Solution Manual For Administrative Procedures for the Canadian Office, Canadian Edition, 11th Editio

Chapter 0 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 1) 5x2 y5 1)

A) Monomial; variables x, y; coefficient 5; degree 2 B) Monomial; variables x, y; coefficient 5; degree 7 C) Monomial; variables x, y; coefficient 5; degree 5 D) Not a monomial

Evaluate the expression. 5 4 2) 7 6 A)

1 21

2) B)

1 7

C)

1 42

Factor the polynomial by removing the common monomial factor. 3) 3x2 - 9x A) 3x(x + 3)

B) 3(x2 - 3x)

C) 3x(x - 3)

D)

2 7

D) 3x2 (x - 3)

Reduce the rational expression to lowest terms. 3x2 - 27x + 54 4) x-6 A)

1 x-6

4) C) 3x2 - 36

B) 3x - 9

D)

3x2 - 27x + 54 x-6

List all the elements of B that belong to the given set. 5 8 5) B = {17, 8, -19, 0, , - , 3.3, 25 , 0.258258258...} 8 5 Integers A) {17, -19}

Factor the polynomial by grouping. 6) 10x2 + 15x - 8x - 12 A) (10x - 4)(x + 3)

5)

B) {17, 0}

C) {17, -19, 0}

D) {17, 0,

B) (5x - 4)(2x + 3)

C) (5x + 4)(2x - 3)

D) (10x + 4)(x - 3)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 7) 1 1x 8+

1 x

A)

8x + 1 x-1

B)

3)

x-1 8x + 1

C)

1

x+1 8x - 1

D)

x-1 8x

8}

6)

7)

8)

8)

2 4+ x x 1 + 3 6

A)

x 12

B) 12

C) 1

D)

12 x

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 9) (3x + 4y)(3x - 4y) 9) A) 9x2 + 24xy - 16y2 B) 9x2 - 24xy - 16y2

C) 9x2 - 16y2

D) 6x2 - 8y2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 1 11 + 10) 3x 12x A)

5 4x

B) 1

C)

15 24x

D)

4 5x

Perform the indicated operations. Express the answer as a single polynomial in standard form. 11) -2x(-5x - 4) A) -5x2 + 8x B) 10x2 + 8x C) 10x2 - 4x D) 18x2 Tell whether the expression is a polynomial. If it is, give its degree. 4 12) 6x2 x A) Polynomial; degree 2 C) Polynomial; degree -1

11)

12)

B) Polynomial; degree 1 D) Not a polynomial

Simplify the expression. Assume that all variables are positive when they appear. 13) (5 11 + 4)2 A) 259 + 40 11

10)

B) 291 + 40 11

C) 279 + 40 11

13) D) 291 - 40 11

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. x-2y2 14) 14) xy7

A)

y5 x3

B)

1 x3 y5

C)

1

xy5

Factor completely. If the polynomial cannot be factored, say it is prime. 15) 4x2 - 24x - 16x + 96 A) 4(x + 6)(x + 4)

B) (x - 6)(4x - 16)

C) 4(x - 6)(x - 4)

2

D)

x y5

D) (x - 6)(x - 4)

15)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 16) B

A) {0, 1, 4, 6, 7, 8, 9} C) {0, 1, 4, 6, 9}

16)

B) {1, 4, 6, 8, 9} D) {0, 1, 4, 6, 8, 9}

Use synthetic division to determine whether x - c is a factor of the given polynomial. 17) 4x3 - 27x2 + 8x + 60; x + 4 A) Yes

17)

B) No

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 18) (x2 + 1) - (4x2 + 7) + (x2 + x - 8)

18)

Graph the numbers on the real number line. 19) x > -3

19)

A) -2x2 + 8x - 7

B) -4x2 + x - 14

C) -3x2 + x - 14

D) -2x2 + x - 14

A)

B)

C)

D)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 20) A B A) {0, 4, 6, 9} Solve. 21) What is the value of A) 16

B) {1, 2, 3, 5, 7, 8}

C) {1, 4, 6, 8, 9}

D) {4, 6, 9}

(6,666)4 ? (3,333)4

20)

21) C) (2,222)4

B) 48

3

D) (3,333)4

Perform the indicated operations and simplify the result. Leave the answer in factored form. 22) 10 11 + 11 - x x - 11

22)

7 4 + x x - 11

A) -

23)

21x 11x - 77

B) -

x 11x - 77

C)

21x 11x - 77

D)

x 11x - 77

23)

x2 - 81 x x-9 x-7

A) (x + 9)(x - 7)

B)

(x - 9)(x2 - 9) x(x - 7)

C)

x (x + 9)(x - 7)

D)

(x + 9)(x - 7) x

Evaluate the expression using the given values. 6x - 7y x = 10, y = 6 24) x+3 A)

34 13

24)

B) 2

C)

18 13

D)

34 9

Perform the indicated operations. Express the answer as a single polynomial in standard form. 25) 6x6 (3x5 + 2x4 - 6) A) 18x11 + 2x4 - 6

B) 18x5 + 12x4 - 36

C) 18x11 + 12x10

D) 18x11 + 12x10 - 36x6

List all the elements of B that belong to the given set. 0 26) B = 19, 5, -8, 0, , 0.2 3 Irrational numbers 0 5, A) 3

26)

B) { 5}

C)

5,

0 , 0.2 3

D) { 5, 0.2}

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 27) (2x2 + 13x - 10) - (7x2 + 16x + 4) A) -5x2 + 20x - 6

B) -5x2 - 3x - 14

C) -5x2 - 3x + 14

D) -5x2 - 3x - 6

Reduce the rational expression to lowest terms. 10x2 + 30x3 28) 9x + 27x2 A)

10 9

25)

B)

27)

28)

10 + 30x3 9x + 27

C)

4

10x2 + 30x3 9x + 27x2

D)

10x 9

Solve the problem. 29) Find the surface area S of a right circular cylinder with radius 10 cm, and height 4 cm. Use 3.14 for . Round your answer to one decimal place. A) 753.6 cm2 B) 879.2 cm2 C) 439.6 cm2 D) 1,256.0 cm2 Simplify the expression. 30) 165/4 A) 35

29)

30) B)

5

8

C) 32

Find the quotient and the remainder. 31) 7x2 + 33x - 54 divided by x + 6 A) 7x - 9; remainder 9 C) 7x + 9; remainder 0

D) 1,024

31)

B) 7x - 9; remainder 0 D) x - 9; remainder 0

Simplify the expression. Assume that all variables are positive when they appear. 32) ( 12 + 2)( 12 - 2) A) 8 B) 10 C) 16

32) D) 12 - 2 2

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 33) (A B) C 33) A) {1, 2, 3} B) {2, 3, 5} C) {1, 2, 3, 4, 5, 9} D) {1, 2, 3, 5} Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x3 + 7x4 34) x2 + 36 A) x = -36

Simplify the expression. 35) 125-4/3 A) 625

B) x = -6

C) x = 0, x = -

1 B) 625

1 C) 625

1 7

D) none

35) D) -625

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x2 + 6x + 9 36) x3 - 9x A) x = 3, x = -3, x = 0 C) x = 3, x = -3

34)

36)

B) x = 3, x = 0 D) x = 0

Write the number in scientific notation. 37) 0.000486 A) 4.86 × 104 B) 4.86 10-4

37) C) 4.86 × 10-5

Factor completely. If the polynomial cannot be factored, say it is prime. 38) x4 - 64 A) (x2 + 8)2 B) prime C) (x2 + 8)(x2 - 8) 5

D) 4.86 × 10-3

D) (x2 - 8)2

38)

Evaluate the expression. 39) -9 - (-2 + 6 · 7 + 8) A) -57

B) 39

C) -61

D) -41

Simplify the expression. Assume that all variables are positive when they appear. 6 40) 7 B) 6 7

A) 55

C)

36 7 7

Use a calculator to evaluate the expression. Round the answer to three decimal places. 41) (4.49)2 A) 20.160

B) 0.050

C) -0.050

39)

40) D)

6 7 7

D) -20.160

Solve the problem. 42) Find the area of the window. Approximate the result to the nearest tenth using 3.14 for .

41)

42)

8 ft

4 ft

A) 35.1 ft2

B) 57.1 ft2

C) 38.3 ft2

D) 82.2 ft2

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 43) A C A) {1, 2, 3, 4, 5, 7, 8, 9} C) {0, 2, 3, 4, 5, 6, 7, 8, 9}

43)

B) {1, 2, 3, 4, 5, 6, 7, 8, 9} D) {1}

Perform the indicated operations and simplify the result. Leave the answer in factored form. 44) x xx+2 x+1

A)

x x+1

B)

x x+2

C)

6

x2 x+2

D)

x x-2

44)

Solve the problem. 45) Find the area of the shaded region. Express the answer in terms of .

45)

9

9

A) 81 -

81 4

square units

B)

D) 81 -

C) 324 - 81 square units

Factor the perfect square. 46) x2 + 12x + 36 A) (x + 6)2

81 4

+ 81 square units 81 2

square units

C) (x - 6)2

B) (x + 12)(x - 12)

46) D) (x + 6)(x - 6)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 47) A C 47) A) {1, 2, 3, 4, 5, 8, 9} B) {1} C) {1, 2, 3, 5, 7, 9} D) {4, 6, 7, 9} Perform the indicated operations. Express the answer as a single polynomial in standard form. 48) -4x5 (3x7 - 10)

48)

Factor the polynomial. 49) 9y2 + 18y + 8

49)

A) -12x7 + 40

A) (9y + 4)(y + 2)

B) -12x12 - 10

C) 28x5

B) (3y + 4)(3y + 2)

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

D) -12x12 + 40x5

D) prime

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 50) (9x1/5 · y1/5 )2 50) A) 81x1/10y1/10

B) 81x2/5 y2/5

C) 81x2 y2

7

D) 81x1/25y1/25

On the real number line, label the points with the given coordinates. 51) -1.75, 1, 3, 5.25

A)

B)

C)

D)

51)

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 52) (13x2 + 4x - 2) + (8x + 2) A) 13x2 + 12x

B) 25x3

C) 13x2 + 4x + 4

D) 13x2 + 12x - 4

Solve the problem. 53) The weekly production cost C of manufacturing x calendars is given by C(x) = 29 + 3x, where the variable C is in dollars. What is the cost of producing 213 calendars? A) $242.00 B) $668.00 C) $639.00 D) $6,180.00 The triangles are similar. Find the missing length x and the missing angles A, B, C. 54)

52)

53)

54)

94° 16

24

36°

50°

12

A) x = 8 units; A = 50°; B = 36°; C = 94° C) x = 16 units; A = 94°; B = 36°; C = 50°

B) x = 16 units; A = 36°; B = 94°; C = 50° D) x = 8 units; A = 94°; B = 36°; C = 50°

Factor completely. If the polynomial cannot be factored, say it is prime. 55) 18x2 - 63x - 36 A) (18x - 9)(x + 4)

B) 9(2x - 1)(x + 4)

C) 9(2x + 1)(x - 4)

8

D) prime

55)

Use synthetic division to find the quotient and the remainder. 56) x4 + 16 is divided by x - 2 A) x3 + 2x2 + 4x + 8; remainder 32 C) x3 + 2x2 + 4x + 8; remainder 0

B) x3 - 2x2 + 4x - 8; remainder 32 D) x3 + 2x2 + 4x + 8; remainder 16

56)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 57) (B C) A 57) A) { } B) {1, 2, 3, 5} C) {1, 2, 3, 4, 5, 7, 9} D) {1, 2, 3} Insert <, >, or = to make the statement true. -3.9 58) 6.7 A) =

58) B) >

C) <

Write the number in scientific notation. 59) 0.00006693 A) 6.693 × 10-5 B) 6.693 × 105

C) 6.693 × 104

59) D) 6.693 ± 10-4

Factor completely. If the polynomial cannot be factored, say it is prime. 60) 98x2 - 112x + 32

60)

B) 2(7x - 4)2

A) 2(7x - 4)(7x + 4) C) 2(7x + 4)2

D) prime

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 61) (8x4 - 17x3 ) - (12x4 + 11x3 ) A) 20x4 - 6x3

B) -32x7

C) -4x4 - 6x3

D) -4x4 - 28x3

61)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 6x 62) 62) y

A) Monomial; variables x, y; coefficient 6; degree -2 B) Monomial; variables x, y; coefficient 6; degree 2 C) Monomial; variables x, y; coefficient 6; degree 1 D) Not a monomial Find the LCM of the given polynomials. 63) x2 - 4x, (x - 4)2 A) x(x - 4)2

B) x(x + 4)2

C) x(x - 4)

Factor completely. If the polynomial cannot be factored, say it is prime. 64) 3x2 - 18x + 24 A) 3(x - 4)(x - 2)

B) (x - 4)(3x - 6)

C) 3(x - 8)(x + 1)

9

D) (x + 4)(x - 4)2

D) prime

63)

64)

Tell whether the expression is a polynomial. If it is, give its degree. 65) -2z 4 + z A) Polynomial; degree 1 C) Polynomial; degree 5

65)

B) Polynomial; degree 4 D) Not a polynomial

Reduce the rational expression to lowest terms. 4x + 2 66) 12x2 + 26x + 10 A)

1 3x + 5

B)

66)

4x + 2 2 12x + 26x + 10

C)

4x 3x + 5

D)

4x + 3 3x + 26

Use synthetic division to determine whether x - c is a factor of the given polynomial. 1 67) 6x5 - 5x4 + x - 4; x + 2 A) Yes Factor the polynomial. 68) 4x2 + 12x + 9

A) (2x - 3)(2x - 3)

67)

B) No

B) (2x + 3)(2x + 3)

Write the statement as an inequality. 69) y is greater than or equal to 65 A) y < 65 B) y 65

C) (4x + 3)(x + 3)

D) prime

C) y > 65

D) y 65

Factor the polynomial by removing the common monomial factor. 70) 9x - 9 A) 9(x + 1) B) x(x + 9) C) x(x - 9)

D) 9(x - 1)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 71) 2 +1 x

68)

69)

70)

71)

2 -1 x

A)

x2 x2 + 2

B)

2+x 2-x

C) x2 + 2

The lengths of the legs of a right triangle are given. Find the hypotenuse. 72) a = 24, b = 7 A) 625 B) 5 C) 20 Simplify the expression. Assume that all variables are positive when they appear. 73) ( 12 + z)( 12 - z) A) 12 - 2 12z B) 12z C) 12 - z

10

D) 2

D) 25

72)

73) D) 12 - 2 z

Factor completely. If the polynomial cannot be factored, say it is prime. 74) 15x4 + 16x2 + 4 A) (5x2 - 2)(3x2 - 2) C) (15x2 + 2)(x2 + 2)

74)

B) (3x2 + 1)(5x2 + 4) D) (3x2 + 2)(5x2 + 2)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 75) x 1 81 x 1+

9 x

A)

81 x+9

B)

x+9 81

C)

x-9 81

D)

81 x-9

Solve the problem. 76) Police use the formula s = 30fd to estimate the speed s of a car in miles per hour, where d is the distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on a certain gravel road is 0.28 and a car skidded 330 feet, find the speed of the car, to the nearest mile per hour. A) 99 mph B) 2,772 mph C) 53 mph D) 288 mph Approximate the number rounded to three decimal places, and truncated to three decimal places. 77) 7.1134 A) 7.112 B) 7.114 C) 7.113 D) 7.113 7.114 7.113 7.113 7.114 Factor the polynomial by grouping. 78) 15x2 - 6x + 10x - 4 A) (15x - 2)(x + 2)

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

C) (15x + 2)(x - 2)

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

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

D) (x2 + 2)(x2 - 2)

Factor the difference of two squares. 79) x2 - 4 A) (x - 2)(x - 2)

B) (x + 4)(x - 4)

75)

Solve the problem. 80) A circular swimming pool, 20 feet in diameter, is enclosed by a circular deck that is 4 feet wide. What is the area of the deck? Use = 3.1416. A) 314.2 ft2 B) 301.6 ft2 C) 703.7 ft2 D) 584.3 ft2

76)

77)

78)

79)

80)

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 81) (x + 5y)(x - 5y) 81) 2 2 2 2 x 10xy 25y x 10xy 25y + A) B)

C) x2 - 25y2

Simplify the expression. 82) 2434/5 A) 19,683

D) x2 - 10y2

B) 2,187

C) 6,561 11

D) 81

82)

Factor the expression. Express your answer so that only positive exponents occur. 83) (3m + 9)-2/5 + (3m + 9) 1/5 + (3m + 9) 7/5

83)

A) (3m + 9)-2/5 [1 + (3m + 9) 4/5 + (3m + 9) 7/5] B) (3m + 9)-2/5 [1 + (3m + 9) 3/5 + (3m + 9) 9/5]

C) (3m + 9)-2/5 [1 + (3m + 9) 3/5 - (3m + 9) 9/5] D) (3m + 9)-2/5 [1 + (3m + 9)-3/5 + (3m + 9) -9/5] An expression that occurs in calculus is given. Factor completely. 84) 3(x + 5)2 (2x - 1)2 + 4(x + 5)3 (2x - 1)

84)

B) (x + 5)2 (2x - 1)(x + 17) D) (x + 5)2 (2x - 1)(10x + 17)

A) (x + 5)(2x - 1)(10x + 17) C) (x + 5)2 (10x + 17)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 3x x-1 1 + 85) x2 - 5x - 36 x2 - 16 x2 - 13x + 36 A)

2x2 - x - 5 (x - 9)(x + 4)(x - 4)

B)

2x - 1 (x - 9)(x + 4)

C)

2x - 1 (x - 9)(x - 4)

D)

2x2 - 21x + 13 (x - 9)(x + 4)(x - 4)

Solve the problem. 86) An electrical circuit contains two resistors connected in parallel. If the resistance of each is R1 and

85)

86)

R2 ohms, respectively, then their combined resistance R is given the formula R=

1

1 1 + R 1 R2

If their combined resistance R is 2 ohms and R2 is 9 ohms, find R 1 .

