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100+ Free AP Calculus AB Practice Questions

Pass your AP Calculus AB (Advanced Placement Calculus AB) exam on the first try — instant access, no signup required.

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Key Facts: AP Calculus AB Exam

45

multiple-choice questions in Section I (50% of the score)

College Board

6

free-response questions in Section II (50% of the score)

College Board

3h 15m

total exam time across both sections

College Board

1-5

AP score scale; a 3 or higher typically earns college credit

College Board

8

units covering limits, derivatives, integrals, and applications

AP Calculus AB and BC CED

17-20%

exam weight of Unit 6, Integration and Accumulation of Change (the largest)

AP Calculus AB and BC CED

$99

approximate standard US AP exam fee for 2025-26

College Board

The AP Calculus AB exam runs 3 hours 15 minutes and is split evenly between Section I (45 multiple-choice questions in 1 hour 45 minutes) and Section II (6 free-response questions in 1 hour 30 minutes). Each section counts for 50% of the composite score, which is reported on the 1-5 AP scale, and a 3 or higher typically earns college credit. The course covers 8 units, with Integration and Accumulation of Change (17-20%) and Analytical Applications of Differentiation (15-18%) carrying the most weight. Some parts allow a graphing calculator and others do not (source: College Board, apcentral.collegeboard.org).

Sample AP Calculus AB Practice Questions

Try these sample questions to test your AP Calculus AB 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 of (x^2 - 9)/(x - 3) as x approaches 3?
A.6
B.3
C.0
D.The limit does not exist
Explanation: Factor the numerator: x^2 - 9 = (x - 3)(x + 3). The (x - 3) factors cancel, leaving x + 3. Substituting x = 3 gives 3 + 3 = 6. This removable discontinuity is a classic indeterminate 0/0 form resolved by factoring.
2A function f is continuous at x = a if which of the following conditions holds?
A.The limit of f(x) as x approaches a exists only
B.f(a) is defined only
C.f(a) is defined, the limit of f(x) as x approaches a exists, and they are equal
D.f is differentiable at a but not necessarily defined there
Explanation: Continuity at a point requires three things: f(a) exists, the limit of f(x) as x approaches a exists, and the limit equals f(a). All three must hold simultaneously. This is the formal definition tested throughout Unit 1.
3What is the limit of (sin x)/x as x approaches 0?
A.0
B.The limit does not exist
C.Infinity
D.1
Explanation: This is a fundamental trigonometric limit: the limit of (sin x)/x as x approaches 0 equals 1, where x is in radians. It can be justified by the Squeeze Theorem and is the basis for the derivative of sin x.
4As x approaches infinity, what is the limit of (3x^2 + 5)/(2x^2 - x)?
A.0
B.3/2
C.Infinity
D.5
Explanation: When the degrees of numerator and denominator are equal, the limit at infinity is the ratio of leading coefficients: 3/2. Dividing every term by x^2 makes the lower-order terms vanish, leaving 3/2.
5Which theorem states that if a function g is between functions f and h near a point, and f and h share the same limit L there, then g also has limit L?
A.Squeeze Theorem
B.Intermediate Value Theorem
C.Mean Value Theorem
D.Extreme Value Theorem
Explanation: The Squeeze (Sandwich) Theorem states that if f(x) <= g(x) <= h(x) near a point and the limits of f and h both equal L, then the limit of g equals L. It is commonly used to evaluate limits like (sin x)/x.
6The function f(x) = 1/(x - 2) has what type of behavior at x = 2?
A.A removable discontinuity
B.A horizontal asymptote
C.A vertical asymptote
D.A point of continuity
Explanation: As x approaches 2, the denominator approaches 0 while the numerator stays nonzero, so the function values grow without bound. This produces a vertical asymptote at x = 2.
7If the limit of f(x) as x approaches 4 from the left is 5 and the limit from the right is 7, what can be concluded about the limit of f(x) as x approaches 4?
A.It equals 6, the average of the one-sided limits
B.It equals 5
C.It equals 7
D.It does not exist
Explanation: A two-sided limit exists only if the left-hand and right-hand limits are equal. Since 5 does not equal 7, the limit as x approaches 4 does not exist. This indicates a jump discontinuity.
8By the Intermediate Value Theorem, if f is continuous on [1, 3] with f(1) = -2 and f(3) = 4, which conclusion is guaranteed?
A.f has a maximum at x = 3
B.There is some c in (1, 3) where f(c) = 0
C.f is differentiable on (1, 3)
D.f is increasing on [1, 3]
Explanation: The Intermediate Value Theorem says a function continuous on [1, 3] takes every value between f(1) = -2 and f(3) = 4. Since 0 lies between -2 and 4, there must be a c in (1, 3) with f(c) = 0.
9What is the limit of (e^x - 1)/x as x approaches 0?
A.1
B.0
C.e
D.The limit does not exist
Explanation: This is a standard limit equal to 1, since it is the definition of the derivative of e^x at x = 0. It can also be confirmed by L'Hospital's Rule, which gives e^x/1 evaluated at 0, equal to 1.
10A graph shows a jump from a closed point at (2, 3) to an open point at (2, 5). What type of discontinuity occurs at x = 2?
A.Removable
B.Infinite
C.Jump
D.Oscillating
Explanation: A jump discontinuity occurs when the left-hand and right-hand limits both exist but are not equal, producing a 'jump' in the graph. Here the function value differs from the limit approached from one side.

