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CLEP® Study Guide
Printable PDF · 30 pages
CLEP Calculus Study Guide
Everything the CLEP Calculus exam tests, in one PDF you can print. Built from the College Board's official outline, heaviest topics first.
- 180 key terms, each with an example
- 41 practice questions with every answer explained
- A 2-page cram sheet for the night before
- 2-, 4- and 8-week study plans built from the exam weights
Last updated 2026 · exam details checked against the College Board's published exam information in 2026
Look inside the guide
Real pages from the 30-page PDF.
What you get for $5
One chapter for each official content area, in the order the exam weighs them.
- 📘30pages, printable
- 🧭3chapters, heaviest first
- 🔑180terms with examples
- ✍️41practice questions, answers explained
- ⚠️9exam traps to avoid
- 📄2page cram sheet
Try 10 free Calculus questions
In the style of the real exam, from all 3 areas. About 20 minutes, with every answer explained and a score by area.
10 questions
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Question 1 · Differential Calculus
What is lim [√(9 + h) − 3]/h as h → 0?
Show the answer
Answer: C. 1/6. This is the limit definition of the derivative of √x at x = 9. The derivative is 1/(2√x), which equals 1/6 at x = 9.
The trap: The answer 1/3 comes from using 1/√x instead of 1/(2√x), dropping the factor 2 from the power rule.
This is the limit definition of the derivative of √x at x = 9. The derivative is 1/(2√x), which equals 1/6 at x = 9.
The trap: The answer 1/3 comes from using 1/√x instead of 1/(2√x), dropping the factor 2 from the power rule.
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Question 2 · Integral Calculus
A function f satisfies f′(x) = 6x² − 2 and f(1) = 5. What is f(2)?
Show the answer
Answer: D. 17. An antiderivative is f(x) = 2x³ − 2x + C. From f(1) = 2 − 2 + C = 5, C = 5. Then f(2) = 16 − 4 + 5 = 17.
The trap: 12 leaves out the constant C = 5. 22 is f′(2), the derivative, not f(2).
An antiderivative is f(x) = 2x³ − 2x + C. From f(1) = 2 − 2 + C = 5, C = 5. Then f(2) = 16 − 4 + 5 = 17.
The trap: 12 leaves out the constant C = 5. 22 is f′(2), the derivative, not f(2).
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Question 3 · Limits
What is lim x→3 (x² − 9)/(x² − 5x + 6)?
Show the answer
Answer: B. 6. Substitution gives 0/0. Factor to (x − 3)(x + 3)/((x − 2)(x − 3)), cancel x − 3, and substitute 3 into (x + 3)/(x − 2) to get 6/1 = 6.
The trap: A limit of 0 comes from noticing only the zero in the numerator. A 0/0 form is indeterminate, so the expression must be simplified.
Substitution gives 0/0. Factor to (x − 3)(x + 3)/((x − 2)(x − 3)), cancel x − 3, and substitute 3 into (x + 3)/(x − 2) to get 6/1 = 6.
The trap: A limit of 0 comes from noticing only the zero in the numerator. A 0/0 form is indeterminate, so the expression must be simplified.
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Question 4 · Differential Calculus
If f(x) = 3x² − 4/x + 2eˣ, what is f′(1)?
Show the answer
Answer: A. 10 + 2e. Rewrite 4/x as 4x⁻¹. Then f′(x) = 6x + 4/x² + 2eˣ, and at x = 1 this is 6 + 4 + 2e = 10 + 2e.
The trap: The answer 2 + 2e comes from differentiating −4/x as −4/x², which has the wrong sign. The derivative of −4x⁻¹ is +4x⁻².
Rewrite 4/x as 4x⁻¹. Then f′(x) = 6x + 4/x² + 2eˣ, and at x = 1 this is 6 + 4 + 2e = 10 + 2e.
The trap: The answer 2 + 2e comes from differentiating −4/x as −4/x², which has the wrong sign. The derivative of −4x⁻¹ is +4x⁻².
