 12 + log 4 9 A) log 4 108

33) B) log 8 21

C) log 4 21

Use composition to verify whether or not the inverse is correct.

1 34) f(x) = 5x + 10, f-1 (x) = x - 5 5 A) Yes

34) B) No

6

D) log 8 108

Graph.

35) f(x) = 4 x

35)

A)

B)

C)

D)

Solve the problem.

36) A computer is purchased for $4500. Its value each year is about 77% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function V(t) = 4500(0.77)t. Find the value of the computer after 6 years.

A) $722.18 B) $556.08

C) $20,790.00

7

D) $937.90

36)

Solve.

37) log 3 A)

1 =x 27

37)

1 81

B)

1 9

C) -3

D) 3

Solve the equation.

38) log 3 x = 5

38)

A) 125

B) 243

C) 15

Determine whether the function is one-to-one.

39) f(x) = x3 + 8 A) Yes

Solve.

D) 1000

39)

B) No

40) log 5 x = -2 A)

40)

1 25

B) -10

C) -25

D) 32

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

3 41) f(x) = x + 3 B) f-1 (x) = (x + 3)3

A) f-1 (x) = x3 - 3 C) f-1 (x) =

3

41)

x-3

D) Not a one-to-one function

Solve the equation.

42) ln(5x - 1) = ln 3 - ln (x - 3) 16 3 A) B) 3, 5 5 43) e-t = 0.9 (Round to the nearest ten-thousandth.)

A) -0.1054 B) 2.4594

8

C)

16 D) 0, 5

C) -2.4594

D) 0.1054

42)

43)

Graph.

44) f(x) = 2 -x

44)

A)

B)

C)

D)

Solve the problem.

45) A size 4 dress in Country C is size 32 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 12). Find a formula for the inverse of the function described. x x - 12 x - 12 + 12 A) f-1 (x) = x - 12 B) f-1 (x) = C) f-1 (x) = D) f-1 (x) = 2 2 2

45)

Solve for x.

46) log a a x = 8 A) a 8

46) B) 8

C) 1

9

D) 8loga a

Determine whether the function is one-to-one.

47) f(x) = 7x2 - 6 A) No

B) Yes

Graph the relation using solid circles and the inverse using open circles.

48) {(-1, 16), (-7, -2), (5, -11)}

A)

B)

C)

D)

47)

48)

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

10

49) y = 2x3 + 3

49)

A)

B)

C)

D)

Convert to an exponential equation.

50) log 10 1000 = 3 A) 10003 = 10

50) B) 3 10 = 1000

C) 103 = 1000

11

D) 100010 = 3

Graph the function.

51) f(x) = 3ln x

51)

A)

B)

C)

D)

Solve the equation.

52) 5 3x = 8 x + 1 (Round to the nearest thousandth.)

A) 1.292 B) 2.292 Using a calculator, find to the nearest ten-thousandth.

53) 10-2.6778 A) 0.0021

B) 16.9991

12

C) 0.756

D) -4.424

C) 0.0210

D) 0.0002

52)

53)

Solve the equation.

54) 4 x = 16 A) 3

Solve.

B) 1

C) 4

D) 2

55) The amount of particulate matter left in solution during a filtering process is given by the equation P = 500(2)-0.4n , where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5.

(Round to the nearest whole number.)

A) 500, 16 B) 500, 125

C) 1000, 125

55)

D) 500, 2000

Express as a product.

56) log b t4 A) b log 40 t4

54)

56) B) b log 4 t

C) 4 log b t

D) 4 log b t4

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

57) y = 7x - 8 57)

A)

B)

13

C)

D)

Graph.

58) x = 2 y

58)

A)

B)

14

C)

D)

Express as a sum of logarithms.

59) log 4 (16 · 64)

Solve.

59)

A) log 4 2 + log 4 3

B) log 4 16 + log 4 64 + log 4 4

C) log 16 4 + log 64 4

D) log 4 16 + log 4 64

60) Given log 10 2 = 0.3010 and log 10 3 = 0.4771, evaluate log 10 24 .

A) 1.7323

B) 1.3801

C) 0.5044

60) D) 0.4308

Find the logarithm.

