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100+ Free CLEP Calculus Practice Questions

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What is the derivative of f(x) = (2x + 3)(x - 1) found by expanding first?

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B
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Key Facts: CLEP Calculus Exam

44

multiple-choice questions on the CLEP Calculus exam

College Board

90 minutes

total testing time across two sections

College Board

20-80

score scale, with 50 the ACE credit-granting score

College Board

4

semester hours typically awarded by ACE for a passing score

ACE / College Board

60% / 40%

split between limits-plus-differential calculus and integral calculus

College Board

$97

exam fee plus a separate test-center administration fee

College Board

The CLEP Calculus exam has 44 multiple-choice questions answered in about 90 minutes across two sections: roughly 27 no-calculator questions and 17 questions where an on-screen TI-84 Plus CE graphing calculator is available. Content is approximately 60% limits and differential calculus and 40% integral calculus, breaking down to about 10% limits, 50% differential calculus, and 40% integral calculus. It is scored on a 20-80 scale, and the ACE-recommended credit-granting score of 50 typically earns 4 semester hours of credit, though each institution sets its own policy (source: College Board, clep.collegeboard.org).

Sample CLEP Calculus Practice Questions

Try these sample questions to test your CLEP Calculus exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the value of the limit as x approaches 3 of (x^2 - 9)/(x - 3)?
A.0
B.3
C.6
D.The limit does not exist
Explanation: Factor the numerator: x^2 - 9 = (x - 3)(x + 3). Cancel (x - 3) to get x + 3. Substituting x = 3 gives 3 + 3 = 6. This removable discontinuity is resolved by factoring before substitution.
2Evaluate the limit as x approaches infinity of (3x^2 + 2x)/(5x^2 - 1).
A.0
B.Infinity
C.1
D.3/5
Explanation: For a rational function where numerator and denominator have the same degree, the limit at infinity equals the ratio of the leading coefficients. Here that is 3/5. Dividing every term by x^2 confirms the lower-order terms vanish.
3What is the limit as x approaches 0 of sin(x)/x?
A.0
B.The limit does not exist
C.Infinity
D.1
Explanation: The limit of sin(x)/x as x approaches 0 is a fundamental trigonometric limit equal to 1. It can be confirmed by the squeeze theorem or L'Hospital's Rule, since the form is 0/0 and the derivative of sin(x) is cos(0) = 1.
4For what value of k is the function f(x) = x^2 for x < 2 and f(x) = kx for x >= 2 continuous at x = 2?
A.1
B.8
C.4
D.2
Explanation: For continuity at x = 2, the left and right pieces must agree there. The left piece gives 2^2 = 4, and the right piece gives k(2) = 2k. Setting 2k = 4 gives k = 2.
5Evaluate the limit as x approaches 0 of (sqrt(x + 4) - 2)/x.
A.0
B.1/2
C.1/4
D.The limit does not exist
Explanation: Multiply numerator and denominator by the conjugate (sqrt(x + 4) + 2). The numerator becomes (x + 4) - 4 = x, giving x/[x(sqrt(x+4)+2)] = 1/(sqrt(x+4)+2). At x = 0 this is 1/(2 + 2) = 1/4.
6What is the limit as x approaches infinity of (2x^3 + x)/(x^2 + 5)?
A.0
B.2
C.Infinity
D.1/5
Explanation: The numerator has degree 3 and the denominator degree 2, so the numerator grows faster. As x approaches infinity the quotient increases without bound, so the limit is infinity.
7Using the limit definition, the derivative of f(x) = x^2 is the limit as h approaches 0 of which expression?
A.(x + h)^2 - x^2
B.(x^2 - (x - h)^2)/x
C.((x + h)^2 - x^2)/h
D.(x^2 + h)/h
Explanation: The derivative is defined as the limit as h approaches 0 of [f(x + h) - f(x)]/h. For f(x) = x^2 this is [(x + h)^2 - x^2]/h, which simplifies to 2x + h and approaches 2x.
8What is the derivative of f(x) = 5x^4 - 3x^2 + 7?
A.5x^3 - 3x
B.20x^3 - 6x + 7
C.20x^3 - 6x
D.20x^4 - 6x^2
Explanation: Apply the power rule term by term: the derivative of 5x^4 is 20x^3, the derivative of -3x^2 is -6x, and the derivative of the constant 7 is 0. The result is 20x^3 - 6x.
9What is the derivative of f(x) = sin(x)?
A.-sin(x)
B.cos(x)
C.-cos(x)
D.tan(x)
Explanation: The derivative of sin(x) is cos(x). This is a standard result for the elementary trigonometric functions and is essential for the CLEP Calculus exam.
10Using the product rule, what is the derivative of f(x) = x^2 * e^x?
A.2x * e^x
B.x^2 * e^x
C.(2x + x^2) * e^x
D.(x^2 - 2x) * e^x
Explanation: The product rule gives f'(x) = (derivative of x^2)(e^x) + (x^2)(derivative of e^x) = 2x*e^x + x^2*e^x. Factoring e^x yields (2x + x^2)*e^x.