A)

18 ohms 7

B) 7 ohms

C)

2 ohms 7

Factor completely. If the polynomial cannot be factored, say it is prime. 87) 8x4 - x A) x(2x - 1)(4x2 + 1) C) x(2x - 1)(4x2 + 2x + 1)

B) x(8x - 1)(x2 + 2x + 1) D) x(2x + 1)(4x2 - 2x + 1)

D)

7 ohm 18

87)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 88) (3x - 8)(x + 5) 88) A) 3x2 - 40x + 7 B) 3x2 + 7x - 40 C) 3x2 + 5x - 40 D) 3x2 + 7x + 7 Use synthetic division to determine whether x - c is a factor of the given polynomial. 89) x3 - 7x2 - 9x + 63; x + 3 A) Yes

B) No

90) x3 - 13x2 + 46x - 48; x - 2 A) Yes

B) No

12

89)

90)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 91) -4xy3 91)

A) Monomial; variables x, y; coefficient -4; degree 1 B) Monomial; variables x, y; coefficient -4; degree 3 C) Monomial; variables x, y; coefficient -4; degree 4 D) Not a monomial

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 92) (6x - 5y)2 92)

A) 6x2 - 60xy + 25y2 C) 6x2 + 25y2

B) 36x2 + 25y2 D) 36x2 - 60xy + 25y2

Evaluate the expression using the given values. 93) x + y x = -8, y = 3 A) -11 B) 5

C) 11

Simplify the expression. Assume that all variables are positive when they appear. 3 3 94) 21 · 49 3 6 3 A) 7 3 B) 1,029 C) 7 21

D) -5

93)

94) D)

3

1,029

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. x5/3 · x3/4 95) 95) x-4/7 A)

1 251/84 x

B) x251/84

C) x155/84

Simplify the expression. 96) -243-4/5

1 81

96)

D) not a real number

Find the LCM of the given polynomials. 97) 3x - 9, x2 - 3x A) 3x2 - 9

1 155/84 x

1 B) 81

A) 81 C)

D)

B) 3x - 3

C) 3x(x - 3)

D) 3x2 - 3

97)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 98) -5x-9 98)

A) Monomial; variable x; coefficient 9; degree -5 B) Monomial; variable x; coefficient -5; degree 9 C) Monomial; variable x; coefficient -5; degree -9 D) Not a monomial

13

List all the elements of B that belong to the given set. 4 9 99) B = 17, 7, -11, 0, , - , 1.8 9 4 Natural numbers 9 A) 17, 0, 4

99)

B) {-11, 0, 17}

C) {17}

D) {17, 0}

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8x2 8x 100) x-1 x-1 A)

8x(x + 1) x-1

B) 8x

C) 0

Simplify the expression. Assume that all variables are positive when they appear. 3 3 101) 8y - 128y 3 3 3 3 3 A) 4 2y - 2 y B) 2 y - 4 2y C) 6 y 102)

147x2

A) 7x 3

D)

100)

8x x-1

101) D) 2 - 4

3

102) C) 3x2 7

B) 7 3x

D) 147x

Perform the indicated operations and simplify the result. Leave the answer in factored form. 3 7 + 103) 2 2 x - 3x + 2 x - 1 A)

10x - 11 (x - 1)(x + 1)(x - 2)

B)

10x - 11 (x - 1)(x - 2)

C)

42x - 11 (x - 1)(x + 1)(x - 2)

D)

11x - 10 (x - 1)(x + 1)(x - 2)

Write the number as a decimal. 104) 5.378 × 105 A) 537,800

2

B) 5,378,000

C) 268.9

D) 53,780

103)

104)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 105) A B 105) A) {1, 2, 3, 5, 7, 8} B) {2, 3, 5, 7} C) {2, 3, 5} D) {1, 2, 3, 5, 8} An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 3 1 (x2 + 2)1/2 · (2x + 1)1/2 · 2 - (2x + 1)3/2 · (x2 + 2)-1/2 · 2x 2 2 106) 106) x2 + 2

A)

(2x + 1)1/2(x2 - x + 6) (x2 + 2)3/2

B) (x2 + 2)3/2(2x + 1)-1/2(x2 - x + 6)

C) (x2 + 2)3/2(2x + 1)1/2(x2 - x + 6)

D)

14

(2x + 1)1/2(x2 - x + 6) (x2 + 2)-3/2

Factor completely. If the polynomial cannot be factored, say it is prime. 107) 7y6 - 39y3 + 20 A) y2 (7y2 - 4)(y2 - 5) C) (7y3 - 5y2 + y - 4)(y3 - 4y2 + y - 5)

107)

B) (7y3 - 4)(y3 - 5) D) y4 (7y - 4)(y - 5)

Simplify the expression. 1 1/2 108) 16 A) 4

108) B)

1 4

C)

-1 4

D) -4

Graph the numbers on the real number line. 109) x < -7

109)

A)

B)

C)

D)

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 110) (8x2 + 8x + 2) + (9x2 + 5x - 6)

110)

Simplify the expression. 111) -4 -2

111)

A) 17x2 + 13x + 4

1 A) 8

B) 17x2 + 13x - 4

B) -16

C) 11x2 + 13x + 2

D) 17x2 - 13x - 4

C) 16

1 D) 16

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 112) (-5x - 11)(-3x + 3) 112) 2 2 2 2 A) -8x + 18x - 33 B) -8x + 18x + 18 C) 15x + 18x + 18 D) 15x + 18x - 33 Express the statement as an equation involving the indicated variables. 113) The area A of a triangle is one-half the product of its base b and its height h. 1 1 A) A = (b + h) B) A = bh C) A = bh 2 2

15

113) D) A = 2bh

Simplify the expression. Assume that all variables are positive when they appear. 114) 7 2 + 5 8 A) 17 2 B) 3 2 C) -17 2 Write the number in scientific notation. 115) A computer compiles a program in 0.0000266 seconds. A) 2.66 × 10-7 B) 2.66 × 104 C) 2.66 × 10-5

114) D) 12 2

115) D) 2.66 × 10-6

An expression that occurs in calculus is given. Reduce the expression to lowest terms. (2x + 5)4x - 2x2 (2) 116) (2x + 5)2 A)

2x

B)

(x + 5)2

4(x + 5) (2x + 5)2

C)

4x

(2x + 5)2

116) D)

4x(x + 5) (2x + 5)2

Reduce the rational expression to lowest terms. x2 + 5x + 6 117) x2 + 9x + 18 A)

5x + 6 9x + 18

B) -

117)

x2 + 5x + 6 x2 + 9x + 18

C)

x+2 x+6

D)

5x + 1 9x + 3

Perform the indicated operations and simplify the result. Leave the answer in factored form. 4 6 118) x+5 x-5 A)

-2 (x + 5)(x - 5)

B)

-2x - 50 (x + 5)(x - 5)

C)

-2x + 50 (x + 5)(x - 5)

D)

-2x + 10 (x + 5)(x - 5)

Find the quotient and the remainder. 119) 45x2 + 35x - 11 divided by 5x A) 9x2 + 7x -

119)

11 ; remainder 0 5

B) 9x + 7; remainder -11

C) 9x - 4; remainder 0

D) 45x + 35; remainder -11

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 120) (2x5 - 5x3) + (3x5 + 3x3 ) A) 3x8

118)

B) 5x5 - 2x3

C) 5x10 - 2x6

121) 6(1 - y3 ) - 4(1 + y + y2 + y3 ) A) -10y3 - 4 - ay2 - 4y + 2

D) 3x16

121)

B) -10y3 + 4y2 - 4y - 2 D) -10y3 - 4y2 - 4y + 2

C) 10y3 - 4y2 - 4y + 2

Write the statement as an inequality. 122) z is less than or equal to 1 A) z > 1 B) z < 1

C) z = 1

16

120)

D) z 1

122)

An expression that occurs in calculus is given. Factor completely. 123) 2(x + 6)(x - 5)3 + (x + 6)2 · 6(x - 5)2 A) (x + 6)(x - 5)2 (4x + 13) C) 2(x + 5)(x - 6)2 (4x + 13)

123)

B) 2(x + 6)(x - 5)2 (4x + 13) D) (x + 6)(x - 5)2 (8x + 26)

Reduce the rational expression to lowest terms. y2 + 11y + 28 124) y2 + 13y + 42 A)

11y + 28 13y + 42

B) -

124)

y2 + 11y + 28 y2 + 13y + 42

C)

11y + 2 13y + 3

Simplify the expression. 125) (4-1 )-2 1 A) 16

B) 4

C) 16

D)

y+ 4 y+ 6

1 D) 4

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x2 - 64 126) x A) x = -8

B) x = 8, x = 0

C) x = 8, x = -8

5 2

B)

5x 2

C)

5x 8

D)

Simplify the expression. Assume that all variables are positive when they appear. 5 3+ 6 129) 6+ 3

130)

1-

10

1+

10

A)

11 + 2 10 -9

B) 5 2 - 3

C) 5 2 - 7

127)

x 2

Solve the problem. 128) The maximum distance d in kilometers that you can see from a height h in meters is given by the formula d = 3.5 h. How far can you see from the top of a 383-meter building? (Round to the nearest tenth of a kilometer.) A) 19.6 km B) 68.5 km C) 36.6 km D) 716.5 km

A) 4 2 - 3

126)

D) x = 0

Perform the indicated operations and simplify the result. Leave the answer in factored form. 4x 10x + 5 · 127) 8x + 4 2 A)

125)

128)

129) D) 6 2 + 7 130)

B)

-9 - 2 10 11

C)

17

11 - 2 10 -9

D) 1

Find the quotient and the remainder. 131) 27x8 - 45x4 divided by 9x

A) 3x8 - 5x4 ; remainder 0 C) 3x7 - 5x3 ; remainder 0

Find the value of the expression using the given values. x = 15, y = 20 132) x2 + y2 A) 24

Factor the polynomial. 133) x2 + 49

A) (x - 7)2

131)

B) 27x7 - 45x3 ; remainder 0 D) 3x9 - 5x5 ; remainder 0

132)

B) 18

C) 25

D) 13

B) (x + 7)2

C) (x + 7)(x - 7)

D) prime

133)

Insert <, >, or = to make the statement true. -4 134) 4

134)

A) >

B) =

C) <

Simplify the expression. Assume that all variables are positive when they appear. 5 135) 3 3 A) 5

3

9

B)

5

3 3

3

C) 5

3

3

135)

D)

5

3 3

9

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 136) (-5x + 11y)(-3x + 11y) 136) 2 2 2 2 A) 15x - 88xy + 121y B) 15x - 55xy + 121y C) 15x2 - 88xy - 88y2

D) 15x2 - 33xy + 121y2

Find the LCM of the given polynomials. 137) x2 + 6x + 8, -3x - 12 A) -3(x - 2)(x + 4)

B) -3(x + 2)(x - 4)

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

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

Evaluate the expression. 1 1 1 138) + · 5 8 9 A)

13 360

138) B)

1 180

C)

49 40

D)

77 360

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. 7x - 2 139) x2 - 16 A) x = 4, x = -4

137)

C) x =

B) x = 16

18

2 7

D) x = 4

139)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 140) (9x10y-16)1/2 140) A)

9x5 y8

B)

3 x5 y8

C) 3x5 y8

D)

3x5 y8

Solve the problem. 141) Find the volume V and surface area S of a sphere of radius 2 centimeters. Express the answer in terms of . 8 32 cm3 ; S = cm2 A) V = 32 cm3 ; S = 1 cm2 B) V = 3 3 C) V = 8 cm3 ; S = 4

cm2

D) V =

32 3

cm3 ; S = 16 cm2

142) A bicycle wheel makes 4 revolutions. Determine how far the bicycle travels in inches if the diameter of the wheel is 22 in. Use 3.14. Round to the nearest tenth. A) 552.6 in. B) 88 in. C) 69.1 in. D) 276.3 in. Find the value of the expression using the given values. x = -9, y = -4 143) x2 + y2 A) 13

B) 97

C) -5

Find the LCM of the given polynomials. 144) x2 - 7x + 12, x2 - 4x + 3 A) (x - 4)(x - 3) C) (x - 3)(x - 1)

A) 16 C)

146)

D) 5

B) -

1 16

143)

145)

1 16

D) not a real number

4

146)

A) 16 C)

142)

144)

B) (x + 4)(x + 3)(x - 1) D) (x - 4)(x - 3)(x - 1)

Simplify the expression. 145) 32-4/5

141)

B) 2

1 4

Evaluate the expression. 147) 2 · [3(7 - 2) - 4] A) 22 148) 2 · [4 + 6 · (3 + 4)] A) 92

D) not a real number

B) 7

C) -10

D) -14

B) 50

C) 136

D) 140

19

147)

148)

The lengths of the legs of a right triangle are given. Find the hypotenuse. 149) a = 6, b = 8 A) 5 B) 10 C) 7 Simplify the expression. Assume that all variables are positive when they appear. 150) 9y10 A) 3y8

B) 3y10

C) 3y5

Use synthetic division to find the quotient and the remainder. 151) x4 - 4 is divided by x - 2 A) x3 + 2x2 + 4x + 8; remainder 12 C) x3 + 4x2 + 16x + 64; remainder 254

D) 9

D) 9y5

B) x3 + 6x2 + 4x + 2; remainder 12 D) x3 + 2x2 + 4x + 8; remainder 254

Perform the indicated operations and simplify the result. Leave the answer in factored form. 6x + 5 6x - 5 152) 2 2 A) 5

B) 25

C) 0

Use synthetic division to find the quotient and the remainder. 153) 3x3 + 16x2 - 14x - 12 is divided by x + 6

149)

150)

151)

152)

D) 6x

A) -3x2 - 6x - 2; remainder 0

8 B) 3x2 x + - 2; remainder0 3

C) 3x2 - 2x - 2; remainder 0

D)

153)

1 2 8 7 x + x - ; remainder 0 2 3 3

Solve. b, 154) If the three lengths of the sides of a triangle are known, Heron's formula can be used to find its area. If a, 154) and c are the three lengths of the sides, Heron's formula for area is: A = s(s - a)(s - b)(s - c) 1 where s is half the perimeter of the triangle, or s = (a + b + c). 2 Use this formula to find the area of the triangle if a = 7 cm, b = 9 cm and c = 14 cm.

A) 19 3.98891967 sq. cm C) 19 1.99445983 sq. cm

B) 139 11.9993789 sq. cm D) 5 1.92 sq. cm

Use the Distributive Property to remove the parentheses. 155) 7(4x + 8) A) 11x + 15 B) 84x

C) 28x + 56

Factor the expression. Express your answer so that only positive exponents occur. 156) x5/4 - x3/4 A) x3/4 (x1/2 - 1)

B) x3/4 (x1/2 + 1)

C) x3/4 (x1/2 )

20

D) 28x + 8

D) x3/4 (x1/2 - x)

155)

156)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 157) 1 x+6

157)

5

x2 - 36

A)

x-6 5

B)

5 x-6

C) x - 6

D)

x+6 5

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 158) B C 158) A) { } B) {0} C) {1, 2, 3, 5, 7, 9} D) {1, 2, 3, 4, 5, 7, 9} Factor the expression. Express your answer so that only positive exponents occur. 159) x8/5 + x2/5 A) x2/5 (x6/5 )

B) x2/5 (x6/5 + x)

C) x2/5 (x6/5 + 1)

D) x2/5 (x6/5 - 1)

Simplify the expression. 8 2/3 160) 64 A) -

1 4

160) B)

1 6

C)

Find the LCM of the given polynomials. 161) 12x - 7, 12x + 7 A) (12x - 7) or (12x + 7) C) (12x - 7)(12x + 7) Write the number as a decimal. 162) 4.13 × 107 A) 4,130,000

1 2

D)

1 4

161)

B) (12x - 7) D) (12x + 7)

B) 289.1

C) 41,300,000

D) 413,000,000

Tell whether the expression is a polynomial. If it is, give its degree. 163) 6x5 - 4 A) Polynomial; degree 6 C) Polynomial; degree 4

2x - 2 45

1 27

B)

9(6x - 6) 2x - 2

C)

21

12(x - 1)2 225

162)

163)

B) Polynomial; degree 5 D) Not a polynomial

Perform the indicated operations and simplify the result. Leave the answer in factored form. 164) 6x - 6 5

A)

159)

D) 27

164)

Write the statement using symbols. 165) The sum of four times x and 5 decreased by 7 is 8. A) 4(x + 5 - 7) = 8 B) 4(x + 5) - 7 = 8

C) 7 - (4x + 5) = 8

D) 4x + 5 - 7 = 8

Perform the indicated operations and simplify the result. Leave the answer in factored form. 2x2 2x 166) x-1 x-1 A)

167)

2x(x + 1) x-1

10

x2 + 2x

A)

+

B) 0

C) 2x

D)

166)

2x x-1

2 5 + x x+2

7 x

Factor the polynomial. 168) x2 + 7x - 44

A) (x - 11)(x + 4)

167) B)

10 x

C)

B) (x - 11)(x + 1)

2 x

C) (x + 11)(x - 4)

D)

5 x

168)

D) prime

Evaluate the expression. 4 1 169) + 5 14 A)

61 19

169) B)

