Algebra and Functions

Algebra and Functions is a foundational topic in OCR A-Level Mathematics, covering the manipulation of algebraic expressions, solving equations, and understanding the behaviour of functions. This topic underpins much of the A-Level course, including calculus, trigonometry, and modelling. You'll explore polynomial operations, factorisation, algebraic division, and the laws of indices and surds. Functions are introduced formally, including domain, range, composite and inverse functions, and transformations of graphs. Mastery here is essential for success in later topics like differentiation and integration.

Why does this matter? Algebra is the language of mathematics, and functions describe how quantities relate. In real-world contexts, you might model population growth with exponential functions or optimise profit using quadratic functions. At A-Level, you'll need to solve equations that arise in mechanics (e.g., projectile motion) and statistics (e.g., probability distributions). A strong grasp of algebraic manipulation and function properties will save you time in exams and reduce errors in more complex problems.

This topic builds on GCSE algebra but introduces greater depth and abstraction. You'll encounter new techniques like completing the square for quadratics, solving simultaneous equations with three unknowns, and working with inequalities. Functions are explored more rigorously, including piecewise definitions and the concept of one-to-one functions. By the end, you should be able to sketch graphs confidently, solve equations analytically, and interpret transformations like translations and stretches.