Name___________________________________ MATH 0021 FINAL EXAM REVIEW UPDATED 10/2020

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

For numbers 1-5: Solve the equation.1) 4(x + 5) - (3x + 4) = -4 1)

A) x = - 20 B) x = 12 C) x = 5 D) x = 20

2) 25

x - 13

x = 3 2)

A) x = -90 B) x = 45 C) x = 90 D) x = -45

3) 3 (y - 2)5

= 1 - 3y 3)

A) y = 1118

B) y = -1118

C) y = 116

D) y = 76

4) -6.2m - 1.3 + 5m = -7.2 - 1.2m + 5.9 4)A) 0 B) 1.1C) all real numbers D) no solution

5) -2(x - 3) - 59 = 3x - 5(x + 7) 5)A) -94 B) -24C) all real numbers D) no solution

6) The length of a rectangular room is 4 feet longer than twice the width. If the room's perimeter is176 feet, what are the room's dimensions?

6)

A) Width = 56 ft; length = 120 ft B) Width = 28 ft; length = 60 ftC) Width = 42 ft; length = 46 ft D) Width = 33 ft; length = 70 ft

7) A 12-ft. board is cut into 2 pieces so that one piece is 8 feet longer than 3 times the shorter piece. Ifthe shorter piece is x feet long, find the lengths of both pieces.

7)

A) shorter piece: 1 ft; longer piece: 11 ft B) shorter piece: 24 ft; longer piece: 44 ftC) shorter piece: 6 ft; longer piece: 36 ft D) shorter piece: 28 ft; longer piece: 36 ft

8) Solve for the indicated variable: A = P + PRT for T 8)

A) T =PR

A - PB) T =

P - APR

C) T =AR

D) T =A - P

PR

9) Solve for the indicated variable: A = 12

h(B + b) for b 9)

A) b =2A + Bh

hB) b =

A - Bhh

C) b =2A - Bh

hD) b = 2A - Bh

10) Solve for the indicated variable: V = 13

Bh for h 10)

A) h = V3B

B) h = 3BV

C) h = 3VB

D) h = B3V

1

Solve the inequality. Graph the results.11) 4x + 2 3x + 6 11)

A) x 4

B) x 4

C) x > 4

D) x < 4

12) -10x - 4 -11x + 1 12)

A) x 5

B) x > -10

C) x < -10

D) x 5

2

13) x + 9 < 3 13)

A) x -6

B) x -6

C) x > -6

D) x < -6

14) Which of the following ordered pairs is a solution to the equation 3x + y = 6? 14)

A) (13

, 5) B) ( - 13

, 5) C) (-3 , 0) D) (- 1, -6)

Identify the intercepts.15) 15)

A) (1, 0), (0, 5) B) (1, 0), (0, -5) C) (-5, 0), (0, 5) D) (-1, 0), (0, 5)

3

16) 16)

A) (4, 0), (-4, 0) B) (4, 0), (-4, 0), (0, 0)C) (0, -4) D) (4, 0), (-4, 0), (0, -4)

Find the slope and the y-intercept.17) -5x + 7y = 11 17)

A) m =75 ; 0, -

115 B) m =

57 ; 0,

117 C) m = 5; (0, 11) D) m = 35; (0, 77)

18) 8x - 6y = 48 18)

A) m =43 ; (0, -8) B) m = 8; (0, 48) C) m =

34 ; (0, 6) D) m = -

43 ; (0, 8)

Find the slope of the line.19) x = 4 19)

A) m = 0 B) m = 1C) m = -1 D) undefined slope

20) y = -3 20)A) m = 0 B) m = 1C) m = -1 D) undefined slope

Model the problem with a linear equation.21) The average value of a certain type of automobile was $13,500 in 2008 and depreciated to $6660 in

2011. Let y be the average value of the automobile in the year x, where x = 0 represents 2008. Writea linear equation that models the value of the automobile in terms of the year x.

21)

A) y = -2280x - 180 B) y = -2280x + 13,500

C) y = - 1

2280 x - 6660 D) y = -2280x + 6660

4

Graph the equation by plotting three points and connecting them.22) y = 3x - 6 22)

A) B)

C) D)

5

Graph the equation by plotting the intercepts.23) 5x - 15y = 30 23)

A) B)

C) D)

6

Graph the equation.24) -9y = -54 24)

A) B)

C) D)

7

Graph.25) x + 4 = 0 25)

A) B)

C) D)

8

Graph the line.