1 61) log8 8

61)

A) -1

B) 8

C) 0

D) 1

Express in terms of logarithms of a single variable or a number.

8 m 62) log7 n B) log7 n - log7 8 -

A) log7 (8 m) + log7 n C) log7 8 + Solve.

62)

1 log7 m - log7 n 2

D) log7 8 ·

63) Given logb 5 = 1.284 and logb 11 = 1.365, evaluate logb 6.

A) 55 B) 16 C) 2.2 D) cannot be found using the properties of logarithms

15

1 log7 m 2

1 log7 m ÷ log7 n 2

63)

Answer Key Testname: C12

1) D 2) C 3) D 4) 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.

5) 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.

6) A sum of logarithms is not equal to a logarithm of a sum. log 2 + log M = log 2M 3 3 3 3 4 3 4 7) Since 3 < < 4, 2 < 2 < 2 ; that is 2 is greater than 2 (or 8), but less than 2 (or 16). This is true because 2 x is an increasing function.

8) 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.

9) It excludes x = 1 y which is not a function.

10) A logarithm of a product is not equal to a product of logarithms. log

4

3y = log

4

3 + log y 4

11) Reflect the graph of f(x) = ex across the line y = x and then translate it up one unit.

12) A difference of logarithms is not equal to the logarithm of the difference.

8 log 6 8 - log 6 N = log 6 N 13) Let log

a

5 = x. Then a x = 5. Replacing x with log

a

5, we have a

14) C 15) D 16) A 17) A 18) B 19) C 20) C 21) B 22) C 23) D 24) C 25) A 26) C 27) B 28) C 29) B 30) A 31) D 32) D 33) A 34) B 35) B 36) D 37) C 38) B 16

log a 5

= 5.

Answer Key Testname: C12

39) A 40) A 41) A 42) A 43) A 44) A 45) B 46) B 47) A 48) D 49) D 50) C 51) A 52) C 53) A 54) D 55) B 56) C 57) B 58) B 59) D 60) B 61) A 62) C 63) D

17

Exam Name___________________________________

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

Use synthetic division to divide.

1) (x4 + 625) ÷ (x - 5)

625 A) x3 + 5x2 + 25x + 125 + x-5

C) x3 - 5x2 + 25x - 125 +

Solve.

1250 B) x3 + 5x2 + 25x + 125 + x-5

1250 x-5

D) x3 + 5x2 + 25x + 125

2) Let f(x) = -6x + 8 and g(x) = 7x2 + 1. Find f(8) · g(8) .

A) -17,960 B) -21,552 C) -17,920

Find the center and the radius of the circle.

3) (x + 7)2 + y2 = 100 A) (7, 0), r = 100

B) (0, 7), r = 10

C) (0, -7), r = 100

Solve the problem.

4) The following is a list of heights, in inches, of six people: Susan 66 Umar 75 Mark 74 Dorota 66 Mike 76 Gina 64 What is the median height?

A) 70.5 inches B) 70 inches C) 74 inches For the pair of functions, find the indicated sum, difference, product, or quotient.

5) Let f(x) = x + 1 and g(x) = x + 6. Find (f + g)(-4).

A) -1 B) -15 C) -3 Solve using Cramer's rule.

6) 3x - 7y - 5z = -58 2x + 6y - 7z = 25 -4x - 6y - 2z = -56 A) (2, -7, -3)

1)

D) -21,504

D) (-7, 0), r = 10

2)

3)

4)

D) 66 inches

D) -13

5)

6)

B) (7, 3, 7)

C) (3, 5, 3)

D) (2, 7, 3)

Find the distance between the pair of points. Where appropriate, give an approximation to three decimal places.

7) (4, -6) and (-6, -1) 7) A) 75

B) 75 3 129.904

Find the midpoint of the segment with the given endpoints.

8) (4, -6) and (6, -2) A) 10, -8 B) 5, - 4

1

C) 15

D) 5 5 11.18

C) - 1, - 2

D) -2, -4

8)

Use synthetic division to divide.

9) (8r3 - 60r2 - 27r - 40) ÷ (r - 8) 5 A) 8r2 + 4r + r- 8

Find the median.

