Page 1
MATH 1453 - COLLEGE ALGEBRA/BUSN - PRACTICE FINAL EXAM - SPRING 2007 - DR. DAVID BRIDGE
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Add or subtract as indicated.
1) (-6x3 + 9x5 + 2 + 8x4) - (-7 + 2x4 + 2x5 - 2x3)
A) 7x5 + 6x4 - 4x3 + 9 B) 7x5 + 10x4 - 8x3 - 5
C) 11x5 + 10x4 - 8x3 + 9 D) 11x5 + 10x4 - 8x3 - 5
Find the product.
2) (-3x + 2)(-4x - 4)
A) -7x2 + 4x - 8 B) 12x2 + 4x + 4 C) 12x2 + 4x - 8 D) -7x2 + 4x + 4
3) (5y - 7)(25y2 + 35y + 49)
A) 125y3 + 343 B) 125y3 - 343
C) 125y3 + 245y2 - 343 D) 25y3 + 343
Solve the problem.
4) The polynomial 0.0039x4 - 0.0057x3 + 0.0055x2 + 0.15x + 1.89 gives the predicted sales volume of a company, in
millions of items, where x is the number of years from now. Determine the predicted sales 14 years from now.
A) 196.83 million B) 139.25 million C) 126.18 million D) 213.92 million
Factor out the greatest common factor.
5) 64x9y9 - 24x4y6 + 48x7y4
A) 8x4y4(8x5y5 - 3y2 + 6x3) B) 8(8x9y9 - 3x4y6 + 6x7y4)
C) 8x4(8x5y9 - 3y6 + 6x3y4) D) No common factor
6) 12m2 - 11r3
A) 3(4m2 - 3r3) B) m2(12 - 11m) C) No common factor D) 2(6m2 + 5r3)
Factor completely.
7) x2 + 10x - 24
A) (x - 12)(x + 1) B) (x + 12)(x - 2) C) Cannot be factored D) (x - 12)(x + 2)
8) x2 - x - 63
A) Cannot be factored B) (x - 63)(x + 1) C) (x + 7)(x - 9) D) (x - 7)(x + 9)
9) 4x2 - 4x - 24
A) Cannot be factored B) 4(x - 2)(x + 3) C) (4x + 8)(x - 3) D) 4(x + 2)(x - 3)
10) x2 + 30x + 225
A) (x - 15)2 B) (x + 15)(x - 15) C) (x + 15)2 D) Prime
Use factoring to solve the equation.
11) (x + 2)(x - 16) = 0
A) -16, 2 B) -2, 16 C) 16, 2 D) 2, -16
Page 2
12) x2 + 7x - 30 = 0
A) -10, 1 B) 10, 3 C) -10, 3 D) 10, -3
Solve by the square-root property.
13) (x - 6)2 = 16
A) 22 B) 10, 2 C) 4, -4 D) 2, -10
14) (x + 7)2 = 44
A) 2 11 - 7, 2 11 + 7 B) -7 + 2 11, -7 - 2 11
C) -7 + 2 22, -7 - 2 22 D) 2 11, -2 11
Use the quadratic formula to solve the equation. Give both exact and approximate answers.
15) 3m2 + 10m + 4 = 0
A)-5 ± 13
6; -0.232, -1.434 B)
-5 ± 37
3; 0.361, -3.694
C)-10 ± 13
3; -2.131, -4.535 D)
-5 ± 13
3; -0.465, -2.869
Use the discriminant to determine the number of real solutions of the equation.
16) t2 + 4t + 4 = 0
A) 2 B) No real solutions C) 1
17) v2 - 6v - 8 = 0
A) No real solutions B) 2 C) 1
18) 8 + 4z2 = -8z
A) 1 B) No real solutions C) 2
Solve the problem.
19) A rectangular garden has dimensions of 25 feet by 12 feet. A gravel path of equal width is to be built around the garden.
How wide can the path be if there is enough gravel for 588 square feet?
A) 8 ft B) 7 ft C) 8.5 ft D) 6 ft
Page 3
Graph the linear equation.