5 19

C)

1 14

D)

61 70

Perform the indicated operations. Express the answer as a single polynomial in standard form. 170) -8x3 (-10x - 3) A) 80x + 24

B) 80x4 - 3

C) 104x3

D) 80x4 + 24x3

Solve. If necessary, round to the nearest tenth. 171) If a flagpole 9 feet tall casts a shadow that is 12 feet long, find the length of the shadow cast by an antenna which is 18 feet tall. A) 6 ft B) 13.5 ft C) 21 ft D) 24 ft Simplify the expression. Assume that all variables are positive when they appear. 3 3 172) 27 + 12 - 18 3 3 3 3 A) 15 18 B) 27 + 12 - 18 C) 15 - 2 9

2 9

B)

1 9

C)

22

1 6

170)

171)

172) D) 15 -

What number should be added to complete the square of the expression? 2 173) x2 + x 3 A)

165)

3

18

173) D)

4 9

Simplify the expression. 174) 2164/3 A) 279,936

B) 1,296

C) 7,776

D) 46,656

174)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 175) (x - 8y)(-5x + 6y) 175) 2 2 2 2 A) x + 46xy + 46y B) x + 46xy - 48y C) -5x2 + 46xy - 48y2

D) -5x2 + 46xy + 46y2

Evaluate the expression using the given values. 176) -10x + y x = -3, y = -3 A) -6 B) 27

C) -13

D) -33

Write the number in scientific notation. 177) 0.000000666012 A) 6.66012 × 107 B) 6.66012 × 10-6

C) 6.66012 × 106

D) 6.66012 × 10-7

177)

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. 2 178) x+2 A) x = 2

B) x = 0

C) x = -2

B)

C)

D)

179)

Use synthetic division to determine whether x - c is a factor of the given polynomial. 180) x3 - 11x2 + 12x + 80; x + 5 A) Yes

180)

B) No

Write the statement as an inequality. 181) x is less than 5 A) x 5 B) x > 5

C) x < 5

178)

D) none

On the real number line, label the points with the given coordinates. 4 4 179) , 3 3

A)

176)

D) x 5

181)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 182) x-2/5 · x3/5 182) A) x6/5

B) x5/6

C) x1/5

23

D) x-1/5

Simplify the expression. Assume that all variables are positive when they appear. 3 183) -27x21 A) -3x18 B) -3x7 C) 3x7

D) -3x21

183)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 184) (-5x3 )-1 184)

A) -

1

125x3

B)

1

C) -

125x3

1

5x3

D)

1

5x3

Perform the indicated operations and simplify the result. Leave the answer in factored form. 185) 7 -7 3x - 1

185)

7 +7 3x - 1

A)

3x 2 - 3x

Write the number as a decimal. 186) 7.306 × 10-6 A) 0.000007306

B)

2-x x

C)

B) 0.00007306

2 - 3x 3x

C) -7,306,000

D)

2 + 3x 3x

D) 0.0000007306

Solve. If necessary, round to the nearest tenth. 187) A flagpole casts a shadow of 20 feet. Nearby, a 5-foot tree casts a shadow of 3 feet. What is the height of the flagpole? A) 0.8 ft B) 33.3 ft C) 300 ft D) 12 ft Write the statement as an inequality. 188) y is greater than -92 A) y > -92 B) y -92

C) y -92

D) y < -92

Factor completely. If the polynomial cannot be factored, say it is prime. 189) x4 + 2x2 - 35 A) (x2 + 5)(x2 + 7)

B) (x2 + 5)(x2 + 1)

C) (x2 - 5)(x2 + 7)

Write the number in scientific notation. 190) 10,913 A) 1.0913 × 104 B) 1.0913 × 101

C) 1.0913 × 105

24

186)

187)

188)

189) D) Prime

190) D) 1.0913 × 10-4

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 - 5x + 4 x2 - 11x + 30 · 191) x2 - 8x + 15 x2 - 14x + 40 A)

(x - 1) (x - 10)

B)

(x2 - 5x + 4)(x2 - 11x + 30) (x2 - 8x + 15)(x2 - 14x + 40)

C)

(x + 1)(x + 6) (x + 3)(x + 10)

D)

(x - 1)(x - 6) (x - 3)(x - 10)

Factor the sum or difference of two cubes. 192) 125x3 + 1 A) (5x + 1)(25x2 - 5x - 1) C) (5x + 1)(25x2 - 5x + 1)

192)

B) (5x + 1)(25x2 + 1) D) (5x + 1)(25x2 + 5x + 1)

Factor completely. If the polynomial cannot be factored, say it is prime. 193) 15x4 + 10x2 - 6x2 - 4 A) (15x2 + 2)(x2 - 2)

D) (5x4 - 2)(3x + 2)

Find the value of the expression using the given values. x=9 194) ( x)2 A) 81

193)

B) (5x2 - 2)(3x2 + 2)

C) (5x2 + 2)(3x2 - 2)

191)

1 B) 9

1 C) 81

194) D) 9

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 195) (x + 7y)(x + 11y) 195) 2 2 A) x + 18xy + 77y B) x + 18xy + 77y C) x2 + 15xy + 77y2

D) x2 + 18xy + 18y2

Factor completely. If the polynomial cannot be factored, say it is prime. 196) (7 - x)3 - x3 A) (7 + 2x)(x2 - 7x + 49) C) (7 - 2x)(x2 - 7x + 49)

196)

B) (7 - 2x)(3x2 - 7x + 49) D) (7 - x)(x2 - 7x + 49)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 197) x2 - 14x + 49

197)

2x - 14 6x - 42 12

A)

x2 - 14x + 49 (x - 7)2

B)

(x - 7)2 4

C) 1

Find the LCM of the given polynomials. 198) x2 + 12x + 36, x2 + 6x A) x(x + 6)

B) x(x + 6)2

C) (x + 6)2 25

D) 12

198) D) x(x + 1)(x + 6)

Simplify the expression. Assume that all variables are positive when they appear. 199) (9 7)(9 70) A) 81 490 B) 3,969 10 C) 567 10

199) D) 567 70

Solve. If necessary, round to the nearest tenth. 200) If a tree 42.5 feet tall casts a shadow that is 17 feet long, find the height of a tree casting a shadow that is 7 feet long. A) 103.2 ft B) 17.5 ft C) 2.8 ft D) 32.5 ft Evaluate the expression. 9 13 201) 6 7 A)

21 26

201)

B)

54 91

C)

26 21

D)

91 54

Multiply the polynomials. Express the answer as a single polynomial in standard form. 202) (3x - 4y)2 A) 3x2 - 24xy + 16y2

202)

B) 9x2 - 24xy + 16y2

C) 3x2 + 16y2

D) 9x2 + 16y2

Insert <, >, or = to make the statement true. -92 203) -38 A) =

203) B) >

C) <

Evaluate the expression using the given values. 4xy + 15 x = 5, y = 7 204) x A) 7

204)

B) 31

C) 3

D) 43

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 205) 2(4x3 + x2 - 1) - 7(4x3 - 4x + 2) A) -20x3 + 2x2 + 28x - 16

205)

B) -20x3 + x2 + 28x - 16

C) -20x3 + 2x2 - 28x - 16

D) -20x3 + 2x2 + 28x + 16

List all the elements of B that belong to the given set. 8 9 206) B = 13, 8, -2, 0, , - , 2.1 9 8 Integers A) {13, -2}

200)

206)

B) {13, 0}

C) {13, -2, 0}

Find the quotient and the remainder. 207) 7x3 + 24x2 - 12x + 16 divided by x + 4 A) 7x2 - 4x + 4; remainder 0 C) 7x2 + 4x + 4; remainder 0

D) {13, 0,

B) x2 + 5x + 6; remainder 0 D) x2 + 4x + 7; remainder 0

26

8}

207)

Simplify the expression. Assume that all variables are positive when they appear. 24 208) 3 x30 2

3

3 A) 27 x

Simplify the expression. 209) 271/3 A) 243

3

2

3

24 B) 10 x

C)

3 10 x

B) 9

C) 81

Factor completely. If the polynomial cannot be factored, say it is prime. 210) 10y2 + 45y - 25 A) (10y - 5)(y + 5)

B) 5(2y - 1)(y + 5)

C) 5(2y + 1)(y - 5)

208) D) 3

24 x30

D) 3

D) prime

Simplify the expression. Assume that all variables are positive when they appear. 4 211) 625 A) 625 B) 5 C) -5 D) not a real number Use the Distributive Property to remove the parentheses. 212) (x + 4)(x - 4) A) x2 + 8x - 16 B) x2 - 8

C) x2 - 16

209)

210)

211)

D) x2 - 8x - 16

212)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 213) (3x2/3 )(6x3/2 ) 213) A) 18x5/6

B) 18x13/6

C) 18x13/5

D) 18x2/3

Simplify the expression. Assume that all variables are positive when they appear. 3 214) 511 A) 63

B) 8

C) 23

214) D) ±8

Factor completely. If the polynomial cannot be factored, say it is prime. 215) (x + 4)2 - 5(x + 4) + 6

B) (x2 + 4x - 3)(x2 + 4x - 2)

A) (x + 1)(x + 2)

D) (x2 - 4x + 3)(x2 - 4x + 2)

C) (x + 7)(x + 6) 216) 15x6 + 8x3 - 16 A) (5x3 + 4)(3x3 - 4)

216)

B) 15(x3 - 4)(x3 + 4)

C) (3x3 + 1)(5x3 - 16)

D) (3x3 + 4)(5x3 - 4)

Simplify the expression. Assume that all variables are positive when they appear. 217) 5x2 - 2 45x2 - 3 45x2 A) -14x 5

215)

B) -5x 36

C) -14x 36

27

217) D) -5x 5

Tell whether the expression is a polynomial. If it is, give its degree. 218) 1 - 3x A) Polynomial; degree 3 B) Polynomial; degree -3 C) Polynomial; degree 1 D) Not a polynomial Simplify the expression. Assume that all variables are positive when they appear. 3 3 219) 20 2 - 4 128 3 3 3 3 A) 16 2 B) -4 2 C) 20 2 - 4 128 Use the formula C =

218)

219) D) 4

3

2

5 (F - 32) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of the 9

Fahrenheit temperature. 220) F = -13° A) -30° C

B) -20° C

C) -15° C

Find the quotient and the remainder. 221) x4 + 81 divided by x - 3

A) x3 + 3x2 + 9x + 27; remainder 162 C) x3 - 3x2 + 9x - 27; remainder 162

B) x3 + 3x2 + 9x + 27; remainder 0 D) x3 + 3x2 + 9x + 27; remainder 81

Use a calculator to evaluate the expression. Round the answer to three decimal places. 222) -(-1.57)-2 A) -2.465

D) -25° C

B) 2.465

C) -0.406

D) 0.406

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 223) (5x5 + 5x3) + (3x5 + 2x3 + 5) A) -5x5 + 7x3 + 5x

B) 8x5 + 7x3 + 5

C) 12x9

D) 5x + 7x5 - 3x3

Solve the problem. 224) Find the volume V of a sphere of radius 2.5 yd. Use 3.14 for . If necessary, round the result to the nearest tenth. A) V = 36.8 yd3 B) V = 65.4 yd3 C) V = 26.2 yd3 D) V = 523.3 yd3 Perform the indicated operations and simplify the result. Leave the answer in factored form. 225) 5 +4 x

220)

221)

222)

223)

224)

225)

25 - 16 x2

A)

x 5x - 4

B)

1 5 - 4x

C)

Evaluate the expression using the given value of the variables. 226) (x + 4y)2 for x = 2, y = 2 A) 20

B) 35

28

1 5x - 4

C) 100

D)

x 5 - 4x

D) 10

226)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 3x + 5 5x - 8 + 227) x 9x A)

22x + 37 9x

Evaluate the expression. 228) 3 + 1 - 9 A) -7

B)

32x + 37 9x

C)

B) 13

32x + 37 9x2

D)

C) -5

32x - 53 9x

D) 11

Perform the indicated operations and simplify the result. Leave the answer in factored form. x-1 5x + 2 + 229) x2 - 7x + 12 x2 - 5x + 4 A)

6x + 1

2x2 - 12x + 16

C) 6x + 1

B)

6x2 - 15x - 5 (x - 4)(x - 3)(x - 1)

D)

6x2 - 15x - 5 (x + 4)(x + 3)(x + 1)

Find the value of the expression using the given values. x = -1, y = 4 230) yx A) 4

1 B) 4

1 D) 4

C) -4

Factor the sum or difference of two cubes. 231) 8 - x3 A) (2 - x)(4 + 2x + x2 )

A) <

A) 16,384

229)

230)

D) (2 + x)(4 - 2x + x2 )

Insert <, >, or = to make the statement true. 1 0.11 232) 9

Simplify the expression. 233) 2565/4

228)

231)

B) (2 - x)(4 + x2 )

C) (2 + x)(4 - x2 )

227)

232) B) =

C) >

B) 1,024

C) 65,536

D) 262,144

233)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. (4x3/4 )3 234) 234) x-6/5 A) 4x69/20 Factor the difference of two squares. 235) 4x2 - 49 A) (2x + 7)(2x - 7)

B) 4x21/20

B) (2x - 7)2

29

C) 64x21/20

D) 64x69/20

C) (4x + 1)(x - 49)

D) (2x + 7)2

235)

Factor completely. If the polynomial cannot be factored, say it is prime. 236) (2x - 2)3 + 125 A) (2x + 3)(4x2 + 2x + 19) C) (2x + 3)(4x2 + 2x + 39)

Write the statement using symbols. 237) The quotient 18 divided by 9 is 2. A) 18 - 9 = 9

Factor the polynomial. 238) x2 - 3x - 54

A) (x + 6)(x - 9)

236)

B) (2x + 3)(4x2 - 18x + 39) D) (2x - 7)(4x2 + 2x + 19)

B) 18 · 9 = 162

C) 18 + 9 = 27

18 =2 D) 9

B) (x - 6)(x + 1)

C) (x - 6)(x - 9)

D) prime

237)

238)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 4 239) 239) x

A) Monomial; variable x; coefficient 4; degree 0 B) Monomial; variable x; coefficient 4; degree -1 C) Monomial; variable x; coefficient 4; degree 1 D) Not a monomial Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 9x-3 -1 240) 240) 8y-3

A)

8x3 9y3

B)

8y3 9x3

C)

9x31 8y31

Simplify the expression. Assume that all variables are positive when they appear. 241) 7 12 - 2 192 A) 30 3 B) 2 3 C) -2 3

D)

9x3 8y3

241) D) -30 3

Solve the problem. 242) Find the volume V of a right circular cylinder with radius 10 cm and height 20 cm. Express the answer in terms of . A) V = 100 cm3 B) V = 200 cm3 C) V = 2,000 cm3 D) V = 500 cm3

242)

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 243) (7x + y)(7x - y) 243) 2 2 2 2 A) 49x - 14xy - y B) 49x - y

C) 14x2 - y2

D) 49x2 + 14xy - y2

30

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 244) 3x2 - 5 244)

A) Monomial; variable x; coefficient 3; degree 1 B) Monomial; variable x; coefficient 3; degree 2 C) Monomial; variable x; coefficient 5 ; degree 2 D) Not a monomial

Solve the problem. 245) Find the surface area S of a rectangular box with length 5 ft, width 3 ft, and height 2 ft. A) 62 ft2 B) 56 ft2 C) 31 ft2 D) 72 ft2 Factor completely. If the polynomial cannot be factored, say it is prime. 246) (x - 2)2 - 9 A) (x - 1)(x + 5)

B) (x - 5)2

246)

C) (x + 7)(x - 11)

D) (x + 1)(x - 5)

List all the elements of B that belong to the given set. 0 247) B = {3, 5, -6, 0, , 9, 0.12, -5 , 0.999...} 8

247)

Rational numbers 0 A) 3, -6, 0, , 9, 0.12, -5 , 0.999... 8

C) 3, -6, 0,

245)

0 , 0.12 8

B) 3, -6, 0,

0 , 0.12, 0.999... 8

D) 3, -6, 0,

0 , 8

9, 0.12, 0.999...

