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
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