20) -9y = x + 3
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Page 4
21) 3y + 21x = 24
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Find the x-intercepts and y-intercepts of the graph of the equation.
22) -5x + y = 0
A) x-intercept: -5; y-intercept: -1 B) x-intercept: -0; y-intercept: 0
C) x-intercept: -1; y-intercept: -5 D) x-intercept: 0; y-intercept: -0
Solve the problem.
23)
x1990 1991 1992 1993 1994 1995 1996 1997
y700
600
500
400
300
200
100
-100x1990 1991 1992 1993 1994 1995 1996 1997
y700
600
500
400
300
200
100
-100
Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a function
of time. What is the approximate number of cars sold in 1993?
A) 550 B) 500 C) 350 D) 400
Page 5
24) Big "D" Sales
1989-1990
Month
What was the increase in sales between month 5 and month 6 of 1990?
A) $4000 B) $800 C) $4 D) $8000
Find the slope of the line, if it is defined.
25) Through (-1, -6) and (-3, 8)
A) 7 B) 14 C) 2 D) -7
26) Through the origin and (5, 8)
A) 8 B) 13
5C) Undefined D) 1
5
3
Write an equation in slope-intercept form of a line satisfying the given conditions.
27) m = - 3
5; b =
21
5
A) y = 3
5x -
21
5B) y =
3
5x +
21
5C) y = -
3
5x +
21
5D) y = -
3
5x -
21
5
Find the slope and the y-intercept of the line.
28) 3x + 4y = 14
A) m = 4
3; b =
7
2B) m = -
3
4; b =
7
2C) m =
3
4; b = 14 D) m = -
4
3; b = 4
Page 6
Identify whether the slope is positive, negative, zero, or undefined.
29)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
A) Positive B) Negative C) Zero D) Undefined
30)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
A) Negative B) Positive C) Zero D) Undefined
31)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
A) Negative B) Positive C) Zero D) Undefined
Page 7
32)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
A) Positive B) Zero C) Undefined D) Negative
Find an equation of the the line satisfying the given conditions.
33) Through (2, 4); m = - 2
3
A) 2x + 3y = 16 B) 2x + 3y = -16 C) 2x - 3y = 16 D) 3x + 2y = -16
Write an equation in standard form for a line passing through the pair of points.
34) (-8, -3) and (5, 7)
A) -5x - 2y = 11 B) 5x + 2y = 11 C) -10x - 13y = -41 D) 10x - 13y = -41
35) (5, -4) and (-2, -4)
A) y = -4 B) x = 5 C) 5x - 2y = 0 D) -2x + 5y = 0
Find an equation of the the line satisfying the given conditions.
36) Through (4, -11); parallel to -4x + 3y = -37
A) -4x - 3y = -49 B) 3x - 4y = -11 C) -4x + 3y = -49 D) 4x + 3y = -37
Solve the problem.
37) Let C(x) = 100 + 10x be the cost to manufacture x items. Find the average cost per item to produce 90 items.
A) $11 B) $12 C) $990 D) $1710
Convert the temperature. You may use the fact that 32°F = 0°C, and 212°F = 100°C.
38) 25°C = °F
A) 45.9°F B) 102.6°F C) 77.0°F D) 8.8°F
Solve the problem.
39) Suppose the sales of a particular brand of appliance satisfy the relationship S(x) = 50x + 1100, where S(x) represents the
number of sales in year x, with x = 0 corresponding to 1982. Find the number of sales in 1995.
A) 3500 B) 1750 C) 1700 D) 3450
Page 8
40) Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $8500 in
1982 and $55,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).
A) S(x) = 47,000x + 8500 B) S(x) = 47,000x + 55,500
C) S(x) = 9400x + 8500 D) S(x) = 9400x + 55,500
Solve and graph the inequality and graph the solution.
