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LearnCambridge97092026–2027Paper 3 · Pure Mathematics 3Algebra

Paper 3 · Module

Algebra

5 subtopics≈ 215 min in total

Start the module: Modulus graphs and equations Open graphing calculator

Modulus graphs and equations
What $|x|$ means, how to sketch $y=|ax+b|$ by reflecting the negative part, and two reliable ways to solve modulus equations: squaring both sides, or splitting into cases and checking.
≈ 40 min
Modulus inequalities
Solving inequalities with moduli: the "between" and "outside" patterns, squaring when both sides are moduli, and using a sketch when a modulus is compared with a line.
≈ 40 min
Polynomials: division, factor and remainder theorems
Long division for polynomials, why the remainder on dividing by $(x-a)$ is just $p(a)$ , and how the factor theorem lets you factorise cubics and find unknown coefficients.
≈ 45 min
Partial fractions
Splitting a complicated fraction into simpler ones, which you need for integrating and for binomial expansions: the right form for each kind of denominator, and quick ways to find the constants.
≈ 45 min
Binomial expansion for any rational n
Extending $(1+x)^n$ to negative and fractional powers: an infinite series that only works for $|x|<1$ , how to handle $(a+bx)^n$ , and how to use the expansion with partial fractions and for approximations.
≈ 45 min