Perform the indicated operations and simplify the result. Leave the answer in factored form. 248) 4x2 - 49

248)

x2 - 16 2x - 7 x-4

A)

2x - 7 x-4

B)

(2x - 7)(4x2 - 49) (x2 - 4)(x -4)

C)

x+4 2x + 7

D)

2x + 7 x+4

Find the quotient and the remainder. 249) x4 + 8x2 + 9 divided by x2 + 1

249)

A) x2 + 7; remainder 2 C) x2 + 7x +

B) x2 + 7x + 1; remainder 2

1 ; remainder 0 2

D) x2 + 7; remainder 0

31

Simplify the expression. 25 3/2 250) 9 A)

27 125

250) B) -

125 27

C)

125 27

D) -

27 125

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 251) (3x + 10y)(-3x + 7y) 251) A) -9x2 - 9xy - 9y2 B) -9x2 + 21xy + 70y2 C) -9x2 - 9xy + 70y2

D) -9x2 - 30xy + 70y2

Multiply the polynomials. Express the answer as a single polynomial in standard form. 252) (x + 12)(x - 12) A) x2 - 24 B) x2 + 24x - 144 C) x2 - 144 D) x2 - 24x - 144 Perform the indicated operations and simplify the result. Leave the answer in factored form. x 10 253) 2 11 A)

x - 10 22

B)

11x - 20 22

C)

Use the Distributive Property to remove the parentheses. 254) 5x(x + 9) A) 45x2 B) 5x2 + 9

x - 10 13

C) 5x2 + 45x

D)

253) 11x + 20 20

D) x2 + 45x

Factor the expression. Express your answer so that only positive exponents occur. 255) 10x1/7 - 13x-4/7 A) x1/3(10 - 13x5/13) C) x-4/7 (10x5/7 - 13x)

B) x = -8

C) x = 8

257)

B) 10x2 - 220x + 121 D) 100x2 - 220x + 121

Simplify the expression. Assume that all variables are positive when they appear. 3 3 258) 4 64x + 4 8x 3 3 3 A) 6 x B) 4 72x C) 24 x

32

256)

D) none

Multiply the polynomials. Express the answer as a single polynomial in standard form. 257) (10x - 11)2 A) 100x2 + 121 C) 10x2 + 121

254)

255)

B) x-4/7 (10x5/7 - 13) D) x1/7 (10x5/7 - 13x5/13)

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x 256) x-8 A) x = 0

252)

258) D) 24x

Perform the indicated operations and simplify the result. Leave the answer in factored form. 259) 3 5 + x x2

259)

9 25 2 x x

A)

3x2 + 5 9 - 25x

B)

1 3x - 5

C)

1 3 - 5x

D)

3x + 5 9 - 25x

Evaluate the expression. 4 2 1 + 260) · 5 5 10 A)

261)

8 25

260) B) 2

C)

1 10

D)

2 5

5+2 9+2

261)

A) 1

B)

Factor the polynomial by grouping. 262) x2 + 4x + 7x + 28 A) (x - 4)(x + 7)

3 11

C)

B) (x + 4)(x + 7)

7 11

C) (x - 4)(x - 7)

Find the quotient and the remainder. 263) x4 + 625 divided by x - 5

A) x3 + 5x2 + 25x + 125; remainder 625

D)

D) prime

B) x3 - 5x2 + 25x - 125; remainder 1,250

C) x3 + 5x2 + 25x + 125; remainder 1,250

C)

262)

263)

D) x3 + 5x2 + 25x + 125; remainder 0

Simplify the expression. 27 -4/3 264) 64 A) -

3 7

264)

2.849934139e+15 9.007199255e+15

B)

9.007199255e+15 2.849934139e+15

2.849934139e+15 9.007199255e+15

D) not a real number

Find the quotient and the remainder. 265) 5x3 - 7x2 + 7x - 8 divided by 5x - 2 A) x2 + x -1; remainder -6

B) x2 - x + 1; remainder -6

C) x2 - x + 1; remainder 10

265)

D) x2 - x + 1; remainder 6

Use synthetic division to determine whether x - c is a factor of the given polynomial. 266) 4x3 - 17x2 + 23x - 10; x - 5 A) Yes

B) No

33

266)

Write the number as a decimal. 267) 4.464 × 10-5 A) 0.0004464

B) 0.000004464

C) -446,400

D) 0.00004464

Solve the problem. 268) Find the area of the shaded region. Express the answer in terms of .

267)

268)

5 5

A)

25 - 25 square units 4

B)

C) 5 - 5 square units

25 2

- 25 square units

D) 25 square units

What number should be added to complete the square of the expression? 269) x2 - x A) 4

B) 1

C)

1 2

D)

1 4

Insert <, >, or = to make the statement true. 270) 3.14 A) <

270) B) =

C) >

Multiply the polynomials. Express the answer as a single polynomial in standard form. 271) (13y + x)(13y - x) A) 169y2 - 26xy - x2 B) 26y2 - x2 C) 169y2 - x2

Simplify the expression. 272) 2 -5 · 2 2 A) 4

269)

271)

D) 169y2 + 26xy - x2

1 B) 16

1 C) 8

Multiply the polynomials. Express the answer as a single polynomial in standard form. 273) (x + 3)3 A) x3 + 3x2 + 3x + 27 C) x3 + 9x2 + 9x + 27

B) x3 + 9x2 + 27x + 27 D) x3 + 9x2 + 3x + 27

34

272) D) 8

273)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 274) A C 274) A) {4, 6, 7, 9} B) {1, 2, 3, 5, 7, 9} C) {1} D) {1, 2, 3, 4, 5, 7, 8, 9} Simplify the expression. 275) -4 2 A) 16

B) -16

C) -8

Factor the sum or difference of two cubes. 276) 512x3 - 343 A) (8x + 7)(64x2 - 56x + 49) C) (8x - 7)(64x2 + 56x + 49)

275)

D) 8

276)

B) (512x - 7)(x2 + 56x + 49) D) (8x - 7)(64x2 + 49)

Simplify the expression. 277) 16-5/4

277)

1 A) 32

C)

B) 32

1 32

278) -321/5 A) -2

D) not a real number

B) -8

C) 32

278)

D) 16

An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. (49 - x2)1/2 + 3x2 (49 - x2 )-1/2 279) 279) 49 - x2

A)

3x2 (49 - x2)3/2

B)

49 - 4x2 (49 - x2)3/2

C)

49 + 2x2 (49 - x2)3/2

D)

3x2 49 - x2

Simplify the expression. Assume that all variables are positive when they appear. 3 280) 343x4y5 3 3 A) 7xy xy B) 2xy xy2 C) 7xy xy2

D) 7xy xy2

Write the number in scientific notation. 281) 754.294 A) 7.54294 × 10-1 B) 7.54294 × 10-2

C) 7.54294 × 101

D) 7.54294 × 102

Evaluate the expression using the given values. 282) |6x + 10y| x = -3, y = -2 A) 18 B) 42

C) 38

D) 2

35

280) 3

281)

282)

List all the elements of B that belong to the given set. 0 283) B = 11, 8, -16, 0, , 0.42 4

283)

Rational numbers 0 8, , 0.42 A) 4

B) {11, 0} D) 11, -16, 0,

C) { 8}

0 , 0.42 4

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 284) 28, 96, 100 284) A) right triangle; 96 B) right triangle; 100 C) right triangle; 28 D) not a right triangle

Solve the problem. 285) The formula v = 2.5r can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the maximum safe speed for a curve in a road with a radius of curvature of 200 feet. A) 14 mph B) 35 mph C) 9 mph D) 22 mph 286) Find the area A of a rectangle with length 7.2 in and width 11.1 in. A) A = 28.8 in2 B) A = 159.84 in2 C) A = 79.92 in2 Express the statement as an equation involving the indicated variables. 287) The area A of a rectangle is the product of its length l and its width w. l A) A = 2(l + w) B) A = lw C) A = w Write the number in scientific notation. 288) 0.0000027813 A) 2.7813 × 10-6 B) 2.7813 × 10-7 Factor the perfect square. 289) 25x2 + 90x + 81 A) (5x - 9)2

C) 2.7813 × 10-5

B) (5x + 9)2

C) (5x - 10)2

D) A = 18.3 in2

C) (3x2 + 6x)(x - 4)

B) 3x(x - 2)(x + 4)

D) A = l + w

D) 2.7813 × 106

288)

289) D) (5x + 9)(5x - 9)

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

Solve the problem. 291) A rectangular patio has dimensions 10 feet by 15 feet. The patio is surrounded by a border with a uniform width of 3 feet. Find the area of the border. A) 114 ft2 B) 186 ft2 C) 84 ft2 D) 162 ft2

36

286)

287)

Factor completely. If the polynomial cannot be factored, say it is prime. 290) 3x3 + 6x2 - 24x A) (x - 2)(3x2 + 12)

285)

291)

Factor the polynomial by grouping. 292) 2x2 + 9x + 18x + 81 A) (2x + 9)(2x + 9)

B) (x + 9)(2x + 9)

C) (2x + 9)(9x + 2)

D) prime

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 - 7x 12 + 293) x-3 x-3 A) x + 3

B) x - 4

C) x - 3

Use synthetic division to find the quotient and the remainder. 294) x3 - x2 + 4 is divided by x + 2 A) x2 - 3x + 6; remainder 2

C) x2 - 3x + 6; remainder -8

Simplify the expression. 295) (-4)3 A) 64

293)

D) x + 4

B) 3x2 - 4x + 2; remainder 0

294)

D) x2 + x + 2; remainder -8

B) -64

C) -12

296) -64-4/3 1 A) 256 C) -

292)

D) 12

295)

296) B) 256

1 256

D) not a real number

Write the number in scientific notation. 297) 0.0000000968011 A) 9.68011 × 108 B) 9.68011 × 10-9

297) C) 9.68011 × 10-8

D) 9.68011 × 10-7

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 298) (6x6 + 8x4 + 7) - (8x6 + 6x4 - 9)

298)

Find the quotient and the remainder. 299) -20x3 - 41x2 - 35x + 5 divided by 5x + 4

299)

A) 16x10

B) -2x6 + 16x4 - 2

C) -2x6 + 2x4 - 2

A) -4x2 - 5x - 3; remainder 20

D) -2x6 + 2x4 + 16

B) x2 - 3; remainder -5

C) -4x2 - 5x - 3; remainder 0

D) -4x2 - 5x - 3; remainder 17

Solve. If necessary, round to the nearest tenth. 300) The zoo has hired a landscape architect to design the triangular lobby of the children's petting zoo. In his scale drawing, the longest side of the lobby is 15 cm. The shortest side of the lobby is 6 cm. The longest side of the actual lobby will be 49 m. How long will the shortest side of the actual lobby be? A) 1.2 m B) 122.5 m C) 19.6 m D) 0.2 m Use the Distributive Property to remove the parentheses. 301) (x - 7)(x - 3) A) x2 - 10x + 21 B) x2 - 10x - 10

C) x2 - 11x + 21 37

D) x2 + 21x - 10

300)

301)

Factor the sum or difference of two cubes. 302) 729y3 - 1 A) (729y - 1)(y2 + 9y + 1) C) (9y + 1)(81y2 - 9y + 1)

302)

B) (9y - 1)(81y2 + 9y + 1) D) (9y - 1)(81y2 + 1)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 303) 8 1x x-

64 x

A) x + 8

304)

303)

B)

1 x+8

C) x - 8

D)

1 x-8

304)

x2 + 9x + 18

x2 + 11x+ 24 x2 + 6x

x2 + 16x + 64

A)

x+8 x

B)

x (x + 8)(x + 3)

C)

x+8 x(x + 8)

D) x + 8

List all the elements of B that belong to the given set. 7 9 305) B = {12, 8, -15, 0, , - , 8.8, 8 , 0.848484...} 9 7 Natural numbers 9 A) 12, 0, 7

305)

B) {12}

C) {12, 0}

Find the quotient and the remainder. 306) x2 + 12x + 27 divided by x + 4 A) x + 8; remainder 0 C) x + 8; remainder -5

D) {-15, 0, 12}

306)

B) x + 9; remainder 0 D) x + 8; remainder 5

Perform the indicated operations and simplify the result. Leave the answer in factored form. 10x2 - 3x - 4 15x2 + 12x · 307) 5x2 - x - 4 1 - 4x2 A)

3x (1 - 2x)(x - 1)

B)

3x(5x + 4) (1 - 2x)(x - 1)

C)

(5x + 4)(5x - 4) (1 - 2x)(x - 1)

D)

3x(5x - 4) (1 - 2x)(x - 1)

Solve the problem. 308) At the beginning of the month, Christopher had a balance of $196 in his checking account. During the next month, he wrote a check for $19, deposited $90, and wrote another check for $180. What was his balance at the end of the month? A) -$87 B) $87 C) $93 D) -$93

38

307)

308)

Evaluate the expression. 5 309) 7 + 6 A)

309)

42 6

B)

47 6

C)

47 5

D)

42 5

Solve the problem. 310) Find the area of the shaded region. Express the answer in terms of .

310)

1 1

square units

B)

1 square units 2

C) 1 square units

D)

1 4

A)

1 2

square units

Find the value of the expression using the given values. x = -3, y = 1 311) x2 + y2 A) 4

B)

311)

10

C) 3

D) -2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8 - x 2x + 4 312) x-2 2-x A) -

x+4 x-2

B)

x+4 x-2

C)

x + 12 x-2

D) -

Insert <, >, or = to make the statement true. -6 313) -5 A) <

312) x + 12 x-2

313) B) =

C) >

Find the quotient and the remainder. 314) x2 + 10x + 16 divided by x + 8 A) x3 - 8; remainder 0

B) x2 + 2; remainder 0

C) x - 8; remainder 0

D) x + 2; remainder 0

39

314)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 4x-1 -3 315) 315) 5y-1

A)

64x3 125y3

B)

125y3 64x3

C)

64y3 125x3

D)

Express the statement as an equation involving the indicated variables. 316) The perimeter P of a rectangle is twice the sum of its length l and its width w. A) P = l + w B) P = 2(l + w) C) P = lw An expression that occurs in calculus is given. Factor completely. 317) (2x + 1)2 + 3(2x + 1) - 4 A) 2x - 6

B) 2x(2x + 5)

C) 2x - 1

125x3 64y3

D) P = 2lw

D) 2x(2x + 1)

Simplify the expression. Assume that all variables are positive when they appear. 3 318) x23 A) x

3

x20

B)

3

x23

C) x7

3

x2

1 x-8

B)

x(x + 7) x-8

C)

D) x9

x

D)

x2 + 15x + 56

319)

x x-8

Insert <, >, or = to make the statement true. 7 320) 2.64 A) =

320) B) <

C) >

Simplify the expression. Assume that all variables are positive when they appear. 11 321) 3 y21 A)

3

11 y7

Simplify the expression. 322) 1,4441/2 A) 38

B)

317)

318)

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 + 14x + 48 x2 + 7x · 319) x2 + 15x + 56 x2 - 2x - 48 A)

316)

11 y7

C) 3

B) 19

11 y21

C) 152

321)

D)

3

11 18 y

D) 76

322)

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 323) (x - 9y)2 323)

A) x2 - 9xy + 81y2 C) x2 - 18xy + 81y2

B) x2 - y2 D) x2 + 18xy + 81y2

40

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 324) 6, 8, 12 324) A) right triangle; 6 B) right triangle; 8 C) right triangle; 12 D) not a right triangle

Simplify the expression. Assume that all variables are positive when they appear. 325) y7 A)

y7

B) y3 y

C) y6 y

Use synthetic division to find the quotient and the remainder. 326) x2 + 12x + 30 is divided by x + 4 A) x + 8; remainder -2 C) x + 8; remainder 2

325) D) y y5

326)

B) x + 8; remainder 0 D) x + 9; remainder 0

Reduce the rational expression to lowest terms. 2x2 - 3x - 2 327) 3x2 - 11x + 10 A)

2x+ 1 3x - 5

B)

327)

x- 1 x+5

C)

Use the Distributive Property to remove the parentheses. 328) 8(x + 7) A) 8x + 7 B) 56x

x+2 x-4

C) x + 56

Write the statement using symbols. 329) The product of 30 and 6 equals 180. 30 =5 A) B) 30 + 6 = 36 6

D)

2x - 2 3x + 2

D) 8x + 56

329) C) 30 · 6 = 180

D) 30 - 6 = 24

Solve the problem. 330) Find the area A and circumference C of a circle of radius 11 yd. Express the answer in terms of . A) A = 22 yd2 ; C = 22 yd B) A = 44 yd2; C = 11 yd C) A = 121 yd2 ; C = 22 yd

330)

D) A = 484 yd2 ; C = 11 yd

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 331) -1(x2 + 6x + 1) + (3x2 - x - 4) A) 2x2 - 7x - 3

328)

B) -4x2 - 7x - 5

C) 2x2 - 6x - 5

Solve the problem. 332) Find the area A of a triangle with height 2 cm and base 5 cm. A) A = 5 cm2 B) A = 10 cm C) A = 5 cm Factor completely. If the polynomial cannot be factored, say it is prime. 333) x9 + 1 A) (x3 + 1)(x6 - x3 + 1) C) (x - 1)(x + 1)(x6 - x3 + 1)

D) 2x2 - 7x - 5

D) A = 10 cm2

B) (x - 1)(x2 + x + 1)(x6 + x3 + 1) D) (x + 1)(x2 - x + 1)(x6 - x3 + 1)

41

331)

332)

333)

Simplify the expression. Assume that all variables are positive when they appear. 3 334) -729 A) 27

B) 81

C) ±9

Write the statement using symbols. 335) Three times the difference of x and 8 is -10. A) 3x - 8 = -10 B) 3(x - 8) = -10

A) (2 - x)2

D) -9

C) 3 - x - 8 = -10

Factor the difference of two squares. 336) 4 - x2

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

Multiply the polynomials. Express the answer as a single polynomial in standard form. 337) (a - b)2 A) a 2 - 2ab - b2

B) a 2 - ab + b2

D) 3 + x - 8 = -10

C) a 2 + 2ab + b2

D) a 2 - 2ab + b2

List all the elements of B that belong to the given set. 0 338) B = 12, 6, -5, 0, 8 Real numbers

A) 12,

6, -5, 0,

0 8

B) 12, -5, 0,

0 8

D) 12, -5

Perform the indicated operations and simplify the result. Leave the answer in factored form. 339) 5 +5 x 5 -5 x x2

5 - x2

337)

338)

C) {12, -5, 0}

A)

335)

336)

C) (2 + x)2

B) prime

334)

B)

1+x 1-x

C)

42

5(1 + x) 1-x

D) 5 - x2

339)

Solve the problem. 340) Find the perimeter. Approximate the result to the nearest tenth using 3.14 for .