About the AP Calculus AB Exam

AP Calculus AB is a College Board Advanced Placement course equivalent to a first-semester college calculus course, organized into 8 units covering limits, derivatives, integrals, and their applications. The May exam has two sections: Section I has 45 multiple-choice questions in 1 hour 45 minutes (a no-calculator part and a calculator part), and Section II has 6 free-response questions in 1 hour 30 minutes. Each section is worth 50% of the score, which is reported on the 1-5 AP scale.

Questions

45 scored questions

Time Limit

3 hours 15 minutes (1h45m multiple choice + 1h30m free response)

Passing Score

Scored 1-5; a 3 or higher typically earns college credit

Exam Fee

About $99 per exam (2025-26, US) (College Board)

AP Calculus AB Exam Content Outline

17-20%

Integration and Accumulation of Change

Riemann sums, definite integrals, the Fundamental Theorem of Calculus, antiderivatives, and u-substitution.

15-18%

Analytical Applications of Differentiation

Mean Value Theorem, extrema, monotonicity, concavity, inflection points, and optimization.

10-15%

Contextual Applications of Differentiation

Motion, related rates, linear approximation, and L'Hospital's Rule.

10-15%

Applications of Integration

Average value, area between curves, and volumes by cross-section and revolution.

10-12%

Limits and Continuity

Evaluating limits, one-sided limits, continuity, the Squeeze Theorem, and asymptotes.

10-12%

Differentiation: Definition and Fundamental Properties

Limit definition of the derivative, differentiability, and basic differentiation rules.

9-13%

Differentiation: Composite, Implicit, and Inverse Functions

Chain rule, implicit differentiation, inverse and inverse trig derivatives, and higher-order derivatives.

6-12%

Differential Equations

Slope fields, separable equations, and exponential growth and decay.

How to Pass the AP Calculus AB Exam

What You Need to Know

  • Passing score: Scored 1-5; a 3 or higher typically earns college credit
  • Exam length: 45 questions
  • Time limit: 3 hours 15 minutes (1h45m multiple choice + 1h30m free response)
  • Exam fee: About $99 per exam (2025-26, US)

Keys to Passing

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

AP Calculus AB Study Tips from Top Performers

1Practice both with and without a calculator — the exam has a no-calculator part, so you must know derivative and integral rules by hand.
2Memorize the Fundamental Theorem of Calculus in both forms; it ties together the heavily weighted integration and accumulation unit.
3Drill the chain rule until it is automatic — it appears throughout differentiation, related rates, and implicit differentiation.
4For free-response practice, always show the setup (the integral or derivative expression) before computing, since the rubric awards setup points.
5Spend extra review time on Units 5 and 6, which together make up roughly a third of the exam.

Frequently Asked Questions

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

Section I has 45 multiple-choice questions in 1 hour 45 minutes, and Section II has 6 free-response questions in 1 hour 30 minutes, for a total of about 3 hours 15 minutes. Each section is worth 50% of the score.

How is the AP Calculus AB exam scored?

Scores are reported on the AP 1-5 scale, where 5 is the highest. A 3 is considered 'qualified,' and most colleges award credit or placement for a score of 3 or higher, though policies vary by institution.

Can I use a calculator on the AP Calculus AB exam?

Yes, on parts of it. Both Section I and Section II are divided into a part where a graphing calculator is required and a part where calculators are not permitted, so you must be able to solve problems both ways.

What units does AP Calculus AB cover?

The course has 8 units: limits and continuity, differentiation definitions and rules, composite/implicit/inverse differentiation, contextual and analytical applications of differentiation, integration and accumulation of change, differential equations, and applications of integration.

Which units are weighted most heavily on the exam?

Unit 6 (Integration and Accumulation of Change) at 17-20% and Unit 5 (Analytical Applications of Differentiation) at 15-18% carry the most weight, followed by the contextual applications and applications of integration units at 10-15% each.

How much does the AP Calculus AB exam cost?

The standard AP exam fee in the United States is about $99 per exam for 2025-26. Fee reductions are available for eligible students, and fees can differ for schools and for testing outside the US.