Free AP Calculus Solver
Paste any AP Calculus AB or BC question and see the full step-by-step working. Covers all 10 AB units and the three additional BC units — from limits through series.
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An AP Calc integral — u-substitution walkthrough
Below is one fully worked example plus a short primer so you can see exactly how our AI reasons through a problem.
Example Problem
DEMO- 1
Spot the u-substitution
The integrand has x multiplied by e to a power of x² — a classic u = −x² setup because du = −2x dx gives us the x dx we need.
- 2
Substitute u = −x²
Change the limits too: x = 0 → u = 0; x = 1 → u = −1.
- 3
Rewrite the integral in terms of u
- 4
Evaluate
- 5
AP exam tip — write the substitution explicitly
On free-response questions, graders award partial credit for showing u = −x², du = −2x dx, and the changed limits. Even if the final answer is wrong, you keep the setup points.
Final Answer
How to approach AP Calculus — AB vs BC, and FRQ strategy
AP Calculus comes in two flavours. AP Calculus AB is a first-year college calculus course covering Units 1–8: limits and continuity, differentiation, applications of derivatives (rates, optimisation, related rates), integration, and applications of integration (area, volume). AP Calculus BC is a superset — everything in AB plus Units 9 and 10: parametric/polar/vector functions, and infinite sequences and series (Taylor, Maclaurin, convergence tests). Both exams are 3 hours 15 minutes with two sections, multiple choice and free response, and both allow a graphing calculator on roughly half the questions. The free response (FRQ) section is where most students gain or lose points — graders reward explicit setup, clearly labelled variables, units on final answers, and justification using specific theorems (IVT, MVT, Fundamental Theorem of Calculus). The College Board releases past FRQs every year — working through the last ten years is the single highest-ROI prep activity, especially with a solver that shows the setup the way AP expects.
AP Calculus problems to practise (AB & BC)
Tap any problem to solve it with full step-by-step working.
- Solve with AI →1.Unit 1 — limitsAB / BCEasy
- Solve with AI →2.Unit 2 — product ruleAB / BCEasy
- Solve with AI →
3. A spherical balloon is inflated at 30 cm³/s. How fast is the radius increasing when r = 5 cm?
Unit 4 — related ratesAB / BCMedium - Solve with AI →4.Unit 6 — integration by partsBCMedium
- Solve with AI →5.Unit 10 — seriesBCHard
Frequently asked questions
What's the difference between AP Calculus AB and BC?+
AB covers Units 1–8 (limits, derivatives, integrals and their applications). BC adds Units 9 (parametric, polar, vector functions) and 10 (sequences and series). BC also goes deeper on some AB topics. Both exams share the same 3:15 length and calculator policy.
How do I maximise free-response (FRQ) points?+
Show every step of your setup: define variables, state the theorem you're using (IVT, MVT, FTC), keep units on final answers, and justify continuity or differentiability when the problem asks. Graders award partial credit generously for clear reasoning even when arithmetic slips.
Which convergence test should I use for a BC series question?+
Start with the nth-term test (does a_n → 0?). If not → diverges. Then try comparison or limit-comparison for series of positive terms, ratio test for factorials or nth powers, alternating-series test for alternating signs, and integral test for series resembling integrable functions. The solver walks through the decision path.
What calculator functions should I master before the exam?+
Graphing, numerical derivative at a point (nDeriv), numerical integral over an interval (fnInt), and finding roots or intersections. The AP exam allows these four calculator-active operations without showing work — learn to reach them in under 10 seconds.
Is the AP Calculus solver free to use?+
SolveGini has a free plan. Guests get 1 solve per day; free accounts unlock 5 daily solves plus quizzes and flashcards tuned to AP syllabus. Full FRQ-style working shown on every solve.
Can I use this alongside Princeton Review or Barron's prep books?+
Yes — use the book for concept introduction and mock tests, and SolveGini for the specific problems where you want worked-out reasoning beyond the book's answer key. The two pair well without overlapping.
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