10) 2.7, 4.7, 8.5, 3.5 A) 3.5

9)

B) 8r2 + 4r + 5

C) 8r2 - 4r - 5

D) r2 + 5r + 4

B) 4.7

C) 8.5

D) 4.1

C) (0, 7), r = 7

D) (7, 0), r = 49

Find the center and the radius of the circle.

11) x2 + (y + 7)2 = 49 A) (0, -7), r = 7

B) (-7, 0), r = 49

10)

11)

Evaluate.

12)

12) 5 -4 -4 2 -3 -4 -2 4 3 A) -237

B) 83

C) 19

D) -19

13)

13) 5 8 9 3 8 5 6 5 2 A) 1060

B) 150

Find the center and the radius of the circle.

14) x2 - 18x + 81 + (y - 6)2 = 64 A) (9, 6), r = 8

B) (6, 9), r = 8

2

C) -150

D) -630

C) (-6, -9), r = 64

D) (-9, -6), r = 64

14)

Graph the circle.

15) (x - 1)2 + y2 = 9

15)

A)

B)

C)

D)

Solve the problem.

16) The following is a list of heights, in inches, of six people: Susan 66 Umar 74 Mark 75 Dorota 66 Mike 76 Gina 65 What is the mode?

A) 70 inches B) 66 inches C) 70.5 inches Graph the circle.

3

16)

D) 74 inches

17) (x - 2)2 + (y - 2)2 = 25

17)

A)

B)

C)

D)

Solve the problem.

18) The Wellspring Company has a fleet of seven trucks which get gas mileages of 19, 8, 16, 14, 18, 8, and 25 miles per gallon, respectively. What is the mean gas mileage for the fleet? Round your answer to the nearest mpg.

A) 14 mpg B) 15 mpg C) 18 mpg D) 16 mpg Find the median.

19) $69.15, $52.55, $81.40, $74.35, $52.55 A) $52.55 B) $69.15

C) $66.00

4

D) $81.40

18)

19)

Find the mean.

20) 27, 39, 11, 35, 8, 39, 9 A) 27

B) 21

C) 39

D) 24

Find the median.

21) 13, 16, 35, 52, 63, 63, 79 A) 35

B) 52

C) 63

D) 46

Solve using Cramer's rule.

22) 5x + 5y = 10 5x + y = -10 A) (5, -3)

21)

22) B) (3, -5)

C) (-5, -3)

D) (-3, 5)

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

23) Let f(x) = x - 2 and g(x) = -5x2 + 18x - 5. Find (f · g)(4).

A) -510

20)

B) -26

C) 166

23)

D) -78

Evaluate.

24)

24) 0

0 9

6 -7 9 0

Solve.

3 3 A) -183

B) 141

C) 162

D) -162

25) Let f(x) = 6x + 3 and g(x) = 3x2 + 7. Find f(9) · g(9) .

A) 13,851 B) 13,122 C) 14,250

Find the midpoint of the segment with the given endpoints.

26) (0, 1) and (8, 5) A) -8, -4 B) 4, 3

25)

D) 13,500

C) - 4, - 2

26)

D) 8, 6

Give the equation for a circle with the given center and radius.

27) Center at (-10, 0), radius 3 A) x2 + (y - 10)2 = 3 B) (x - 10)2 + y2 = 9 C) (x + 10)2 + y2 = 9

D) x2 + (y + 10)2 = 3

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

28) Let f(x) = 5x2 + 5 and g(x) = x + 3. Find (f - g)(-4).

A) 92

27)

B) -81

C) 86

28)

D) 78

Find the distance between the pair of points. Where appropriate, give an approximation to three decimal places.

5 1 1 19 , and , 29) 29) 11 22 5 22 A)

13 11

1.182

B)

2221 55

40.382

C)

5

2221 55

0.857

D)

2 34 11

1.06

Find the center and the radius of the circle.

30) x2 + y2 - 10x - 16y + 53 = 0 A) (8, 5), r = 6

31) x2 + y2 = 36 A) (6, 6), r = 36 Solve using matrices.

32) 3x - y - 8z = 6 9x + 5z = 91 3y + z = 17 A) (9, 2, 5)

B) (-8, -5), r = 36

C) (-5, -8), r = 36

D) (5, 8), r = 6

B) (0, 0), r = 36

C) (0, 6), r = 36

D) (0, 0), r = 6

B) (9, 5, 2)

C) (5, 2, 9)

D) (-9, 5, 18)

33)

34) B) (12, -2)

C) (-2, 3)

D) (3, 7)

Solve the problem.

