AP Calculus study guides

Recognize when a function is a composition, then differentiate it with the chain rule: outer derivative times inner derivative, with trig examples.

Recognize when u-substitution applies, choose u as the inner function whose derivative appears, convert definite-integral bounds, and avoid failed choices.

Decide between u-substitution, integration by parts, and partial fractions by reading the integrand. Includes a decision table and worked examples.

The 5-step method for related rates: diagram, equation, differentiate with respect to time, substitute, solve. Ladder and cone examples fully worked.

How to set up optimization word problems: objective vs constraint, reduce to one variable, then justify the max or min with a derivative test.

The order to evaluate AP Calculus limits: direct substitution, factoring, conjugates, trig limits, and the squeeze theorem, plus when to use each.

L'Hopital's Rule works only on 0/0 or infinity/infinity forms. Learn to verify the indeterminate form, apply the rule, and avoid the classic misuse.

Learn to recognize when to use implicit differentiation and find dy/dx step by step, with a circle example, a product-rule case, and the second derivative.

How FTC Part 1 (accumulation functions) and Part 2 (evaluating definite integrals) differ, when to use each, and how to tell which the problem wants.

Approximate definite integrals with left, right, midpoint, and trapezoidal Riemann sums, and tell instantly whether your estimate is too high or too low.

Pick disk vs washer fast by matching a perpendicular slice to the axis; shell (a college topic) uses a parallel slice and is not on the AP exam.

Find the area between two curves: top minus bottom vs right minus left, choosing dx or dy, finding intersections, and handling curves that cross.

Learn when to use the product rule versus the quotient rule in AP Calculus, plus when rewriting a fraction lets you skip the quotient rule entirely.

All six trig derivatives, inverse trig (Topic 3.4), and the co-function negative trick, with complete worked examples for AP Calculus AB and BC.

Derivatives of ln x, e^x, and a^x with answer-first formulas and full proofs via inverse functions and rewriting a^x = e^(x ln a). AP Calc CED 2.7 and 3.3.

Recognize, separate, integrate, and solve any separable differential equation, with initial conditions and the domain restrictions AP rubrics require.

How to read and sketch slope fields (AB and BC) and run Euler's method (BC only), with a full worked Euler table and the over/underestimate rule.

Test continuity at a point with the 3-part definition, classify removable, jump, and infinite discontinuities, and apply the Intermediate Value Theorem.

A weight-by-unit AP Calculus AB study plan: where the points are, how to spot which method each problem needs, and where students lose easy marks.

How AP Calculus AB and BC differ: the two BC-only units, the identical exam format, what the 2025 score gap really means, and how to choose.

The AP Calculus AB and BC exam format: two sections, four parts, 3 hours 15 minutes, the calculator rules per part, and how the 1 to 5 score is built.

Which AP Calculus exam parts allow a graphing calculator, the four calculator skills the exam expects, and the radian-mode and rounding mistakes to avoid.

Thirty five-minute AP Calculus openers organized by unit, from limits to BC series, each stating what a correct answer must include.

A complete first-day AP Calculus plan: a physical ten-minute limit hook, one-paragraph syllabus, full-period timing, and the first homework.

40+ discussion questions for AP Calculus AB/BC grouped by the real conceptual tension in each topic, plus notes on how to run the discussion.

A 40-minute Riemann sum lesson on the slider: predict left, right, and midpoint sums, watch error shrink as n grows, plus a no-tech graph-paper version.

Four AP Calculus sub plans built around the interactives: a projector step, plain instructions, and a worked answer key.

Ten AP Calculus review games with exact rules, timing, and prep, including three built on the site's own interactive tools.

Twelve AP Calculus AB/BC projects, each with a deliverable, duration, unit, and rubric line, plus math blocks and a fair-grading section.

Thirty two-minute AP Calculus exit tickets organized by unit, from limits to BC series, each naming the one line a correct answer must contain.

A week by week pacing guide for AP Calculus AB across all 32 teaching weeks before the exam, with the BC additions and what to cut when a unit runs long.

A 40-minute tangent line tracer lesson: predict slope sign, locate zero slope, and test a corner by hand, plus a no-tech graph-paper version.

How to recognize when integration by parts applies, use LIATE to choose u, and work the classic integrals of x e^x and ln x. BC-only, CED Topic 6.11.

A decision tree for AP Calculus BC: choose the right series convergence test (nth-term, geometric, p-series, alternating, ratio, comparison, integral) fast.

How the ratio test decides convergence: L < 1, L > 1, and the inconclusive L = 1 case, plus how to recognize when it is the right tool. AP Calc BC Topic 10.8.

Building a Taylor or Maclaurin series: the derivative formula, five series to memorize, and when to substitute instead. AP Calc BC Topics 10.11, 10.14, 10.15.

How to find dy/dx and d^2y/dx^2 for parametric curves, compute arc length, and set up polar area integrals in AP Calculus BC Unit 9.