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Every CLEP and DSST exam in one subscription, with real timed practice exams and a live pass-readiness score.
7 day free trial. iPhone only, for now.
So, you’re thinking about taking the CLEP Calculus exam? Great choice if you’ve already got a solid handle on algebra, functions, and trigonometry. This is where that foundation starts paying off in a single 90-minute sitting instead of a full semester.
Trying to plan your order? see which CLEP exams are the easiest to pass.
This page works as a full CLEP Calculus study guide, not just a page of trivia. Read the guide section below topic by topic, take the free practice test to see where you actually stand, then check the FAQ if you have questions about scope or credit. That’s the whole game plan.
The exam runs 90 minutes and covers roughly 44 questions on single-variable calculus: limits, derivatives and their applications, and an introduction to integrals, at about the level of a one-semester college Calculus I course. An online graphing calculator is built into the testing software, so you won’t need to bring your own. Scores are reported on a 20–80 scale, and most colleges that grant credit for this exam set the cutoff around 50, though policies vary by school, so confirm the specific score your college requires before you register.
The exam opens with limits: evaluating limits algebraically, graphically, and numerically, one-sided limits, and the formal idea of continuity at a point. You'll want to be comfortable with limits that require algebraic manipulation (factoring, rationalizing) before you can plug in a value directly, and with recognizing when a limit doesn't exist. This unit is the foundation everything else in the course is built on, so it's worth getting solid before you move on.
The largest chunk of the exam. You'll need the definition of the derivative as a limit, plus fluency with the power rule, product rule, quotient rule, and chain rule. Derivatives of trigonometric, exponential, and logarithmic functions are tested directly, and implicit differentiation shows up for relationships that aren't solved explicitly for y. Make sure you can differentiate quickly and accurately, since later applications assume that skill is already second nature.
Once you can find a derivative, the exam asks what it's for. Expect questions on finding relative and absolute extrema using the first and second derivative tests, determining intervals of increase/decrease and concavity, related rates problems (where two changing quantities are linked by an equation), and optimization problems that ask you to maximize or minimize a real-world quantity. Motion problems (using derivatives to relate position, velocity, and acceleration) are a reliable source of exam questions too.
Integration is introduced as the reverse of differentiation and as a way to measure accumulated change. You'll need basic antiderivative rules, the Fundamental Theorem of Calculus connecting derivatives and definite integrals, and simple techniques like u-substitution. Definite integrals are frequently tied to finding the area under a curve or the area between two curves, and you should be comfortable setting up an integral from a word problem, not just evaluating one you're handed.
CLEP Calculus corresponds to a single semester of college calculus (Calculus I), not a full-year sequence. That means topics like infinite series, multivariable calculus, and more advanced integration techniques generally fall outside its scope. If your goal is credit for a full-year calculus sequence or you need Calculus II-level content, talk to your school about whether this exam actually covers what you need before you register.
Correct Answer: A. f'(x) = 12x^3 - 10x
Explanation: Apply the power rule term by term: the derivative of 3x^4 is 12x^3, the derivative of -5x^2 is -10x, and the derivative of the constant 7 is 0. Putting it together gives f'(x) = 12x^3 - 10x. A common mistake is forgetting to drop the constant term entirely, since its rate of change is always zero.
Correct Answer: C. 4
Explanation: Plugging in x = 2 directly gives 0/0, an indeterminate form, so you factor first: x^2 - 4 factors into (x - 2)(x + 2). The (x - 2) terms cancel (valid everywhere except exactly at x = 2, which doesn't affect the limit), leaving lim (x→2) (x + 2) = 4. This factor-and-cancel approach is one of the most frequently tested limit techniques on the exam.
Correct Answer: B. t = 2
Explanation: The ball reaches maximum height when its velocity, h'(t), equals zero. Differentiating gives h'(t) = -32t + 64. Setting this equal to zero and solving gives t = 2. This is a classic application of using the derivative to find a maximum: the object is momentarily at rest at the peak of its trajectory before gravity pulls it back down.
Correct Answer: C. 8
Explanation: The antiderivative of 2x is x^2. By the Fundamental Theorem of Calculus, the definite integral equals the antiderivative evaluated at the upper bound minus the antiderivative evaluated at the lower bound: (3)^2 - (1)^2 = 9 - 1 = 8. Geometrically, this matches the area of the trapezoid formed under the line y = 2x between x = 1 and x = 3.
Correct Answer: B. dy/dx = -x/y
Explanation: Differentiating both sides with respect to x gives 2y(dy/dx) + 2x = 0, treating y as an implicit function of x and applying the chain rule to the y^2 term. Solving for dy/dx: 2y(dy/dx) = -2x, so dy/dx = -x/y. This is the standard setup for a circle (here, radius 5) where y isn't isolated on one side of the equation, which is exactly why implicit differentiation is needed.
No. Precalculus covers the algebra, trigonometry, and function background you need before calculus, while CLEP Calculus tests actual limits, derivatives, and integrals from a first-semester college calculus course. If you haven't taken precalculus or a strong algebra/trig course yet, that's usually the better place to start.
Yes, the Free Practice Test section above walks through original sample questions with the answer and explanation hidden behind a click, so you can check yourself honestly before moving on to the next one.
No. CLEP Calculus corresponds to a single semester (Calculus I): limits, derivatives and their applications, and an introduction to integrals. Series, multivariable calculus, and more advanced integration techniques generally fall outside its scope, so double-check with your school if you need credit for more than one semester of calculus.
Full disclosure: this one's ours, so I'm about as biased as it gets. It's the study app I always wished existed back when I was doing this: every CLEP and DSST exam in one subscription, real timed practice exams, and a live pass-readiness score so you're not left guessing whether you're actually ready to book the test. It's iPhone-only for now (sorry, Android folks). But there's a 7 day free trial, so you can judge for yourself whether I'm too biased to be trusted here.
Built by a former student, Flying Prep's got what we need: easy to learn flashcards (with mobile-first design), full length practice exams, and complete coverage of every CLEP exam. Plus a dual guarantee including a 30 day satisfaction no-questions-asked guarantee and 6 month exam protection.
While quite short on the study side of things, the official CLEP book is the go-to final practice test. Since this is the only official practice test available, I normally use it as my final spot check before taking the test.
REA offers a great combination of study guide and practice questions. This book functions well as the central pillar of a strong CLEP prep strategy, with resources like the Official CLEP Study Guide (above) providing a great final practice test at the end.
Though the design is now quite dated, InstantCert is one of the OGs in the space. They offer flashcards to study for the exam, but their coverage is somewhat limited and I'm not sure whether they use spaced repetition or other modern study science.