Multiple choice
42 questions · 1 hour 40 minutes · 50%
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AP Calculus AB exam prep
Build conceptual and procedural fluency in limits, derivatives, integrals, differential equations, and accumulation across graphs, tables, formulas, and context.
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AP Calculus AB exam format
Hybrid digital · 2027 format. Formats can change, so verify the linked official page before exam day.
Official College Board exam page ↗Free response
6 questions · 1 hour 30 minutes · 50%
AP Calculus AB unit roadmap
Each unit is a connected part of the course, not an isolated chapter. The focus says what you must know and the weighting says how much exam time it is worth. Use the weighting to order your review, never as permission to skip a prerequisite.
Limits and Continuity
Limit estimates, properties, asymptotes, continuity, IVT
- Define the vocabulary you need to explain limit estimates, properties, asymptotes, continuity, ivt.
- Draw and label the graph, model, diagram, or evidence that best represents limits and continuity.
- Solve one direct limits and continuity question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: FTC in both directions
Differentiation: Definition and Properties
Derivative definitions, rules, tangent lines
- Define the vocabulary you need to explain derivative definitions, rules, tangent lines.
- Draw and label the graph, model, diagram, or evidence that best represents differentiation: definition and properties.
- Solve one direct differentiation: definition and properties question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Derivative meaning from tables and graphs
Composite, Implicit, and Inverse Differentiation
Chain rule, implicit and inverse derivatives
- Define the vocabulary you need to explain chain rule, implicit and inverse derivatives.
- Draw and label the graph, model, diagram, or evidence that best represents composite, implicit, and inverse differentiation.
- Solve one direct composite, implicit, and inverse differentiation question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Sign charts and justification
Contextual Applications of Differentiation
Motion, rates, related rates, local linearity
- Define the vocabulary you need to explain motion, rates, related rates, local linearity.
- Draw and label the graph, model, diagram, or evidence that best represents contextual applications of differentiation.
- Solve one direct contextual applications of differentiation question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Calculator-active FRQ commands
Analytical Applications of Differentiation
MVT, extrema, monotonicity, concavity, optimization
- Define the vocabulary you need to explain mvt, extrema, monotonicity, concavity, optimization.
- Draw and label the graph, model, diagram, or evidence that best represents analytical applications of differentiation.
- Solve one direct analytical applications of differentiation question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Units on rates and accumulated quantities
Integration and Accumulation of Change
FTC, antiderivatives, substitution, Riemann sums
- Define the vocabulary you need to explain ftc, antiderivatives, substitution, riemann sums.
- Draw and label the graph, model, diagram, or evidence that best represents integration and accumulation of change.
- Solve one direct integration and accumulation of change question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: FTC in both directions
Differential Equations
Slope fields, separation, exponential models
- Define the vocabulary you need to explain slope fields, separation, exponential models.
- Draw and label the graph, model, diagram, or evidence that best represents differential equations.
- Solve one direct differential equations question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Derivative meaning from tables and graphs
Applications of Integration
Average value, area, volume, accumulation
- Define the vocabulary you need to explain average value, area, volume, accumulation.
- Draw and label the graph, model, diagram, or evidence that best represents applications of integration.
- Solve one direct applications of integration question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Sign charts and justification
Use a diagnostic to find the first knowledge gap
This short check is not a score prediction. It identifies which part of the course deserves your next focused session.
- Answer without notes.
- Explain your choice before revealing feedback.
- Record every uncertain answer, including lucky guesses.
Question 1 of 3
Scored skills for the AP Calculus AB exam
Knowing an idea internally is not enough. Practice producing observable evidence under time pressure.
Carry out mathematical procedures
Connect analytical, graphical, tabular, and verbal representations
Justify conclusions with definitions and theorems
Use correct notation, units, and endpoint language
Highest-value review targets
- FTC in both directions
- Derivative meaning from tables and graphs
- Sign charts and justification
- Calculator-active FRQ commands
- Units on rates and accumulated quantities
AP Calculus AB formulas and reference relationships
A useful sheet records meaning and conditions, not isolated symbols. Rebuild it from a blank page until every line comes back with its conditions attached.