340)

6 cm

3 cm A) 19.7 cm

B) 27.4 cm

C) 22.7 cm

D) 24.4 cm

An expression that occurs in calculus is given. Reduce the expression to lowest terms. (x2 + 2) · 3 - (3x + 4) · 3x 341) (x2 + 2)3 A)

-9x2 - 12x + 3 (x2 + 2)2

B)

-6x2 - 12x + 6 (x2 + 2)3

C)

6x2 + 12x - 6 (x2 + 2)3

D)

-12x2 - 12x + 6 (x2 + 2)3

341)

Graph the numbers on the real number line. 342) x 4

342)

A)

B)

C)

D)

Use synthetic division to determine whether x - c is a factor of the given polynomial. 343) 3x3 - 20x2 - 9x + 126; x - 6 A) Yes

343)

B) No

Express the statement as an equation involving the indicated variables. 344) The volume V of a cube is the cube of the length x of a side. 3 A) V = 3x B) V = x C) V = x2 43

344) D) V = x3

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 345) 10x4 345)

A) Monomial; variable x; coefficient 4; degree 10 B) Monomial; variable x; coefficient 10; degree 4 C) Monomial; variable x; coefficient 4; degree 0 D) Not a monomial

Simplify the expression. Assume that all variables are positive when they appear. -9 346) 28 A) -

9 7 7

B) -

9 7 14

C) -9 7

346) D) -28

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 + 14x + 45 x2 + 8x · 347) x2 + 17x + 72 x2 + 12x + 35 A)

1 x+7

B)

x x+7

C)

x 2 x + 17x + 72

Write the number in scientific notation. 348) In a certain city, the bus system carried a total of 11,800,000,000 passengers. A) 1.18 × 1011 B) 11.8 × 1010 C) 1.18 × 1010

D)

x2 + 8x x+7

D) 1.18 × 109

Multiply the polynomials. Express the answer as a single polynomial in standard form. 349) (9x + 10)2 A) 9x2 + 180x + 100 C) 9x2 + 100

347)

348)

349)

B) 81x2 + 100 D) 81x2 + 180x + 100

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. x-3y8 350) 350) x5 y11

A)

y3 x8

B)

1 x8 y3

C) x8 y3

D)

x8 y3

Solve the problem. 351) Find the area A and circumference C of a circle of diameter 22 in.. Use 3.14 for . Round the result to the nearest tenth. A) A = 69.1 in.2 ; C = 69.1 in. B) A = 138.2 in.2 ; C = 34.5 in. C) A = 379.9 in.2 ; C = 69.1 in.

351)

D) A = 1,519.8 in.2 ; C = 34.5 in.

Factor the sum or difference of two cubes. 352) 8 - 125x3 A) (8 - 5x)(1 + 10x + 25x2 )

B) (2 - 5x)(4 + 25x2 )

C) (2 + 5x2 )(4 - 10x + 25x2 )

D) (2 - 5x)(4 + 10x + 25x2 ) 44

352)

Use the Distributive Property to remove the parentheses. 1 1 353) 4 x + 2 8 A) 2x +

1 4

B) 2x +

353)

1 8

C)

1 1 x+ 2 2

D) 2x +

1 2

Factor completely. If the polynomial cannot be factored, say it is prime. 354) 15x2 - 9xy - 20xy + 12y2

354)

Simplify the expression. 355) 16-7/4

355)

A) (15x - 4y)(x - 3y) C) (3x + 4y)(5x - 3y)

A) -128

B) (3x - 4)(5x - 3) D) (3x - 4y)(5x - 3y)

B)

1 128

C) -

1 128

D) -16,384

Evaluate the expression. 9-6 356) 6-9 A) 3

356) B) -

3 2

C) -1

D)

3 2

What number should be added to complete the square of the expression? 4 357) x2 - x 5 A)

4 25

B)

16 25

C) -

1 5

357) D) -

8 25

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 + 11x + 18 x2 + 14x + 48 · 358) x2 + 8x + 12 x2 + 17x + 72 A)

x+6 x+8

B)

x+9 x+6

C)

1 x+8

358)

D) 1

Use synthetic division to determine whether x - c is a factor of the given polynomial. 359) x3 + 12x2 + 29x - 42; x - 4 A) Yes

359)

B) No

Multiply the polynomials. Express the answer as a single polynomial in standard form. 360) (13x + 6)(13x - 6) A) 169x2 + 156x - 36 B) 169x2 - 36

360)

Simplify the expression. Assume that all variables are positive when they appear. 3 361) 2x2 - 375 + 242x2 3 3 A) 12x 2 - 5 15 B) 12x 2 - 5 3 C) 12 2x2 - 375

361)

C) 169x2 - 156x - 36

D) x2 - 36

45

D) 11x 2 - 5

3

3

362)

16 11

A) 125

362) B) 4 11

C)

16 11 11

D)

4 11 11

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 363) x3/8 · x5/8 363) A) x

B) x15/64

Write the number in scientific notation. 364) 308.57 A) 3.0857 × 10-2 B) 3.0857 × 102

1 x

C) x15/8

D)

C) 3.0857 × 10-1

D) 3.0857 × 101

Approximate the number rounded to three decimal places, and truncated to three decimal places. 24 365) 7 A) 3.429 3.428

B) 3.43 3.429

C) 3.429 3.429

365)

D) 3.43 3.428

Tell whether the expression is a polynomial. If it is, give its degree. 366) -2y5 - 3 A) Polynomial; degree 3 C) Polynomial; degree 5

364)

366)

B) Polynomial; degree -2 D) Not a polynomial

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 3x6 367) 367) y2

A) Monomial; variables x, y; coefficient 3; degree 2 B) Monomial; variables x, y; coefficient 3; degree 6 C) Monomial; variables x, y; coefficient 3; degree 4 D) Not a monomial Evaluate the expression using the given value of the variables. 368) 4x2 + 5y2 for x = -3, y = 3 A) -9

B) 51

C) 81

D) 33

Perform the indicated operations and simplify the result. Leave the answer in factored form. 369) x+6 x-6 + x-6 x+6 x+6 x-6 x-6 x+6

A) 1

B)

x2 + 36 12x

C)

46

(x + 6)2 12x

D)

(x + 6)3 24x(x + 7)

368)

369)

370)

1 3 (x + 5)(x + 4) (x + 4)(x + 7)

370)

A)

-2(x + 6) (x + 5)(x + 4)(x + 7)

B)

2(2x + 11) (x + 5)(x + 4)(x + 7)

C)

2(x + 4) (x + 5)(x + 4)(x + 7)

D)

-2(x + 4) (x + 5)(x + 4)(x + 7)

Use the given real number line to compute the distance. 371) Find d(A, B)

A) 3 Factor the polynomial. 372) x2 - x - 35

A) (x - 35)(x + 1)

371)

B) 1

C) -2

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

C) (x + 5)(x - 7)

D) 2

D) prime

The triangles are similar. Find the missing length x and the missing angles A, B, C. 373) 13° 27° 48 7 21 140°

A) x = 16; A = 140; B = 13; C = 27 C) x = 48; A = 13; B = 27; C = 140

373)

B) x = 16; A = 27; B = 13; C = 140 D) x = 48; A = 27; B = 13; C = 140

Factor completely. If the polynomial cannot be factored, say it is prime. 374) 3x2 - 75 A) 3(x + 5)(x - 5) 375) x3 + 12x2 + 36x A) x(x - 6)2

B) 3(x + 5)2

C) 3(x - 5)2

374) D) prime 375)

B) x(x + 6)2

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

D) prime

Perform the indicated operations and simplify the result. Leave the answer in factored form. 7x 5 + 376) x-8 8-x A)

2x x-8

Factor the perfect square. 377) x2 + 40x + 400 A) (x + 20)(x - 20)

B)

372)

7x - 5 x-8

C)

B) (x + 20)2

7x + 5 x-8

C) (x - 20)2 47

D)

376)

7x - 5 8-x

D) x2 + 40x + 400

377)

Factor the polynomial. 378) 20z 2 - 3z - 9

A) (20z - 3)(z + 3)

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

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

Factor completely. If the polynomial cannot be factored, say it is prime. 379) 10x2 - 34x + 28 A) (5x - 7)(2x - 2)

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

C) 2(5x - 7)(x - 2)

Write the number in scientific notation. 380) A business projects next year's profits to be $741,000,000. A) 7.41 × 107 B) 7.41 × 109 C) 7.41 × 108

D) prime

D) prime

B)

11

C)

11 11

D) 7.41 × 10-9

381) D) 11 11

Find the LCM of the given polynomials. 382) x2 - 5x - 36, x2 - 16, x2 - 13x + 36

382)

A) (x - 9)(x + 4) C) (x + 9)(x - 4)2

B) (x - 9)(x + 4)(x - 4) D) (x + 9)(x + 4)(x - 4)

Simplify the expression. Assume that all variables are positive when they appear. 3 383) - -8x12y24 A) -2x12y8

Factor the polynomial. 384) 15z 2 - 4z - 4

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

B) 4x4 y8

C) 2x4 y12

D) 2x4 y8

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

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

D) prime

Simplify the expression. Assume that all variables are positive when they appear. 56x5 y6 385) 2y4 A) 28xy x

379)

380)

Simplify the expression. Assume that all variables are positive when they appear. 1 381) 11 A) 11

378)

B) 2x2 y 7x

C) 4x2 y 7x

383)

384)

385) D) 2x4 y2 7xy

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 386) (x - y)2 386)

A) x2 - 2x2 y2 + y2

B) x2 - xy + y2

C) x2 - y2

D) x2 - 2xy + y2

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 387) 15, 36, 39 387) A) right triangle; 36 B) right triangle; 39 C) right triangle; 15 D) not a right triangle

48

Factor the difference of two squares. 388) 36x2 - 1 A) (6x - 1)(6x + 1)

B) (6x - 1)2

C) prime

Find the LCM of the given polynomials. 389) x, x + 4 A) x2 (x + 4) B) x

D) (6x + 1)2

389) C) x(x + 4)

D) x + 4

Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet. 390) A person who is 5 feet tall is standing on the beach and looks out onto the ocean. Suddenly, a ship appears on the horizon. How far is the ship from the shore? Round to the nearest tenth of a mile. A) 5,600.3 mi B) 3.9 mi C) 2.7 mi D) 199.1 mi Write the statement using symbols. 391) The difference 21 less 7 equals 14. 21 =3 A) 21 + 7 = 28 B) 7 Factor the polynomial. 392) 20z 2 + 7z - 6

A) (4z - 3)(5z + 2)

390)

391)

B) (20z + 3)(z - 2)

C) 21 - 7 = 14

D) 21 · 7 = 147

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

D) prime

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 393) (6x5 - 12x3 - 8) - (8x3 + 3x5 - 2) A) 3x5 - 20x3 - 10

388)

B) 3x5 - 9x3 - 10

Write the number in scientific notation. 394) 33,000,000 A) 3.3 × 10-7 B) 3.3 × 107

C) -23x8

D) 3x5 - 20x3 - 6

C) 3.3 × 10-8

D) 3.3 × 108

Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet. 395) A guard tower at a state prison stands 117 feet tall. How far can a guard see from the top of the tower? Round to the nearest tenth of a mile. A) 969.7 mi B) 18.7 mi C) 13.2 mi D) 5,600.3 mi Evaluate the expression using the given values. 396) 4 x + 5 y x = 9, y = -6 A) -66 B) 6

C) 66

D) -6

392)

393)

394)

395)

396)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 397) 7, 24, 25 397) A) right triangle; 25 B) right triangle; 7 C) right triangle; 24 D) not right triangle

49

Express the statement as an equation involving the indicated variables. 4 398) The volume V of a sphere is times times the cube of the radius r. 3 A) V =

4 3

3

r

B) V =

4 3 r 3

C) V =

4 2 r 3

398) D) V =

4 r 3

Factor completely. If the polynomial cannot be factored, say it is prime. 399) 12x3 + 7x2 - 12x

399)

B) (3x2 + 4)(4x - 3)

A) x(3x + 4)(4x - 3) C) x2 (3x + 4)(4x - 3)

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

Find the value of the expression using the given values. x = -6 400) x2 A) -2 3

400) C) 2 3

B) 6

What number should be added to complete the square of the expression? 401) x2 - 6x A) -3

B) 18

C) 5

D) -6

D) 9

401)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 402) 2, 3, 4 402) A) right triangle; 3 B) right triangle; 4 C) right triangle; 2 D) not right triangle

Evaluate the expression using the given value of the variables. 403) -3x-1y2 for x = -2, y = -2 3 A) 8

Simplify the expression. 404) 165/4 A) 256

403)

B) 24

2 C) 3

D) 6

B) 512

C) 128

D) 32

404)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 405) (27x6 y6 )1/3 405) A) 3x2 y2

B) x2 y2

C) 3x2 y

50

D) 3x6 y2

On the real number line, label the points with the given coordinates. 406) -11, -9, -7, -5

A)

B)

C)

D)

406)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 407) 4 1x 1+

407)

4 x

A)

x+4 x-4

B) x + 4

C) x - 4

D)

Express the statement as an equation involving the indicated variables. 408) The surface area S of a cube is 6 times the square of the length x of a side. A) S = 6x2 B) S = x2 C) S = 6 + x2

x-4 x+4

408) D) S = 6x

List all the elements of B that belong to the given set. 0 409) B = {2, 5, -4, 0, , , 0.29, -5 , 0.161616...} 5

409)

Irrational numbers

5,

0 -5 5,

A) { 5}

B)

C) { 5 , -5 }

D) { 5, -5 , 0.161616...}

Find the quotient and the remainder. 410) 6x3 - 13x2 - 4x + 35 divided by -2x + 3 A) -3x2 + 2x + 5; remainder 20

B) -3x2 + 2x + 5; remainder 0

C) x2 + 5; remainder 2

410)

D) -3x2 + 2x + 5; remainder 23

Tell whether the expression is a polynomial. If it is, give its degree. -10x10 - 45x6 411) -5x2 A) Polynomial; degree 10 C) Polynomial; degree 6

B) Polynomial; degree 0 D) Not a polynomial

51

411)

Simplify the expression. 412) (-5)2 A) 5

1 B) 25

C) 625

D) not a real number

Write the number in scientific notation. 413) 820,000 A) 8.2 × 104 B) 8.2 × 10-4 Write the statement using symbols. 414) The sum of 18 and 6 is 24. A) 18 · 6 = 108

C) 8.2 × 105

412)

413) D) 8.2 × 10-5

414)

18 =3 B) 6

C) 18 + 6 = 24

Factor the polynomial. 415) 9x2 - 18xt + 8t2

A) (9x - 2t)(x - 4t) C) (3x + 2t)(3x + 4t)

D) 18 - 6 = 12

415)

B) (3x - 2t)(3x - 4t) D) prime

Factor completely. If the polynomial cannot be factored, say it is prime. 416) 12(x - 7)2 - 19(x - 7) - 21 A) (3x + 7)(4x + 3) C) (3x + 24)(4x + 35)

417) 6x4 - 5x2 - 6 A) (2x2 + 1)(3x2 - 6)

417) B) (3x - 2)(2x + 3) D) (6x2 - 3)(x2 + 2)

C) (2x2 - 3)(3x2 + 2)

Factor the polynomial. 418) x2 - x - 30

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

416)

B) (3x + 14)(4x + 10) D) (3x - 28)(4x - 25)

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

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

D) prime

418)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 419) (x - 7)(x - 6) 419) A) x2 - 14x + 42 B) x2 + 42x - 13 C) x2 - 13x + 42 D) x2 - 13x - 13 Factor completely. If the polynomial cannot be factored, say it is prime. 420) 24x2 + 68x + 48 A) (2x + 1)(3x + 12) C) 4(12x + 3)(x + 4)

B) 4(2x + 3)(3x + 4) D) 4(2x + 1)(3x + 12)

52

420)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8x - 8 2x2 · 421) x 9x - 9 A)

72x2 + 144x + 72 2x3

B)

9 16x

C)

16x 9

D)

16x3 - 16x2 9x2 - 9x

Simplify the expression. 422) (-64)4/3 A) -256 C) 256

422)

B) 4,096 D) not a real number

Find the LCM of the given polynomials. 423) x - 7, 7 - x A) (x - 7)(7 - x) B) x + 7

C) -1

421)

D) (x - 7) or (7 - x)

423)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 424) (x5 y2 )3/4 424) A) x15/4 y3/2

B) x20/3 y8/3

C) x23/4 y11/4

Simplify the expression. Assume that all variables are positive when they appear. 3 3 425) 10 7 · 11 6 3 3 3 3 A) 110 13 B) 110 7 · 6 C) 21 42 Factor completely. If the polynomial cannot be factored, say it is prime. 426) 27x2 - 117x - 90 A) 9(3x - 2)(x + 5)

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

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

427) 12x3 + 8x2 y - 15xy2 - 10y3 A) (4x2 - 5y2)(3x + 2y)

D) x3/2 y15/4

425) 3 D) 110 42

D) prime

427)

B) (12x2 - 5y2 )(x + 2y)

C) (4x2 + 5y2)(3x - 2y)

D) (4x2 - 5y)(3x + 2y)

Simplify the expression. Assume that all variables are positive when they appear. -5 428) 3 9 A) -5

3

3

426)

B) -5

3

9

C)

3 -5 3 3

428)

D)

3 -5 9 3

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 429) (x-2 y)6 429)

A)

y6 x12

B)

1 12 x y6

C) x12y6

53

D)

y6 x2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 430) 3 1 x2 - 3x - 18 x - 6

430)

1 +1 x+3

A)

x 2 x - 4x - 24

B) -1

C) -

Solve the problem. 431) The focal length f of a lens with index of refraction n is

x 2 x - 3x - 18

D) -

x 2 x - 2x - 24

1 1 + 1 = (n - 1) R1 R2 where R1 and R2 are f

431)

the radii of curvature of the front and back surfaces of the lens. Express f as a rational expression. R1 R 2 R1 R 2 A) f = B) f = (n - 1)(R1 + R2 ) (n + 1)(R1 - R2 )

