---
title: "CLEP Calculus Prep and CLEP Precalculus Prep: Exam Guide"
description: "CLEP Calculus prep and CLEP Precalculus prep: question counts, the two timed sections and calculator rules, topic weights, ACE credit and original practice."
canonical: https://learn.modernagecoders.com/clep-calculus-prep
source: src/pages/clep-calculus-prep.html
---
> CLEP Calculus prep and CLEP Precalculus prep: question counts, the two timed sections and calculator rules, topic weights, ACE credit and original practice.

In short

CLEP Calculus is a 44-question, roughly 90-minute College Board exam covering one semester of college calculus, about 60% limits and differential calculus and 40% integral calculus; ACE recommends 4 semester hours for a score of 50. CLEP Precalculus has about 48 questions in roughly 90 minutes, and ACE recommends 3 semester hours at 50. Modern Age Coders teaches both live online, 1-on-1 or in a 15 to 20 batch, through our AP Calculus course.

Credit-level calculus

## Three courses for CLEP Calculus and Precalculus

The AP Calculus course carries the calculus content; AP Precalculus covers the other exam; the college course goes further.

[![AP Calculus AB & BC Exam Prep, Live Online, Score 5 Goal course thumbnail](/images/ap-calculus-prep.webp)  CLE / 01 AP Calculus Limits, derivatives and integrals: the CLEP Calculus content. Open the syllabus →](/courses/ap-calculus-exam-prep)[![AP Precalculus course thumbnail](/images/ap-precalculus.webp)  CLE / 02 AP Precalculus Functions, trigonometry and modeling for CLEP Precalculus. Open the syllabus →](/courses/ap-precalculus-exam-prep-course)[![College Maths Course course thumbnail](/images/college-level-maths.webp)  CLE / 03 College math Multivariable topics and linear algebra after Calculus I. Open the syllabus →](/courses/college-mathematics-complete-masterclass)

CLEP Calculus

## How many questions are on CLEP Calculus, and when can you use a calculator?

The content is "approximately 60% limits and differential calculus and 40% integral calculus", set as 44 questions over two sections in roughly an hour and a half. No calculator is allowed in the first section.

| Feature | CLEP Calculus | CLEP Precalculus |
| --- | --- | --- |
| Level | A one-semester college course in calculus | Readiness for a first-semester calculus course |
| Questions | 44, in two sections | Approximately 48, in two sections |
| Time | Approximately 90 minutes | Approximately 90 minutes |
| Section 1 | About 27 questions, about 50 minutes, no calculator | 25 questions, about 50 minutes, graphing calculator allowed |
| Section 2 | About 17 questions, about 40 minutes, graphing calculator allowed | 23 questions, about 40 minutes, no calculator |
| Calculator | TI-84 Plus CE (non-CAS), built in | TI-84 Plus CE (non-CAS), built in |
| Answer types | Multiple choice | Mostly multiple choice, some numerical entry |
| ACE recommendation | Score 50, 4 semester hours | Score 50, 3 semester hours (Introductory Precalculus) |

Sources: [CLEP Calculus](https://clep.collegeboard.org/clep-exams/calculus) and [CLEP Precalculus](https://clep.collegeboard.org/clep-exams/precalculus), College Board.

| Topic | Share | Examples from College Board's list |
| --- | --- | --- |
| Limits | 10% | Properties of limits; limits involving infinity; continuity |
| Differential calculus | 50% | Definitions of the derivative; chain rule; implicit differentiation; derivatives of inverse functions including arcsin and arctan; Mean Value Theorem; L'Hospital's Rule; curve sketching; extreme values; related rates |
| Integral calculus | 40% | Antiderivatives; substitution; y' = ky growth and decay; Riemann sums; the Fundamental Theorem; average value; area between curves |

### Intuition first

College Board says the exam "is primarily concerned with an intuitive understanding of calculus and experience with its methods and applications." About half the questions are routine technique; the other half test understanding of concepts and applications.

It also warns that "Knowledge of preparatory mathematics is assumed, including algebra, geometry, trigonometry, and analytic geometry." Weak trigonometry costs marks across the whole paper.

