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Math-120 Final Practice Problems (all chapters)
This is a 85 minute, closed-book exam. One cheat sheet of 8½ in by 11 in. is allowed. Show
your work! The answer without work will not receive full credit.
1. A bag of fertilizer covers 2500 ft2. How many bags are needed to cover an area of 32,000 ft2?
Sol. 13 bags
(1.3)
2. Let
(2.2)
U = {1, 2, 3, 4, 5, 6}
A = {1, 3, 4}
B = {2, 3, 6}
C = {1, 5}
Determine the following:
a. A’  B
Sol.
A’ = { 2,
5, 6}
B = { 2, 3,
6}
b.
A’  B = {2, 3, 5, 6}
A  B’
Sol.
A = {1, 3, 4}
B’ ={1,
4, 5}
A  B’ = {1, 4}
3. Real Estate. The Maiellos are moving to Wilmington, Delaware. Their real estate agent
located 83 houses listed for sale, in the Wilmington are, in their price range. Of these houses
listed for sale,
(2.3)
47 had a family room, (R)
42 had a deck,
(D)
30 had a family room and a deck.
How many had
a) a family room but not a deck?
Sol.
II = 30
R but no D = I = 47 – 30 = 17
b) a deck but not a family room?
Sol.
D but no R = III = 42 – 30 = 12
U
R
I
II
III
D
IV
c) either a family room or a deck?
Sol.
I  II  III = 30 + 17 + 12 = 59
1
4. Let p = T, q = r = F, determine the value of the following statement:
[p ⋀ (q ∨ p)]
(3.2)
[T ⋀ (F ∨ T)]
= [F ⋀ (T ∨ T)]
= [F ⋀ T]
= F
Sol.
=T
5. Let p = r = T, q = F, determine the value of the following statement:
(r ⋀ q) ⋀ (r ∨ ~p)
(3.2)
(T ⋀ F) ⋀ (T ∨ ~T)
= (F ⋀ T) ⋀ (F ∨ F)
=F⋀F
Sol.
=F
6. Add in the indicated base:
Sol.
567 + 357
(4.4)
1247
7. Convert the numeral to a numeral in base 10: 4537
Sol.
5637 = 5(72) + 6(7) + 3 = 245 + 42 + 3 = 290
8. Subtract in the indicated base:
Sol.
3335
(4.3)
4215 – 335
(4.4)
9. Perform the rigid motion indicated in each case:
(a) In figure (a), reflect the triangle w.r.t. the x-axis.
(b) In figure (b), rotate the triangle by 90 counterclockwise, w.r.t. the origin.
y
y
B’
5
4
3
2
1
6 5 4 3 2 1 0 1 2 3 4 5 6
1
2
3
4
5
6
(a)
(9.5)
C’
x
5
A’4
3
2
1
C
B
A
0
1
2 3 4 5 6
6 54 3 2 1
1
2
3
4
5
6
x
(b)
2
10. Use the compound interest formula to compute the total amount accumulated:
$20,000 for 6 years at 2.5% compounded semiannually.
Sol. $23,215.09
(11.3)
11. Use the sinking fund formula to determine annual payments (pay once a year) with 7.9%
interest rate compounded annually for 10 years to accumulate to $8000. Round the answers
to the nearest cent.
(11.6)
Sol.
$554.86
12. The Gift Basket Store had the following premade gift baskets containing the following
combinations in stock.
(12.6)
Cookies
Mugs
Candy
Coffee
20
15
15
Tea
15
10
25
Choose 1 basket at random, find the probability that it contains
a. Coffee or candy.
Sol.
total = 50 + 50 = 100,
P(coffee or candy) = (20+15+15+25)/100 = 75/100 = 3/4
b. Tea and cookies.
Sol.
P(tea and cookies) = 15/100 = 3/20
13. Two marbles are drawn from a box with 3 white, 2 green, 2 red, and 1 blue marbles. (12.6)
a. Without replacement, find the probability that the first is white and the second is red?
Sol.
P(one white and one red) = P(1st white and 2nd red) = (3/8)(2/7) = 3/28
b. With replacement, find the probability that the first is white and the second is red?
Sol. P(one white and one red) = P(1st white and 2nd red) = (3/8)(2/8) = 3/32
14. A bag contains 4 red balls and 5 green balls. Select 3 at random, what is the probability that 2
green balls and 1 red ball are selected?
(12.10)
Sol.
10/21
15. The following is the grades for a Statistics test.
52
66
63
61
88
60
74
70
75
(13.3)
80
65
78
a. Construct the frequency distribution (table).
Class
frequency
50 – 59
1
60 – 69
5
70 – 79
4
80 – 89
2
3
b. Construct the stem-leaf display.
Sol.
5
6
7
8
2
01356
0458
08
16. A student obtains the following grades in 8 quizzes.
65
75
80
85
70
90
Find the following:
1) Mean
Ans. 76.25
2) Median
Ans. 75
3) Mode Ans. 70, 75 (bi-modal)
4) Standard Deviation Ans. 8.35
5) Range Ans. 25
(13.4, 13.5)
70
75
17. The average middle-distance runner at a local high school runs the mile in 5.6 minutes, with
a standard deviation of 0.2 minutes. Find the percentage of runners that will run the mile in
greater than 5.2 minutes. Ans. 0.9772 = 97.72%
(13.6)
4