C) f =

(n - 1)(R1 + R2 )

D) f =

R1 R 2

n(R1 - R2 ) R1 R2

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 432) (12x - y)2 432)

A) 144x2 + y2 C) 144x2 - 24xy - 2y2

B) 144x2 - 24xy + y2 D) 144x2 - 12xy + y2

Perform the indicated operations. Express the answer as a single polynomial in standard form. 433) (x - 11)(x2 + 2x - 7) A) x3 + 13x2 + 29x + 77

B) x3 - 9x2 - 15x - 77

C) x3 - 9x2 - 29x + 77

Simplify the expression. 434) 5 4 A) 625

433)

D) x3 + 13x2 + 15x - 77

B) 20

C) -20

D) -625

434)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 435) B C A) {1, 2, 3, 4, 5, 7, 9} C) {0, 6, 8}

435)

B) {6, 8} D) { }

Solve the problem. 436) Find the area A of a rectangle with length 20 yd and width 24 yd. A) A = 44 yd2 B) A = 480 yd2 C) A = 80 yd2

54

D) A = 960 yd2

436)

Perform the indicated operations. Express the answer as a single polynomial in standard form. 437) (5y + 11)(8y2 - 2y - 10)

437)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 438) (5x + 4)3

438)

A) 40y3 + 78y2 - 72y - 110 C) 40y3 + 98y2 + 72y + 110

B) 40y3 - 10y2 - 50y + 11 D) 128y2 - 32y - 160

A) 25x6 + 20x3 + 4,096

B) 125x3 + 299x2 + 240x + 64

C) 125x3 + 299x2 + 299x + 64

D) 25x2 + 40x + 16

Tell whether the expression is a polynomial. If it is, give its degree. 439) 2 A) polynomial, degree 2 B) polynomial, degree 1 C) polynomial, degree 0 D) not a polynomial

439)

Evaluate the expression using the given values. 15x - 5y x = 9, y = 7 440) 5 A) 20

440)

B) 34

C) 26

D) 12

Perform the indicated operations and simplify the result. Leave the answer in factored form. 441) 7 14 + x+5 x+7

441)

3x + 17

x2 + 12x + 35

A) 21

442)

B)

1 7

C) 7

D) 3x + 17

x3 + 1 7x · 3 2 -42x - 42 x -x +x

A) -

x3 + 1 6(x + 1)

442) B) -

1 6

C) -

x2 + 1 6

D)

x+1 6(-x - 1)

Solve the problem. 443) Find the volume V of a sphere of diameter 10 m. Use 3.14 for . If necessary, round the result to the nearest tenth. A) V = 523.3 m 3 B) V = 104.7 m 3 C) V = 4,186.7 m 3 D) V = 294.4 m 3 Multiply the polynomials. Express the answer as a single polynomial in standard form. 444) (x - 5)2 A) x2 - 10x + 25

B) x2 + 25

C) x + 25

55

D) 25x2 - 10x + 25

443)

444)

Express the statement as an equation involving the indicated variables. 445) The circumference C of a circle is the product of and its diameter d. A) C = d

Write the number as a decimal. 446) 5.0458 × 10-7 A) 0.00000050458

B) C = 2 d

C) C =

B) 0.000000050458

C) -504,580,000

d

445) D) C =

+d

D) 0.0000050458

Perform the indicated operations and simplify the result. Leave the answer in factored form. 447) 2x - 2 x

446)

447)

7x - 7 9x2

A)

18x2 (x - 1) 7x(x - 1)

B)

7 18x

C)

14(x + 1)2 9x3

What number should be added to complete the square of the expression? 448) x2 + 16x A) 64

B) 128

C) 8

D)

18x 7

D) 32

Factor completely. If the polynomial cannot be factored, say it is prime. 449) x4 - 256

449)

B) (x2 - 16)2

A) (x2 + 16)(x + 4)(x - 4) C) (x2 + 16)2

448)

D) prime

450) x3 - 4x + 5x2 - 20 A) (x2 - 4)(x + 5)

450) B) (x + 2)(x - 2)(x + 5)

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

D) prime

Evaluate the expression using the given values. 451) x + 8y x = -2, y = -3 A) 6 B) -5

C) -19

Simplify the expression. Assume that all variables are positive when they appear. 452) -10 48 + 7 27 - 10 147 A) -89 3 B) -10 3 C) 17 3

D) -26

452) D) -17 3

Approximate the number rounded to three decimal places, and truncated to three decimal places. 453) 0.28571429 A) 0.287 B) 0.286 C) 0.286 D) 0.285 0.285 0.285 0.286 0.286

56

451)

453)

Simplify the expression. 454) 8 4/3 A) 64

B) 16

C) 128

Express the statement as an equation involving the indicated variables. 455) The surface area S of a sphere is 4 times times the square of the radius r. r A) S = 4 r2 B) S = 4 C) S = r2

454)

D) 32

455) D) S = 4 r

Simplify the expression. Assume that all variables are positive when they appear. 2 456) 5+9 A)

3 10 + 5 2 45

10 - 9 2 -76

B)

C)

10 + 9 2 -76

456) 10 - 9 2 14

D)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 457) 10, 20, 25 457) A) right triangle; 10 B) right triangle; 20 C) right triangle; 25 D) not a right triangle

Factor the sum or difference of two cubes. 458) 343x3 + 729 A) (343x - 9)(x2 + 63x + 81) C) (7x + 9)(49x2 - 63x + 81)

458)

B) (7x - 9)(49x2 + 63x + 81) D) (7x + 9)(49x2 + 63x + 81)

Factor completely. If the polynomial cannot be factored, say it is prime. 459) 2y3 + 6y2 - 14y2 - 42y A) 2y(y - 3)(y + 7) C) (y + 3)(2y2 - 14y)

459)

B) (y + 3)(y - 7) D) 2y(y + 3)(y - 7)

Simplify the expression. Assume that all variables are positive when they appear. 125x2y 460) 49 A)

5 5x2 y 7

Simplify the expression. 461) 5 -2 A) 25

B)

5x 5y 7

C) 25x 5y

1 B) 25

1 C) 10

460) D) x

125y 7

461) D) -25

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 462) (x9 y-1 )8 462)

A)

x72 y8

B)

y8 x72

C) x72y8

57

D)

1 72 x y8

Factor the expression. Express your answer so that only positive exponents occur. 463) x7/8 + 3x6/8 A) x1/8 (x1/8 + 3)

B) x3/4 (x1/8 + 3)

C) x3/4 (x-1/8 + 3)

D) x1/8 (x7/8 + 3)

Tell whether the expression is a polynomial. If it is, give its degree. 464) 9 A) Polynomial, degree 9 B) Polynomial, degree 0 C) Polynomial, degree 1 D) Not a polynomial

464)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 465) (7x + 8y)2 A) 49x2 + 64y2

465)

B) 7x2 + 112xy + 64y2

C) 49x2 + 112xy + 64y2

D) 7x2 + 64y2

Use synthetic division to find the quotient and the remainder. 466) x5 - 2x4 - 12x3 - 13x2 - 12x + 11 is divided by x - 5 A) x4 + 3x3 + 3x2 + 2x + 2; remainder 3 C) x3 + 3x2 + 3x + 2; remainder 1

B) x4 + 3x3 + 3x2 + 2x - 2; remainder 1 D) x4 + 3x3 + 3x2 + 2x + 1; remainder 0

Simplify the expression. Assume that all variables are positive when they appear. 4 467) x+h- x A)

4 x+h+ h

x

C)

4( x + h + h

x)

463)

B)

4( x + h h

D)

4 h h

466)

467)

x)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. -4x4 y-4 -1 468) 468) 5z 7

A)

5z 7 -4x4 y4

B)

5y4z 7 -4x4

C)

5y4 -4x4 z 7

D)

-4x4 5y4z 7

Simplify the expression. Assume that all variables are positive when they appear. 3 469) 6- 7 A)

18 + 3 7 29

B)

18 + 3 7 1

C)

3 3 6 7

469) D)

18 - 3 7 29

Solve the problem. 470) Find the volume V of a rectangular box with length 4 in., width 6 in., and height 7 in.. A) V = 168 in.3 B) V = 294 in.3 C) V = 112 in.3 D) V = 144 in.3

58

470)

Write the statement using symbols. 471) The quotient of x and the sum of 5 and x. x+5 A) B) x + 5 + x x

x C) 5+x

471) D) x(5 + x)

Simplify the expression. Assume that all variables are positive when they appear. 2 472) 2 7- 2 A)

7+1 13

14 + 1 13

B)

14 - 1 13

C)

Factor the sum or difference of two cubes. 473) x3 + 512 A) (x + 8)(x2 + 64)

472) 14 + 1 15

D)

473)

B) (x + 8)(x2 - 8x + 64)

C) (x - 512)(x2 - 1)

D) (x - 8)(x2 + 8x + 64)

Solve. 474) When an object is dropped to the ground from a height of h meters, the time it takes for the object h to reach the ground is given by the equation t = , where t is measured in seconds. If an object 4.9

474)

falls 176.4 meters before it hits the ground, find the time it took for the object to fall. A) 9 seconds B) 6 seconds C) 36 seconds D) 7 seconds

Evaluate the expression using the given value of the variables. 475) 7x3 + 4x2 - 2x - 3 for x = 1 A) -2

Factor the perfect square. 476) x4 - 14x2 + 49 A) (x - 7)2

B) 12

C) 6

D) 10

B) (x2 - 7)2

C) (x2 + 7)2

D) (x - 7)(x + 7)

476)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 1 8 477) - 2 5x A)

5x - 16 10x

B)

-5x + 16 10x

C)

Find the quotient and the remainder. 478) x2 + 3x - 49 divided by x + 9 A) x - 5; remainder 6 C) x - 6; remainder 5

-13 10 - 5x

D)

35x - 13 x(7 - x)

B)

478)

B) x - 6; remainder 0 D) x + 6; remainder 5

35x - 13 x(x - 7)

C)

59

13x - 35 x(x - 7)

477)

-5x - 16 10x

Perform the indicated operations and simplify the result. Leave the answer in factored form. 5 8 479) + x x-7 A)

475)

D)

13x - 35 x(7 - x)

479)

Simplify the expression. 64 -1/2 480) 25

480)

A)

32 25

B)

8 5

C)

5 8

D) not a real number

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8 6 481) x2 x A)

2(4x + 3) x2

B)

2(3x - 4) x

C)

2(4 - 3x) x2

D)

2(4 + 3x) x2

Simplify the expression. Assume that all variables are positive when they appear. 3 482) 10 A)

9 10 10

B)

3 10 10

C) 103

481)

482) D) 3 10

An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 3 1 483) (x2 - 1)1/2 · (2x + 5)1/2 · 2 + (2x + 5)3/2 · (x2 - 1)-1/2 · 2x 483) 2 2

A) (x2 - 1)1/2 (2x + 5)1/2(5x2 + 5x - 3) C)

B)

(2x + 5)1/2(5x2 + 5x - 3) (x2 - 1)-1/2

(2x + 5)1/2(5x2 + 5x - 3) (x2 - 1)1/2

D) (x2 - 1)1/2 (2x + 5)-1/2(5x2 + 5x - 3)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 484) 15, 20, 25 484) A) right triangle; 20 B) right triangle; 25 C) right triangle; 15 D) not a right triangle

Simplify the expression. 485) 729-1/3 1 A) 9

1 C) 27

B) -9

485) D) 9

Reduce the rational expression to lowest terms. x2 - 36 486) x-6 A)

1 x-6

B)

486)

1 x+6

C) x - 6

60

D) x + 6

Factor the sum or difference of two cubes. 487) x3 - 125 A) (x + 5)(x2 - 5x + 25) C) (x + 125)(x2 - 1)

487)

B) (x - 5)(x2 + 25) D) (x - 5)(x2 + 5x + 25)

Use synthetic division to find the quotient and the remainder. 1 488) 6x5 - 5x4 + x - 4 is divided by x + 2 B) 6x4 - 2x3 - x2 +

A) 6x4 - 8x3 + 4x2 - 2x + 2; remainder -5 C) 6x4 - 2x3 + x2 -

488)

1 5 37 x + ; remainder 2 4 8

1 5 27 x + ; remainder 2 4 8 13 2

D) 6x4 - 8x3 + 5; remainder -

489) x5 + x3 + 2 is divided by x + 3 A) x4 - 2x2 ; remainder 8

489)

B) x4 - 3x3 + 10x2 - 30x + 90; remainder -268 C) x4 - 3x3 + 9x2 - 26x + 78; remainder -232

D) x4 - 2; remainder 8

Perform the indicated operations and simplify the result. Leave the answer in factored form. 4x 5 8 + 490) x + 1 x - 1 x2 - 1 A)

x+1 x-1

Write the number as a decimal. 491) 3.66 × 10-4 A) 0.00366

Simplify the expression. 492) 4,0961/4 A) 32

B)

4x - 3 x-1

C)

4x - 3 x+1

D)

4x x-1

B) 0.0000366

C) -366,000

D) 0.000366

B) 8

C) 32,768

D) 256

Perform the indicated operations and simplify the result. Leave the answer in factored form. 2 8 493) + x x-6 A)

10x - 12 x(x - 6)

Factor the perfect square. 494) 25x2 - 20x + 4 A) (5x + 2)(5x - 2) Write the number as a decimal. 495) 2.9135 × 107 A) 2,913,500

B)

12x - 10 x(6 - x)

C)

10x - 12 x(6 - x)

D)

491)

492)

493)

12x - 10 x(x - 6)

B) (5x - 2)2

C) (5x - 3)2

D) (5x + 2)2

B) 203.945

C) 29,135,000

D) 291,350,000

61

490)

494)

495)

Use the Distributive Property to remove the parentheses. 496) (x + 4)(x + 7) A) x2 + 11x + 28 B) x2 + 10x + 28

C) x2 + 11x + 11

D) x2 + 28x + 11

Write the statement as an inequality. 497) y is positive A) y 0 B) y 0

C) y < 0

D) y > 0

Evaluate the expression using the given values. 498) x + y x = -8, y = 2 A) 6 B) -10

C) -6

D) 10

Graph the numbers on the real number line. 499) x 1

496)

497)

498)

499)

A)

B)

C)

D)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 500) (x-9 y2 )-4 z 3 500)

A)

x36z 3 y8

B)

x36 y8 z3

C)

y8 x36z 3

D)

y8 z3 x36

Tell whether the expression is a polynomial. If it is, give its degree. 25 +1 501) x A) Polynomial, degree 25 C) Polynomial, degree 0

501)

B) Polynomial, degree -1 D) Not a Polynomial

An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 502) 10x3/2(x3 + x2 ) - 12x5/2 - 12x3/2 502)

A) x3/2(x - 1)[10(x2 - 1) - 2] + 10x3 C) 10x3/2(x + 1)(5x2 - 6)

B) 10x3/2(x3 - 1) + 10x3 - 2x3/2(x - 1) D) 2x3/2(x + 1)(5x2 - 6)

62

Evaluate the expression using the given values. |x| |y| x = 6 and y = -3 + 503) x y A) -1

503)

B) 2

C) 0

Simplify the expression. 504) 64-4/3

1 256

D) not a real number

505) 25-1/2

1 A) 5

504)

1 B) 256

A) 256 C) -

D) 1

1 C) 5

B) 5

505) D) -5

Solve the problem. 506) A formula used to determine the velocity v in feet per second of an object (neglecting air resistance) after it has fallen a certain height is v = 2gh, where g is the acceleration due to gravity and h is the height the object has fallen. If the acceleration g due to gravity on Earth is approximately 32 feet per second, find the velocity of a bowling ball after it has fallen 20 feet. (Round to the nearest tenth.) A) 1,280 ft per sec B) 35.8 ft per sec C) 25.3 ft per sec D) 6.3 ft per sec Evaluate the expression. 30 2 · 507) 14 5 A)

7 5

507) B)

6 7

C)

15 7

Write the number as a decimal. 508) There are 2.711 × 102 miles of highways, roads, and streets in a certain city. A) 271.1

506)

B) 27.11

C) 27,110

D)

7 6

D) 2,711

Multiply the polynomials. Express the answer as a single polynomial in standard form. 509) (x + 12y)(x - 12y) A) x2 - 24y2 B) x2 + 24xy - 144y2 C) x2 - 24xy - 144y2

508)

509)

D) x2 - 144y2

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 510) (x14y7 )1/7 510) A) x2 |y|

B) x2 y

C) x2

D) x14y

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 511) (6xy)3 511)

A)

1

216x3 y3

B) 216x3 y3

C) 6x3 y3

63

D) 216xy

Perform the indicated operations and simplify the result. Leave the answer in factored form. 17 6 + 512) x-5 x-5 A)

23 x-5

B)

11 x

C)

11 x-5

D)

512)

17(x - 5) 6(x - 5)

Factor the expression. Express your answer so that only positive exponents occur. 513) (x + 8)-3/5 + (x + 8)-1/5 + (x + 8) 1/5

513)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 514) (x + 10)2

514)

A) (x + 8)-3/5 [1 + (x + 8)1/5 + (x + 8)3/5 ] C) (x + 8)-3/5 [1 + (x + 8) 2/5 + (x + 8)4/5 ]

B) (x + 8)-3/5 [1 + (x + 8)4/5 + (x + 8)6/5 ] D) (x + 8)-3/5 [1 + (x + 8) -2/5 + (x + 8) -4/5 ]