26) y = -34

x - 2 26)

A) B)

C) D)

27) Determine the intercepts of the graph 6x - y = 6 27)A) (0, -6) and (1 , 0) B) (0 , -6) and (0, 1)C) (0 , 6) and (-1, 0) D) (6, 1) and (0, 0)

Find the slope of a straight line that passes through the given pair of points.28) (-18, 4) and (16, -9) 28)

A)52 B) -

3413 C) -

1334 D)

1334

29) (8, 3) and (-8, 3) 29)A) 5 B) 2 C) 10 D) 0

9

Determine the rate of change. Don't forget to attach the proper units.30) A mini-van driven 6000 miles cost $800 to own and operate. A mini-van driven 10,000 miles cost

$1333.33 to own and operate. Determine the rate of change.30)

A) $7.50 per mile B) cannot be determinedC) $17.00 per mile D) $0.13 per mile

Find the slope and the y-intercept.31) 2x - 3y = 6 31)

A) m =23 ; (0, -2) B) m = 2; (0, 6) C) m = -

23 ; (0, 2) D) m =

32 ; (0, 3)

32) x + 3y = 1 32)

A) m = -13 ; 0,

13 B) m =

13 ; 0,

13 C) m = -3; (0, 3) D) m = 1; (0, 1)

Write the equation of the line in slope-intercept form.33) m = -9, y-intercept (0, -2) 33)

A) y = 9x + 2 B) y = -2x - 9 C) y = 2x + 9 D) y = -9x - 2

Write an equation of the line passing through the given points.34) (5, -6) and (8, -12) 34)

A) y = - 12 x -

72 B) y = -2x + 4 C) y = 2x - 16 D) y =

12 x -

172

Find an equation of the line described. Write the equation in slope-intercept form if possible.

35) Slope 23

, through (8, 3) 35)

A) y = 23

x + 73

B) y = -23

x + 73

C) y = 23

x - 73

D) y = -23

x - 73

Solve.36) Find the slope of a line parallel to the line passing through (-4, 3) and (2, 1). 36)

A) -7 B) - 3 C) -13

D) - 4

10

37) The equation of a line is y =29 x - 1. What is the slope of a line parallel to it? 37)

A)29 B)

92 C) -

29 D) -

92

38) The equation of a line is y =13 x. What is the slope of a line perpendicular to it? 38)

A) - 3 B) - 13 C)

13 D) 0

Find an equation of the line. Write the equation using function notation.39) Through ( , -3); perpendicular to f(x) = x - 3 39)

A) f(x) = -2x - 2 B) f(x) = -12

x - 2 C) f(x) = x - 2 D) f(x) = x - 2

40) Through (-5, -2); perpendicular to x - 4y = 4 40)

A) f(x) = -14

x - 134

B) f(x) = -4x - 18

C) f(x) = -4x - 22 D) f(x) = 14

x - 134

Find the domain and range of the relation.41) {(9, 9), (-10, -2), (-13, 3), (11, -3), (-1, 6)} 41)

A) Domain = {6, -2, 9, 3, -3}; range = {-1, -10, 9, -13, 11}B) Domain = {-1, 6, -10, -2, 9}; range = {9, -13, 3, 11, -3}C) Domain = {9, -13, 3, 11, -3}; range = {-1, 6, -10, -2, 9}D) Domain = {-1, -10, 9, -13, 11}; range = {6, -2, 9, 3, -3}

Find the domain and range of the relation. Also determine whether the relation is a function.42) 42)

A) domain: [3, ); range: (- , ); not a functionB) domain: (- , ); range: [3, ); functionC) domain: (- , ); range: [3, ); not a functionD) domain: (- , ); range: ( , 3]; function

11

For numbers 43-44: Given the function, find the indicated value.43) f(x) = x2 + 4x + 6; f(-1) 43)

A) 11 B) -1 C) -9 D) 3

44) f(x) = 6 - 7x2; f(-8) 44)A) 118 B) 454 C) -442 D) 62

For number 45-46: Solve.45) x - 5y = -38

9x - 6y = -6945)

A) (-4, 8) B) (-3, 7) C) (3, 8) D) No solution

46) 7x + 15y = 154x - 5y = -5

46)

