Sample Questions: College Mathematics

The following College Mathematics sample questions aren't used in actual CLEP exams and aren't presented here as they will be on the test. Use them to get a sense of question format and difficulty level.

Directions

An online scientific calculator will be available for the questions on this test. For each of the questions below, select the best of the choices given.

Questions

1. Audrey deposited $10,000 into a 3-year certificate of deposit that earned 10% annual interest, compounded annually. Audrey made no additional deposits to or withdrawals from the certificate of deposit. What was the value of the certificate of deposit at the end of the 3-year period?
   1. $13,000
   2. $13,300
   3. $13,310
   4. $13,401
2. Which of the following is the smallest value?
   1. $2\times {10}^{-28}$
   2. $1.3\times {10}^{-2}$
   3. $1.6\times {10}^{10}$
   4. $2\times {10}^{14}$
3. If $P$ dollars is invested in a savings account that pays 5% annual interest, compounded continuously, in how many years will the account value be equal to $2P$ dollars?
   1. In $20\ln \left(2\right)$ years
   2. In $5\ln \left(2\right)$ years
   3. 10 years
   4. 20 years

4. Assume that $a$ and $b$ are positive integers. For each statement below, determine whether the statement is true or false, and indicate your answer in the appropriate box.

   Divisibility statements for $a$ and $b$

   Statement	True	False
   If $a$ is divisible by $b$, then $a^2$ is divisible by $b^2$.	□	□
   If $a^2$ is divisible by $b$, then $a$ is divisible by $b$.	□	□
   If $a$ is divisible by $b^2$, then $a$ is divisible by $b$.	□	□

5. From 1950 to 1990, the population of Country W increased by 40%. From 1990 to 2012, the population of Country W increased by 10%. What is the percent increase in the population of Country W from 1950 to 2012?

    

   %
6. Let $P$(E) represent the probability of event E. Let $A$ and $B$ be events with $P\left(A\right)$ = 0.4, $P\left(B\right)$ = 0.7, and $P\left(A\cap B\right)$ = 0.2. What is the value of $P\left(A\cup B\right)$?
   1. 1.0
   2. 0.9
   3. 0.8
   4. 0.7

7. 

   The chart above shows the number of teachers in City A, City B, City C, and City D in 2005 and 2010. Which city had the greatest percent increase in the number of teachers from 2005 to 2010?

   1. City A
   2. City B
   3. City C
   4. City D
8. If $f\left(x\right)=x^2+x-4$ and $g\left(x\right)=\frac{x-2}{x+3}$, then $f\left(g\right(-4\left)\right)$ =
   1. $\frac{6}{11}$
   2. 26
   3. 38
   4. 48
9. There are 220 seniors at a certain school. Among all seniors at the school, 45 took calculus, 55 took physics, and 10 took both. How many seniors took neither calculus nor physics?
   1. 90
   2. 100
   3. 120
   4. 130

10. There are 10 Airmoon flights and 15 Airsun flights daily from Yorktown to Newcity, as shown in the table below. The table shows that 4 Airmoon and 7 Airsun flights depart in the morning and the remaining flights depart in the afternoon. If a flight is to be selected at random from among the flights that depart in the afternoon from Yorktown to Newcity, what is the probability that the flight selected will be an Airmoon flight?

    Daily flights from Yorktown to Newcity by airline and time of day

    Airline / Departure	Morning	Afternoon	Total
    Airmoon flights	4	6	10
    Airsun flights	7	8	15
    Total	11	14	25

    1. $\frac{6}{25}$
    2. $\frac{6}{14}$
    3. $\frac{10}{25}$
    4. $\frac{14}{25}$

11. In a sleep study, there are 50 people who are 20 years old, 50 people who are 25 years old, and 50 people who are 30 years old. If an additional 20-year-old person participates in the study, what happens to the average age, the median age, and the age range of the participants in the study?

    Effect of adding one 20-year-old participant

    	Increases	Decreases	Does Not Change
    Average age	□	□	□
    Median age	□	□	□
    Age range	□	□	□

Answers

1) C    2) A    3) A    4) True, False, True    5) 54%    6) C    7) B    8) C    9) D    10) B    11) Average decreases; Median no change; Range no change