MATH 1453 - COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #3 - SPRING 2007 - DR. DAVID BRIDGE
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the interest. Round to the nearest cent.
1) $900 at 12% simple interest for 4 years.
A) Interest = $18.75
B) Interest = $432.00
C) Interest = $2700.00
D) Interest = $43.20
C) Interest = $3.30
D) Interest = $475.20
2) $360 at 11% simple interest for 12 months
A) Interest = $39.60
B) Interest = $3960.00
Solve the problem.
3) Gan-Lin borrowed $3700 from his father to buy a car. He repaid him after 6 months with simple interest of 3%. Find the
total amount he repaid.
A) $55.50
B) $3755.50
C) $3746.25
D) $3811.00
4) Tuition of $2500 is due when the spring term begins, in 3 months. What amount should a student deposit today, at
12% simple interest, to have enough to pay tuition?
A) $72.82
B) $2450.98
C) $2427.18
D) $2232.14
C) $29,280.00
D) $47,643.67
C) $14,326.78
D) $14,098.73
Find the compound amount for the deposit. Round to the nearest cent.
5) $12,000 at 9% compounded annually for 16 years
A) $43,709.79
B) $28,200.00
6) $8000 at 12% compounded semiannually for 5 years
A) $10,705.80
B) $12,800.00
Find the compound interest earned by the deposit. Round to the nearest cent.
7) $10,000 at 7% compounded annually for 6 years
A) $5007.30
B) $4025.52
C) $4200.00
D) $3500.00
C) $32.15
D) $30.00
8) $200 at 5% compounded quarterly for 3 years
A) $207.59
B) $31.53
Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points.
9) 18% compounded quarterly
A) 19.25%
B) 18.81%
C) 18.00%
D) 19.56%
B) 4.07%
C) 0.60%
D) 3.06%
10) 4% compounded monthly
A) 4.04%
Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.
11) $3800 at 5% compounded annually for 9 yr
A) $5895.05
B) $2449.51
C) $1350.49
D) $2571.99
12) $3900 at 6% compounded quarterly for 7 yr
A) $5917.17
B) $2593.72
C) $1329.51
D) $2570.49
Solve the problem. Round to the nearest cent.
13) A small company borrows $21,000 at 6% compounded monthly. The loan is due in 2 years. How much interest will the
company pay?
A) $23,670.36
B) $2656.34
C) $2670.36
D) $2552.59
14) Nora Oretega's savings account has a balance of $2362. After 6 years, what will the amount of interest be at 4%
compounded semiannually?
A) $944.80
B) $624.59
C) $633.59
D) $638.59
Solve the problem.
15) Maria and Julio are establishing a fund for their son's college education. What lump sum must they deposit in an account
that gives 6% annual interest rate, compounded monthly, in order for them to have $65,000 in the fund at the end of 10
years?
A) $51,608.69
B) $40,302.13
C) $38,046.13
D) $37,026.13
B) 682
C) 692
D) 686
B) 93
C) 5
D)
B) 65.974
C) 15.974
D) 14.68
B) 39.993
C) 33.76
D) 53.452
Find the sum of the first five terms of the geometric sequence.
16) a = 2, r = 4
A) 684
17) a =
3
,r=2
2
A)
1
8
93
2
Find the value.
s
18) 14 0.02
A) 17.293
s
19) 20 0.06
A) 36.786
Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.
20) R = $100, i = 0.07, n = 12
A) $1578.36
B) $3217.42
C) $300.69
D) $1788.85
C) $879,433.98
D) $129,433.98
21) R = $7500, i = 2% interest compounded semiannually for 8 years
A) $430,757.13
B) $120,726.72
Find the periodic payment that will render the sum.
22) S = $23,000, interest is 8% compounded annually, payments made at the end of each year for 12 years
A) $1381.76
B) $2162.34
C) $1869.97
D) $1211.99
23) S = $27,000, interest is 18% compounded monthly, payments made at the end of each month for 3 years
A) $7557.94
B) $719.26
C) $571.11
D) $598.46
Solve the problem.
24) If Bucy deposits $5000 at the end of each year for 9 years in an account paying 6% interest compounded annually, find the
amount she will have on deposit.
A) $49,487.34
B) $57,456.58
C) $65,903.97
D) $52,456.58
25) At the end of every 3 months, Teresa deposits $100 into an account that pays 5% compounded quarterly. After 2 years, she
puts the accumulated amount into a certificate of deposit paying 7.5% compounded semiannually for 1 year. When this
certificate matures, how much will Teresa have accumulated?