### What the calculator is for

In Section 2 the built-in graphing calculator can numerically evaluate a definite integral, find zeros, intersections and extrema, and solve equations numerically. College Board adds that "Only some of the questions will require the use of the calculator."

Section 1 comes first and has no calculator, so derivatives, limits and antiderivatives by hand must be quick before test day.

CLEP Precalculus

## What is on the CLEP Precalculus exam?

Functions, above all. College Board says "A large portion of the exam is devoted to testing a student's understanding of functions and their properties."

| Topic | Share |
| --- | --- |
| Algebraic Expressions, Equations, and Inequalities | 20% |
| Functions: Concept, Properties, and Operations | 15% |
| Representations of Functions: Symbolic, Graphical, and Tabular | 30% |
| Analytic Geometry | 10% |
| Trigonometry and its Applications | 15% |
| Functions as Models | 10% |

### Trigonometry is bigger than it looks

The table gives trigonometry 15%, but College Board adds a note that it "permeates most of the major topics and accounts for more than 15% of the exam." By its estimate, roughly 30 to 40 percent of questions need right triangle trigonometry or the properties of the trigonometric functions.

For many adults returning to math, trigonometry is the most faded skill, so it deserves the biggest share of review time.

### Which functions appear

College Board lists linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions, presented "symbolically, graphically, verbally" and in tables.

Analytic geometry covers lines, circles, parabolas, ellipses and hyperbolas, which some Algebra 2 courses skip.

Note the reversed calculator order: on Precalculus the calculator section comes first, and the 23-question no-calculator section second. Students who sit both exams should rehearse each order separately.

Scores and credit

## What CLEP Calculus score earns college credit?

ACE, the American Council on Education, suggests a 50 on either exam. Whether that earns credit, and how much, is up to your college.

### The 20 to 80 scale

Each correct answer adds one raw point, and College Board turns the raw total into a reported score between 20 and 80. Blank and wrong answers score the same, zero, which means a guess never hurts.

For Calculus, ACE recommends 4 semester hours at a score of 50; for Introductory Precalculus, 3 semester hours at 50.

### The college decides

Each exam page carries the same note: "Each institution reserves the right to set its own credit-granting policy, which may differ from the American Council on Education (ACE)."

Check whether your college gives Calculus I credit, elective credit or none, and whether a precalculus credit will count toward your degree at all.

1. **Pick the right exam.** If your degree needs Calculus I, CLEP Calculus is the one that may replace it; CLEP Precalculus usually replaces a precalculus requirement.
2. **Read your college's CLEP policy.** Note the score it requires and the course it maps the credit to.
3. **Take College Board's free sample questions untimed.** Mark which topic each miss belongs to.
4. **Study by weight.** For Calculus, differential calculus is half the exam; for Precalculus, representations of functions are 30%.
5. **Rehearse the section order.** Calculus starts without a calculator; Precalculus starts with one.
6. **Book when ready.** College Board says a candidate "may not retake an exam of the same title within three months of the test date."

Worked problems

## Is the CLEP Calculus exam hard? Eight problems at its level

It is a full semester of calculus in 90 minutes, so fluency matters. These problems are ours, matched to College Board's topic list; they are not College Board sample questions.

| Topic | Problem | Reasoning | Result |
| --- | --- | --- | --- |
| Limits | lim as x goes to 2 of (x^2 - 4)/(x - 2) | Factor: (x - 2)(x + 2)/(x - 2) = x + 2 near 2 | 4 |
| Chain rule | Differentiate sin(3x^2) | Outer cos, times the inner derivative 6x | 6x cos(3x^2) |
| Implicit | Slope of x^2 + y^2 = 25 at (3, 4) | 2x + 2y y' = 0, so y' = -x/y | -3/4 |
| L'Hospital | lim as x goes to 0 of (e^x - 1)/x | Form 0/0; differentiate top and bottom: e^x / 1 | 1 |
| Related rates | A circle's radius grows at 2 cm/s. How fast is the area growing when r = 5? | dA/dt = 2 pi r dr/dt = 2 pi x 5 x 2 | 20 pi square cm per second |
| Substitution | Integral of 2x cos(x^2) dx | Let u = x^2, du = 2x dx | sin(x^2) + C |
| Area | Area between y = x and y = x^2 from 0 to 1 | Integral of (x - x^2) = 1/2 - 1/3 | 1/6 |
| Growth | y' = ky, y(0) = 100, and y doubles in 5 years. Find k. | 200 = 100e^(5k), so 5k = ln 2 | k = ln 2 / 5, about 0.139 |