A) (1, 0) B) (0, 1) C) (1, 1) D) (0, 0)

For numbers 47-61: Perform the indicated operation and simplify. Write the results using positive exponents only.47) (-7x9)(-4x7) 47)

A) -28x63 B) 28x63 C) 28x16 D) -28x16

48) (5x3y4)2 48)A) 25x6y8 B) 5x5y6 C) 10x3y4 D) 5x6y8

49) (4a3b6c0)2 49)A) 16a6b12 B) 4a6b12 C) 0 D) 16a6b12c2

50) -9x(2x + 8) 50)A) -18x2 - 72x B) -90x2 C) 2x2 - 72x D) -18x2 + 8x

51) 5x5(8x3 - 2x2 - 9) 51)A) 40x8 - 10x7 - 45x5 B) 40x3 - 10x2 - 45C) 40x8 - 2x2 - 9 D) 40x8 - 10x7

52) -9x2(10x5 + 3x3) 52)A) -117x7 - 117x5 B) -90x7 - 27x5 C) -117x2 D) -90x7 + 3x3

53) (5x + 6)2 53)A) 25x2 + 60x + 36 B) 5x2 + 60x + 36 C) 5x2 + 36 D) 25x2 + 36

54) (x - 6)(5x + 9) 54)A) 5x2 - 21x - 54 B) 5x2 - 21x - 21 C) 5x2 - 23x - 54 D) 5x2 - 54x - 21

12

55) (x-2y5)-2 55)

A) x-4

y3B) y3

x-4C) 1

x4y10D) x4

y10

56) xy6

x5y

-256)

A) 1x7y13

B) x8

y10C) 1

x12y14D) y10

x8

57) 3x2y3

z3

457)

A) 81x8y12

z12B) 3x8y12

z7C) 81x6y7

z7D) 3x8y12

z12

58) (6a6b5c0)2 58)A) 36a12b10c2 B) 6a12b10 C) 36a12b10 D) 0

59) 21m12n11

3m11n759)

A) 7n4 B) 21mn4 C) 7mn4 D) 7m23n18

60) xy3

x3y

-260)

A) 1x5y7

B) 1x8y8

C) y4

x4D) x4

y4

61) 5x-3y-3

2z-261)

A) 4z2

125x3y3B) 2z2

5x3y3C) 5z2

2x3y3D) 5

2x3y3z2

For numbers 62-63: Perform the operation using long division.

62) p2 + 5p - 11p + 7

62)

A) p + 2 +3

p + 7B) p - 3 +

2p + 7

C) p - 2 D) p - 2 +3

p + 7

13

63) x2 + 8x + 13x + 5

63)

A) x + 3 -2

x + 5B) x + 3

x + 5C) x + 3 +

2x + 5

D) x + 4

For numbers 64-66: Perform the indicated operation.64) (28x + 2) - (-4x2 - 14x + 2) 64)

A) -4x2 + 14x + 4 B) 4x2 + 42x C) 4x2 + 42x - 4 D) 4x2 - 42x

65) (15x2 - 8) - (8x2 + 14) 65)A) 23x2 - 22 B) 23x2 + 6 C) 7x2 + 6 D) 7x2 - 22

66) (x + 1)(x2 - x + 1) 66)A) x3 - 1 B) x3 + 2x2 + 2x + 1C) x3 - 2x2 - 2x - 1 D) x3 + 1

For numbers 67-69: Factor out the GCF from the polynomial.67) 27y3 - 9y2 + 12y 67)

A) 3y(9y3 - 3y2 + 4y) B) y(27y2 - 9y + 12)C) 3y(9y2 - 3y + 4) D) 3(9y3 - 3y2 + 4y)

68) -21y3 + 15y 68)A) -3(7y3 + 5y) B) -3y(7y2 - 5) C) -3y2(7y - 5) D) -3y(7y2 + 5)

69) -4x6 + 12x5 - 4x3 69)A) -4x3(x3 - 3x2 + 1) B) -4x3(x3 - 3x2 - 1)C) -4x3(x3 - 3x2 + x) D) -4x3(x3 - 3x2 - x)

For numbers 70-76: Factor the polynomial completely. If the polynomial cannot be factored write "prime".70) x3 + 6x2 + x + 6 70)

A) (x2 + 1)(x + 6) B) (x2 + 6)(x + 1) C) (x2 + 1)(6x + 6) D) (6x2 + 6)(x + 1)