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Question 5 · Integral Calculus
What is ∫₁⁹ 3/√x dx?
Show the answer
Answer: E. 12. Write 3x^(−1/2). An antiderivative is 3·2x^(1/2) = 6√x. Then 6√9 − 6√1 = 18 − 6 = 12.
The trap: 9 is 3√9 evaluated only at the upper limit and missing the factor 2. The power rule divides by 1/2, which doubles the coefficient.
Write 3x^(−1/2). An antiderivative is 3·2x^(1/2) = 6√x. Then 6√9 − 6√1 = 18 − 6 = 12.
The trap: 9 is 3√9 evaluated only at the upper limit and missing the factor 2. The power rule divides by 1/2, which doubles the coefficient.
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Question 6 · Limits
What is lim x→∞ (4x³ − 2x)/(2x³ + 7x²)?
Show the answer
Answer: D. 2. The numerator and denominator have the same degree, so the limit is the ratio of leading coefficients: 4/2 = 2.
The trap: A limit of 1/2 inverts the ratio of leading coefficients. The numerator's coefficient goes on top.
The numerator and denominator have the same degree, so the limit is the ratio of leading coefficients: 4/2 = 2.
The trap: A limit of 1/2 inverts the ratio of leading coefficients. The numerator's coefficient goes on top.
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Question 7 · Differential Calculus
If g(x) = x²/(x + 1), what is g′(1)?
Show the answer
Answer: C. 3/4. By the quotient rule, g′(x) = [2x(x + 1) − x²]/(x + 1)². At x = 1 this is (4 − 1)/4 = 3/4.
The trap: The answer 3/2 comes from forgetting to square the denominator. The quotient rule divides by (x + 1)², which is 4 here.
By the quotient rule, g′(x) = [2x(x + 1) − x²]/(x + 1)². At x = 1 this is (4 − 1)/4 = 3/4.
The trap: The answer 3/2 comes from forgetting to square the denominator. The quotient rule divides by (x + 1)², which is 4 here.
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Question 8 · Integral Calculus
What is ∫₀¹ 6x(x² + 1)² dx?
Show the answer
Answer: A. 7. Let u = x² + 1, so 6x dx = 3 du. The limits become u = 1 to 2. Then 3∫₁² u² du = [u³]₁² = 8 − 1 = 7.
The trap: 1 comes from keeping the old limits 0 and 1 after substituting u. Convert the limits or go back to x first.
Let u = x² + 1, so 6x dx = 3 du. The limits become u = 1 to 2. Then 3∫₁² u² du = [u³]₁² = 8 − 1 = 7.
The trap: 1 comes from keeping the old limits 0 and 1 after substituting u. Convert the limits or go back to x first.
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Question 9 · Limits
Let f(x) = (x² − 4)/(x − 2) for x ≠ 2, and f(2) = 1. What kind of discontinuity does f have at x = 2?
Show the answer
Answer: B. Removable, because the limit is 4 but f(2) = 1. For x ≠ 2, f(x) = x + 2, so the limit as x → 2 is 4. It exists but differs from f(2) = 1, which is a removable discontinuity.
The trap: "None, because f(2) is defined" is wrong: continuity also needs the limit to equal f(2), and 4 ≠ 1.
For x ≠ 2, f(x) = x + 2, so the limit as x → 2 is 4. It exists but differs from f(2) = 1, which is a removable discontinuity.
The trap: "None, because f(2) is defined" is wrong: continuity also needs the limit to equal f(2), and 4 ≠ 1.
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Question 10 · Differential Calculus
If f(x) = x·e^(3x), then f′(x) =
Show the answer
Answer: E. (1 + 3x)e^(3x). Use the product rule with the chain rule on e^(3x): f′ = 1·e^(3x) + x·3e^(3x) = (1 + 3x)e^(3x).
The trap: The choice (1 + x)e^(3x) forgets the chain-rule factor 3 when differentiating e^(3x).
Use the product rule with the chain rule on e^(3x): f′ = 1·e^(3x) + x·3e^(3x) = (1 + 3x)e^(3x).
