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Contemporary Mathematics
Midterm Review 2013-2014
** Show ALL work on problems. **
Unit 1: Critical Thinking Skills (Reasoning & Problem Solving)
Find the next three numbers in the pattern.
1. 8, 13, 18, 23, …
1 1
1
2. 1, − , , − , …
2
4
8
3. Below is a chart that indicates how Kerry spent her $1500 monthly paycheck.
a) How much (in dollars) did Kerry spend on her mortgage?
b) How much more (in dollars) did Kerry Spend on her mortgage?
4. Jason has a checking account at the First Financial Bank. For this service, the bank charges a $3.50 monthly fee
which includes the fee for the first ten checks written. For any checks written during the month after the first
ten checks, the bank charges $0.07 per check. If Jason had to pay a total fee of $4.55 in the month of February,
how many checks did he write during that month? Please show all work.
1
5. If it takes Irene 6 4 hours to plant 25 geraniums, how long does it take Irene to plant each geranium?
6. On a map, if 4 inches represents 50 miles, how many inches would represent 125 miles?
7. Steve Ray gets paid $15.50 per hour with double time for any time worked over 40 hours per week. If he works a
60-hour work week and gets paid $1240, was Steve underpaid? If so, by how much?
8. Create a magic square by using the numbers 4, 8, 12, 16, 20, 24, 28, 32, and 36. The sum of the numbers in every
row, column, and diagonal must be 60.
9. Create a magic square by using the numbers 5, 7, 9, 11, 13, 15, 17, 19, 21. The sum of the numbers in every row,
column, and diagonal must be 39.
10. Larry wants to purchase four lamps for his house. Sunrise has lamps on sale at two for $60. He has a coupon for
15% off the original price of $35 per lamp, for an unlimited number of lamps. Show all work.
a. Determine the cost of purchasing four lamps at sale price.
b. Determine the cost of purchasing four lamps if the coupon is used.
c. Which is the least expensive way to purchase the four lamps, AND by how much?
11. How many rectangles are there in the last two figures?
12. Use each number 26, 27, 28, 29, 30, 31, 32, 33, 34 once.
13. Jeff Howard parked his car in a lot that charged $2.00 for the first hour and $1.50 for each additional hour. He
left the car in the lot for 8 hours. How much change did he receive forma $20 bill?
14. The profit earnings for XYZ company are reported quarterly. The earnings as a percentage of the yearly earnings
for 1995 are shown in the pie chart. If the earnings in the first quarter were $52,000, what were the earnings for
the whole year?
15. Is this a Fibonacci Sequence? 1, 1, 2, 3, 5, 8, 13…
Unit 2: Sets
16. Express the set in roster form: The different grade levels (in terms)
Tell whether the statement is true or false. If false, explain why.
17. 9 ∈ { 18, 27, 36, 45, 54}
18. 6 ∈ { 4, 5, 6, 7}
19. 9 ∈ {3, 8, 10, 13}
20. 2 ∉ {𝑥 | 𝑥 𝑖𝑠 𝑎𝑛 𝑜𝑑𝑑 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟}
21. {c, a, t} = {d, o, g}
22. {8, 11, 13} = {0, 8, 11, 13}
23. For a class project, Ben asked 130 of his classmates what reality shows they watched. The results are as follows:
87 students watch American Idol
76 students watch Survivor
60 students watch The Apprentice
55 students watch American Idol and Survivor
40 students watch Survivor and The Apprentice
45 students watch American Idol and The Apprentice
35 students watch all three reality shows
Construct a Venn diagram and then determine how many students watch:
a)
b)
c)
d)
e)
f)
Exactly one of these reality shows
None of these reality shows
All three of these reality shows
Only American Idol
Survivor and The Apprentice, but not American Idol
At least two of these reality shows
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = { 1, 2, 3, 4, 5, 6, 7, 8}
Determine whether the statement is true or false.
24. D ⊆ B
Unit 3: Logic
Find the truth value of the statements.
25. If 6 ⋅ 3 = 18, then 4 + 3 = 8.
26. If height can be measured in pounds then a dollar bill is paper money, and Hawaii is an island.
27. Write the converse, inverse, and contrapositive of the conditional statement:
Conditional: “If I get paid today, then I will go shopping.
Converse:
Inverse:
Contrapositive:
Let p represent a true statement, while q and r are false statements. Find the truth value of the compound statement.
28. ~ [ ( ~ p Ʌ ~ q) ∨ ~ q ]
Unit 12: Probability
29. Fifty people who visited the Humane Society adopted a pet. Twenty of them adopted a cat. Find the
experimental probability that the next person who adopts a pet at the Humane Society adopts a cat.
30. Marcus is going to wear a blue sport coat and is trying to decide what tie he should wear to work. In his closet,
he has 27 ties, 8 or which he feels go well with the sport coat. If Marcus selects one tie at random, determine:
a. The probability it goes well with the sport coat.
b. The probability it does not go well with the sport coat.
c. The odds against it going well with the sport coat.
d. The odds in favor of it going well with the sport coat.
In the following exercises, one card is selected from a deck of play8ing cards. Find the probability of selecting:
31. An ace or 2.
32. A picture card or a red card.
In the following exercises, each of the numbers 5-15 is written on a sheet of paper. The eleven sheets of paper are
placed in a small wicker basket. If one sheet of paper is selected at random from the basket, find the probability that
the number is selected is:
33. Less than 10.
34. Even.
35. Odd or greater than 8.
36. Even and greater than 8.
In the following exercises 37-40, if two of the same eleven sheets of paper mentioned in the above problems are
selected from the basket, without replacement, find the probability that :
37. Both numbers are less than 10.
38. Both numbers are odd.
39. The first number is even and the second number is greater than 10.
40. Neither number is odd.
41. One card is selected at random from a deck of cards. Find the probability that the selected card is a spade or a
queen.