41) z - 12 < -2
A) (10, ∞)
3 4 5 6 7 8 9 10 11 12 13 14 15 16 173 4 5 6 7 8 9 10 11 12 13 14 15 16 17
B) (-∞, 10]
3 4 5 6 7 8 9 10 11 12 13 14 15 16 173 4 5 6 7 8 9 10 11 12 13 14 15 16 17
C) (-∞, 10)
3 4 5 6 7 8 9 10 11 12 13 14 15 16 173 4 5 6 7 8 9 10 11 12 13 14 15 16 17
D) [10, ∞)
3 4 5 6 7 8 9 10 11 12 13 14 15 16 173 4 5 6 7 8 9 10 11 12 13 14 15 16 17
42) -11z + 9 ≥ -12z + 13
A) (-∞, -11)
-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4
B) (-11, ∞)
-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4
C) (-∞, 4]
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
D) [4, ∞)
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
Solve the problem.
43) The equation y = 0.005x - 0.40 can be used to determine the approximate profit, y in dollars, of producing x items. How
many items must be produced so the profit will be at least $4340?
A) x ≥ 911,484.00 B) 0 < x ≤ 868,079 C) x ≥ 868,080 D) x ≥ 867,920
44) The equation y = 0.002x - 0.10 can be used to determine the approximate cost, y in dollars, of producing x items. How
many items must be produced so the cost will be no more than $195?
A) 0 < x ≤ 102,427.50 B) 0 < x ≤ 97,551 C) 0 < x ≤ 97,450 D) 0 < x ≤ 97,550
Page 9
Solve the inequality and graph the solution.
45) (x - 2)(x + 5) > 0
A) (-5, ∞)
-5
B) (-∞, -2) or (5, ∞)
-2 5
C) (-5, 2)
-5 2
D) (-∞, -5) or (2, ∞)
-5 2
46) t2 - 3t - 28 ≤ 0
A) [7, ∞)
7
B) (-∞, -4]
-4
C) (-∞, -4] or [7, ∞)
-4 7
D) [-4, 7]
-4 7
State the domain of the given function.
47) y = 8 - x
A) (-∞, 8] B) [8, ∞) C) (-∞, 8) D) (-∞, ∞)
Page 10
48) y = x
x - 9
A) 9 B) (-∞, ∞)
C) (9, ∞) D) all real numbers except 9
49) f(x) = 4x2 + 8x - 9
A) all real numbers except 0 B) all whole numbers
C) (0, ∞) D) (-∞, ∞)
For the given function, find f(x + h) -f(x)
h.
50) x2 - 8x
A) 2x - 8 + h B) 2x + h C) 2x + 8 + h D)2xh + h2 - 8h - 16x
h
Graph the piecewise linear function.
51) f(x) = 3 - x, x ≤ 2
1 + 2x, x > 2
A)
x-10 10
y
10
-10
x-10 10
y
10
-10
B)
x-10 10
y
10
-10
x-10 10
y
10
-10
C)
x-10 10
y
10
-10
x-10 10
y
10
-10
D)
x-10 10
y
10
-10
x-10 10
y
10
-10
Page 11
Graph the function.
52) y = 9∣x∣ - 7
A)
x-10 10
y
10
-10
x-10 10
y
10
-10
B)
x-10 10
y
10
-10
x-10 10
y
10
-10
C)
x-10 10
y
10
-10
x-10 10
y
10
-10
D)
x-10 10
y
10
-10
x-10 10
y
10
-10
Page 12
53) y = ∣x - 2∣ - 9
A)
x-10 10
y
10
-10
x-10 10
y
10
-10
B)
x-10 10
y
10
-10
x-10 10
y
10
-10
C)
x-10 10
y
10
-10
x-10 10
y
10
-10
D)
x-10 10
y
10
-10
x-10 10
y
10
-10
Write a cost function for the problem. Assume that the relationship is linear.
54) Fixed cost, $110; 10 items cost $990 to produce
A) C(x) = 88x + 110 B) C(x) = 176x + 990 C) C(x) = 88x + 990 D) C(x) = 176x + 110
55) Marginal cost, $50; 40 items cost $2100 to produce
A) C(x) = 3x + 100 B) C(x) = 50x + 100 C) C(x) = 50x + 2100 D) C(x) = 3x + 2100
Solve the problem.
