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Sample Questions: Calculus

 

The following Calculus sample questions don’t appear on an actual CLEP exam. They’re intended to give potential test-takers an indication of the format and difficulty level of the exam and to provide content for practice and review. For more sample questions and information about the test, see the CLEP Official Study Guide.

Section I (No Calculator)

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

Questions

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

  1. Evaluate: limx → π (ln x − ln π)/(x − π)

    (A) 0
    (B) 1⁄π
    (C) ln|π|
    (D) (ln π + 1)/π2
    (E) nonexistent

     

  2. limx → 1 (1 − x2)/(x2 − x) is

    (A) −2
    (B) −1
    (C) 0
    (D) 2
    (E) nonexistent

     

  3. ∫ (√x − 5/x + ex) dx =

    (A) (2/3)x3/2 + 5/x2 + ex + C
    (B) (2/3)x3/2 − 5 ln|x| + ex + C
    (C) x3/2 − 5 + (1/2)e2x + C
    (D) x3/2 + 5 ln|x| + 2ex2 + C
    (E) 1/(2x2) + 5/x2 + ex + C

     

  4. Let f be a differentiable function such that f(1) = 10 and f′(x) = √(x3 + 15). What is the approximation of f(1.2) found by using the line tangent to the graph of f at x = 1?

    (A) 10.1
    (B) 10.2
    (C) 10.4
    (D) 10.8
    (E) 11.0

     

  5. The function f is defined by f(x) = ln(sin x + 1). What is the slope of the line tangent to the graph of f at x = 0?

    (A) −ln(π)
    (B) −1/2
    (C) 0
    (D) 1
    (E) ln(π + 1)

     

  6. Let f be the piecewise function defined below, where k is a constant. For what value of k is f continuous at x = 3?
     

    f(x) = x2 − 4    for x < 3
    k cos(πx) + 1    for x ≥ 3 

    k = 

     

  7. If x3 + x y = 0, what is the value of dy/dx at the point (−1, −1)?
    (A) −3
    (B) −1
    (C) 1
    (D) 2
    (E) 3

Section II (Calculator Available)

Directions: A calculator will be available for questions in this section. Some questions will require you to select from among five choices—choose 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 the value. Some questions will require you to enter a numerical answer in the box provided.

  1. The curve y = ex and the line y = 2x + 2 intersect at two points in the xy-plane. Of the following, which is closest to the area of the region bounded by the curve and the line?


    (A) −4.891
    (B) −1.286
    (C) 1.492
    (D) 2.227
    (E) 3.525

     

  2. Oil is poured on a flat surface and spreads out, forming a circle. The area of the circle is increasing at a constant rate of 5 square centimeters per second. At what rate, in centimeters per second, is the radius increasing at the instant when the radius is 5 centimeters?


    (A) 1/(2π)
    (B) 1/π
    (C) 1
    (D) π
    (E) 2π

Graph of f′(x): shows intervals where f′ is positive or negative and zeros at key x-values. See following description for details.
  1. The graph of f′, the derivative of the function f, is shown above. Which of the following statements CANNOT be true?
    1. f is decreasing on (0, 1).
    2. f is concave up on (0, 1).
    3. f has a local maximum at x = 3.
    4. f has an absolute minimum at x = 1.
    5. f has an absolute maximum at x = 2.

Answers to Sample Questions

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

Learn more about the Calculus exam.

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