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Principles of Math Practice Test (Most Answers are in your Content Files)
1. A rectangle has an area of 15 square feet. Its length is 4 more than 4 times its width.
What are the dimensions of this rectangle?
2. Write the negations of the statements "Some movies are comedies" and “All math
teachers can not spell”.
3. Let F = "My car is fast", N = "My car is new", and R="My car needs repair". Represent
each of the statements below in symbolic form:
A) My car is slow and needs to be repaired.
B) My car is fast or it does not need repair
B) It is not the case that if my car is fast, then it needs to be repaired.
C) It is not the case that my car is old if and only if it is not fast.
4. Construct a truth table for (~Q) V(P^Q)
5. Construct a truth table for PQ and also construct a truth table for QP.
6. Is “x = 2 if and only if x+3 = 5” an example of a if-and-only-if statement that is always
true in a real-life situation? What about “A car will not start if and only if the car is out of
gas”?
7. Use DeMorgan’s Laws to write the negations of (P V ~Q) and (~P ^ ~Q).
8. Answer the following:
Assume it true that If you study hard, then you get a good grade. Also assume Albert
E. got a good grade. What incorrect conclusion would we reach about Albert E. that
demonstrates the Fallacy of the Converse?
Assume that it is true that if you join an outdoors club you are in favor of preserving the
outdoors. Also assume that you refuse to join any membership to an outdoors
club. What incorrect conclusion would you reach that demonstrates the Fallacy of the
Inverse?
9. How does a company using fine print protect them legally?
10. How many 6 character computer passwords are possible if each character can be an
upper or lower case letter?
11. One must choose from a list of 20 candidates to fill the positions of President, Vice
President, and Secretary. How many ways are there to do this assuming a single person
can not fill two positions?
12. In how many ways may you choose a committee of 4 from a list of 30 candidates?
13. What is the probability of drawing an ace or a three from a regular deck of 52 cards?
Write this probability as a ratio, a fraction, a decimal, and a percent.
14. 100 people are surveyed and 45 are found to prefer a certain political candidate.
From this experimental data we obtain a probability of 45/100. Is this a theoretical
probability or an empirical probability?
15. In the game of "Powerball", 5 white balls are drawn from a tank containing 53 balls
numbered 1 through 53, and 1 red "powerball" is drawn from a tank containing 42 balls
numbered 1 through 42. If you have a game ticket that matched the first 5 white ball
numbers in any order and it also matches the red "powerball" exactly, you win the
jackpot. What is the probability of winning this jackpot?
16. If you flip a coin four times, what is the probability that you will get exactly 2 heads
and 2 tails?
17. What is the probability of drawing a card from a deck of 52 that is an ace or a jack?
18. If the odds in favor of the Vikings winning are 3 to 2, what is the probability of the
Vikings winning?
There is a 20% chance of rain. What are the odds in favor of rain occurring?
19. Which of the following represent pairs of independent events?
In a deck of 52 draw an ace, replace the card and shuffle, and then draw
another ace.
In a deck of 52 draw an ace, don't replace the card, and then draw
another ace.
Flip a coin and get heads, flip the coin again and get heads.
Roll 1 die and get a 2 four times in a row.
20. Calculate the expected gross winnings for the $1 ticket with probabilities given
below.
Prize
Probability
$1 prize with probability 1/10
$2 prize with probability 1/10.64
$3 prize with probability 1/20
$10 prize with probability 1/166.67
$20 prize with probability 1/500
$30 prize with probability 1/750
$500 prize with probability 1/60,000
$5,000 prize with probability 1/240,000
21. Find the mean of the data {2,3,3,4,4,4,4,4,5,5}. This is the same as
Data Value
2
3
4
5
Frequency
1
2
5
2
22. Find the median, mode, and midrange of the data {3, 2, 5, 8, 9, 4, 3}.
23. Find standard deviation of (2,3,4,5,6) and show the steps. (See Formula Sheet)
24. The mean of a normally distributed population is 20 and the standard deviation is 2.0
What percent of the data is found between values 16 and 24? What are the Z-scores of
16 and 24? Use one the graphic figures below showing a normal distribution.
25. $1000 is placed in an account that earns 7% interest compounded monthly for 10
years. How much is in the account after 10 years? (See Formula Sheet)
26. A person contributes $100 each month to an annuity that earns 8% interest
compounded monthly. How much will this person have in the account after 10 years?
(See Formula Sheet)
27. You buy a home that sells for $189,000. You place 15% down, and finance the
balance at 6% interest, compounded monthly for 30 years and your monthly payment is
$963.18 How much is paid in interest?
28. List 2 things you must consider when deciding whether or not to refinance a home