A) x2 + 20x + 100 C) x2 + 100

B) 100x2 + 20x + 100

D) x + 100

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 515) (x + 8y)(x - 3y) 515) A) x2 + 5xy - 24y2 B) x + 5xy - 24y C) x2 + 2xy - 24y2 D) x2 + 5xy + 5y2 Use synthetic division to determine whether x - c is a factor of the given polynomial. 516) 3x3 - 22x2 - 3x + 70; x - 7 A) Yes

516)

B) No

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 517) -15x 517) A) Monomial,; variable x; coefficient -15; degree 0 B) Monomial, variable x; coefficient 1; degree -15 C) Monomial; variable x; coefficient -15; degree 1 D) Not a monomial

Perform the indicated operations and simplify the result. Leave the answer in factored form. 6 4 518) 7x 7x A)

519)

1 7x

B)

2 7x

C)

7 2x

x 4 2 2 x - 16 x + 5x + 4

518)

D) 1

519)

A)

x2 - 3 (x - 4)(x + 4)(x +1)

B)

x2 - 3x + 16 (x - 4)(x + 4)(x + 1)

C)

x2 + 3x + 16 (x - 4)(x + 4)(x + 1)

D)

x2 - 3x + 16 (x - 4)(x + 4)

64

Evaluate the expression. 1 1 +8 520) · 10 4 5 A)

57 20

520) B)

89 5

C)

209 20

D)

103 10

Perform the indicated operations and simplify the result. Leave the answer in factored form. 9x4 - 72x x2 + x - 2 · 521) 2 3 3x - 12 4x + 8x2 +16x A)

3(x - 1) 4

B)

3x(x - 1)(x - 2)2 4(x + 2)2

C)

3x(x + 1) 4

D)

3x(x - 1) 4

Factor completely. If the polynomial cannot be factored, say it is prime. 522) (x + 8)2 - 49 A) (x - 1)(x - 15) Simplify the expression. 523) 36-3/2 A) -216

B) (x + 57)(x - 41)

C) x2 + 16x + 15

1 B) 216

1 C) 216

522) D) (x + 15)(x + 1)

523) D) 216

Find the quotient and the remainder. 524) x2 - 121a 2 divided by x - 11a A) x2 - 22xa

524)

B) x2 + 22xa

C) x - 11a

D) x + 11a

Simplify the expression. Assume that all variables are positive when they appear. 3 525) -64x24y36 A) 16x8 y12

526)

x7x +

A) C)

B) -4x8 y12

C) -4x12y18

D) 4x8 y12

y 3y

525)

526)

x 7-

3xy - 7xy + y 3 7x - 3y

B)

x 7-

3xy - 7xy + y 3 7x + 3y

D)

7x -

10xy + 7x + 3y

3y

7x -

10xy + 7x - 3y

3y

Perform the indicated operations and simplify the result. Leave the answer in factored form. x+4 x+4 527) x+2 x-6 A)

521)

8(x + 4) (x + 2)(x - 6)

B)

-8(x + 4) (x + 2)(x - 6)

C) 0

65

D)

-4(x + 4) (x + 2)(x - 6)

527)

Reduce the rational expression to lowest terms. y3 - 64 528) y- 4 A) y2 + 4y + 16

528)

B) y2 - 16

C)

1 y-4

D)

y3 - 64 y- 4

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 529) (12x3 )-2 529)

A)

1

144x6

B) 144x6

C)

144 x6

D)

x6 144

Perform the indicated operations and simplify the result. Leave the answer in factored form. 530) x +1 x-4 12

x2 - 16

A)

530)

+1

x+4 x+2

B)

2x + 8 x-2

C)

2x - 8 x-2

D)

2x + 8 x+2

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x-8 531) x-3 A) x = 3

B) x = 0

C) x = -3

D) none

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 532) (8x2 + 5) - (-x3 - 10x2 + 4) A) 9x3 - 5x2 - 4

B) x3 - 2x2 + 9

Evaluate the expression using the given values. 533) -6xy + 6y - 4 x = -2, y = -1 A) -14 B) -22 Find the quotient and the remainder. 534) 20x3 - 29x2 + 15x + 12 divided by 5x - 1 A) 4x2 - 5x + 2; remainder 17 C) x2 + 2; remainder -5

Simplify the expression. 535) (-5)-4 A) 625

C) 9x3 - 10x2 + 1

D) x3 + 18x2 + 1

C) -18

D) 2

B) 4x2 - 5x + 2; remainder 14 D) 4x2 - 5x + 2; remainder 0

1 B) 625

C) -625

66

531)

1 D) 625

532)

533)

534)

535)

Use a calculator to evaluate the expression. Round the answer to three decimal places. 536) (-1.57)-5 A) -9.539

B) -0.105

C) 9.539

536)

D) 0.105

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 537) (9x6 + 6x5 - 2x) + (6x6 + 7x5 - 8x) A) 4x6 + 16x5 - 2x

537)

B) 15x + 13x6 - 10x5

C) 15x6 + 13x5 - 10x

D) 18x12

Simplify the expression. Assume that all variables are positive when they appear. 3 3 538) 4 81x - 3 192x 3 3 3 A) 24 x B) 12 x - 3 192x C) 0

538)

D) cannot simplify

Evaluate the expression using the given values. 539) 6x - 7y x = 9, y = 9 A) -9 B) -117

C) 117

539)

D) 9

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 540) (2x + 9y)2 540)

A) 2x2 + 36xy + 81y2 C) 2x2 + 81y2

B) 4x2 + 81y2 D) 4x2 + 36xy + 81y2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 541) 1 1 + x+8 x-8

541)

1

x2 - 64

A) x2

B) 16

C) -16

D) 2x

Simplify the expression. Assume that all variables are positive when they appear. 542) 27x7 y8 A) 3y4

3x7

B) 3x3 y4

C) 3x3 y4

3

Factor completely. If the polynomial cannot be factored, say it is prime. 543) 2x2 - 2x - 12 A) 2(x + 2)(x - 3)

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

3x

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

67

542) D) 3x7 y8

D) prime

3x

543)

Answer Key Testname: CHAPTER 0 1) B 2) A 3) C 4) B 5) C 6) B 7) B 8) D 9) C 10) A 11) B 12) D 13) B 14) B 15) C 16) D 17) B 18) D 19) D 20) A 21) A 22) D 23) D 24) C 25) D 26) B 27) B 28) D 29) B 30) C 31) B 32) A 33) C 34) D 35) B 36) A 37) B 38) C 39) A 40) D 41) A 42) C 43) C 44) B 45) A 46) A 47) A 48) D 49) B 50) B 68

Answer Key Testname: CHAPTER 0 51) D 52) A 53) B 54) D 55) C 56) A 57) B 58) B 59) A 60) B 61) D 62) D 63) A 64) A 65) B 66) A 67) B 68) B 69) B 70) D 71) B 72) D 73) C 74) D 75) C 76) C 77) C 78) D 79) C 80) B 81) C 82) D 83) B 84) D 85) A 86) A 87) C 88) B 89) A 90) A 91) C 92) D 93) B 94) A 95) B 96) B 97) C 98) D 99) C 100) B 69

Answer Key Testname: CHAPTER 0 101) B 102) A 103) A 104) A 105) C 106) A 107) B 108) B 109) D 110) B 111) D 112) D 113) B 114) A 115) C 116) D 117) C 118) B 119) B 120) B 121) D 122) D 123) B 124) D 125) C 126) D 127) B 128) B 129) A 130) C 131) C 132) C 133) D 134) A 135) D 136) A 137) D 138) D 139) A 140) D 141) D 142) D 143) A 144) D 145) C 146) B 147) A 148) A 149) B 150) C 70

Answer Key Testname: CHAPTER 0 151) A 152) A 153) C 154) C 155) C 156) A 157) A 158) D 159) C 160) D 161) C 162) C 163) B 164) D 165) D 166) C 167) A 168) C 169) D 170) D 171) D 172) D 173) B 174) B 175) C 176) B 177) D 178) C 179) B 180) B 181) C 182) C 183) B 184) C 185) C 186) A 187) B 188) A 189) C 190) A 191) D 192) C 193) B 194) D 195) B 196) C 197) C 198) B 199) C 200) B 71

Answer Key Testname: CHAPTER 0 201) A 202) B 203) B 204) B 205) A 206) C 207) A 208) C 209) D 210) B 211) B 212) C 213) B 214) B 215) A 216) D 217) A 218) C 219) D 220) D 221) A 222) C 223) B 224) B 225) D 226) C 227) B 228) C 229) B 230) D 231) A 232) C 233) B 234) D 235) A 236) B 237) D 238) A 239) D 240) A 241) C 242) C 243) B 244) D 245) A 246) D 247) D 248) D 249) A 250) C 72

Answer Key Testname: CHAPTER 0 251) C 252) C 253) B 254) C 255) B 256) C 257) D 258) C 259) D 260) D 261) C 262) B 263) C 264) C 265) B 266) B 267) D 268) B 269) D 270) A 271) C 272) C 273) B 274) C 275) B 276) C 277) C 278) A 279) C 280) D 281) D 282) C 283) D 284) B 285) D 286) C 287) B 288) A 289) B 290) B 291) B 292) B 293) B 294) C 295) B 296) C 297) C 298) D 299) D 300) C 73

Answer Key Testname: CHAPTER 0 301) A 302) B 303) B 304) A 305) B 306) C 307) D 308) B 309) B 310) A 311) B 312) C 313) C 314) D 315) D 316) B 317) B 318) C 319) D 320) B 321) A 322) A 323) C 324) D 325) B 326) A 327) A 328) D 329) C 330) C 331) D 332) A 333) D 334) D 335) B 336) D 337) D 338) A 339) B 340) A 341) B 342) B 343) A 344) D 345) B 346) B 347) B 348) C 349) D 350) B 74

Answer Key Testname: CHAPTER 0 351) C 352) D 353) D 354) D 355) B 356) C 357) A 358) D 359) B 360) B 361) B 362) D 363) A 364) B 365) A 366) C 367) D 368) C 369) B 370) D 371) D 372) D 373) B 374) A 375) B 376) B 377) B 378) C 379) C 380) C 381) C 382) B 383) D 384) A 385) B 386) D 387) B 388) A 389) C 390) C 391) C 392) C 393) D 394) B 395) C 396) C 397) A 398) B 399) A 400) B 75

Answer Key Testname: CHAPTER 0 401) D 402) D 403) D 404) D 405) A 406) D 407) D 408) A 409) C 410) A 411) D 412) A 413) C 414) C 415) B 416) D 417) C 418) B 419) C 420) B 421) C 422) C 423) D 424) A 425) D 426) B 427) A 428) C 429) A 430) D 431) A 432) B 433) C 434) A 435) C 436) B 437) A 438) B 439) C 440) A 441) C 442) B 443) A 444) A 445) A 446) A 447) D 448) A 449) A 450) B 76

Answer Key Testname: CHAPTER 0 451) D 452) A 453) B 454) B 455) A 456) B 457) D 458) C 459) D 460) B 461) B 462) A 463) B 464) B 465) C 466) B 467) C 468) B 469) A 470) A 471) C 472) B 473) B 474) B 475) C 476) B 477) D 478) C 479) C 480) C 481) C 482) B 483) B 484) B 485) A 486) D 487) D 488) A 489) B 490) B 491) D 492) B 493) A 494) B 495) C 496) A 497) D 498) D 499) D 500) A 77

Answer Key Testname: CHAPTER 0 501) D 502) D 503) C 504) B 505) C 506) B 507) B 508) A 509) D 510) B 511) B 512) A 513) C 514) A 515) A 516) A 517) C 518) B 519) B 520) C 521) A 522) D 523) B 524) D 525) B 526) A 527) B 528) A 529) A 530) D 531) A 532) D 533) B 534) B 535) B 536) B 537) C 538) C 539) D 540) D 541) D 542) C 543) A

78

Chapter 1 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the real solutions of the equation. 1) (x - 4)2 + 3(x - 4) - 18 = 0 A) {-6, 1}

B) {-1, 6}

C) {-7, 2}

1)

D) {-2, 7}

Solve the problem. 2) Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. How long will they take to paint the fence if they work together? 13 1 17 3 hr hr A) 5 B) 11 hr C) 5 D) 5 hr 24 2 23 4 3) Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If Susan's investment amounts to $19,000 and the annual income is $1590, how much money is invested in bonds and how much is invested in certificates of deposit? A) $5500 in bonds; $13,500 in certificates of deposit B) $13,000 in bonds; $6000 in certificates of deposit C) $6000 in bonds; $13,000 in certificates of deposit D) $13,500 in bonds; $5500 in certificates of deposit SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the equation by factoring. 4) x2 - x = 72

4)

Solve the problem. 5) Two pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pump alone to fill the tank? 6) At Bargain Car Rental, the cost of renting an economy car for one day is $19.95 plus 20 cents per mile. At Best Deal Car Rental, the cost of renting a similar car for one day is $24.95 plus 15 cents per mile. Solve the inequality 24.95 + 0.15x < 19.95 + 0.20x to find the range of miles driven such that Best Deal is a better deal than Bargain. Find the real solutions of the equation. 3 7) 4x - 5 + 7 = 8

5)

6)

7)

Solve the problem. 8) What is the domain of the variable in the expression

1

4x - 12 ?

8)

2)

3)

9) Marianne is planning a shopping trip to buy birthday gifts for her son. She estimates that the total price of the items she plans to purchase will be between $350 and $400 inclusive. If sales are taxed at a rate of 8.375% in her area, what is the range of the amount of sales tax she should expect to pay on her purchases? If Marianne's budget for the shopping trip is $425, will she necessarily be able to buy all the gifts that she has planned? Find the real solutions of the equation. 3 10) 4x - 5 + 7 = 8

9)

10)

Solve the problem.

11) The surface area A of a right circular cylinder is A = 2 r2 + 2 rh, where r is the radius and h is the height. Find the radius of a right circular cylinder whose surface area is 95.36 square inches and whose height is 11.7 inches.

11)

12) Chi is assigned to construct a triangle with the measure b of the base and the measure h of the height differing by no more than 0.2 centimeters. Express the relationship between b and h as an inequality involving absolute value.

12)

13) Martin purchased some municipal bonds yielding 8% annually and some certificates of deposit yielding 11% annually. If Martin's investment amounts to $23,000 and the annual income is $2230, how much money is invested in bonds and how much is invested in certificates of deposit?

13)

Write the expression in the standard form a + bi. 14) If z = 3 - 6i and w = 1 + 5i, evaluate z + w.

14)

Solve the problem. 15) Express that x differs from -7 by more than 3 as an inequality involving absolute value. Solve for x.

15)

16) In his algebra class, Rob has scores of 79, 85, 81, and 65 on his first four tests. To get a grade of C, the average of the first five tests must be greater than or equal to 70 and less than 80. Solve an inequality to find the range of scores that Rob can earn on the fifth test to get a C.

16)

17) A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds. Over what range may the weight of a 40-pound bag of to soil vary?

17)

Solve the equation by completing the square. 18) x2 - 4x + 1 = 0

18)

2

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the inequality. Express your answer using interval notation. 19) -2x + 5 > -3x + 3

19)

A) [-2, )

B) (- , -2]

C) (8, )

D) (-2, )

Write the inequality using interval notation, and illustrate the inequality using the real number line. 20) -1 < x < 3

A) [-1, 3]

B) (-1, 3)

C) [-1, 3)

D) (-1, 3)

Find the real solutions of the equation. 21) (2x - 4)2 - 6(2x - 4) + 5 = 0 A) {-

3 1 , } 4 2

3 1 B) { , - } 2 2

5 9 C) { , } 2 2

3

D) {-

5 9 ,- } 2 2

20)

21)

Solve the inequality. Express your answer using interval notation. 22) x - 4 < -5

22)

A) (-1, )

B) (- , -9)

C) (- , -9]

D) (- , -1)

Solve the equation.

