A-Level Maths Integration Cheat Sheet & Summary (Year 1 & 2) - Edexcel, AQA, OCR

A comprehensive, print-ready 3-page Integration Summary Cheat Sheet and Knowledge Organiser covering every Year 1 (AS) and Year 2 Pure Mathematics integration technique for UK A-Level Maths (Edexcel, AQA, OCR A, and OCR MEI).

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Each of the 18 colour-coded revision cards states the clear general rule, key exam pitfalls to watch out for, and a fully worked A-Level exam-style example — ideal for topic summaries, folder dividers, independent Year 13 mock/summer revision, or classroom wall displays.

Topics Covered Across All 18 Cards:
• Page 1 (Core & Year 1/Early Year 2 Foundations):

1. Indefinite Integration & Finding +c (fractional & negative powers)
2. Definite Integrals & Negative Areas below the x-axis (splitting at roots)
3. Areas Between Curves, Lines & Axes (composite regions with triangles)
4. Standard Functions (e^x, 1/x, trig, sec^2 x, cosec^2 x, sec x tan x, cosec x cot x)
5. Integrating f(ax + b) (reverse linear chain rule & power rule vs ln trap)
6. Trigonometric Identities in Integration (double-angle sin^2 x, cos^2 x, tan^2 x & sin x cos x)

• Page 2 (Advanced Techniques — Reverse Chain Rule, Substitution & Parts):
7. Reverse Chain Rule (“Consider, Then Scale” — f’(x)/f(x), f’(x)e^f(x), f’(x)[f(x)]^n)
8. Integration by Substitution u = g(x) (converting x-limits to u-limits)
9. Root Substitutions (u^2 = ax + b with implicit differentiation)
10. Integration by Parts (LATE rule, integrating ln x & definite IBP)
11. Integration by Parts Twice (x^2 e^kx and x^2 sin kx)
12. Cyclic Integration by Parts (“Closing the Loop” for e^ax cos bx)

• Page 3 (Rational Functions, Parametrics, Differential Equations & Numerical Methods):
13. Partial Fractions in Integration
14. Top-Heavy Algebraic Fractions (algebraic division before integrating)
15. Parametric Integration (area under parametric curves & changing limits to t)
16. Solving First-Order Differential Equations (separating variables & + ln k)
17. Forming Differential Equations in Modelling (rates of change & connected rates)
18. The Trapezium Rule (concavity overestimate/underestimate test & worked table)

Format: Crisp 3-page A4 high-resolution PDF, ready to print in colour or black-and-white.