Derivative definition
\[f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}\]
What it tells you: Defines instantaneous rate of change and tangent slope from secant slopes.
Use it when: The limit must exist and be finite for differentiability at $a$.
Example: For $f(x)=x^2$, the quotient approaches $2a$.
Chain rule
\[\frac{d}{dx}f(g(x))=f'(g(x))g'(x)\]
What it tells you: Differentiates a composition from the outside inward.
Use it when: Both required derivatives must exist at the relevant inputs.
Example: $d[(3x+1)^4]/dx=12(3x+1)^3$.
Fundamental Theorem
\[\int_a^b f(x)dx=F(b)-F(a),\quad F'=f\]
What it tells you: Connects accumulated change with antiderivatives.
Use it when: The course typically assumes $f$ is continuous on the interval.
Example: $\int_0^2 3x^2dx=[x^3]_0^2=8$.
Average value
\[f_{\mathrm{avg}}=\frac1{b-a}\int_a^b f(x)dx\]
What it tells you: Finds the constant height with the same signed accumulation over an interval.
Use it when: $a<b$ and $f$ must be integrable.
Example: The average of $x^2$ on $[0,3]$ is $(1/3)[x^3/3]_0^3=3$.
What the AP Calculus AB exam hands you, and what you have to recall
| Section or part | What you may use | What that means for your work |
|---|---|---|
| Multiple choice, Part A | No calculator | Derivative and integral rules by hand, limits, and algebraic simplification. |
| Multiple choice, Part B | Graphing calculator required | Numerical answers and graph reading; some choices are close together on purpose. |
| Free response, Part A | Graphing calculator required | Only four uses are expected: graph in any window, find zeros, evaluate a derivative at a point, evaluate a definite integral. |
| Free response, Part B | No calculator | Antiderivatives, chain rule, implicit differentiation, and exact values. |
Anything the table does not hand you, you have to remember. The AP Calculus AB study plan puts these rules on a week-by-week schedule.
Your AP Calculus AB preparation plan
Repeat this loop weekly: retrieve, diagnose, repair, mix, time, and reflect.
01
AP-style practice
Original questions, immediate explanations, and local progress.
Start →02Full course test
A timed mixed-unit test with a complete answer review.
Test →03Study plan and strategy
Eight weeks, plus the timing, calculator, and task-verb decisions.
Plan →04Unit roadmap
Every unit, its weighting, and what mastery looks like.
Review →05Formula review
Key relationships, their conditions, and what the exam provides.
Recall →Questions about the AP Calculus AB exam
Can I use a graphing calculator on the AP Calculus AB exam?
Rules change from section to section. Multiple choice, Part A: no calculator. Multiple choice, Part B: graphing calculator required. Free response, Part A: graphing calculator required. Free response, Part B: no calculator. Practise each section under its own rule.
How long is the AP Calculus AB exam?
Multiple choice: 1 hour 40 minutes, 42 questions. Free response: 1 hour 30 minutes, 6 questions. Multiple choice — About 2.4 minutes each. If a Part A question takes more than three minutes of algebra, you missed a shortcut. Free response — About 15 minutes per question. Answer every part you can even after you get stuck on part (a) - later parts are scored separately.
Which AP Calculus AB unit is weighted most heavily?
Analytical Applications of Differentiation (15–20%) and Integration and Accumulation of Change (15–20%) tie for the largest published weighting. Use the weighting to order your review, not to skip a prerequisite that a heavier unit depends on.
What does “Justify” mean on the AP Calculus AB exam?
Name the theorem AND verify its hypotheses. 'By the Mean Value Theorem' earns nothing unless you state that f is continuous on [a, b] and differentiable on (a, b). Answering a different verb can be mathematically correct and still score zero.
Use AI responsibly during AP exam preparation
Attempt first. Ask for a hint or critique. Close the explanation and solve again from memory. Never use outside help on a live or prohibited assessment.
Turn the guide into exam-day skill
Start a focused AP Calculus AB practice set, check each explanation, and use every miss to choose your next review session.
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