A Level Math Paper 3 (P3) complete revision

The complete revision of Cambridge A Level Math 9709 Paper 3 (Pure Mathematics 3), in three videos on this page. For each topic, they go through the key concepts and the types of questions you meet in the exam.

Each video has its own chapter list, so you can jump straight to the topic you want.

Jump to: Part 1 · Part 2 · Part 3

Press a chapter in any part and that video starts at the topic.

Part 1

Play the video

It covers concepts and question types for modulus inequalities, polynomials, partial fractions and binomial expansion.

1. 0:00Modulus InequalitiesSketching modulus graphs, solving modulus equations and inequalities, and inequalities that include a constant.Quiz
2. 27:57Polynomials (Remainder and Factor Theorem)Algebraic long division, the remainder and factor theorems, factorising cubics, and solving polynomial equations and inequalities.Quiz
3. 1:31:19Partial FractionsSplitting a fraction by substitution or by comparing coefficients, repeated factors, and improper fractions that need an extra constant.Quiz
4. 2:05:40Binomial ExpansionExpansions with negative and fractional powers, the values of x for which they are valid, and expanding a fraction by first writing it in partial fractions.Quiz

Part 2

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It covers concepts and question types for vectors, complex numbers, and logarithms with linear law.

1. 0:00VectorsPosition and unit vectors, ratios and parallelograms, equations of lines in three dimensions, angles between lines, points of intersection, perpendiculars and reflections in a line.Quiz
2. 1:47:30Complex NumbersCartesian form and equality, conjugates and roots of polynomials, modulus and argument, products and square roots, and loci and shaded regions on an Argand diagram.Quiz
3. 4:01:02Logs and Linear LawThe laws of logarithms and ln, solving exponential and logarithmic equations and inequalities, converting to y = mx + c, and growth and doubling-time questions.Quiz

Part 3

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It covers concepts and question types for trigonometry, differentiation, integration, differential equations and iteration.

1. 0:00P3 TrigonometryReciprocal functions, compound-angle, double-angle and half-angle identities, solving equations with them, and writing an expression in the form R sin(x + α).Quiz
2. 58:08P3 DifferentiationThe chain, product and quotient rules, exponential and logarithmic functions, implicit differentiation, tangents and normals, and showing a derivative takes a given form.Quiz
3. 2:25:23P3 IntegrationIntegrals with a linear expression inside, integration by parts, substitution, using identities and partial fractions first, exact answers, areas and volumes of revolution.Quiz
4. 4:23:00P3 Differential EquationsForming a differential equation from a description, separating variables, using the given conditions, and what happens after a long time.Quiz
5. 5:18:48P3 IterationShowing a root lies between two values, iterative formulae, finding the equation a root satisfies, and sketching graphs to count the roots.Quiz

How to use these videos

1. Pick the topic you want to revise and start there, rather than watching from the top.
2. Pause before each worked question and try it yourself first.
3. Note any topic that still feels shaky, then practise it with topical past paper questions.