The trap: The choice (1 + x)e^(3x) forgets the chain-rule factor 3 when differentiating e^(3x).
The CLEP Calculus exam at a glance
The CLEP Calculus exam is a computer-based test from the College Board. It has 44 questions in two sections, to be answered in approximately 90 minutes. A score of 50 on the 20–80 scale earns an ACE credit recommendation of 4 semester hours, though each college sets its own policy. The exam covers 3 content areas; the heaviest is Differential Calculus at 50%.
- Questions
- 44mostly multiple choice
- Time
- 90 minseparately timed sections
- Passing score
- 50on a 20–80 scale
- ACE credit
- 4semester hours
- Exam fee
- $97paid to College Board
- Calculator
- Section 2 onlyon-screen graphing calculator
Source: official CLEP Calculus exam page.
What the exam covers
3 areas, heaviest first. The guide's chapters follow this order.
- Differential Calculus50%
- Integral Calculus40%
- Limits10%
How it works
- 1Buy once, $5Secure checkout. No subscription needed.
- 2Download the PDFFrom your TransferCredit.org account, right away and any time later.
- 3Study the heaviest areas firstFollow the 2-, 4- or 8-week plan, then read the cram sheet the night before.
Questions students ask
What's in the full CLEP Calculus study guide?
30 pages: 3 chapters, one per official content area, heaviest first. 180 terms, each with a plain-English definition and an example, 2 key people, common traps and memory tricks, 41 practice questions with an answer key that explains every answer, question tactics, 2-, 4- and 8-week study plans and a 2-page cram sheet.
How much is the full CLEP Calculus study guide?
The full 30-page PDF is $5, a one-time payment. The 10 practice questions on this page are free, with no account.
What does the $29 plan include?
$29 a month gives you all 28 CLEP subjects: every CLEP study guide plus the full prep course for each subject, and you can cancel anytime. If you only need this exam, the guide on its own is a one-time $5.
How do I get the full guide?
Choose Buy this guide ($5) and check out. Then sign in to your TransferCredit.org account, then open the course and its Download Your Study Guide lesson. The PDF is yours to keep, and you can download it again from your account at any time.
Can I print the guide or use it on my phone?
Yes. It's a PDF, so it opens on phones, tablets and computers, and printing is allowed. Its tick boxes and answer bubbles work in PDF readers that support forms. Copying and editing are turned off.
Is this an official CLEP study guide?
No. CLEP® is a registered trademark of the College Board, which was not involved in producing this guide and does not endorse it. TransferCredit.org is independent. We built the guide from the official exam outline, and the exam details were checked against the College Board's published exam information in 2026.
Why is this study guide better than a generic review?
It follows the official outline area by area and spends the most pages on what the exam weighs most. Every term comes with an example, each chapter names the traps the exam sets, and the answer key explains why the most tempting wrong answer is wrong, not just which answer is right. It ends with a 2-page cram sheet for the night before.
What is the CLEP Calculus exam?
The CLEP Calculus exam is a computer-based test from the College Board. It has 44 questions in two sections, to be answered in approximately 90 minutes. A score of 50 on the 20–80 scale earns an ACE credit recommendation of 4 semester hours, though each college sets its own policy. The exam covers 3 content areas; the heaviest is Differential Calculus at 50%.
More questions about the CLEP Calculus exam (19)
How many questions are on the CLEP Calculus exam, and how long is it?
It has 44 questions in two sections, to be answered in approximately 90 minutes. Section 1 (about 27 questions, about 50 minutes) allows no calculator; Section 2 (about 17 questions, about 40 minutes) provides an online graphing calculator (non-CAS), needed for only some questions.
What is the passing score for CLEP Calculus?
The passing score is 50 on a 20–80 scale. At 50 or above, the American Council on Education (ACE) recommends 4 semester hours. Each college sets its own passing score and credit award, so check your school's policy before you book.
How much does the CLEP Calculus exam cost?
