Sample Questions: Precalculus

The following Precalculus 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

Each of the questions or incomplete statements below is followed by five suggested answers or completions. Select the one that is best in each case.

Questions

SECTION I

Directions: A graphing calculator will be available for the questions in this section. Some questions will require you to select from among five choices. For these questions, select the BEST of the choices given. If the exact numerical value of your answer is not one of the choices, select the choice that best approximates this value. Some questions will require you to enter a numerical answer in the box provided.

1. Abigail built a table with a rectangular top. The width of the tabletop is 3.5 feet less than the length. The tabletop has a surface area of 24.5 square feet. What is the perimeter of the tabletop?

   A. 10.5 feet
   B. 18.5 feet
   C. 21.0 feet
   D. 28.0 feet
   E. 35.0 feet

    

2. A tank is in the shape of a right circular cylinder. It has radius r, and the height is 3 times the diameter. Which of the following is the volume of the tank?

   A. (1/3)πr³
   B. (4/3)πr³
   C. 3πr³
   D. 6πr³
   E. 27πr³

    

3. The cost of 3 granola bars and 2 bottles of water is $7. The cost of 2 granola bars and 1 bottle of water is $4. How much does each item cost?

   A. A granola bar costs $1, and a bottle of water costs $1.
   B. A granola bar costs $1, and a bottle of water costs $2.
   C. A granola bar costs $1, and a bottle of water costs $3.
   D. A granola bar costs $2, and a bottle of water costs $1.
   E. A granola bar costs $2, and a bottle of water costs $2.

    

4. How many solutions does the equation x²cos(x²) = 0 have on the interval [−π, π]?

   (Enter a numerical answer.)   [       ]

    

5. Carter began walking from a campsite. He walked 2 miles due east from his campsite, and then he walked 4 miles in a direction that was 45 degrees east of north. What was his distance from the campsite, in miles?

   A. 2.9
   B. 3.8
   C. 4.5
   D. 5.1
   E. 5.6

SECTION II

Directions: A calculator will not be available for the questions in this section. Some questions will require you to select from among five choices. For these questions, select the BEST of the choices given. Some questions will require you to enter a numerical answer in the box provided.

6. Let f be the piecewise function defined below:
   f(x) = { −2x + 5   for   x ≤ 1;    1 − 3x²   for   x > 1 }
   What is the range of f?

   A. (−∞, 3] only
   B. (−2, 3] only
   C. [3, ∞) only
   D. (−∞, −2) ∪ (−2, ∞)
   E. (−∞, −2) ∪ [3, ∞)

    

7. What are the solutions to the equation shown below?

   (4 − 3/x + 10/x²)  /  (3 + 4/x − 2/x²) = 1 
   A. x = −8 and x = 1
   B. x = −4 and x = 3
   C. x = −3 and x = 4
   D. x = −1 and x = 8
   E. x = 3 and x = 4

    

8. The function f is defined by f(x) = 2 sin(x/3). On which of the following intervals is f decreasing for all values of x in the interval?

   A. 0 ≤ x ≤ π/2
   B. 0 ≤ x ≤ 3π
   C. π/2 ≤ x ≤ 3π/2
   D. 3π/2 ≤ x ≤ 9π/2
   E. 3π ≤ x ≤ 9π

9. Which of the following is an equation of the figure shown in the xy-plane above?

A. x²/4 + y²/9 = 1
B. x² + y² = 36
C. 2x² + 3y² = 1
D. x²/9 − y²/4 = 1
E. x² − y² = 36

10. If 2 log t = log(3 − 2t), then t =

A. −2/3 only
B. 1/3 only
C. 1 only
D. −3 and 1
E. −2/3 and 1/3

Answers

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