56) At a manufacturing plant, the total cost (in dollars) to produce x items is
C(x) = 5.58x + 27,000.
What is the marginal cost per item?
A) $26,994.42 B) $27,005.58 C) $5.58 D) $27,000
Determine the vertex of the parabola.
57) f(x) = x2 - 20x + 107
A) (0, 7) B) (10, 0) C) (7, 10) D) (10, 7)
58) f(x) = 4x2 - 8x + 6
A) (1, 0) B) (2, 1) C) (1, 2) D) (0, 2)
Page 13
59) y = 1
2(x - 2)2 + 3
A) (-2, 3) B) (3, 2) C) (-3, -2) D) (2, 3)
Find the x- and y-intercepts. If no x-intercepts exist, state so.
60) f(x) = 2x2 + 8x + 1
A)-8 ± 14
2, 0 , (0, 1) B)
-4 ± 2
2, 0 , (0, -1)
C)-4 ± 14
2, 0 , (0, 1) D)
-4 ± 14
4, 0 , (0, -1)
61) f(x) = (x + 2)2 - 16
A) x-intercepts: (-2, 0), (6, 0); y-intercept: (0, -16) B) x-intercepts: (2, 0), (-6, 0); y-intercept: (0, -12)
C) x-intercepts: (-2, 0), (6, 0); y-intercept: (0, -12) D) x-intercepts: (2, 0), (-6, 0); y-intercept: (0, -16)
Find the rule of a quadratic function whose graph has the given vertex and passes through the given point.
62) vertex (1, -3); point (2, -8)
A) f(x) = (x - 1)2 - 3 B) f(x) = 2(x - 1)2 - 3 C) f(x) = -5(x - 1)2 - 3 D) f(x) = -5(x + 1)2 - 3
Graph the parabola.
63) y = -x2 + 3
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Page 14
64) y = 4(x + 1)2 + 5
A)
x-10 10
y
10
-10
x-10 10
y
10
-10
B)
x-10 10
y
10
-10
x-10 10
y
10
-10
C)
x-10 10
y
10
-10
x-10 10
y
10
-10
D)
x-10 10
y
10
-10
x-10 10
y
10
-10
Page 15
65) f(x) = x2 - 3x - 8
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Solve the problem.
66) The manager of a CD store has found that if the price of a CD is p(x) = 56 - x
6, then x CDs will be sold. An expression for
the total revenue from the sale of x CDs is
R(x) = 56x - x2
6
Find the number of CDs that will produce maximum revenue.
A) 148 B) 168 C) 336 D) 208
67) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c = 3x2 - 300x + 70, where c is
cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?
A) 35 watches B) 30 watches C) 50 watches D) 70 watches
Page 16
Graph the rational function.
68) f(x) = - 1
x + 1
A)
x-6 6
y6
-6
x-6 6
y6
-6
B)
x-6 6
y6
-6
x-6 6
y6
-6
C)
x-6 6
y6
-6
x-6 6
y6
-6
D)
x-6 6
y6
-6
x-6 6
y6
-6
Page 17
69) f(x) = 4x - 5
2x + 1
A)
x-12 12
y12
x-12 12
y12
B)
x-12 12
y12
x-12 12
y12
C)
x-12 12
y12
x-12 12
y12
D)
x-12 12
y12
x-12 12
y12
Give the equation of the vertical asymptote(s) of the rational function.
70) g(x) = 3x + 2
x - 1
A) x = -1 B) y = 3 C) x = 1 D) y = 1
Give the equation of the horizontal asymptote of the rational function.
71) f(x) = 9x + 9
8x - 3
A) x = 3
8B) y = 9 C) y = 0 D) y =
9
8
Page 18
Graph the function.
72) f(x) = 5x
A)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
B)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
C)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
D)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
Provide an appropriate response.
73) The graph of an exponential function is given. Which of the following is the correct equation of the function?