A) $895.42
B) $903.00
C) $965.97
D) $899.76
26) Mark wants to start an IRA that will have $240,000 in it when he retires in 21 years. How much should he invest quarterly
in his IRA to do this if the interest is 5% compounded quarterly?
A) $4451.57
B) $1006.50
C) $1618.22
D) $1631.22
B) 12.3996
C) 9.8226
D) 9.929
B) 2.554
C) 21.7583
D) 1.7711
Find the value.
a
27) 25 0.09
A) 9.7066
a
28) 2 0.085
A) 0.9217
Find the present value of the ordinary annuity.
29) Payments of $400 made annually for 13 years at 6% compounded annually
A) $3353.52
B) $3539.80
C) $4868.98
D) $3718.00
30) Payments of $90 made quarterly for 10 years at 8% compounded quarterly
A) $1531.91
B) $2478.19
C) $2421.23
D) $3382.51
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).
31) $1000 at 3%
A) $14,877.50
B) $15,415.00
C) $14,323.20
D) $14,867.50
B) $560,799.45
C) $560,619.00
D) $543,838.50
C) $241.55
D) $305.05
32) $45,000 at 5%
A) $576,954.00
Find the payment necessary to amortize the loan.
33) $1500; 6% compounded annually; 7 annual payments
A) $268.70
B) $271.33
34) $12,800; 12% compounded monthly; 48 monthly payments
A) $1542.69
B) $337.07
C) $337.31
D) $331.71
Find the monthly house payment necessary to amortize the following loan.
35) In order to purchase a home, a family borrows $55,000 at 13% for 30 yr. What is the monthly payment?
A) $595.83
B) $620.31
C) $19.86
D) $608.41
Solve the problem.
36) Tasha borrowed $13,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly
payments over a 5 year period. What is her monthly payment?
A) $282.65
B) $325.29
C) $23.83
D) $119.17
37) What is the least amount that should be deposited in a bank account today at 12% compounded quarterly to allow $650
withdrawals at the end of each quarter for 8 years?
A) $13,497.76
B) $30,080.64
C) $13,252.70
D) $13,000.28
B) (7, -5)
C) (8, -6)
D) No solution
B) (7, 0)
C) (0, -7)
D) (1, -8)
B) (1, -6)
C) No solution
D) (1, -5)
B) (1, 0)
C) No solution
D) (0, -3)
Solve the system of two equations in two variables.
38) x + 5y = -22
3x + 4y = 0
A) (-8, -5)
39) x - 7y = 49
-2x - 6y = 42
A) No solution
40) 9x + 9y = -45
-5x + 2y = -17
A) (0, -5)
41) 3x - 2y = 6
6x - 4y = 30
A) (1, -1.5)
42) 2x + 5y = 6
6x + 15y = 18
1
A) , 1
2
B) 3, 0
C) No solution
D) -
5
y + 3, y for any real number y
2
Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system.
1
1
43) x + y = -3
2
2
x- y=8
A) (0, -6)
B) (-1, -6)
C) No solution
D) (1, -7)
44)
1
1
x + y = -1
2
2
1
1
x- y=5
2
2
A) No solution
45)
B) (3, -5)
C) (-4, -5)
D) (4, -6)
3x 3y 33
=
8
5
80
4x 4y 37
+
=
7
5
35
A)
3 3
,
2 4
B)
3 1
,
4 2
C)
3 1
,
2 4
D)
1 1
,
4 2
Solve the problem by writing and solving a suitable system of equations.
46) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $114 for 3 days and 300 miles,
while Mary was charged $204 for 5 days and 600 miles. What does Best Rental charge per day and per mile?
A) $24 per day and 14 cents per mile
B) $25 per day and 15 cents per mile
C) $14 per day and 24 cents per mile
D) $23 per day and 15 cents per mile
47) A shopkeeper orders 56 pounds of cashews and peanuts. If the amount of cashews he orders is 24 pounds less than the
amount of peanuts, how many pounds of peanuts did he order?
A) 28 pounds
B) 16 pounds
C) 32 pounds
D) 40 pounds
48) Carole's car averages 12.5 miles per gallon in city driving and 22.8 miles per gallon in highway driving. If she drove a total
of 299.3 miles on 19 gallons of gas, how many of the gallons were used for city driving?
A) 6 gallons
B) 11 gallons
C) 15 gallons
D) 13 gallons
49) If 20 pounds of tomatoes and 30 pounds of bananas cost $21 and 40 pounds of tomatoes and 50 pounds of bananas cost $
39, what is the price per pound of tomatoes and bananas?