About the CLEP Calculus Exam

The CLEP Calculus exam awards college credit for content typically covered in a one-semester college Calculus I course. It contains 44 multiple-choice questions to be answered in about 90 minutes, split into two sections: Section 1 (about 27 questions, no calculator) and Section 2 (about 17 questions, where an integrated TI-84 Plus CE graphing calculator is available). The exam emphasizes limits and differential calculus (about 60%) and integral calculus (about 40%), and is scored on a 20-80 scale.

Questions

44 scored questions

Time Limit

90 minutes

Passing Score

50 (on a 20-80 scale)

Exam Fee

$97 plus a test-center administration fee (College Board)

CLEP Calculus Exam Content Outline

~10%

Limits

Properties of limits (constant, sum, product, quotient), limit calculations including limits involving infinity, and continuity of functions.

~50%

Differential Calculus

Definition of the derivative, derivatives of elementary and composite functions, the chain and product/quotient rules, implicit differentiation, higher-order derivatives, L'Hospital's Rule, and applications such as tangent lines, extreme values, concavity, curve sketching, and related rates.

~40%

Integral Calculus

Antiderivatives and basic integration formulas, integration by substitution, Riemann sums, the definite integral, the Fundamental Theorem of Calculus, and applications such as area under and between curves, accumulated change, and average value of a function.

How to Pass the CLEP Calculus Exam

What You Need to Know

  • Passing score: 50 (on a 20-80 scale)
  • Exam length: 44 questions
  • Time limit: 90 minutes
  • Exam fee: $97 plus a test-center administration fee

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

CLEP Calculus Study Tips from Top Performers

1Memorize the core derivative rules (power, product, quotient, chain) and the matching basic antiderivative forms until you can apply them without hesitation.
2Practice limit problems by factoring, rationalizing, and using L'Hospital's Rule on 0/0 and infinity/infinity indeterminate forms.
3Drill the Fundamental Theorem of Calculus in both directions: evaluating definite integrals and differentiating an integral with a variable upper limit.
4Work Section 1 problems by hand without a calculator, since the first section forbids one and rewards clean algebra.
5Use related-rates and optimization word problems to connect derivatives to real applications, a frequently tested category.

Frequently Asked Questions

How many questions are on the CLEP Calculus exam and how long is it?

The CLEP Calculus exam has 44 multiple-choice questions and takes about 90 minutes. It is divided into Section 1 (about 27 questions, no calculator, about 50 minutes) and Section 2 (about 17 questions, about 40 minutes, with a graphing calculator available).

What score do I need to pass the CLEP Calculus exam?

CLEP exams are scored on a 20-80 scale. The American Council on Education (ACE) recommends a credit-granting score of 50, which typically earns 4 semester hours. Each college sets its own minimum, so confirm your school's policy.

Can I use a calculator on the CLEP Calculus exam?

A graphing calculator (TI-84 Plus CE) is integrated into the exam software and available only during Section 2. Section 1 must be completed without a calculator, and only some Section 2 questions actually require one.

What topics does the CLEP Calculus exam cover?

The exam covers single-variable Calculus I: limits and continuity (about 10%), differential calculus including derivatives and their applications (about 50%), and integral calculus including antiderivatives, the definite integral, and applications (about 40%).

How much does the CLEP Calculus exam cost?

The CLEP exam fee is $97, paid to the College Board, plus a separate administration fee charged by the test center. Many test takers qualify for funding or institutional vouchers, including DANTES funding for eligible military members.

How does CLEP Calculus credit compare to AP Calculus?

CLEP Calculus covers material similar to a one-semester Calculus I course and the AP Calculus AB scope. A passing CLEP score typically grants 4 semester hours, while AP credit depends on your 1-5 score and the college's AP policy.