# AP Calculus AB: Units, Exam Format, Study Guide and Free Practice

> A free AP Calculus AB study guide: all 8 units and their exam weights, the 2027 exam format and date, sample questions, and practice for every topic.

Source: https://practicecalculus.com/ap-calculus/ab
Updated: 2026-11-06

## At a glance

- **Exam date:** Monday, May 10, 2027
- **Exam length:** 3 hours 10 minutes
- **Questions:** 42 multiple choice and 6 free response
- **Format:** Hybrid digital: answer in the Bluebook app, write free-response work on paper
- **Calculator:** Graphing calculator for some parts only
- **College equivalent:** A first-semester college calculus course
- **Units:** 8, from limits to applications of integration
- **Practice here:** [Calculus 1](/learn/calculus-1), plus [slope fields](/learn/calculus-2/improper-integrals-and-applications/slope-fields) and [separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations)

## Key takeaways

- AP Calculus AB covers the same material as a first-semester college calculus course: limits, derivatives, integrals and their applications.
- The 2027 exam is on Monday, May 10, lasts 3 hours 10 minutes and has 42 multiple-choice and 6 free-response questions.
- Units 5 and 6, analytical applications of differentiation and integration, carry the most weight at 15 to 20 percent each.
- Half of the score comes from free response, where you must show your work and justify answers in words.

**AP Calculus AB** is College Board's course in differential and integral calculus. It matches a first-semester college calculus course, and a good score on the May exam can earn you college credit. This guide covers all 8 units, how much each one counts, how the exam works, and where to practice every topic with instant feedback.

## The 2027 AP Calculus AB exam

The exam is on **Monday, May 10, 2027**. It is a hybrid digital exam: you answer multiple-choice questions and read the free-response questions in the Bluebook app, then write your free-response work by hand in a paper booklet.

| Section | Questions | Time | Calculator | Share of score |
| --- | --- | --- | --- | --- |
| Multiple choice, Part A | 29 | 1 hr 40 min for both parts | No | 35% |
| Multiple choice, Part B | 13 | (shared with Part A) | Graphing calculator for some | 15% |
| Free response, Part A | 2 | 30 min | Graphing calculator for some | 16.7% |
| Free response, Part B | 4 | 60 min | No | 33.3% |

In total that is **3 hours 10 minutes**: 42 multiple-choice questions and 6 free-response questions. About two thirds of the score comes from parts where calculators are not allowed, so fast, accurate hand skills matter most.

## AP Calculus AB units and what to practice

College Board splits the course into 8 units. Each row shows the unit's share of the exam, a lesson where you can practice it, and pages that explain the ideas.

| Unit | Exam weight | Practice | Read |
| --- | --- | --- | --- |
| 1. Limits and Continuity | 10–15% | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [Intermediate Value Theorem](/theorems/intermediate-value-theorem) |
| 2. Differentiation: Definition and Fundamental Properties | 10–15% | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative), [power rule](/rules/power-rule) |
| 3. Differentiation: Composite, Implicit, and Inverse Functions | 5–10% | [Chain rule: powers](/learn/calculus-1/derivative-rules/chain-rule-powers) | [Chain rule](/rules/chain-rule), [implicit differentiation](/rules/implicit-differentiation) |
| 4. Contextual Applications of Differentiation | 10–15% | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates), [linear approximation](/blog/linear-approximation) |
| 5. Analytical Applications of Differentiation | 15–20% | [Critical points](/learn/calculus-1/applications-of-derivatives/critical-points) | [Mean Value Theorem](/theorems/mean-value-theorem), [optimization problems](/blog/optimization-problems) |
| 6. Integration and Accumulation of Change | 15–20% | [Accumulation functions](/learn/calculus-1/integrals/accumulation-functions) | [Riemann sums](/blog/riemann-sums), [Fundamental Theorem of Calculus](/theorems/fundamental-theorem-of-calculus-part-1) |
| 7. Differential Equations | 5–10% | [Slope fields](/learn/calculus-2/improper-integrals-and-applications/slope-fields) | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) |
| 8. Applications of Integration | 10–15% | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves), [volumes of revolution](/blog/volumes-of-revolution) |

Units 5 and 6 together are up to 40% of the exam, so give them the most practice time. Unit 6 also feeds almost every free-response question, because accumulation, the Fundamental Theorem and Riemann or trapezoid sums from tables show up again and again.

