# Summary of changes

This guide outlines the main changes to our AS and A-level Maths qualifications, for first teaching from September 2017.

## Overview of changes

The main changes to our new AS and A-levels in Maths are:

• the qualifications will now be linear, meaning that all the exams are sat in the same series
• AS Maths will no longer count towards A-level Maths – they can be co-taught but they are assessed separately
• the applied content (statistics and mechanics) is all now compulsory. The applied content contains a sample of topics from the legacy MM1B, MM2B MS1B and MS2B topics, along with some additional material for statistics
• there will be no optional content; all students sit the same exams covering the same content
• there is no longer any decision maths content in AS or A-level Maths.

## Subject content

The AS and A-level Maths subject content is 100% defined by the Department for Education (DfE).

The content is the same for all exam boards offering Maths AS and A-levels for exams in June 2018 and onwards.

Below is a broad summary of how the new content differs from that of the legacy specification. Please see the AS and A-level specifications for full details.

### Changes to pure maths content

What’s new What’s gone What’s moved from A-level to AS What’s moved from AS to A-level
• A greater overarching emphasis on modelling and problem solving (AS and A-level).
• Specific methods of proof eg disproof by counter example (AS and A-level) and proof by contradiction, including irrationality of and the infinity of primes (A-level only).
• Use of functions, parametric equations, sequences and series in modelling (A-level only).
• Use of logarithmic graphs for estimating parameters in exponential relationships (AS and A-level).
• Trigonometric exact values, small angle approximations, trigonometric functions, geometric proofs of formulae (A-level only).
• Gradient functions of a curve (AS and A-level).
• Differentiation from first principles for polynomials (AS and A-level), sin and cos (A-level only).
• Connected rates of change (A-level only).
• Integration as the limit of a sum (A-level only).
• Use of second derivatives for determining convexity, concavity and points of inflection (A-level only).
• The Newton-Raphson method (A-level only).
• Remainder Theorem.
• Volumes of revolution.
• Mid-ordinate and Simpson’s rule.
• Vector equations of lines.
• Scalar product (of vectors).

Use of exponential and logarithmic models using base e.

• Sequences given by a formula for the n th term; increasing, decreasing and periodic sequences; sigma notation; arithmetic sequences and series; geometric sequences and series.
• Radian measure, arc length, area of sector, area between two curves.
• Trapezium rule.

### Changes to applied content

#### Mechanics

What’s new What’s gone What’s moved from A-level to AS What’s moved from AS to A-level

Derivation of formulae for constant acceleration for motion in a straight line (AS and A-level).

• Use of vectors in two dimensions, magnitude and direction of a vector, position vectors, vector addition and multiplication by scalars.
• Use of calculus in kinematics for motion in a straight line.
• Derivation of formulae for constant acceleration for motion in two dimensions (using vectors).
• Resolution of forces using Newton’s second law.
• Forces and dynamics for motion in a plane.
• Use of the model.

#### Statistics

What's new What's gone What’s moved from A-level to AS What’s moved from AS to A-level
• Selection and critique of sampling methods and data presentation techniques (AS and A-level).
• Greater emphasis on making connections when calculating probability (AS and A-level).
• Correlation coefficients (A-level only).
• Statistical hypothesis testing (AS and A-level).
Application of the language of statistical hypothesis testing.
• Conditional probability.
• Normal and binomial distribution models.