Sample Questions: College Algebra

The following College Algebra 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. Some items may ask for a numerical answer.

Questions

1. What is the remainder when the polynomial  $x^{53}-12x^{40}-3x^{27}-5x^{21}+x^{10}-3$ is  divided by $x+1$?
   1. −21
   2. −7
   3. −3
   4. 4
   5. 21
2. Let $a$, $b$, and $c$ be real numbers, where $a\ne 0$. If the equation   $a{x}^2+bx+c=0$ has two real solutions, which of the following statements could be true? Indicate all such statements.
   1. $a>0$, $b>0$, and $c<0$
   2. $b=\pm \sqrt{ac}$
   3. $ac<0$

3. A science class launched a rocket from level ground. The height $h$ , in feet, of the rocket above the ground $t$ seconds after it was launched can be modeled by the function $h\left(t\right)=-16t^2+64t$. How many seconds did it take for the rocket to return to the ground?

   Enter your numerical answer.

4. At a certain shipping company, the cost to deliver a package depends on its weight. The company charges a flat rate of $7.00 for the first 5 kilograms plus $1.50 for each additional kilogram or fraction thereof. For this company, which of the following functions represents the cost $C$, in dollars, to deliver a package with a weight of $k$ kilograms, where $k$ is an integer greater than or equal to 5?
   1. $C\left(k\right)=7+1.5k$
   2. $C\left(k\right)=7\left(5\right)+1.5k$
   3. $C\left(k\right)=7+1.5(k-5)$
   4. $C\left(k\right)=7\left(5\right)+1.5(k-5)$
   5. $C\left(k\right)=7+5(k-1.5)$

5. 

   The graph of the quadratic function $f$ is shown in the $xy$-plane. The linear function $g$ is defined by $g\left(x\right)=cx$ for all real numbers $x$, where $c$ is a positive constant. Which of the following must be true?

   1. $f\left(0\right)>g\left(0\right)$
   2. $f\left(a\right)>g\left(0\right)$
   3. $f\left(a\right)>g\left(a\right)$
   4. $f\left(a\right)>g\left(b\right)$
   5. $f\left(b\right)>g\left(b\right)$

6. The table shows some values of the functions $f$ and $g$. Based on the table, what is the value of $g\left(f\right(2\left)\right)$?

   Values of functions f and g

   Input $x$	$f\left(x\right)$	$g\left(x\right)$
   0	9	1
   1	2	5
   2	1	3
   3	3	8

   1. 0
   2. 3
   3. 5
   4. 8
   5. 9
7. At the beginning of each year, the population of a small town is predicted to be 2 percent greater than its population at the beginning of the preceding year. If $P$ is the population of the town on January 1, 2018, what is the predicted population of the town on January 1, 2023?
   1. $\left(5\cdot 0.02\right)P$
   2. $\left(1+5\cdot 0.02\right)P$
   3. $\left(1.02+5\right)P$
   4. ${0.02}^{5}P$
   5. ${1.02}^{5}P$

8. Let ${\log }_{a}x=2$, ${\log }_{a}y=3$, and ${\log }_{a}z=4$, where $a$ is a positive number that is not equal to 1. What is the value of ${\log }_a\frac{x^{3}y}{\sqrt{z}}$?

   Enter your numerical answer.

9. Which of the following is equal to $\frac{\left(i+3\right)\left(i+2\right)}{i^2}$?
   1. $5i+7$
   2. $5i+5$
   3. $5i-5$
   4. $-5i+7$
   5. $-5i-5$
10. What is the highest-degree term in the expansion of $\frac{{\left(x+2\right)}^5-x^5}{2}$?
    1. $\frac{x^4}{2}$
    2. $5x^4$
    3. $10x^4$
    4. $\frac{x^5}{2}$
    5. $x^5$

Answers

1) B   2) A, C   3) 4   4) C   5) C   6) C   7) E   8) 7   9) E   10) B