Algebra and Functions
The toolkit for every other topic in the course: manipulating expressions, solving equations and inequalities, sketching and transforming graphs, and expanding brackets with the binomial theorem.
- An Overview — the big idea, the language, the core techniques and the common mistakes
The content statements
- Indices and Surds — the laws of indices, including negative and fractional powers; simplifying surds and rationalising denominators
- Quadratic Functions — graphs, the discriminant, completing the square, and quadratics in a function of x
- Simultaneous Equations — elimination and substitution, one linear and one quadratic, and what the solutions mean graphically
- Linear and Quadratic Inequalities — solving inequalities, set notation, and shading regions on a graph
- Polynomials and the Factor Theorem — expanding, factorising, simple algebraic division and the factor theorem
- Curve Sketching and Proportion — cubics, quartics, reciprocal graphs, asymptotes, and direct and inverse proportion
- Transformations of Graphs — stretches and translations of y = f(x), and simple combinations
- The Binomial Expansion — expanding (a + bx)ⁿ for a positive integer n, Pascal’s triangle and approximations
Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.