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
A) y = 2.4x B) y = 0.45x C) y = 0.31x D) y = 1.8x
Page 19
Solve the equation.
74) 45 - 3x = 1
256
A) 128 B) 3 C)1
64D) -3
Solve the problem.
75) Assume exponential decay; that is, use the formula y = Poat. A bacterial culture has an initial population of 10,000. If its
population declines to 7000 in 2 hours, what will it be at the end of 4 hours?
A) 2450 B) 9031 C) 1500 D) 4900
Convert to exponential form.
76) log5 1
125 = -3
A) 5-3 = 1
125B)
1
125
3 = 5 C) 5125 = 3 D) 35 =
1
125
Write in logarithmic form.
77) 4 -3 = 1
64
A)1
64 = log4 -3 B) -3 = log1/ 64 4 C) -3 = log4
1
64D) 4 = log -3
1
64
Find the value of the expression.
78) log9 81
A) 9 B) 81 C) 18 D) 2
79) log9 1
81
A) -2 B) 9 C) -9 D) 2
Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent
positive numbers.
80) 2 log w + 6 log z - log (x - 5)
A) log w6*z2
(x - 5)B) log
(x - 5)
w2*z6C) log
w2*z6
(x - 5)D) log
w2*(x - 5)
z6
Write the expression as a sum and/or a difference of logarithms with all variables to the first degree.
81) log 3r4s3
A) log 3 + 4 log r + 3 log s B) log 12r + log 3s
C) 12log r + 3 log s D) log 7 + log r + 3 log s
Evaluate the expression.
82) log2 82.15
A) 0.1572 B) 1.9146 C) 6.3602 D) 41.0750
Page 20
Graph the function.
83) y = log5 x
A)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
B)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
C)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
D)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
Page 21
84) y = log1/8
x
A)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
B)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
C)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
D)
x-4 -2 2 4 6
y
4
2
-2
-4
-6
x-4 -2 2 4 6
y
4
2
-2
-4
-6
Find the interest. Round to the nearest cent.
85) $1430 at 14% simple interest for 2 months
A) Interest = $400.40 B) Interest = $3336.67 C) Interest = $100.10 D) Interest = $33.37
Solve the problem.
86) Gan-Lin borrowed $6400 from his father to buy a car. He repaid him after 8 months with simple interest of 10%. Find the
total amount he repaid.
A) $6826.67 B) $7040.00 C) $6773.33 D) $426.67
Find the compound amount for the deposit. Round to the nearest cent.
87) $16,000 at 5% compounded annually for 5 years
A) $20,420.51 B) $19,200.00 C) $20,000.00 D) $19,448.10
Find the compound interest earned by the deposit. Round to the nearest cent.
88) $1000 at 7% compounded quarterly for 2 years
A) $1035.31 B) $144.90 C) $140.00 D) $148.88
Page 22
Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points.
89) 6% compounded monthly
A) 6.09% B) 1.01% C) 5.14% D) 6.17%
Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.
90) $8800 at 4% compounded quarterly for 3 yr
A) $9916.06 B) $7809.55 C) $7823.17 D) $990.45
Solve the problem. Round to the nearest cent.
91) Ibrahim made an initial deposit of $4000 in a bank account. Assuming an interest rate of 10% compounded quarterly, how
much will the account be worth in 20 years?
A) $11,008.76 B) $28,838.27 C) $28,134.90 D) $28,159.95
Find the value.
92) 14 0.05s
A) 21.579 B) 19.599 C) 39.599 D) 17.713
Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.
93) R = $7500, i = 6% interest compounded semiannually for 8 years
A) $139,491.85 B) $187,953.78 C) $151,176.61 D) $401,176.61
Find the periodic payment that will render the sum.
94) S = $47,000, interest is 18% compounded monthly, payments made at the end of each month for 3 years
A) $994.16 B) $13,156.42 C) $1041.77 D) $1252.04
Solve the problem.
95) Courtney wants to start an IRA that will have $980,000 in it when she retires in 29 years. How much should she invest
annually in her IRA to do this if the interest is 16% compounded annually?