71) 15x2 + 20x + 6x + 8 71)A) (15x - 2)(x - 4) B) (15x + 2)(x + 4) C) (5x - 2)(3x - 4) D) (5x + 2)(3x + 4)

72) x3 + 6x2 - 4x - 24 72)A) (x - 2)2(x + 6) B) (x + 2)(x - 2)(x + 6)C) (x2 - 4)(x + 6) D) Prime

73) 100x2 + 160x + 64 73)A) 4(5x - 4)2 B) 4(5x + 4)2

C) 4(5x + 4)(5x - 4) D) 4(25x + 16)2

14

74) 2x3 - 26x2 + 72x 74)A) 2x(x + 9)(x + 4) B) 2x(x - 9)(x - 4) C) x(x + 9)(2x + 8) D) x(2x + 9)(x + 4)

75) 5x2 + 6x - 8 75)A) (5x + 2)(x - 4) B) (5x + 4)(x - 2) C) (5x - 4)(x + 2) D) (5x - 2)(x + 4)

76) 12x2 - 42x - 24 76)A) 12x2 - 42x - 24 B) (12x - 6)(x + 4) C) 6(2x + 1)(x - 4) D) 6(2x - 1)(x + 4)

Solve.77) The perimeter of the quadrilateral is 40 inches. Find the lengths of the sides. 77)

A) 7 in., 14 in., 18 in., 1 in. B) 8 in., 13 in., 18 in., 1 in.C) 3 in., 3 in., -2 in., -4 in. D) 9 in., 15 in., 28 in., 2 in.

For numbers 78-81: Solve the equation.78) x2 - x = 56 78)

A) x = -7, 8 B) x = 1, 56 C) x = 7, 8 D) x = -7, -8

79) 11d2 - 4d = 0 79)

A) d = -114

, 0 B) d = 114

, 0 C) d = 411

, 0 D) d = -411

, 0

80) 2x2 = 3x + 5 80)

A) x = 25

, x = 1 B) x = 25

, x = 0 C) x = 52

, x = -1 D) x = 25

, x = -1

81) x2 = 4x 81)A) x = 0, x = -4 B) x = 0, x = 4 C) x = -4 D) x = 4

Solve the problem.82) A window washer accidentally drops a bucket from the top of a 144-foot building. The height h of

the bucket after t seconds is given by h = -16t2 + 144. When will the bucket hit the ground?82)

A) -3 sec B) 9 sec C) 48 sec D) 3 sec

15

83) The demand for a rooftop-mounted industrial air conditioner is given by the demand function

D(x) = 9800x2 + 5x

where x is the number of units produced each day and D(x) is the number sold each day. Assumethat x is an integer. What is the domain of the demand function from a purely mathematical pointof view?

83)

A) All integers greater than 0 B) All integers other than -5 or 0C) All integers D) All integers other than 5 or 0

For number 84-90: Perfrom the indicate operation and simplify.

84) x + 85 - x

÷x2 - 7x - 8

x2 - 13x + 4084)

A) x - 8x + 1

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

(x - 5)2C) -

x - 8x + 1

D) -x + 8x + 1

85) (x + 6) ÷x2 - 15x + 54

9 - x85)

A) -x - 6x + 6

B) -1 C) -x + 6x - 6

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

86) x2 + 6x + 8x2 + 13x + 36

÷x2 + 2x

x2 + 7x - 1886)

A) x - 2x2 + 9x

B) xx2 + 13x + 36

C) x - 2 D) x - 2x

87) (x - 10)25

÷5x - 50

2587)

A) 1x - 10

B) x - 10 C) 5(x - 10)25x - 50

D) (x - 10)325

88) x2 - 164y

÷4 - x28xy

88)

A) 7x(x + 4) B) -7x(x - 4) C) -7x(x + 4) D) 7x(x - 4)

89) 14x - 8

+x

x2 - 6489)

A) 15x + 112(x + 8)(x - 8)

B) 14x(x + 8)(x - 8)

C) 15x - 112(x + 8)(x - 8)

D) 14x + 112(x + 8)(x - 8)

16

90) 3x2 - 3x + 2

+7

x2 - 190)

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

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

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

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

For numbers 91-93: Solve the compound inequality. Graph the solution set.91) 7 3t + 1 19 91)

A)

B)

C)

D)

