Math 110 Chapter 8, 9, 11 Practice Exam
Bro. Daris Howard
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) The perimeter of a rectangle is 22 cm. The length of the rectangle is 5 cm longer than the width. Find the width
and length of the rectangle.
A) 3, 5
B) 6, 11
C) 3, 8
D) 4, 9
Page Ref: 541-548
2) There were 33,000 people at a ball game in Los Angeles. The day's receipts were $212,000. How many people
paid $14 for reserved seats and how many paid $4 for general admission?
A) 8000 paid $14 and 25,000 paid $4
B) 20,000 paid $14 and 13,000 paid $4
C) 13,000 paid $14 and 20,000 paid $4
D) 25,000 paid $14 and 8000 paid $4
Page Ref: 541-548
Solve the problem by using a system of three linear equations in three variables.
3) 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. They used 100 black, 110 white and 80 red wires. How
many of each cable were made?
A) 20 cable A, 20 cable B, 83 cable C
B) 10 cable A, 20 cable B, 20 cable C
C) 20 cable A, 93 cable B, 10 cable C
D) 20 cable A, 20 cable B, 10 cable C
Page Ref: 553-561
4) Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income
from all three investments is $1600. The combined income from the 5% and 6% investments is the same as the
income from the 8% investment. Find the amount invested at each rate.
A) $10,000 at 5%, $10,000 at 6%, $5000 at 8%
B) $8000 at 5%, $10,000 at 6%, $7000 at 8%
C) $10,000 at 5%, $5000 at 6%, $10,000 at 8%
D) $5000 at 5%, $10,000 at 6%, $10,000 at 8%
Page Ref: 553-561
5) A grain dealer sold to one customer 9 bushels of wheat, 2 of corn, and 5 of rye, for $50.50; to another, 2 of wheat,
5 of corn, and 9 of rye, for $65.40; and to a third, 5 of wheat, 9 of corn, and 2 of rye, for $56.90. What was the price
per bushel for corn?
A) $4.50
B) $4.10
C) $2.20
D) $2.70
Page Ref: 553-561
6) The sum of three numbers is -4. The first, minus the second, plus 3 times the third, equals 10. The third, plus 3
times the first, plus the second, equals -6. What are the numbers? (Express your answer as an ordered triple.)
A) (-1, -1, -5)
B) (1, 5, -2)
C) (-1, -5, 2)
D) No solution
Page Ref: 553-561
Use a system of equations to find the parabola of the form y = ax2 + bx + c that goes through the three points.
7) (-2, -12), (-3, -25), (-5, -69)
A) y = -3x2 + 2x - 4
B) y = -3x2 - 2x + 4
C) y = 3x2 - 2x - 4
D) y = -3x2 - 2x - 4
Page Ref: 553-561
1
Solve the system of equations.
8) 2x - 6y + 7z = -53
-8x + 24y - 28z = 212
8x - 24y + 28z = -212
A) M
B) {(x, y, z)|8x - 24y + 28z = -53}
C) {(x, y, z)|2x - 6y + 7z = -53}
D) {(-3, 2, -5)}
Page Ref: 553-561
9) x - y + 5z = 5
-4x + 4y - 20z = 5
x + 5y + z = -10
A) {(0, -3, 5)}
B) M
C) {(5, 0, -3)}
D) {(5, -3, 0)}
Page Ref: 553-561
Solve the problem.
10) A $108,000 trust is to be invested in bonds paying 7%, CDs paying 6%, and mortgages paying 9%. The bond and
CD investment together must equal the mortgage investment. To earn a $8220 annual income from the
investments, how much should the bank invest in bonds?
A) $54,000
B) $10,000
C) $42,000
D) $12,000
Page Ref: 603-613
11) The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year younger than Ben.
Which of these people were teenagers 7 years ago?
A) Ben
B) Art and Ben
C) Art
D) Art, Ben, and Cal
Page Ref: 603-613
Solve the system using Gaussian elimination.