## What the free-response questions look like

Free response is half of the score, and it rewards clear reasoning as much as correct numbers. Most years include questions like these:

- **Rate in, rate out.** Water flows into and out of a tank at given rates. Find the amount at a given time with an integral, and decide when it is greatest.
- **Data in a table.** Estimate a derivative from nearby values, approximate an integral with a [trapezoid sum](/learn/calculus-1/integrals/trapezoid-sums), and explain what it means in context.
- **The graph of f'.** Read where $f$ increases, has extrema or changes concavity, and evaluate an [accumulation function](/learn/calculus-1/integrals/accumulation-functions) from areas.
- **Motion on a line.** Use velocity to find position, total distance and when the particle changes direction.
- **A differential equation.** Sketch a [slope field](/learn/calculus-2/improper-integrals-and-applications/slope-fields), write a tangent line approximation and solve with separation of variables.

Always state the theorem or reason you use, such as "since $f'$ changes from positive to negative at $x = 3$, $f$ has a relative maximum there". Answers without justification lose points even when the number is right.

## Example problems at the AP Calculus AB level

**1. A limit (Unit 1).** Find $\displaystyle\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$.

$$\frac{x^2 - 9}{x - 3} = \frac{(x - 3)(x + 3)}{x - 3} = x + 3 \to 6$$

**2. The chain rule (Unit 3).** Differentiate $y = \sin(x^2)$.

$$\frac{dy}{dx} = \cos(x^2) \cdot 2x = 2x\cos(x^2)$$

**3. An accumulation function (Unit 6).** If $g(x) = \int_0^x (3t^2 - 4)\,dt$, then by the Fundamental Theorem of Calculus

$$g'(x) = 3x^2 - 4, \qquad g(2) = \left[t^3 - 4t\right]_0^2 = 8 - 8 = 0$$

## How to prepare for AP Calculus AB

- **Practice a little every day.** Short daily sessions build the hand skills you need for the no-calculator parts. Every lesson here gives new numbers each time, so you can repeat a topic until it feels automatic.
- **Learn the justifications.** Know when to cite the [Intermediate Value Theorem](/theorems/intermediate-value-theorem), the [Mean Value Theorem](/theorems/mean-value-theorem) and the [Extreme Value Theorem](/theorems/extreme-value-theorem), and practice writing one clear sentence for each.
- **Keep the formulas close.** The [calculus formula sheet](/formulas) has every derivative and integral on one page. No formula sheet is provided on the exam.
- **Take timed practice exams** in the final weeks using [practice exams](/practice), then review every mistake.
- **Avoid the classic slips.** Our list of [common calculus mistakes](/blog/common-calculus-mistakes) covers the errors that cost the most points.

Thinking about the faster course instead? See the [AP Calculus BC guide](/ap-calculus/bc) and our comparison of [AP Calculus AB vs BC](/blog/ap-calculus-ab-vs-bc).

> AP and Advanced Placement are registered trademarks of College Board, which is not affiliated with PracticeCalculus and does not endorse this guide. Exam details come from College Board's AP Calculus AB pages; check them for any changes.

## Frequently asked questions

### What is on the AP Calculus AB exam?

Eight units: limits and continuity, the definition and basic rules of derivatives, the chain rule with implicit and inverse functions, applied rates of change, analytical uses of derivatives, integration and accumulation, differential equations, and applications of integration.

### When is the 2027 AP Calculus AB exam?

College Board lists the 2027 AP Calculus AB exam for Monday, May 10, 2027. Your AP coordinator confirms the exact time and room.

### Can I use a calculator on AP Calculus AB?

Only on some parts. Multiple-choice Part B and free-response Part A need a graphing calculator for some questions. Multiple-choice Part A and free-response Part B do not allow one, which is about two thirds of the score.

### Is AP Calculus AB hard?

It covers a full semester of college calculus, so it takes steady work. Students who practice a few problems every day, and who write out their reasoning on free-response style questions, find it very manageable.

### Should I take AP Calculus AB or BC?

BC includes everything in AB plus two more units, parametric and polar curves and infinite series, so it moves faster. Take AB if you want more time on the core ideas, and BC if you are comfortable with fast pacing and want credit for two college courses.