| Topic | Problem | Reasoning | Result |
| --- | --- | --- | --- |
| Inverse functions | Inverse of f(x) = 2 ln(x - 1) | Swap and solve: x/2 = ln(y - 1), so y - 1 = e^(x/2) | e^(x/2) + 1 |
| Trig equations | Solve 2 sin x = 1 for 0 ≤ x < 2 pi | sin x = 1/2 in quadrants I and II | pi/6 and 5 pi/6 |
| Analytic geometry | Describe x^2/9 + y^2/4 = 1 | Ellipse centered at the origin, a = 3 on the x-axis, b = 2 | Vertices (3, 0) and (-3, 0) |
| Identities | Simplify sin^2 x / (1 - cos x) | sin^2 x = (1 - cos x)(1 + cos x) | 1 + cos x |

College Board's notes for CLEP Calculus say that unless stated otherwise "all angles are measured in radians", and that ln x is the natural logarithm. Students who learned trigonometry in degrees should switch their practice to radians from the first week.

Practice and plans

## Original CLEP Calculus and Precalculus practice, and two study plans

Twelve problems we wrote, eight for Calculus and four for Precalculus, then a plan for each exam.

| # | Exam | Problem | Answer |
| --- | --- | --- | --- |
| 1 | Calculus | lim as x goes to infinity of (3x^2 + 1)/(x^2 - 5) | 3 |
| 2 | Calculus | Derivative of x^3 e^x | e^x (x^3 + 3x^2) |
| 3 | Calculus | Derivative of arctan(2x) | 2/(1 + 4x^2) |
| 4 | Calculus | Where is f(x) = x^3 - 3x decreasing? | -1 < x < 1 |
| 5 | Calculus | Linear approximation of the square root of 4.1 using x = 4 | 2.025 |
| 6 | Calculus | Integral of 1/x from 1 to e | 1 |
| 7 | Calculus | Average value of x^2 on [0, 3] | 3 |
| 8 | Calculus | A particle has v(t) = 6t, s(0) = 2. Find s(t). | 3t^2 + 2 |
| 9 | Precalculus | Domain of g(x) = root(x - 4) / (x - 6) | x ≥ 4, x not 6 |
| 10 | Precalculus | Exact value of cos(2 pi / 3) | -1/2 |
| 11 | Precalculus | Solve log base 3 of (x + 1) = 2 | x = 8 |
| 12 | Precalculus | Center and radius of (x + 1)^2 + (y - 2)^2 = 16 | (-1, 2), radius 4 |

1. **CLEP Calculus, week 1:** sample questions untimed, then limits, continuity and the limit definition of the derivative.
2. **Week 2:** derivative rules, the chain rule, implicit differentiation and inverse trig derivatives, all without a calculator.
3. **Week 3:** applications: curve sketching, extrema, the Mean Value Theorem, motion and related rates.
4. **Week 4:** antiderivatives, substitution and y' = ky.
5. **Week 5:** Riemann sums, the Fundamental Theorem, area and average value, plus TI-84 practice for numerical integrals.
6. **Week 6:** two timed rehearsals: 27 questions in 50 minutes without a calculator, then 17 in 40 with one.

1. **CLEP Precalculus, week 1:** algebra review and function concepts: domain, range, composition, inverses.
2. **Week 2:** representations: reading and transforming graphs and tables of every listed function type.
3. **Week 3:** trigonometry: the unit circle in radians, identities, equations and inverse trig functions.
4. **Week 4:** analytic geometry and functions as models.
5. **Week 5:** timed rehearsal in the exam's order: 25 questions with a calculator, then 23 without, including numerical-entry answers.

College Board's Calculus study-resources page points to free university courses and textbooks, with a caution that they were not written with CLEP in mind. Our plans track the exam's own topic weights, and the only official questions we use are College Board's free samples, untouched.