A) tomatoes: $0.70 per pound; bananas: $0.30 per pound
B) tomatoes: $0.50 per pound; bananas: $0.37 per pound
C) tomatoes: $0.70 per pound; bananas: $0.23 per pound
D) tomatoes: $0.60 per pound; bananas: $0.30 per pound
Solve the problem.
50) What is the size of the matrix?
8 5 -6
-4 6 1
A) 3 x 2
B) 2 x 3
C) 3
D) 6
B) 4 x 1
C) 1 x 4
D) 4
51) What is the size of the matrix?
3 -9 2 7
A) 1
52) What is the size of the matrix?
2 6
-5 -1
A) 1
B) 4
C) 2
D) 2 x 2
B) 3 × 1
C) 1 × 3
D) 3 × 0
B) 4 × 4
C) 4 × 3
D) 3 × 4
C)
D)
53) What is the size of the matrix?
7
12
5
A) 3 × 3
54) What is the size of the matrix?
-11 -10 -4 -4
5 4 -1 -7
12 0 -5 17
A) 3 × 3
Perform the indicated operation where possible.
62
-7 1
55)
+
23
25
A)
B)
34
48
56) 5 4
-1 -5
-5 -4
14
-3
8
+
A)
B) Not defined
C)
5 -3
4 8
-1 5
57) 0 4
6 -4
-1 3
48
D)
2
12
2 12
21
- 74
42
A)
B)
3 -4
7 0
-2 6
C)
-3 4
-7 0
2 -6
D)
1 6
7 8
10 -2
1 4
7 0
2 -2
Perform the indicated operation.
-3 1
58) Let A =
. Find 4A.
02
A)
B)
15
46
C)
-12 4
08
D)
-12 1
02
-12 4
02
59) Let B = -1 3 6 -3 . Find -4B.
A) -3 1 4 -5
B) 4 3 6 -3
C) -4 12 24 -12
D) 4 -12 -24 12
6
1
60) Let C = -2 . Find
C.
2
12
A)
B)
3
-2
12
61) Let A =
C)
6
-1
12
13
26
and B =
B)
2 10
1 12
C)
2 10
3 18
and D =
12
-4
24
04
. Find 2A + B.
-1 6
A)
1
62) Let C = -3
2
D)
3
-1
6
D)
2 7
3 12
2 14
2 24
-1
3 . Find C - 3D.
-2
A)
B)
-2
6
-4
C)
4
-12
8
D)
-4
12
-8
4
-6
4
Write a matrix to display the information.
63) A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1
red. C requires 2 black, 1 white, and 2 red. Make a 3 x 3 matrix showing the wire requirements. Assign the cable types to
the rows and the wire types to the columns.
A)
B)
212
121
233
C)
212
321
312
D)
332
121
212
312
321
212
64) Factory A makes 9 model-A, 6 model-D, and 6 model-M train sets. Factory B makes 8 model-A, 8 model-D, and 6
model-M train sets. If model-A sells for $16, model-D for $21, and model-M for $31, write a 2 x 3 matrix to summarize the
income by model.
A)
B)
144 128
126 168
186 186
C)
144 126 186
128 168 186
D)
144 168
96 168
96 126
144 96 96
168 168 126
Solve the problem.
65) Barnes and Able sell life, health, and auto insurance. Sales for May and June are given in the matrices.
Life Health Auto
20,000 15,000 6000
M = 30,000
0 17,000
70,000
0 30,000
J =
10,000 20,000 32,000
Able
Barnes
Able
Barnes
Find the matrix that would give total sales for the months of May and June.
A)
B)
130,000 35,000 85,000
90,000 15,000 36,000
40,000 20,000 49,000
C)
D)
90,000 15,000 36,000
40,000 20,000 32,000
90,000 0 36,000
40,000 0 49,000
66) Carney and Dobler sell home and mortgage insurance. Their sales for the months of May and June are given in the
matrices.
Home Mortgage
22,000 45,000 Carney
M=
J =
18,000 27,000
Dobler
25,000 43,000
Carney
14,000 21,000
Dobler
Find the matrix that would give the change in sales from May to June.
A)
B)
C)
7000 -8000
-7000 8000
D)
-3000 2000
4000 6000
3000 -2000
-4000 -6000
67) 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
6
10 Ford
9
3 Morton
T=
8
5 Porter
A)
B)
32
24
26
C)
20 12
6 18
10 16
D)
12 20
18 6
16 10
12 20
18 6
15 10
Find the order of the matrix product AB and the product BA, whenever the products exist.
68) A is 3 x 4, B is 4 x 3.
A) AB is 4 x 4, BA is 3 x 3.
B) AB is 3 x 3, BA is nonexistent.
C) AB is 3 x 3, BA is 4 x 4.
