# A-Level Maths (first teaching from 2017)

**A-Level Maths** is typically taught over two years – **AS Maths** is taught in the first year followed by **A2 Maths** in the second year. **Pure Maths**, **Statistics** and **Mechanics** are taught in both of the A-Level Maths years. The content of these years can be split into the topic areas seen below. Click on the links to find out more about the topics or see the content for individual **A-Level Maths lessons**. On each of these pages you should find notes on A-Level Maths, helpful examples, informative videos, questions by topic and much more. To find out more about the **A-Level Maths** **exams** go to the AS Maths page or the A2 Maths page. Also see below for what you need to know on the Edexcel Large Dataset.

## Topics covered in AS Maths

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

**AS Maths STATISTICAL SAMPLING**– sampling**AS Maths DATA PRESENTATION & INTERPRETATION**– box plots, frequency polygons and cumulative frequency diagrams, histograms, correlation, measures of central tendency, measures of variation, linear interpolation and coding**AS Maths PROBABILITY**– mutual exclusivity and independence, tree diagrams, Venn diagrams**AS Maths STATISTICAL DISTRIBUTIONS**– discrete probability distributions**AS Maths STATISTICAL HYPOTHESIS TESTING**– hypothesis tests, conducting hypothesis tests

**AS Maths QUANTITIES & UNITS IN MECHANICS**– quantities and units**AS Maths KINEMATICS**– motion in a straight line, the SUVAT equations**AS Maths FORCES & NEWTON’S LAWS**– motion under gravity, forces and Newton’s first law, Newton’s second law, Newton’s third law**AS Maths Moments**– not covered in AS Maths

## Topics covered in A2 Maths

**A2 Maths PROOF**– proof by contradiction**A2 Maths ALGEBRA & FUNCTIONS**– modulus of a function, partial fractions, inverse and composite functions, compound transformations**A2 Maths COORDINATE GEOMETRY**– parametric equations**A2 Maths SEQUENCES & SERIES**– arithmetic series (and sigma notation), geometric series, sequences, binomial expansion**A2 Maths TRIGONOMETRY**– radians, arc length & area of a sector, small angle approximations, reciprocal trigonometric functions, inverse trigonometric functions, double & compound angle formulae**A2 Maths EXPONENTIALS & LOGARITHMS**– compound transformations**A2 Maths DIFFERENTIATION**– concavity, convexity & inflection points, derivatives of trigonometric functions, product, quotient & chain rule, parametric & implicit differentiation, differentiating exp/log functions, differential equations & rates**A2 Maths INTEGRATION**– further integration, integration using trigonometric identities, integration by substitution, integration by parts, integration using partial fractions, solving differential equations,**A2 Maths NUMERICAL METHODS**– locating roots using iteration (including Newton-Raphson), trapezium rule**A2 Maths VECTORS**– 3D vectors

**A2 Maths Statistical Sampling –**(not covered in A2 Maths)**A2 Maths Data Presentation & Interpretation****–**(not covered in A2 Maths)**A2 Maths PROBABILITY –**conditional probability**A2 Maths STATISTICAL DISTRIBUTIONS –**the normal distribution**A2 Maths STATISTICAL HYPOTHESIS TESTING –**more hypothesis testing

**A2 Maths Quantities & Units in Mechanics****–**(not covered in A2 Maths)**A2 Maths KINEMATICS –**2D kinematics**A2 Maths FORCES & NEWTON’S LAWS –**2D forces**A2 Maths MOMENTS –**moments

## The Large Dataset

‘Big data’ is no longer a thing of the future and is creeping into A-Level Maths specifications across the board. You may be expected to answer questions based on a dataset that you are already familiar with. The more you are familiar with it, the more of an advantage you will have when answering questions. You may also be expected to recall trends in the data without being given the data.

The following links are provided by CrashMaths and provide guidance on the A-Level Maths Edexcel large dataset. This dataset contains weather statistics provided by the MET Office: