Exam #4 Extra Practice Problems, Math 100, Professor Wilson
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Kate decides to replace all the lights in her college apartment with energy saving light bulbs
beginning this month. The packaging says the new bulbs will use 25% less electricity. If Kate's
electric bill last month was $10.00 from bulb use alone, project how much Kate's electric bill will be
this month for bulb use.
A) $9.75
B) $2.50
C) $5.00
D) $7.50
E) $12.50
Express the percentage as a simplified fraction
2) 4.75%
18
19
A)
B)
400
400
38
C)
800
9
D)
200
4
E)
75
Solve the problem.
3) A savings bond currently worth $7600 collects 5.5% annual simple interest each year. If the bond
was purchased seven years ago, how much was it bought for?
A) $11,780.00
B) $5487.36
C) $4903.23
D) $2673.21
E) $1381.81
1)
2)
3)
4) A loan worth $1000 collects simple interest each year for 6 years. At the end of that time, a total of
$1270 is paid back. Determine the APR for this loan.
A) 4.25%
B) 5.75%
C) 5%
D) 4.5%
E) 5.5%
4)
5) Suppose you buy a $9000 savings bond that pays 4.75% annual simple interest. When you cash in
the bond, you have to pay 16% federal taxes on the interest you earned. How much money would
you net if you cash in the bond after six years?
A) $11,565.60
B) $10,915.20
C) $11,154.60
D) $13,275.30
E) $10,440.70
5)
6) A bank offers a 7.3% annual interest rate compounded daily. The periodic interest rate is
A) 0.02%.
B) 0.00002%.
C) 0.00073%.
D) 0.00068%.
E) none of these
6)
7) Suppose that $3500 is invested in a savings account with an APR of 8.25%. What is the future value
of the account in 8 years?
A) $5631
B) $1320
C) $6599
D) $6579
E) $180
7)
1
8) Suppose that $575.75 is invested in a savings account with an APR of 12% compounded monthly.
What is the future value of the account in 5 years?
0.12 60
A) $575.75 1 +
12
8)
B) $575.75(1.12)60
C) $575.75
1.12 60
12
D) $575.75(1.12)5
E) none of these
9) Suppose that $P is invested in a savings account with an APR of i% compounded quarterly. What
is the future value of the account in 10 years?
1 + i 40
A) P
4
B) P 1 +
C) P 1 +
D) P 1 +
9)
i 40
400
i 40
4
100i 40
4
E) none of these
Consider a geometric sequence that has initial term G0 = 75 and a common ratio c = 2.2.
10) Find G 1.
A) 144
11) Find G 4.
A) 2250.32
10)
B) 150
C) 155
D) 35
E) 165
B) 1650.52
C) 7522.30
D) 798.60
E) 1756.92
11)
As summer approaches the size of Matt's wardrobe increases weekly by 6%. Assume that Matt's wardrobe contained
112 pieces in March, and let GN denote the number of pieces in his wardrobe N months after March.
12) How many pieces does Matt have in his wardrobe in July (N = 5)? Round to the nearest whole
number.
A) 151
B) none of these
C) 96
D) 150
E) 124
2
12)
13) Give an explicit formula for GN.
13)
A) GN = N · (1.06)112
B) GN = N · (112)1.6
C) GN = 112 · (1.06)N
D) GN = 112 · (1.6)N
E) GN = 112 · (N)1.06
Solve the problem.
14) 4 + 4 × 3 + 4 × 32 + . . . + 4 × 3 88 =
A) 2 × (3 89 - 1)
14)
B) 4 × (3 89 - 1)
C) 4 × (3 88 - 1)
D) 2 × (3 88 - 1)
E) none of these
15)
$22
$22
$22
$22
+
+
+...+
(1.025) (1.025)2 (1.025)3
(1.025)50
A) $655.23
B) $611.01
15)
C) $671.92
D) $623.97
E) $617.57
16) Starting at age 22, Khalfani invests $1800 at the beginning of each year in an IRA with an APR of
7% compounded annually. How much money will there be in Khalfani's retirement account when
he retires at the age of 65? (Assume that his 43rd and last deposit generates interest for one year.)