A) $143.16 B) $2134.69 C) $2062.39 D) $2147.69
Find the value.
96) 20 0.05
a
A) 12.4622 B) 27.5378 C) 12.8212 D) 12.0853
Find the present value of the ordinary annuity.
97) Payments of $67 made quarterly for 10 years at 8% compounded quarterly
A) $1531.91 B) $1802.47 C) $3382.51 D) $1844.88
Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for
20 years at the given interest rate, compounded annually).
98) $80,000 at 5%
A) $996,976.80 B) $996,656.00 C) $966,824.00 D) $1,025,696.00
Page 23
Find the payment necessary to amortize the loan.
99) $5500; 6% compounded annually; 7 annual payments
A) $1118.50 B) $885.70 C) $985.24 D) $994.86
Find the monthly house payment necessary to amortize the following loan.
100) In order to purchase a home, a family borrows $45,000 at 11% for 30 yr. What is the monthly payment?
A) $441.05 B) $13.75 C) $428.55 D) $412.50
Solve the problem.
101) Tasha borrowed $13,000 to purchase a new car at an annual interest rate of 15%. She is to pay it back in equal monthly
payments over a 5 year period. What is her monthly payment?
A) $351.23 B) $309.27 C) $32.50 D) $162.50
Solve the system of two equations in two variables.
102) x + 6y = 18
5x + 5y = 40
A) (6, 2) B) (5, 3) C) No solution D) (-6, 3)
103) -7x + 9y = 29
-3x - 7y = -31
A) No solution B) (1, 4) C) (1, 5) D) (0, 5)
104) 4x - 2y = 6
16x - 8y = 12
A) (1, 0) B) No solution C) (1, -1) D) (0, -3)
105) 4x + 3y = 5
8x + 6y = 10
A) - 3
4y +
5
4, y for any real number y B) No solution
C)1
2, 1 D)
5
4, 0
Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system.
106)1
5x +
1
5y = 0
x - y = 10
A) No solution B) (5, -5) C) (-5, -4) D) (4, -4)
Solve the problem by writing and solving a suitable system of equations.
107) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $75 for 3 days and 300 miles,
while Mary was charged $133 for 5 days and 600 miles. What does Best Rental charge per day and per mile?
A) $17 per day and 8 cents per mile B) $8 per day and 17 cents per mile
C) $16 per day and 9 cents per mile D) $18 per day and 9 cents per mile
Page 24
108) A shopkeeper orders 12 pounds of cashews and peanuts. If the amount of cashews he orders is 8 pounds less than the
amount of peanuts, how many pounds of peanuts did he order?
A) 10 pounds B) 2 pounds C) 4 pounds D) 6 pounds
Solve the problem.
109) What is the size of the matrix?
2 5 7
-4 -9 1
A) 6 B) 3 C) 3 x 2 D) 2 x 3
Perform the indicated operation where possible.
110) 3 4 + -4
7
A)
3 -4
4 7
B)
-1
11
C)
-1 11
D) Not defined
111)
-1 2
0 4
7 -4
- 2 1
7 4
2 2
A)
1 1
7 0
5 -2
B)
-3 1
-7 0
5 -6
C)
1 3
7 8
9 1
D)
3 -1
7 0
-5 6
Perform the indicated operation.
112) Let C =
1
-3
2
and D =
-1
3
-2
. Find C - 4D.
A)
5
-15
10
B)
5
-6
4
C)
-5
15
-10
D)
-3
9
-6
Page 25
Solve the problem.
113) Barnes and Able sell life, health, and auto insurance. Sales for May and June are given in the matrices.
Life Health Auto
M =
20,000 15,000 8000
30,000 0 17,000
Able
Barnes
J =
70,000 0 30,000
20,000 22,000 32,000
Able
Barnes
Find the matrix that would give total sales for the months of May and June.
