Integration by Substitution | 40 Worked Examples | AQA A-Level Maths

A complete, fully worked set of 40 integration by substitution questions for AQA A-Level Mathematics (7357), covering the calculus specification in full. Every solution is broken down one atomic step at a time, with a plain-English note on every working line and mark-scheme codes (M1, A1) placed exactly where the real AQA scheme rewards them, so students see not just the answer but precisely how marks are earned. The pack runs from gentle entry-level integrals up to genuinely demanding problems, split into 12 Easy, 16 Standard and 12 Challenging questions with continuous numbering. It teaches the whole toolkit: linear substitutions such as u = ax + b, spotting when the derivative of the inside function already sits in the integrand, rewriting a stray x factor in terms of u, definite integrals with careful conversion of the limits (the single most common lost mark on this topic), odd powers of sine and cosine via u = cos x or u = sin x, exponential and logarithmic substitutions, root substitutions such as u = sqrt(x), and the given trigonometric substitutions x = sin(theta) and x = 2 sin(theta) and x = tan(theta) that turn a surd into an exact expression. Extra-verbose explanations are woven into the harder questions to build genuine understanding of why each method works and to flag the classic sign-flip and limit-conversion traps that lose marks. Ideal for Year 13 revision, homework, cover lessons or targeted intervention. Answers are given in exact form throughout and every integral has been computer-verified for accuracy.