A) $512,548.76
B) $502,293.32
C) $482,349.03
D) $507,404.89
E) $477,217.53
16)
17) Starting at age 22, Celine invests $1800 at the end of each year in an IRA with an APR of 7%
compounded annually. How much money will there be in Celine's retirement account when he
retires at the age of 65? (Assume that his 43rd and last deposit generates no interest.)
A) $477,217.53
B) 443,997.69
C) $454,778.22
D) $445,997.69
E) 421,236.16
17)
18) Find the present value of an installment loan consisting of 20 annual payments of $1500 assuming
an APR of 5.5% compounded annually. (Assume each of the payments are made at the end of
each year.)
A) $18,911.48
B) $18,455.79
C) $17,925.57
D) $18,693.31
E) $19.627.98
18)
19) Find the present value of a 30-month installment loan consisting of 30 monthly payments of $24
assuming an APR of 7% compounded annually. (Assume each of the payments are made at the
end of each year.)
A) $662.61
B) $654.94
C) $702.33
D) $631.91
E) $658.76
19)
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20) George plans to donate $10 per week to the World Wildlife Fund for the next 25 years. Assuming
an annual interest rate of 6% compounded weekly, find the present value of this annuity to the
World Wildlife Fund.
A) $6731.20
B) $6338.96
C) $6721.20
D) $6738.97
E) $6454.38
20)
The figure below is a square ABCD with center O. (M, N, P, and Q are the midpoints of the sides.)
21) The image of A under the reflection with axis the line passing through M and P is
A) B.
B) D.
C) C.
D) O.
E) none of these
21)
The figure below is a regular hexagon ABCDEF with center O. (P, Q, R, S, T, and U are the midpoints of the sides.)
22) The image of A under the reflection with axis the line passing through B and E is
A) T.
B) C.
C) Q.
D) D.
E) none of these
22)
23) The image of A under a 300° counterclockwise rotation with center O is
A) E.
B) F.
C) B.
D) C.
E) none of these
23)
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24) Which of the following reflections is not a symmetry of the regular hexagon?
A) the reflection with axis the line passing through R and S
B) the reflection with axis the line passing through A and D
C) the reflection with axis the line passing through A and B
D) the reflection with axis the line passing through P and Q
E) all of these are symmetries of the regular hexagon.
24)
25) Which of the following rotations is not a symmetry of the regular hexagon?
A) a 180° clockwise rotation with center O
B) a 60° clockwise rotation with center O
C) a 120° counterclockwise rotation with center O
D) a 90° clockwise rotation with center O
E) none of these
25)
Solve the problem.
26) What are the symmetries of the letter B?
A) a reflection with axis a vertical line
B) a reflection with axis a horizontal line
C) a 90° rotation
D) all of these
E) none of these
26)
27) Which of the following are symmetries of the letter D?
A) a reflection with axis a diagonal line
B) a 90° rotation
C) a reflection with axis a vertical line
D) a reflection with axis a horizontal line
E) none of these
27)
28) The letter B has symmetry type
A) Z 1 .
28)
B) Z 2 .
C) D2 .
D) D1 .
E) none of these
29) The greek letter
A) D1 .
(gamma) has symmetry type
29)
B) Z 2 .
C) D2 .
D) Z 1 .
E) none of these
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30)
The symbol
30)
has symmetry type
A) Z 1 .
B) Z 2 .
C) D1 .
D) D2 .
E) none of these
31) Which of the following letters has the same symmetry type as the letter X?
A) E
B) M
C) U
D) H
E) none of these
31)
32) The kind of symmetries found in the border pattern . . . S S S S S S . . . are the identity and
A) translations and vertical reflections only.
B) translations and half-turns only.
C) translations only.
D) translations and horizontal reflections only.
E) none of these
32)
33) The kind of symmetries found in the border pattern . . . A A A A A A . . . are the identity and
A) translations and vertical reflections only.
B) translations and horizontal reflections only.
C) translations only.
D) translations and half-turns only.
E) none of these
33)
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