The exam at a glance
| Section | Weight | Timing | What you do |
|---|---|---|---|
| I · Multiple choice | 50% | 1 hr 40 min · 42 questions | Part A: 29 questions in 62 minutes, no calculator (35% of score). Part B: 13 questions in 38 minutes, graphing calculator required for some (15%). Functions appear as equations, graphs, tables and words. |
| II · Free response | 50% | 1 hr 30 min · 6 questions | Part A: 2 questions in 30 minutes, graphing calculator required (about 17%). Part B: 4 questions in 60 minutes, no calculator (about 33%). At least two questions use a real-world context. |
Click in Bluebook, write on paper
You answer multiple-choice questions and read the free-response questions in the Bluebook app, then handwrite free-response answers in a paper booklet.
Know your four calculator skills
On calculator parts you are expected to graph a function, solve an equation, find a numerical derivative and evaluate a definite integral. Check that your model is on College Board's approved list.
The multiple-choice section
Part A gives you 29 questions in 62 minutes without a calculator (about 2 minutes each). Part B gives 13 questions in 38 minutes with a calculator (about 3 minutes each). Wrong answers lose no points.
Strategies that work
- Read graphs of f′ carefully. Many questions show the derivative, not the function: increasing f means f′ > 0, not f′ increasing.
- Know your limits toolkit: factoring, conjugates, the special trig limits and L'Hospital's Rule.
- Units tell you the answer type. A rate in gallons per hour, integrated over hours, gives gallons.
- In Part B, use the calculator for definite integrals and solving. Store intermediate values; don't round.
- Eliminate with estimates. A quick sketch often rules out two choices.
- Flag and move on after 3 minutes. Come back once the quick points are banked.
The 8 units, in plain English
Limits & Continuity
What a function approaches, and where it breaks.
Be ready to: Evaluate limits from graphs, tables and algebra; use the squeeze theorem; find asymptotes; apply the definition of continuity and the IVT.
Differentiation: Definition & Rules
The derivative as a limit and an instantaneous rate.
Be ready to: Use the limit definition; apply power, product and quotient rules and trig/exponential derivatives; connect differentiability and continuity.
Composite, Implicit & Inverse
Harder derivative rules.
Be ready to: Apply the chain rule; differentiate implicitly; find derivatives of inverse functions and inverse trig functions; find second derivatives.
Contextual Applications
Derivatives describing real change.
Be ready to: Interpret derivatives with units; solve motion and related-rates problems; use local linearization; apply L'Hospital's Rule.
Analytical Applications
Using derivatives to analyze a function's shape.
Be ready to: Apply the MVT and EVT; find intervals of increase and concavity; justify extrema with the first and second derivative tests; solve optimization problems.
Integration & Accumulation
The integral as accumulated change.
Be ready to: Compute Riemann and trapezoidal sums; apply both parts of the FTC; find antiderivatives; use u-substitution; interpret accumulation functions.
Differential Equations
Equations that describe how something changes.
Be ready to: Verify solutions; sketch and read slope fields; solve separable equations with initial conditions; model exponential growth.
Applications of Integration
Average value, motion, area and volume.
Be ready to: Find average value; use integrals for position and total distance; find areas between curves; find volumes by cross sections and discs/washers.
Units 5 and 6, analyzing functions with derivatives and the meaning of the integral, are the biggest and drive most free-response questions. AB covers Units 1–8; BC adds Units 9–10 (parametric, polar and series).
The free-response section
90 minutes, 6 questions, 9 points each (54 raw points). Part A (2 questions, calculator) gets 30 minutes; Part B (4 questions, no calculator) gets 60 minutes, and you may return to Part A questions without a calculator.
Rates in and out
Water, people or cars enter and leave. You integrate rates for amounts, compare rates to decide increasing or decreasing, and find maximums. Often in Part A.
Amount at time t = starting amount + ∫(in − out).
Data in a table
Estimate integrals with left, right, midpoint or trapezoidal sums, interpret them with units, and apply the MVT or IVT to the data.
Check the hypotheses aloud: "f is differentiable, so…".
Graph of f′
Given the graph of a derivative, find extrema, concavity, inflection points and values of f using areas.
Justify with f′, never with "the graph goes up".
Particle motion
Position, velocity and acceleration: direction, speeding up or slowing down, displacement versus total distance, and position at a given time.