12) w - x + 2y + z = 4
x + y
=4
y-z =1
A) {(5, 3, 1, 0)}
B) {(5 - 4z, 3 - z, 1 + z, z) z is any real number}
C) M
D) {(1, 2, 2, 1)}
Page Ref: 603-613
Find all the terms of the finite sequence.
13) an = n - 6 , 1 ² n ² 5
A) -5, -4, -3, -2, -1
B) 5, 4, 3, 2, 1
C) 5, 4, -3, -2, -1
D) -6, -5, -4, -3, -2
Page Ref: 719-725
Find the first five terms of the infinite sequence whose nth term is given.
n+1
14) an = (-1) n - 1
2n - 1
4 5 2
A) 2, 1, , ,
5 7 3
B) - 2, 1, -
4 5 2
, ,5 7 3
4 5 2
C) 2, - 1, , - ,
5 7 3
Page Ref: 719-725
2
4 5 2
D) - 2, 1, , - ,
5 7 3
Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.
15) 4, 16, 64, 256, 1024, . . .
A) an = 12n - 4
B) an = 4n
C) an = 4n-1 + 3
D) an = 4n
Page Ref: 719-725
Find the first six terms of the sequence.
16) a1 = 8, an = an-1 + 4
A) 8, 4, 8, 12, 16, 20
B) 8, 12, 16, 20, 24, 28
C) 0, 4, 8, 12, 16, 20
D) 12, 16, 20, 24, 28, 32
Page Ref: 719-725
Find the indicated part of the arithmetic sequence.
17) Find the common difference of the sequence in which the first term is 3 and the 55th term is 9.
1
1
A) B) -6
C) 6
D)
9
9
Page Ref: 719-725
18) Find the common difference of the sequence in which the first term is 7 and the 44th term is -79.
43
43
A) -2
B) C) 2
D)
22
22
Page Ref: 719-725
Find the requested sum of the arithmetic sequence.
19) 10, 5, 0, . . . , -190
A) -3600
B) -180
C) -175
D) -3690
Page Ref: 729-734
Solve the problem.
20) Suppose Janet could save $3 at the end of January, $6 at the end of February, $12 at the end of March, and so on.
What amount would she have saved by the end of one year? Round to the nearest cent.
A) $189.00
B) $4095.00
C) $6142.50
D) $12,285.00
Page Ref: 729-734
21) If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and
so forth, how much money will be in the bank after 50 days?
A) $12.75
B) $0.50
C) $25.50
D) $6.38
Page Ref: 729-734
22) A pendulum is released and swings until it stops. If it passes through an arc of 35 inches the first pass, and if on
4
each successive pass it travels the distance of the preceding pass, how far will it travel before stopping?
5
A) 140 in.
B) 175 in.
C) 210 in.
Page Ref: 738-746
3
D) 315 in.
23) After a person stops pedaling a bicycle, the wheel rotates 490 times the first minute. Each subsequent minute, it
9
rotates
as many times as in the previous minute. How many times will the wheel rotate before coming to a
10
complete stop?
A) 4900 rotations
B) 544.4 rotations
C) 9310 rotations
D) 9800 rotations
Page Ref: 738-746
Find the required part of the geometric sequence.
24) Find the first term of a geometric sequence with the sixth term -354,294 and common ratio of -3.
2
A)
B) -2
C) 1458
D) -6
3
Page Ref: 738-746
25) Find the common ratio for a geometric sequence with the first term 4 and fifth term 1024.
1
A) ±4
B)
C) 64
D) 4
4
Page Ref: 738-746
4
ARITHMETIC
an = a1 +(n-1)d
Sn = na1 +
Sn =
d
n( n - 1)
2
n
(a + an )
2 1
GEOMETRIC
an = a1 rn-1
Sn =
a1 (1 - r n )
r¹1
1- r
S¥ =
a1
1- r