Detailed revision guide for the Algebra topic in AQA GCSE Mathematics covering definitions, examples, methods, advantages, disadvantages, and practice questions.
Algebra – AQA GCSE Mathematics (8300)
Key Concepts
Expressions, equations, inequalities
Substitution and formulae
Sequences (arithmetic and geometric)
Graphs of functions and lines
Factorising and expanding brackets
Solving linear and quadratic equations
Simultaneous equations
Definitions & Examples
Expression: A combination of numbers, variables and operators, e.g., 2x + 5.
Equation: A statement that two expressions are equal, e.g., 3x + 2 = 11.
Inequality: Shows that one side is greater or less than the other, e.g., x + 5 > 7.
Sequence: Ordered list of numbers following a pattern, e.g., 2, 5, 8, 11 (arithmetic +3).
Function: A rule that assigns each input exactly one output, e.g., f(x) = 2x + 1.
Methods
Substitute values into formulae to calculate unknowns
Expand and simplify brackets
Factorise expressions to solve equations
Use graphical methods to solve linear and quadratic equations
Solve simultaneous equations by substitution or elimination
Generate and continue sequences
Advantages & Disadvantages
Advantages: Develops reasoning, problem solving, transferable to science/CS, allows generalisation of patterns.
Disadvantages: Can be abstract, requires careful manipulation to avoid errors, quadratic factorisation can be tricky.
Practice Questions
Simplify: 3(x + 2) + 5x
Solve: 2x + 7 = 15
Factorise: x^2 + 5x + 6
Solve simultaneous equations: x + y = 10, 2x - y = 3
Find the 10th term of the sequence 4, 7, 10, 13,...