A-level maths / Pure 1 / Algebraic methods
Algebraic methods
Simplify expressions, factor polynomials and explain why a mathematical statement is true.
Choose a skill below. Written steps stay available; models and short animations run at your pace.
- Algebraic fractionsSimplify algebraic fractions by factorising, divide a polynomial term by term and retain excluded values. Worked examples, a missing-point model and practice questions.
- Polynomial divisionDivide polynomials by linear factors using selectable worked steps. Handle missing powers, non-unit divisors and remainders, with full solutions to practice questions.
- Factor theoremUse the factor theorem to factorise cubics and quartics, solve polynomial equations and find unknown coefficients. Includes fractional roots, repeated roots and graph connections.
- Proof by deductionLearn to write algebraic and geometric proofs using identities, integer definitions, inequalities and coordinate geometry. Includes Pythagoras, parameter conditions and geometric bounds for pi.
- Proof by exhaustion and counterexamplesProve statements by checking every possible case and disprove universal claims with valid counterexamples. Explore parity, remainders and common errors in proof.
Useful foundations
Review algebraic expressions, quadratics and circles when a proof uses those methods.