23) (x + 9)(x - 1) = (x + 1)2 5 A) 3 24) 13x - 8 = 5x - 72 A) {8}

B) {10}

3 C) 2

10 D) 9

B) {-9}

C) {-8}

D) {9}

C) {5, -9}

D) { 7, -1}

Solve the equation by completing the square. 25) x2 + 4x - 45 = 0 A) {-5, 9}

Find the real solutions of the equation. 26) (x2 - 1)1/2 = 12 B) { 145, -

26) 145}

C) { 13}

D) {145, -145}

Solve the inequality. Express your answer using interval notation. 27) |5x - 1| 5 4 6 4 6 A) [- , ] B) (- , ) 5 5 5 5 C) (- , -

4 6 ) or ( , ) 5 5

D) (- , -

1 9 B) {- , - } 2 2

1 9 C) { , } 2 2

4

27)

4 6 ] or [ , ) 5 5

Find the real solutions, if any, of the equation. Use the quadratic formula. 28) 4x2 + 9 = -20x 1 9 A) {- , - } 4 4

24)

25)

B) {-36, -9}

A) {13}

23)

9 9 D) {- , } 4 2

28)

Solve the problem. 29) Two cars start from the same point and travel in the same direction. If one car is traveling 60 miles per hour and the other car is traveling at 53 miles per hour, how far apart will they be after 9.4 hours? A) 65.8 mi B) 564 mi C) 498.2 mi D) 1,062.2 mi Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 30) The profit derived from the sale of x video cameras is $350 per unit less the sum of $2,000 costs plus $150 per unit. A) If P is profit and x the units sold, then P = 350x - (2,000 + 150x) or P = 200x - 2,000. B) If P is profit and x the units sold, then P = 350x + 2,000 - 150x or P = 200x + 2,000. 350 150 200 ) or P = - (2,000 + - 2,000. C) If P is profit and x the units sold, then P = x x x

29)

30)

D) If P is profit and x the units sold, then P = 350x - (2,000 - 150x) or P = 500x - 2,000. Find the real solutions of the equation. 31) x4 - 5x2 + 4 = 0

32)

3

A) {-4, 4}

B) {-2, 2}

2x + 1 = -5 125 } A) {2

127 } B) {2

C) {-5, 5}

D) {-1, 1, -2, 2}

32) C) {- 63}

D) {12}

C)

D) >

Fill in the blank with the correct inequality symbol. 0. 33) If x < -8, then x + 8 A)

31)

33)

B) <

Find the real solutions, if any, of the equation. Use the quadratic formula. 34) 2x2 = -10x - 6 A) {

-5 - 37 -5 + 37 , } 2 2

B) {

-5 - 13 -5 + 13 , } 4 4

C) {

-10 - 13 -10 + 13 , } 2 2

D) {

-5 - 13 -5 + 13 , } 2 2

Find the real solutions of the equation. 5 35) 1 - x = -2 A) {-33} B) {32}

C) {33}

Write the expression in the standard form a + bi. 36) (9 + 7i)(3 - 4i) A) 55 + 15i B) -28i2 - 15i + 27

34)

D) {-32}

35)

36) C) 55 - 15i

D) -1 + 57i

Solve the problem. 37) During an intramural basketball game, Team A scored 17 fewer points than Team B. Together, both teams scored a total of 151 points. How many points did Team A score during the game? A) 67 points B) 84 points C) 75 points D) 68 points

5

37)

Without solving, determine the character of the solutions of the equation in the complex number system. 38) x2 + 2x - 5 = 0

38)

Find the real solutions of the equation. 39) x + 3x1/2 + 2 = 0

39)

A) two complex solutions that are conjugates of each other B) a repeated real solution C) two unequal real solutions

1 A) { } 4

B) {1, 4}

C) {- 1, - 2}

D) no real solution

B) {0}

11 , 0} C) {2

11 D) { , 0} 2

Solve the equation by factoring. 40) 2x2 - 11x = 0 11 11 } A) { , 2 2

40)

Write the expression in the standard form a + bi. 41) If z = 9 - 3i, evaluate z + z. A) 18 + 6i B) 18 - 6i Find the real solutions of the equation. 3 42) 1 + x = -1 A) {-2} B) {1} Solve the equation. 43) 6x - 17 = 0 17 A) 6 44) 7x - 6 = x - 4 1 ,- 1 A) 3

B)

6 17

D) 18

C) {2}

D) {-1}

C) -

1 5 B) - , 3 4

Write the expression in the standard form a + bi. 45) i15 A) 1

C) -6i

B) -1

6 17

D)

17 6

D)

C) i

D) -i

equation for h. Use the result to determine the height from which an object was dropped if it hits the ground after falling for 6 seconds. A) h = 24.01t2 ; 864.4 meters B) h = 24.01t; 144.1 meters

D) h = 4.9t2 ; 176.4 meters

6

42)

43)

44)

1 5 , C) 3 4

Solve the problem. 46) When an object is dropped to the ground from a height of h meters, the time it takes for the object h to reach the ground is given by the equation t = , where t is measured in seconds. Solve the 4.9

C) h = 4.9t; 29.4 meters

41)

45)

46)

Find the real solutions of the equation. 47) x2 - 3x + 83 = x + 7 A) {-2}

B) {2}

C) {-5}

D) {9}

Solve the problem. 48) Sue can sew a precut dress in 3 hours. Helen can sew the same dress in 2 hours. If they work together, how long will it take them to complete sewing that dress? Give your answer rounded to one decimal place, if necessary. A) 1.2 hr B) 2.5 hr C) 5 hr D) 1.8 hr Solve the equation by the Square Root Method. 49) x2 = 25 A) {5}

B) {6, -6}

C) {12.5}

D) {5, -5}

Solve the problem. 50) A bank loaned out $56,000, part of it at the rate of 13% per year and the rest at a rate of 8% per year. If the interest received was $5,730, how much was loaned at 13%? A) $30,000 B) $31,000 C) $26,000 D) $25,000 Write the interval as an inequality involving x, and illustrate the inequality using the real number line. 51) [-2, )

A) x > -2

B) x -2

C) x -2

D) x > -2

Solve the equation. 52) -7.4x + 1.8 = -15.9 - 1.5x A) {3}

B) {2.6}

C) {-24}

Solve the inequality. Express your answer using interval notation. 53) |x - 1| < 0 A) (-1, ) B) (- , 1) C) (-1, 1)

D) {2.4}

D) no solution

Write the expression in the standard form a + bi. 2 2 2 i + 54) 2 2 A) i

B)

47)

48)

49)

50)

51)

52)

53)

54)

i 2

C) -i

55) If w = 8 + 6i, evaluate w - w. A) 0 B) 16

C) 12i

7

D) -

i 2

D) -16 + 12i

55)

Solve the equation. 56) |x| - 12 = -13 A) {-1}

B) {1, -1}

C) {1}

D) no solution

56)

Find the real solutions, if any, of the equation. Use the quadratic formula and a calculator. Express any solutions rounded to two decimal places. 57) x2 + 3x - 3 = 0 57)

A) {-2.8, 2.8}

B) {-1.07, 2.8}

Solve the equation. The letters a, b, and c are constants. 58) ax - b = c, a 0 c-b b-c A) x = B) x = a a

C) {-2.8, 1.07}

D) {-2.8, -1.07}

b+c C) x = a

b+ c D) x = a

Find the real solutions, if any, of the equation. Use the quadratic formula. 59) 4x2 + 12x + 2 = 0

59)

A) {

-3 - 11 -3 + 11 , } 2 2

B) {

-12 2

C) {

-3 - 7 -3 + 7 , } 2 2

D) {

-3 - 7 -3 + 7 , } 8 8

7 -12 + , 2

7

}

Write the expression in the standard form a + bi. 9 60) 6 - 8i A) -

27 18 i 14 7

B) -

60)

27 18 i + 14 7

C)

27 18 i + 50 25

D)

27 18 i 50 25

Solve the problem. 61) During the first five months of the year, Len earned commissions of $3,850, $2,790, $2,450, $2,360, and $3,580. If Len must have average monthly earnings of at least $3,140 in order to qualify for retirement benefits, what must he earn in the sixth month in order to qualify for benefits? A) at least $3,140 B) at least $3,810 C) at least $3,028 D) at least $3,006 Write the inequality obtained by performing the indicated operation on the given inequality. 62) Add 4 to each side of the inequality 5 + 5x < -4. A) 9 + 5x > 0 B) 9 + 5x < 0 C) 9 + 9x < 0 D) 9 + 9x > 0 Find the real solutions of the equation. 63) x2 + 5x - x2 + 5x = 12

61)

62)

63)

A) {25, -25} C) {

58)

B) {3}

-5 + 89 -5 - 89 , } 2 2

D) {5}

8

Find the real solutions, if any, of the equation. Use the quadratic formula. 64) x2 + 4x - 3 = 0 A) {-1 - 7, -1 + C) {2 + 7}

7}

64)

B) {-2 - 7, -2 + 7} D) {-2 - 2 7, -2 + 2 7}

Solve the problem. 65) For a cone, the formula r =

3V describes the relationship between the radius r of the base, the h

65)

volume V, and the height h. Find the volume if the radius is 7 inches and the cone is 9 inches high. (Use 3.14 as an approximation for , and round to the nearest tenth.) A) 461.6 cubic in. B) 4,154.2 cubic in. C) 51.3 cubic in. D) 65.9 cubic in.

Solve the equation by factoring. x-4 15 = 66) x x+4 A) {16, 1}

66) B) {4, -1}

C) {4, 1}

D) {16, -1}

Solve the equation. The letters a, b, and c are constants. a b 67) + = c, c 0 x x A) x =

a+b c

B) x =

67)

ab c

C) x =

Find the real solutions of the equation. 68) x + 7 + x = 3 1 A) { } B) {1} 9 69) x3/2 - 9x1/2 = 0 A) { 2}

c ab

D) x =

c a+b

68) C) {4}

D) no real solution

C) {3}

D) {0, 81}

69) B) {0, 9}

Solve the equation. 5 8 = 70) 1 8x 7 A) -

35 8

70) B) - 7

Solve the equation by the Square Root Method. 71) (2x - 5)2 = 25 A) {0, -10}

35 8

D) - 5

C) {10, 0}

D) {5, 0}

C)

B) {0, -5}

9

71)

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 72) The total cost of producing refrigerators in one production line is $5,000 plus $500 per unit produced. 5,000 . A) If C is the total cost and x is the number of units produced, then C = 500x

72)

B) If C is the total cost and x is the number of units produced, then C = 5,000 + 500x. C) If C is the total cost and x is the number of units produced, then C = (5,000 + 500)x. D) If C is the total cost and x is the number of units produced, then C = 5,000x + 500. Write the expression in the standard form a + bi. 73) (9 + 5i)(9 - 5i) A) 56

B) 81 - 25i

C) 106

D) 81 - 25i2

C) {-3}

3 D) {- } 2

Find the real solutions of the equation. 74) x2 - 3x + 64 = x + 5 A) {8}

B) {3}

Solve the inequality. Express your answer using interval notation. 75) 4x + 5 < 37

73)

74)

75)

A) (- , 8] B) [8, )

C) (8, )

D) (- , 8)

Find the real solutions of the equation. 76) 2x + 3 - x + 1 = 1 A) {-3, -1} B) {3}

C) {3, -1}

D) no real solution

77) x5/4 - 4x1/4 = 0 A) {-4, 0, 4}

B) {0}

C) {0, 2}

D) {0, 4}

78) 4x-2 - 11x-1 - 3 = 0 1 A) {- 4, } 3

1 B) {- , -3} 4

1 C) {4, } 3

1 D) {- , 3} 4

10

76)

77)

78)

Fill in the blank with the correct inequality symbol. -28. 79) If x > -7, then 4x A) <

79)

B)

C) >

D)

Find the real solutions, if any, of the equation. Use the quadratic formula. 80) 5x2 + x - 5 = 0 A) { C) {

-1 1-

2

101 -1 + ,

2

101

80)

-1 - 101 -1 + 101 , } B) { 10 10

}

101 1 + 101 , } 10 10

D) no real solution

Solve the inequality. Express your answer using interval notation. 3 5 81) 0 < < x 2

81)

6 A) ( , ) 5

B) (- ,

6 ) 5

5 D) ( , ) 6

C) (- ,

Write the expression in the standard form a + bi. 82) 8(8 - 8i) A) 64 + 64i B) 8 - 64i

5 ) 6

C) 64 - 64i

D) 64i - 8i

82)

Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 83) x2 + 3x + 3 = 0 83)

A) repeated real solution B) two unequal real solutions C) no real solution

Solve the equation by the Square Root Method. 84) (x - 3)2 = 9 A) {3, -3}

B) {0, -6}

C) {12}

11

D) {6, 0}

84)

Write the inequality using interval notation, and illustrate the inequality using the real number line. 85) 1 x 7

A) (1, 7)

B) [1, 7]

C) (1, 7]

D) [1, 7]

Find the real solutions of the equation by factoring. 86) 2x4 = 128x A) {0, 4}

B) {0, 2, 4}

C) {0}

D) {-4, 0, 4}

Solve the problem. 87) The formula v = 2.5r can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the radius of curvature if the maximum safe velocity is 15 miles per hour. A) 563 ft B) 90 ft C) 36 ft D) 225 ft Express the graph shown using interval notation. Also express it as an inequality involving x. 88)

A) (1, 9] 1<x 9

B) [1, 9] 1 x 9

Write the expression in the standard form a + bi. 89) i10 A) 1

B) i

C) [1, 9) 1 x<9

D) (1, 9) 1<x<9

C) -1

D) -i

Solve the equation. 90) |2x2 - x - 1|= 3 A) {C) {

1-

1-

4

4

33

85)

86)

87)

88)

89)

90) ,-

33 1 + ,

1+

4

33

4

33

}

B) {

}

1-

4

33

,-

1+

4

33

}

D) no solution

Solve the problem. 91) x represents the number of cassette tapes sold at $8.75 per tape, and y represents the total cost of the cassette tapes. After writing an equation for this situation, what is the total cost of 14 cassettes? A) $122.5 B) $0.62 C) $245 D) $61.25

12

91)

Solve the equation. 3 7 4 = 92) x + 2 x - 2 x2 - 4 A) { 21} 93)

92) B) {6}

C) {-6}

D) {24}

2x x =3+ 5 3

93)

A) {-45}

B) {-90}

C) {45}

D) {90}

Solve the inequality. Express your answer using interval notation. 94) (3x + 5)-1 < 0

A) (-

5 , ) 3

C) (- , -

94)

B) [-

5 ) 3

5 , ) 3

D) (- , -

5 ] 3

Find a and b.

95) If 0 < 2x < 6, then a < x2 < b. A) a = 0, b = 9 B) a = 0, b = 16

C) a = 0, b = 3

D) a = 0, b = 36

95)

Find the real solutions of the equation. Use a calculator to express the solutions rounded to two decimal places. 96) (1 + x)2 - 5 = 2(1 + x) 96) A) {0.62, -1.98}

B) {-1.62, -0.62}

C) {-0.62, -0.18}

D) {-0.62, 0.82}

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 97) Speed is measured by distance divided by time. d A) If S represents speed, d distance, and t time, then S = . t B) If S represents speed, d distance, and t time, then t =

S . d

C) If S represents speed, d distance, and t time, then S =

t . d

D) If S represents speed, d distance, and t time, then d =

S . t

13

97)

Write the inequality using interval notation, and illustrate the inequality using the real number line. 98) y < -4

A) (- , -4]

B) (- , -4)

C) [- , -4)

D) [- , -4]

98)

Find the real solutions, if any, of the equation. Use the quadratic formula and a calculator. Express any solutions rounded to two decimal places. Use 3.14 to approximate . 99) x2 + x - 4 = 0 99)

A) {0.73, 1.73}

B) {-0.73, 1.73}

C) {-1.73, 0.73}

D) {-1.73, -0.73}

Find the real solutions, if any, of the equation. Use the quadratic formula. 100) 2x2 - x + 4 = 0 -1 - 33 -1 + 33 , } A) { 4 4

C) {

100)

-1 - 33 1 + 33 , } B) { 4 4

-1 + 33 1 + 33 , } 4 4

D) no real solution

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 101) The surface area of a sphere is 4 times the square of the radius. A) If S represents the surface area and r the radius, then 4 S =r2 .

101)

B) If S represents the surface area and r the radius, then S = 4 r. C) If S represents the surface area and r the radius, then S = 4 r2 .

D) If S represents the surface area and r the radius, then S = r2 . Find the real solutions of the equation. 102) x + x = 20 A) {25} B) {4}

C) {5}

D) {16}

Solve the problem. 103) The radiator in a certain make of car needs to contain 60 liters of 40% antifreeze. The radiator now contains 60 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze to get the desired strength? A) 20.0 L B) 15.0 L C) 30 L D) 24 L

14

102)

103)

Solve the inequality. Express your answer using interval notation. 104) x(4x - 6) (2x + 6)2

104)

A) (- , -

6 ] 5

6 B) [ , ) 5

C) (- , -

6 ] 5

D) [-

Write the expression in the standard form a + bi. 105) (-7 + i)(-7 - i) A) 49 B) -7

6 , ) 5

C) -48

D) 50

Express the graph shown using interval notation. Also express it as an inequality involving x. 106)

A) (-4, 1] -4 < x 1

B) [-4, 1) -4 x < 1

C) [-4, 1] -4 x 1

D) (- , 1) x<1

C) { 7i, i}

D) { 7, 7}

Solve the equation in the complex number system. 107) x4 - 6x2 - 7 = 0 A) {- 7i, -i}

B) {-

7,

105)

106)

107)

7, i, -i}

Solve the inequality. Express your answer using interval notation. 108) 8 < 2x 12

A) (4, 6]

B) [-6, -4)

C) (-6, -4]

D) [4, 6)

15

108)

Solve the problem. 109) BJ can overhaul a boat's diesel inboard engine in 20 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency? A) 6 hr B) 15 hr C) 80 hr D) 12 hr Solve the equation. 5-x 3 7 + = 110) x 4 x A) -

8 7

109)

110) B) {-8}

C) {8}

D) {-4}

Solve the problem. 111) A loan officer at a bank has $100,000 to lend and is required to obtain an average return of 13% per year. If he can lend at the rate of 14% or the rate of 11%, how much can he lend at the 11% rate and still meet his required return? A) $33,333.33 B) $7,142.86 C) $900,000.00 D) $4,000.00 Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 112) The volume of a right prism is the area of the base times the height of the prism. 1 A) If V represents the volume, B the area of the base, and h the height, then V = Bh. 2

111)

112)

B) If V represents the volume, B the area of the base, and h the height, then V = Bh. C) If V represents the volume, B the area of the base, and h the height, then V = B + h. B D) If V represents the volume, B the area of the base, and h the height, then V = . h Solve the inequality. Express your answer using interval notation. 113) |x + 8| 0 A) {8} B) (- , -8) C) {-8} Find the real solutions of the equation by factoring. 114) x3 + 3x2 + 4x + 12 = 0 A) {3}

B) {-2, 2, -3}

C) {-3}

D) no solution

D) no real solution

Write the inequality using interval notation, and illustrate the inequality using the real number line. 115) -2 x < 8

A) (-2, 8]

B) [-2, 8)

C) (- , 8)

D) [-2, 8)

16

113)

114)

115)