GCSE Maths: Algebra Revision

Foundation and Higher Algebraic notation — writing an expression from a description Substitution — evaluating expressions and formulae, including negatives Simplifying expressions — collecting like terms and using the index laws Expanding brackets — single, double and triple brackets Factorising — common factors, quadratics and the difference of two squares Linear equations — unknowns on both sides, brackets and fractional coefficients Forming equations — setting up an equation from a perimeter, an age or a total Linear graphs — gradient, intercept, and the equation of a line Coordinates and midpoints — including working back to an endpoint Rearranging formulae — changing the subject, including when it appears twice Quadratic equations — solving by factorising and by formula Sequences — the nth term, term-to-term rules, and quadratic sequences Simultaneous equations — elimination and substitution Inequalities — linear, double-sided, and integer solution sets Indices — including zero and negative powers Algebraic proof — expanding and simplifying to show a result Higher tier as well Completing the square — and reading off the turning point Quadratic inequalities — solution sets and integer solutions Algebraic fractions — simplifying, adding, subtracting and dividing Functions — composite fg(x), gf(x) and inverse f⁻¹(x) Gradients and rates of change — including the gradient of a chord Differentiation — gradients at a point, stationary points and kinematics Proportion — direct and inverse, including squares and roots Arithmetic series — first term, common difference and the sum of n terms Fractional and negative indices — evaluating exactly Parallel and perpendicular lines — finding equations through a given point