Speeding up: v and a have the same sign.
Differential equations
Sketch a slope field, use a tangent-line approximation, and solve a separable equation with an initial condition.
Separate, integrate, add +C, use the initial condition, then solve for y.
Area and volume
Area between curves and volumes by discs, washers or cross sections. Sometimes replaced by an implicit-differentiation question.
Write the integral setup clearly; it earns points even without evaluating.
Time plan: About 15 minutes per question.
Habits that earn points
- Label every part: (a), (b), (c).
- Justify with f′ or f″ signs, not words like "the graph".
- Include units in every contextual answer.
- Give decimals to 3 places on calculator parts.
- Stuck? Write the setup integral or equation. It still scores.
10 traps that cost points
Justifying with "the graph"
Readers need a reason based on f′ or f″: "f′ changes from + to −", not "the graph peaks".
Displacement vs distance
Total distance is ∫|v(t)| dt. Displacement is ∫v(t) dt. They differ whenever the particle turns around.
Forgetting the chain rule
d/dx[sin(x²)] = 2x cos(x²). The inner derivative is the most common missing piece.
Rounding too early
Store calculator values and round only the final answer to 3 decimal places.
Dropping +C or the initial condition
In separable equations, add +C right after integrating and solve for it before isolating y.
Mixing up f, f′ and f″
If the graph shown is f′, its zeros are f's critical points and its slopes give f's concavity.
Using a theorem without its conditions
The MVT needs f continuous on [a, b] and differentiable on (a, b). Say so when you use it.
Wrong limits after u-substitution
Either change the limits to u-values or switch back to x before evaluating.
Missing units in context
A rate in liters per minute integrated over minutes gives liters. Write it.
Leaving a part blank
Each part is scored separately. A correct setup can earn points even if the next step fails.
A study roadmap to May
A steady plan beats a last-minute rush. Shift the months to match your teacher's pacing.
- Sep – Oct
Units 1–2: limits and derivatives
Master limit techniques and every derivative rule. Do 10 derivative drills a day until you rarely make sign errors.
- Nov – Dec
Units 3–5: applications
Chain rule, implicit, related rates, MVT, extrema and optimization. Start writing justifications in full sentences.
- Jan – Mar
Units 6–8: integrals
Riemann sums, FTC, u-substitution, differential equations, area and volume. One released free-response question per week.
- April
Timed sections
Alternate full multiple-choice and free-response sections under real timing, splitting calculator and no-calculator parts.
- Early May
Justification polish
Rewrite your weakest justifications until they match rubric language. Review the traps list.
- May 2027
Exam day
Monday, May 10, 2027 (morning session). Sleep well and confirm your start time with your AP coordinator.
3 practice questions
Original questions written by ACT SAT GO in the style of the exam. The free PDF has 10, with full explanations.
- Unit 3 · Implicit differentiation
For the curve x² + xy + y³ = 3, what is dy/dx at the point (1, 1)?
- A −3/4
- B −1
- C 3/4
- D −1/2
Show answer
Answer: A · −3/4. Differentiate: 2x + y + xy′ + 3y²y′ = 0. At (1, 1): 3 + 4y′ = 0, so y′ = −3/4.
- Unit 5 · Extrema
The derivative of f is f′(x) = (x − 2)²(x + 1)(x − 4). At which value(s) of x does f have a relative minimum?
- A x = −1 only
- B x = 2 and x = 4
- C x = −1, x = 2 and x = 4
- D x = 4 only
Show answer
Answer: D · x = 4 only. f′ changes sign only at −1 (+ to −, a maximum) and 4 (− to +, a minimum). (x − 2)² never changes sign, so x = 2 is not an extremum.
- Unit 8 · Motion
A particle moves along a line with velocity v(t) = t² − 4t + 3 for 0 ≤ t ≤ 4. What is the total distance it travels?
- A 4/3
- B 8/3
- C 4
- D 16/3
Show answer
Answer: C · 4. v = (t − 1)(t − 3) changes sign at 1 and 3. Distances: 4/3 + 4/3 + 4/3 = 4. Choice A is the displacement.
How students score
Ranges reflect recent College Board score distributions and shift a little each year. Credit and placement policies vary by college.
Aiming for a 5 in AP Calculus AB?
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