Calculus Tips & Tricks: Review

Calculus Tips and Tricks teaches the shortcuts, quick checks and common mistakes that make calculus faster and safer: 45 short pages on limits, derivatives, integrals and series.

Each calculus trick is shown in a worked example, then you try it yourself in practice questions with tap-to-reveal answers. It all works offline.

This is not another formula list. Each page answers a practical question: which technique should I use, how do I set this up, and how do I check my answer? Decision charts help you choose a method, and every topic warns about the calculus mistakes students make most often.

What you will learn

• Algebra and Trig Skills: factoring patterns, simplifying fractions and roots, completing the square, exponent and log rewrites, the trig identities you actually use, unit circle tricks

• Limits: which limit technique to use, factor, cancel or conjugate, squeeze and trig limits, dominant terms at infinity, L'Hôpital's rule: uses and pitfalls

• Derivatives: choosing the right rule, the chain rule layer by layer, avoiding the quotient rule, logarithmic differentiation, implicit differentiation steps, quick derivative checks, common derivative mistakes

• Applications of Derivatives: a related-rates recipe, an optimisation checklist, finding extrema fast, sign charts for curve sketching, reading a graph of f′, linear approximation checks

• Integrals: rewrite before you integrate, spotting a u-substitution, FTC shortcuts, integration by parts and choosing u, tabular (DI) integration, partial fractions and the cover-up method, trig integrals, which integration technique to use, symmetry shortcuts, setting up area between curves, checking by differentiating

• Series: choosing a convergence test, quick convergence checks, Taylor series to memorise, building new series from old ones

• Exam Strategy: managing your time, showing your work, calculator habits, checking units and signs, free-response habits, and the top 30 calculus mistakes

Features

• 45 topic pages in 7 sections

• 119 worked examples, all checked with computer algebra

• 139 practice questions with tap-to-reveal answers

• 20 original drawings: decision charts for limits, derivative rules and convergence tests, sign charts, a DI table, the unit circle, the squeeze theorem, area between curves and more

• A list of the top 30 mistakes to read before a test

• Search all pages from the home screen

• Dark mode

• Works offline, no account needed

• Available in 8 languages: English, Español, Português, Français, Deutsch, العربية, हिन्दी and Bahasa Indonesia

Who it is for

• High school students taking calculus; useful when revising for AP Calculus AB and BC

• College and university students in a first-year calculus course (Calculus I and II)

• Anyone who knows the formulas but wants calculus shortcuts, quick checks and fewer mistakes

• Teachers and tutors looking for clear calculus tips and tricks to share with students

Calculus Tips and Tricks is an independent study aid. Content is checked against the OpenStax Calculus textbooks (Volumes 1 and 2), OpenStax College Algebra and Precalculus, and the College Board's AP Calculus AB and BC Course and Exam Description. It is not affiliated with or endorsed by the College Board, any exam board, textbook publisher or university.