35) The following prices per pound of ocean perch were found at seven supermarkets: $6.59, $7.49, $7.39, $7.59, $6.59, $7.29, $6.39 What is the mode?

A) $6.59 B) $7.29 C) $7.59 D) $7.39 Give the equation for a circle with the given center and radius.

36) Center at (-6, -4), radius 19 A) (x - 4)2 + (y - 6)2 = 361 B) (x + 4)2 + (y + 6)2 = 361 C) (x + 6)2 + (y + 4)2 = 19

Solve.

31)

32)

Solve the problem.

33) The five sales people at Southwest Appliances earned commissions last year of $20,000, $29,000, $48,000, $17,000, and $29,000. Find the mean commission.

A) $31,460 B) $27,170 C) $30,030 D) $28,600 Solve using matrices.

34) x + 7y = -2 3x + y = 34 A) (7, 12)

30)

35)

36)

D) (x - 6)2 + (y - 4)2 = 19

37) Let f(x) = 6x + 8 and g(x) = 5x2 + 7. Find f(7) - g(7) .

A) -210 B) -203 C) -195

D) -202

38) Let f(x) = 3x + 8 and g(x) = 3x2 + 2. Find f(7) + g(7) .

A) 178 B) 176 C) 168

D) 170

37)

38)

Find the distance between the pair of points. Where appropriate, give an approximation to three decimal places.

39) (-2.5, 4.8) and (9.5, 9.8) 39) A) 169 B) 17 C) 13 D) 17 Find any modes that exist.

40) 106, 150, 156, 106, 188, 199, 162 A) 85 B) 156

C) 150

6

D) 106

40)

Find the median.

41) 13, 57, 275, 215, 378, 470 A) 201.5

B) 215

C) 275

D) 245

Use synthetic division to divide.

42) (y9 + 1) ÷ (y + 1)

41)

42)

-2 A) y8 - y7 + y6 - y5 + y4 - y3 + y2 - y + 1 + y+ 1

B) y8 + y7 + y6 + y5 + y4 + y3 + y2 + y + 1 +

2 y+ 1

C) y8 - y7 + y6 - y5 + y4 - y3 + y2 - y + 1 D) y8 + y7 + y6 + y5 + y4 + y3 + y2 + y + 1 For the pair of functions, find the indicated sum, difference, product, or quotient.

43) f(x) = 7x2 - 4x, g(x) = x2 - 2x - 8

43)

Find (f/g)(x).

A)

7x x+1

Solve using matrices.

44) 2x + 4y = - 1 7x - y = 4 1 1 A) , 2 2 Solve.

B)

7-x 8

C)

7x - 4 -2

D)

7x2 - 4x x2 - 2x - 8

44) B) -

1 ,0 2

C)

1 1 , 2 2

45) Let f(x) = 7x + 4 and g(x) = 5x2 + 9. Find g(3) - f(3) .

A) 24 B) 33 C) 20

D) -

1 1 , 2 2

D) 29

Give the equation for a circle with the given center and radius.

46) Center at (0, -9), radius 7 A) x2 + (y + 9)2 = 49 B) x2 + (y - 9)2 = 7 C) (x - 9)2 + y2 = 49

Find any modes that exist.

47) 20, 21, 46, 21, 49, 21, 49 A) 21 Solve using matrices.

48) 5x + 6y = 20 2x + 8y = 36 A) (-2, -5)

45)

46)

D) (x + 9)2 + y2 = 49

B) 32.4

C) 49

D) 46

47)

48) B) (5, -2)

C) (5, 2)

Give the equation for a circle with the given center and radius.

49) Center at (0, 1), radius 5 A) (x + 1)2 + y2 = 25 B) x2 + (y - 1)2 = 5 C) (x - 1)2 + y2 = 25

D) x2 + (y + 1)2 = 5

7

D) (-2, 5)

49)

Find the mean.

50) 33, 43, 19, 39, 16 A) 30

B) 33

C) 43

8

D) 25

50)

Answer Key Testname: C13

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