A)
90,000 0 38,000
50,000 0 49,000
B)
140,000 37,000 87,000
C)
90,000 15,000 38,000
50,000 22,000 32,000
D)
90,000 15,000 38,000
50,000 22,000 49,000
114) The matrix shows the average number of wax and buff treatments each of 3 workers in a car wash can do in a day. Give the
matrix that shows what each worker can do in 2 days.
Wax Buffs
T =
6 10
9 3
8 5
Ford
Morton
Porter
A)
12 20
18 6
16 10
B)
32
24
26
C)
20 12
6 18
10 16
D)
12 20
18 6
15 10
Find the order of the matrix product AB and the product BA, whenever the products exist.
115) A is 2 x 3, B is 3 x 2.
A) AB is 2 x 2, BA is nonexistent. B) AB is 2 x 2, BA is 3 x 3.
C) AB is 3 x 3, BA is 2 x 2. D) AB is nonexistent, BA is 3 x 3.
116) A is 2 x 1, B is 1 x 1.
A) AB is nonexistent, BA is 1 x 2. B) AB is 2 x 1, BA is nonexistent.
C) AB is 1 x 2, BA is 1 x 1. D) AB is 2 x 2, BA is 1 x 1.
Given the matrices A and B, find the matrix product AB.
117) A = -1 3
2 2 , B =
-2 0
-1 5 Find AB.
A)
2 0
-2 10
B)
2 -6
-1 7
C)
15 -1
10 -6
D)
-1 15
-6 10
Page 26
118) A = -1 3
3 2 , B =
0 -2 5
1 -3 2 Find AB.
A) AB is not defined. B)
3 -7 1
2 -12 19
C)
3 2 -7
-12 1 19
D)
0 -6
15 3
-6 4
119) A = 3 -2 1
0 4 -3 , B =
4 0
-2 2 Find AB.
A) AB is not defined. B)
12 -8 4
-6 12 -8
C)
12 -6
-8 12
4 -8
D)
12 0
0 8
Solve the problem.
120) Three different high schools plan to order the same three text books. School A plans to order 50 of book 1, 90 of book 2,
30 of book 3. School B plans to order 80 of book 1, 90 of book 2, 30 of book 3. School C plans to order 20 of book 1, 50
of book 2, 30 of book 3. The cost of book 1 is $15 per copy, the cost of book 2 is $20 per copy, and the cost of book 3 is
$25 per copy. What matrix product displays the cost to each school of buying the textbooks? Display the two matrices
which must be multiplied and their product.
A) 15 20 25
150
230
90
= 2250 4600 2250 B) 15 20 25
170
200
100
= 2550 4000 2500
C) 15 20 25
50 80 20
90 90 50
30 30 30
= 3300 3750 2050 D) 15 20 25
50 90 30
80 90 30
20 50 30
= 2850 4400 1800
Page 27
Answer Key
Testname: MATH 1453 - PRACTICE FINAL EXAM
1) A
2) C
3) B
4) B
5) A
6) C
7) B
8) A
9) D
10) C
11) B
12) C
13) B
14) B
15) D
16) C
17) B
18) B
19) D
20) D
21) B
22) B
23) A
24) A
25) D
26) B
27) C
28) B
29) A
30) A
31) C
32) C
33) A
34) D
35) A
36) C
37) A
38) C
39) B
40) C
41) C
42) D
43) C
44) D
45) D
46) D
47) A
48) D
49) D
50) A
51) A
52) A
53) B
54) A
55) B
56) C
57) D
58) C
59) D
60) C
61) B
62) C
63) B
64) D
65) D
66) B
67) C
68) B
69) A
70) C
71) D
72) B
73) B
74) B
75) D
76) A
77) C
78) D
79) A
80) C
81) A
82) C
83) B
84) C
85) D
86) A
87) A
88) D
89) D
90) B
91) B
92) B
93) C
94) A
95) D
96) A
97) A
98) A
99) C
100) C
101) B
102) A
103) B
104) B
105) A
106) B
107) A
108) A
109) D
110) D
111) B
112) A
113) D
114) A
115) B
116) B
117) D
118) B
119) A
120) C