Which exam

## Should you take CLEP Calculus or CLEP Precalculus?

It depends on the course your degree needs and what you already know. Our guide below; your college's policy has the final word.

| Your situation | Usually the better fit |
| --- | --- |
| Degree requires Calculus I; you finished a calculus course | CLEP Calculus |
| Degree requires precalculus or college algebra and trigonometry | CLEP Precalculus |
| You finished precalculus but never studied calculus | CLEP Precalculus now, Calculus later |
| You took AP Calculus but scored below your college's cut | Check whether the college accepts a CLEP Calculus score instead |

### For homeschool families

A full calculus year followed by six weeks of CLEP review is a realistic route. Check two or three target colleges' policies before the year starts.

Some colleges limit credit if a student has already attempted a similar college course, so plan the order.

### For adult learners

Precalculus is often the safer first exam for adults away from math for years; it rebuilds trigonometry and functions that calculus assumes.

Remember the three-month wait before retaking the same exam title.

The catalogue

## Math courses from precalculus to college calculus

Live courses for credit-by-exam candidates and for the math beyond.

I

### Before calculus

Functions and trigonometry

CLE / P / 01

#### AP Precalculus

For CLEP Precalculus.

[Open the syllabus](/courses/ap-precalculus-exam-prep-course)

CLE / P / 02

#### High school math

Trig and functions refresher.

[Open the syllabus](/courses/complete-high-school-mathematics-mastery)

CLE / P / 03

#### Placement and CLEP algebra

Including CLEP College Algebra.

[Open the syllabus](/courses/college-math-placement-test-prep-course)II

### Calculus

Credit level

CLE / C / 01

#### AP Calculus

For CLEP Calculus.

[Open the syllabus](/courses/ap-calculus-exam-prep)

CLE / C / 02

#### College math

Series, vectors, matrices.

[Open the syllabus](/courses/college-mathematics-complete-masterclass)

CLE / C / 03

#### Math through coding

Riemann sums in Python.

[Open the syllabus](/courses/maths-through-coding)III

### After the credit

Applied math

CLE / A / 01

#### Math for data science

Calculus put to use.

[Open the syllabus](/courses/data-analytics-mathematics-masterclass)

CLE / A / 02

#### Statistics

Another common requirement.

[Open the syllabus](/courses/statistics-probability-maths-course)

CLE / A / 03

#### Quantitative reasoning

For graduate admissions.

[Open the syllabus](/courses/gre-gmat-quant-maths-prep-course)

How lessons run

## Calculus lessons around a test date

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Weekdays

Daytime for homeschoolers, evening for adults.

Weekends

Timed section rehearsals.

1-on-1

Paced to your booked exam date.

### By topic weight

Differential calculus gets half the time.

### No-calculator speed

Hand techniques drilled first.

### TI-84 fluency

Numerical integrals and zeros.

### Radians always

As the exam assumes.

### Concepts explained

For the nonroutine half.

### Batch or private

Fifteen to twenty, or one learner.

Student work

## Work from our students

Some learners model motion and growth in code after calculus. See [student labs](/student-labs).

![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp)

AI and ML

#### NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app)

![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp)

AI and ML

#### Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · [Open it](https://misti.modernagecoders.com)

![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp)

AI and ML

#### GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app)

![SkyCast weather forecast application screenshot](/images/projects/skycast.webp)

Web app

#### SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

## Fees

Lessons cost a monthly fee in US dollars, with no term to sign up for. College Board's exam fee is separate and paid to College Board, not to us.

Free first class

USD 0

no card required

- A first class without charge
- Bring your college's CLEP policy
- No card details

Book it

Group batch

USD 100

a month, billed in US dollars

- Fifteen to twenty learners
- A consistent teacher
- Choose your slot
- Paid by the month

Start here

One to one

USD 150

a month, billed in US dollars

- A private teacher
- Planned back from your exam date
- Your choice of times

Enquire

What families say

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Google reviews from families and adult learners, quoted in full.

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Questions learners ask

## CLEP Calculus and Precalculus: common questions

### How many questions are on CLEP Calculus?

College Board says 44 questions in two sections, answered in approximately 90 minutes: about 27 questions in about 50 minutes without a calculator, then about 17 in about 40 minutes with a built-in graphing calculator.

