Algebra — GCSE Revision Notes

12 notes on Algebra for GCSE Maths.

Solving Linear EquationsA linear equation contains a letter (the unknown) to the power 1 — no… Expanding and FactorisingExpanding means multiplying out brackets. Multiply the term outside… Quadratic EquationsA quadratic equation has the form ax² + bx + c = 0, where the highest… Simultaneous EquationsSimultaneous equations are two equations with two unknowns (usually x… Straight-Line Graphs (y = mx + c)A straight line has the equation y = mx + c, where: m = the gradient… Sequences and the nth TermA sequence is a list of numbers (terms) that follow a rule. Common… Quadratic EquationsA quadratic equation has the form ax² + bx + c = 0 where a ≠ 0.… Simultaneous EquationsSimultaneous equations are two (or more) equations that are both true… Sequences: nth Term, Quadratic & GeometricA sequence is an ordered list of numbers that follows a rule. GCSE… Algebraic Fractions & ProofAlgebraic fractions follow the same rules as numerical fractions. To… Functions & Graph TransformationsA function is a rule that takes an input and produces exactly one… Iteration & InequalitiesInequalities use the symbols (greater than), ≤ (less than or equal…

What these notes cover

Solving Linear Equations — What a linear equation is; The balance method; Unknowns on both sides; Equations with brackets; Equations with fractions; Forming equations from words
Expanding and Factorising — Expanding brackets; Expanding double brackets; Factorising
Quadratic Equations — Quadratic equations; Method 1: Factorising; Method 2: The quadratic formula; Method 3: Completing the square; The discriminant
Simultaneous Equations — Simultaneous equations; Method 1: Elimination; Method 2: Substitution; Graphical meaning
Straight-Line Graphs (y = mx + c) — Straight-line graphs; Gradient; The y-intercept; Reading an equation; Parallel and perpendicular lines; Plotting a line
Sequences and the nth Term — What a sequence is; Arithmetic (linear) sequences; The nth term of a linear sequence; Using the nth term; Geometric sequences; Special sequences
Quadratic Equations — Quadratic Equations; Method 1: Factorising; Method 2: The Quadratic Formula; The Discriminant (Higher); Method 3: Completing the Square (Higher); Forming Quadratic Equations
Simultaneous Equations — Simultaneous Equations; Linear Simultaneous Equations; Linear-Quadratic Simultaneous Equations (Higher); Graphical Interpretation
Sequences: nth Term, Quadratic & Geometric — Sequences: nth Term, Quadratic & Geometric; Arithmetic (Linear) Sequences; Quadratic Sequences (Higher); Geometric Sequences (Higher); Other Sequences to Recognise
Algebraic Fractions & Proof — Algebraic Fractions & Proof (Higher); Simplifying Algebraic Fractions; Adding and Subtracting Algebraic Fractions; Multiplying and Dividing; Solving Equations with Algebraic Fractions; Algebraic Proof
Functions & Graph Transformations — Functions & Graph Transformations (Higher); Function Notation; Composite Functions; Inverse Functions; Graph Transformations; Using Vectors for Translations
Iteration & Inequalities — Iteration & Inequalities; Inequalities; Iteration (Higher)

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