Algebraic methods
Build a convincing argument and work confidently with rational expressions.
Available lessons include notes you control, visual explanations and independent practice with full solutions.
- Proof by contradictionLearn A-level proof by contradiction: negate a claim, prove parity and irrationality results, and check each logical step. Interactive diagrams and practice with worked solutions.
- Algebraic fractionsSimplify, multiply, divide, add and subtract algebraic fractions. Keep track of excluded values, explore cancellation and practise with fully worked solutions.
- Partial fractionsDecompose algebraic fractions with distinct linear factors. Learn substitution and coefficient comparison, including non-monic factors and three-term examples, with worked practice.
- Partial fractions with repeated factorsLearn partial fractions with repeated linear factors: include every power, isolate coefficients and use an extra equation. Original worked examples, a manual model and practice.
- Algebraic divisionLearn algebraic division with linear and quadratic divisors, missing powers and remainders. Step through an original worked example and practise with full solutions.
- Improper partial fractionsLearn improper partial fractions by dividing first, then decomposing the proper remainder. Equal-degree, higher-degree and repeated-factor examples with worked practice.
These six lessons cover the chapter, from proof by contradiction to improper partial fractions.