D) AB is nonexistent, BA is 4 x 4.
69) A is 2 x 1, B is 1 x 1.
A) AB is 1 x 2, BA is 1 x 1.
B) AB is 2 x 1, BA is nonexistent.
C) AB is 2 x 2, BA is 1 x 1.
D) AB is nonexistent, BA is 1 x 2.
70) A is 4 x 2, B is 4 x 2.
A) AB is 4 x 4, BA is 2 x 2.
B) AB is 4 x 2, BA is 2 x 4.
C) AB is 2 x 4, BA is 4 x 2.
D) AB is nonexistent, BA is nonexistent.
Given the matrices A and B, find the matrix product AB.
-2 3
-2 0
71) A =
, B=
Find AB.
-1 4
42
A)
B)
1 12
-10 8
72) A =
0 -2
4 1
, B=
-2 0
-1 1
A)
B)
-1 3
32
C)
04
-4 1
, B=
0 -2 4
1 -3 2
A)
, B=
C)
30
-2 3
B)
C)
30
-2
1
, B=
03
0 -6
12 3
-6 4
D)
9 -6
-6 16
3 -11
9 0
0 12
Find AB.
B)
3 -6 0
0 0 9
D)
Find AB.
9 -6 3
-6 16 -11
A)
-8 -2
4 3
3 2 -7
-12 2 16
A) AB is not defined.
1 3 -2
75) A =
4 0 3
D)
Find AB.
B) AB is not defined.
3 -2 1
0 4 -3
4 -6
-6 5
2 -2
-9 1
3 -7 2
2 -12 16
74) A =
D)
12 1
8 -10
Find AB.
-2 2
-7 -9
73) A =
C)
40
-4 8
C)
-3 -3
9 12
D)
-3 -3
12 9
AB is not defined.
Find the inverse, if it exists, of the given matrix.
5 12
76)
2 5
A)
B)
-5 2
12 -5
77) A =
B)
1
5
5 -12
-2 5
C)
2
5
D)
2 1
5 3
1 1
3 3
-
1
5
1
3
-
1 1
3 3
1 1
3 3
2
5
1 2
5 5
1
5
0 -3
-3 -5
A)
B)
1
3
C)
0
-
1
3
D)
5 1
9 3
1
0 3
5 1
9 3
79) A =
D)
52
12 5
6 5
3 5
A)
78) A =
C)
-5 -12
-2 -5
5
9
1
3
5 1
9 3
0
-
1
3
0
2 2
5 5
A)
B)
5
21
2
21
5
2
21 21
C)
5
2
21 21
-
5
2
21 21
D)
2
5
21 21
No inverse
-
5
21
2
21
Solve the problem.
80) Three different high schools plan to order the same three text books. School A plans to order 40 of book 1, 30 of book 2,
20 of book 3. School B plans to order 80 of book 1, 60 of book 2, 100 of book 3. School C plans to order 40 of book 1, 60
of book 2, 90 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.
40 30 20
40 80 40
A) 15 20 25
80 60 100 = 3200 3150 4550
B) 15 20 25
30 60 60 = 1700 4900 4050
40 60 90
20 100 90
160
90
C) 15 20 25
150 = 2400 3000 5250
D) 15 20 25
240 = 1350 4800 4750
210
190
81) Three different clothing stores order the following amounts of clothing by a certain designer:
Jackets
Shirts
Suits
Store 1:
40
10
30
Store 2:
30
50
10
Store 3:
20
20
30
The unit prices of each product are given below for two suppliers:
Supplier A Supplier B
Jacket
85
90
Shirt
30
30
Suit
180
200
What matrix product displays the cost to each store of buying the clothes from each supplier? Display the two matrices
which must be multiplied and their product.
40 10 30
19,000
40 10 30
85 90
85
A) 30 50 10
B) 30 50 10
30 30 = 12,050
30 = 9100 5850 7700
20 20 30
16,100
20 20 30
180 200
180
40 30 20
7900 8500
40 10 30
9100 9900
85 90
85 90
C) 10 50 20
D) 30 50 10
30 30 = 5950 6400
30 30 = 5850 6200
30 10 30
8250 9000
20 20 30
7700 8400
180 200
180 200
Solve the matrix equation for X.
53
1
82) A =
,B=
, AX = B
85
-8
A)
B)
-69
43
83) A =
D)
29
-48
-19
-32
-1 3
-1 15
, B=
, AX = B
22
-6 10
A)
B)
-2 0
-1 5
84) A =
C)
27
-46
C)
-2 5
-1 0
D)
2 -6
-1 7
2 0
-2 10
0 -1
1 -1
, B=
, AX = B
4 1
-9 1
A)
B)
-8 -2
4 2
C)
02
-4 1
D)
-1 -1
1 0
-2 0
-1 1
C) (8, 19)
D) (-9, 4)
Solve the system by using the inverse of the coefficient matrix.