### Is the CLEP Calculus exam hard?

It packs a semester of college calculus into one sitting, with roughly equal routine and concept questions. Learners who have completed a calculus class and then review by topic usually cope; rusty trigonometry and algebra cause most trouble.

### How many credits is CLEP Calculus worth?

The ACE guideline is 4 semester hours at a score of 50. Colleges are free to award more, fewer or none, and to set a different cut score, so read the CLEP page of yours.

### How many credits is CLEP Precalculus worth?

Under the name Introductory Precalculus, ACE suggests 3 semester hours at 50. Whether those hours count toward your degree is a question for your college.

### Is a calculator allowed on CLEP Precalculus?

Only in the first section. College Board says Section 1 has 25 questions with a TI-84 Plus CE graphing calculator built in, and Section 2 has 23 questions with no calculator.

### What topics are on CLEP Precalculus?

Algebraic expressions, equations and inequalities (20%), functions (15%), representations of functions (30%), analytic geometry (10%), trigonometry (15%) and functions as models (10%). College Board notes that trigonometry runs through most topics.

### What is a passing score on CLEP Calculus?

CLEP does not pass or fail anyone. You get a reported score between 20 and 80, ACE treats 50 as the credit line, and your college may choose another number.

### What is the best prep book for CLEP Calculus?

College Board sells an official CLEP Calculus Examination Guide and lists free study resources, while noting that none of those resources are designed specifically for CLEP. Our lessons follow the official content outline, using problems our teachers write.

### When are your CLEP classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

### Are you connected with College Board?

No. Modern Age Coders is independent of College Board and CLEP. We teach the published content and direct you to College Board's own free sample questions.

Elsewhere on this site

## Related pages

More pages for credit-by-exam candidates and calculus students.

### [CLEP College Algebra prep](/clep-college-algebra-prep)

The CLEP exam one step below.

### [Calculus tutoring](/calculus-tutoring-online)

Ongoing calculus help.

### [Precalculus tutoring](/precalculus-tutoring-online)

Functions and trigonometry.

### [AP Calculus tutoring](/ap-calculus-tutoring-online)

The exam-based alternative.

### [Trigonometry tutoring](/trigonometry-tutoring-online)

Radians and identities.

### [Homeschool math](/homeschool-math-curriculum-usa)

Planning toward CLEP credit.

## Related pages in this guide

Part of the guide: [US math placement and college readiness tests](/us-math-placement-and-college-readiness-tests)

### College placement and credit

- [ACCUPLACER math prep](/accuplacer-math-prep)
- [ALEKS math placement test prep](/aleks-math-placement-test-prep)
- [TSIA2 math prep](/tsia2-math-prep)
- [CLEP College Algebra prep](/clep-college-algebra-prep)
- [Dual enrollment math help](/dual-enrollment-math-help)

### School placement and growth tests

- [MAP Growth math test prep](/map-growth-math-test-prep)
- [i-Ready math help](/i-ready-math-help)
- [Middle school math placement test prep](/middle-school-math-placement-test-prep)
- [Accelerated math program online](/accelerated-math-program-online)

### High school math courses

- [Integrated Math 1 tutoring](/integrated-math-1-tutoring)
- [Integrated Math 2 tutoring](/integrated-math-2-tutoring)
- [Integrated Math 3 tutoring](/integrated-math-3-tutoring)
- [Trigonometry tutoring online](/trigonometry-tutoring-online)
- [Statistics tutoring online](/statistics-tutoring-online)
- [AP Precalculus tutoring online](/ap-precalculus-tutoring-online)

### PSAT and PreACT

- [PSAT 8/9 and PSAT 10 math prep](/psat-8-9-math-prep)
- [PSAT math prep](/psat-math-prep)
- [PreACT math prep](/preact-math-prep)
- [SAT math tutoring online](/sat-math-tutoring-online)
- [ACT math tutoring online](/act-math-tutoring-online)

More guides: [US state math tests by state](/us-state-math-tests-by-state) · [US gifted and selective school tests](/us-gifted-and-selective-school-tests-guide) · [Homeschool and school math curricula guide](/homeschool-math-curriculum-guide-usa) · [US math and coding competitions guide](/us-math-and-coding-competitions-guide)

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## Keep exploring Modern Age Coders

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