# Algebra and Functions in A-Level Maths

## Algebra and Functions

**Algebra and Functions** are fundamental to most aspects of Pure Maths. For this reason, especially in the first year, this is one of the more important sections and we cover a relatively large number of topics.

At GCSE, we learn about surds and indices and a large emphasis is put on introducing quadratics (see more about GCSE Maths). In particular, we learn to solve quadratics by factorising, using the quadratic formula or by completing the square. We also start to learn how to solve simultaneous equations and inequalities. At A-Level, we develop these areas first seen at GCSE and we learn how to use the discriminant of a quadratic. We also advance our knowledge of Algebra and Functions by looking at other polynomials such as cubics. Curve Sketching and Transformations of graphs (not necessarily just quadratics and cubics) are also an important part of Algebra & Functions. In the second year, we introduce a new function: the modulus function and we learn how to invert and compound functions.

The following lists of topics show the areas covered in the first year (AS Maths) and in the second year (A2 Maths) of A-Level Maths or equivalent. Click on the links to look at our lessons in more detail.

## Other Areas in AS-Maths

- PROOF – proof by deduction, proof by exhaustion, disproof by counterexample
- COORDINATE GEOMETRY – straight lines, equation of a circle
- SEQUENCES & SERIES – binomial expansion
- TRIGONOMETRY – non-right-angled triangles, trigonometric equations, trigonometric graphs, trigonometric identities
- EXPONENTIALS & LOGS – exponential & logarithmic graphs, logs, their rules and solving log equations, growth & decay, differentiating e to the kx
- DIFFERENTIATION – differentiation from first principles and differentiating polynomials, increasing & decreasing functions, stationary points, tangents & normals, differentiating e to the kx
- INTEGRATION – fundamental theorem of calculus and integrating powers of x, definite integrals
- NUMERICAL METHODS – (not covered at AS Level)
- VECTORS – two-dimensional vectors, vector arithmetic, vectors in context

## Other Areas in A2 Maths

- PROOF – proof by contradiction
- COORDINATE GEOMETRY – parametric equations
- SEQUENCES & SERIES – arithmetic series (and sigma notation), geometric series, sequences, binomial expansion
- TRIGONOMETRY – radians, arc length & area of a sector, small angle approximations, reciprocal trigonometric functions, inverse trigonometric functions, double & compound angle formulae
- EXPONENTIALS & LOGARITHMS – compound transformations
- DIFFERENTIATION – concavity, convexity & inflection points, derivatives of trigonometric functions, product, quotient & chain rule, parametric & implicit differentiation, differentiating exp/log functions, differential equations & rates
- INTEGRATION – further integration, integration using trigonometric identities, integration by substitution, integration by parts, integration using partial fractions, solving differential equations,
- NUMERICAL METHODS – locating roots using iteration (including Newton-Raphson), trapezium rule
- VECTORS – 3D vectors