85) 3x + 7y = 1
5x + 12y = 2
A) (10, -4)
B) (-2, 1)
Graph the linear inequality.
86) 5x + y ≤ -6
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
87) x + 3y ≥ 1
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
88) y ≤ -x + 6
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Graph the feasible region for the system of inequalities.
89) 2x + y ≤ 4
x-1≥0
A)
B)
4
y
4
4 x
-4
y
4 x
-4
-4
-4
C)
D)
4
y
4
4 x
-4
-4
y
4 x
-4
-4
90) 2x + y ≤ 4
y-1≤0
A)
B)
4
y
4
4 x
-4
y
4 x
-4
-4
-4
C)
D)
4
y
4
4 x
-4
-4
y
4 x
-4
-4
91) 3x - 2y ≤ 6
x-1≥0
A)
B)
5
y
5
5 x
-5
y
5 x
-5
-5
-5
C)
D)
5
y
5
5 x
-5
-5
y
5 x
-5
-5
92) 3x + 2y ≤ -6
x-1≥0
A)
B)
5
y
5
5 x
-5
y
5 x
-5
-5
-5
C)
D)
5
y
5
5 x
-5
-5
y
5 x
-5
-5
93) x + 2y ≤ 2
x+y≥0
A)
B)
5
y
5
5 x
-5
y
5 x
-5
-5
-5
C)
D)
5
y
5
5 x
-5
5 x
-5
-5
y
-5
Find the value(s) of the function on the given feasible region.
94) Find the maximum and minimum of z = 22x + 14y.
A) 220, 42
B) 290, 220
C) 290, 42
D) 70, 42
95) Find the minimum of z = 18x + 9y + 11.
A) 38
B) 11
C) 29
D) 20
C) 30, -60
D) -60, 0
96) Find the maximum and minimum of z = 6x - 10y.
A) 30, 0
B) -42.5, -60
Use graphical methods to solve the linear programming problem.
97) Maximize
subject to:
z = 6x + 7y
2x + 3y ≤ 12
2x + y ≤ 8
x≥0 & y≥0
A) Maximum of 32 when x = 2 and y = 3
B) Maximum of 52 when x = 4 and y = 4
C) Maximum of 32 when x = 3 and y = 2
D) Maximum of 24 when x = 4 and y = 0
98) Maximize
subject to:
z = 8x + 12y
40x + 80y ≤ 560
6x + 8y ≤ 72
x≥0 & y≥0
A) Maximum of 96 when x = 9 and y = 2
B) Maximum of 92 when x = 4 and y = 5
C) Maximum of 100 when x = 8 and y = 3
D) Maximum of 120 when x = 3 and y = 8
Find the value(s) of the function, subject to the system of inequalities.
99) Find the maximum and minimum of P = 24x + 19y subject to:
0 ≤ x ≤ 10, 0 ≤ y ≤ 5, 3x + 2y ≥ 6.
A) 95, 57
B) 335, 240
C) 335, 57
D) 240, 57
C) 65, -120
D) 65, 0
100) Find the maximum and minimum of P = 13x - 20y subject to:
0 ≤ x ≤ 5, 0 ≤ y ≤ 8, 4x + 5y ≤ 30, and 4x + 3y ≤ 20.
A) -120, 0
B) -83.75, -120
Answer Key
Testname: MATH 1453 - PRACTICE EXAM #3
1) B
2) A
3) B
4) C
5) D
6) C
7) A
8) C
9) A
10) B
11) B
12) D
13) C
14) C
15) A
16) B
17) D
18) C
19) A
20) D
21) D
22) D
23) C
24) B
25) D
26) D
27) C
28) D
29) C
30) A
31) A
32) B
33) A
34) B
35) D
36) A
37) C
38) C
39) C
40) B
41) C
42) D
43) D
44) D
45) C
46) A
47) D
48) D
49) D
50) B
51) C
52) D
53) B
54) D
55) D
56) B
57) B
58) B
59) D
60) C
61) B
62) B
63) C
64) B
65) A
66) D
67) C
68) C
69) B
70) D
71) A
72) C
73) A
74) A
75) C
76) D
77) C
78) D
79) C
80) B
81) D
82) C
83) A
84) D
85) B
86) C
87) B
88) C
89) C
90) C
91) C
92) A
93) D
94) C
95) D
96) C
97) C
98) C
99) C
100) C