The exam fee is $97, paid to the College Board. Test centers may add their own administration fee. Eligible U.S. military service members can usually test for free through DANTES.
How many college credits is CLEP Calculus worth?
ACE recommends 4 semester hours for a passing score of 50. Your college decides how many credits it awards and which course they replace. Check your college's policy.
Can I use a calculator on the CLEP Calculus exam?
Section 1 (about 27 questions, about 50 minutes) allows no calculator; Section 2 (about 17 questions, about 40 minutes) provides an online graphing calculator (non-CAS), needed for only some questions.
Is there a penalty for guessing on CLEP Calculus?
No. Your score counts only correct answers, so a wrong answer costs nothing. Never leave a question blank: rule out what you can and pick your best guess.
What topics are on the CLEP Calculus exam?
3 content areas, from the official outline: Differential Calculus (50%); Integral Calculus (40%); Limits (10%).
Which CLEP Calculus topics should I study first?
Start with Differential Calculus (50%), the largest of the exam's 3 areas, then Integral Calculus (40%) and Limits (10%). The guide's chapters run in that order, heaviest first.
Is the CLEP Calculus exam hard?
It depends on what you already know. The exam has only 3 content areas, so each one carries real weight: Differential Calculus (50%), Integral Calculus (40%) and Limits (10%). Take the free diagnostic above to see where you stand in about 20 minutes.
What kinds of questions are on the CLEP Calculus exam?
The guide sorts them into 5 types: “Evaluate”, “Apply a theorem”, “Read a table or graph”, “Rate and application word problem” and “Which statement must be true?”. Multiple-choice questions have 5 answer choices, and some items use other formats. Try the 10 free questions above to see the style.
How long should I study for CLEP Calculus?
Use the diagnostic to decide. If you already know most areas, two weeks of daily review is often enough; if the subject is new to you, plan on eight. The full guide has 2-, 4- and 8-week plans built from the exam weights.
How should I pace myself on the CLEP Calculus exam?
On average you have about 2 minutes per question (90 minutes for 44 questions). The sections are timed separately, so pace each one on its own: divide its minutes by its questions and check your place halfway through. If a question takes more than about 4 minutes, pick your best guess, mark it and come back.
What happens if I don't pass CLEP Calculus?
You can retake a CLEP exam after three months. Use the wait to work through the areas the score report and the diagnostic show you missed.
Do colleges accept CLEP Calculus for credit?
CLEP exams are accepted at more than 2,900 U.S. colleges and universities, but each school decides which exams it accepts, the score it requires and the credit it gives. Look up your college's CLEP policy before you book.
How up to date is this CLEP Calculus guide?
Last updated 2026. The exam details were checked against the College Board's published exam information in 2026. Exams change, so confirm the details on the official exam page before you register.
What should I do the night before the exam?
Read the cram sheet once, slowly. Check your test time, the location or remote-proctoring setup, and the ID you need. Then sleep: a rested brain recalls more than a crammed one. In the morning, skim the memory tricks and common traps, then stop studying.
Are angles in degrees or radians on CLEP Calculus?
Radians, unless a question says otherwise. The College Board's notes also say ln x means the natural logarithm, and inverse trig functions may be written either as sin⁻¹ x or as arcsin x.
Which derivatives and integrals should I memorize for CLEP Calculus?
Section 1 allows no calculator, so know by heart the derivatives of polynomial, exponential, logarithmic and trigonometric functions, including tan x, cot x, arcsin x and arctan x, plus the product, quotient and chain rules. For integrals, know the basic antiderivative formulas, u-substitution and both parts of the Fundamental Theorem.
Does CLEP Calculus include Calculus II topics?
No. It matches a one-semester Calculus I course: limits, derivatives and basic integration including substitution. Integration by parts, series and other Calculus II topics are not tested.
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CLEP® is a registered trademark of the College Board, which was not involved in producing this guide and does not endorse it. TransferCredit.org is independent and not affiliated with the College Board. © 2026 UPI Globale Edu Inc.