92) -32 -5c + 3 < -17 92)

A)

B)

C)

D)

17

93) 6x - 4 < 2x or -2x -6 93)

A) [1, 3]

B) (- , 1) [3, )

C)

D) (1, 3)

For numbers 94-95: Simplify. Assume that all variables represent positive numbers.94) 75y2 94)

A) 5y 3 B) 5y2 3 C) 5 3y2 D) 5 3

95) 175x2y 95)A) 5xy2 7 B) 5xy 7 C) 5x2 7y D) 5x 7y

Find the root. Assume that all variables represent nonnegative real numbers.96)

3 125x6

96)

A) x25

B) 1253

x2 C) 5x2

D) 53

x2

Simplify the radical expression. Assume that all variables represent positive real numbers.

97)3

-27a11b7 97)

A) -3a3b2 3a2b B) 3 a7b11 C) 3a2b

3a3b2 D) 3ab

3a3b4

For numbers 98-99: Divide and simplify. Assume that all variables represent positive numbers.

98)3

500a4b6

34a

98)

A) 5ab2 35ab B) 5ab4 3

5a2 C) 5a2b4 D) 5ab2

18

99) 128x92x

99)

A) 8 x9 B) 8x4 C) 8x8 D) 8x4 2

For numbers 100-101: Use radical notation to write the expression. Simplify if possible.100) 6x2/9 100)

A)9

6x2 B) 69

x2 C)2

6x9 D)9

36x2

101) (5x)2/9 101)

A) 59

x2 B)2

5x9 C)9

5x2 D)9

25x2

For numbers 102-103: Combine the following, if possible.102) -3 2 - 8 50 102)

A) -43 2 B) -11 2 C) -37 2 D) 43 2

103) 2 + 7 50 + 7 72 103)A) 14 124 B) 14 2 C) 78 124 D) 78 2

For numbers 104-105: Rationalize the denominator and simplify. Assume that all variables represent positive realnumbers.

104) 26 - 5

104)

A) 12 - 2 531

B) 26

-25

C) 12 + 2 5-1

D) 12 + 2 531

105) 217x

105)

A) 21 7x7x

B) 21 xx

C) 3 7xx

D) 3 7x7x

Use the Pythagorean theorem to find the unknown side of the right triangle.106)

6

14

106)

A) 10 B) 2 58 C) 116 D) 232

For numbers 107-108: Multiply, and then simplify if possible. Assume all variables represent positive real numbers.107) (6 5 + 7)(2 5 + 5) 107)

A) 35 + 12 52 + 30 5 B) 77 5

C) 47 5 + 30 D) 95 + 44 5

19

108) ( 2 + 13)( 2 - 13) 108)A) 2 - 2 2 B) 15 C) -11 D) 2 - 2 13

For numbers 109-110: Solve the radical equation. Check all proposed solutions.109) 6x - 5 = 5 109)

A) x = 25 B) x = 103

C) x = 256

D) x = 5

110) 4x + 5 - 5= 0 110)

A) x = 152

B) x = 25 C) x = 5 D) x = 254

For number 111-112:Simplify. Express in terms of i.111) -25 111)

A) 5i B) -i 5 C) ±5 D) -5i

112) -148 112)A) -2 37 B) 2i 37 C) 2 37 D) -2i 37

20

Answer KeyTestname: MATH0021 REVIEW (2020)

1) A2) B3) A4) C5) D6) B7) A8) D9) C

10) C11) B12) D13) D14) A15) A16) D17) B18) A19) D20) A21) B22) C23) A24) B25) D26) B27) A28) C29) D30) D31) A32) A33) D34) B35) C36) C37) A38) A39) B40) C41) D42) B43) D44) C45) B46) B47) C48) A49) A50) A

21

Answer KeyTestname: MATH0021 REVIEW (2020)

51) A52) B53) A54) A55) D56) B57) A58) C59) C60) D61) C62) D63) A64) B65) D66) D67) C68) B69) A70) A71) D72) B73) B74) B75) C76) C77) B78) A79) C80) C81) B82) D83) B84) D85) C86) D87) B88) C89) A90) D91) B92) C93) B94) A95) D96) C97) A98) D99) B

100) B22

Answer KeyTestname: MATH0021 REVIEW (2020)

101) D102) A103) D104) D105) C106) B107) D108) C109) D110) C111) A112) B

23