# Further Mathematics AS/A Level at S. Peter's Collegiate School - A CofE Academy

## Course description

This course will build upon GCSE Mathematics knowledge to a greater extent than single Mathematics – extending familiar algebraic, spatial and statistical concepts. It therefore has to be taken in conjunction with single mathematics at A Level.

- There is no coursework component in this specification, which allows students more time to concentrate on practising their techniques.
- All students have to complete three compulsory Further Pure Modules over the two years (one at AS and two at A2)
- The Advanced (A Level) award comprises six units
- Students will have the opportunity of completing two Applied Modules in Year 12 (Decision 1 and Statistics 1). In Year 13 the final applied modules will depend on student interest and numbers.
- Each paper will consist of short (4 or 5 marks) and long questions (up to 18 marks).
- Students studying Further Mathematics must opt for Mechanics 1 in single Mathematics lessons.
- All units will be examined in the summer.
- Candidates for AS are expected to have already obtained (or to be obtaining concurrently) an AS and/or A Level award in Mathematics.

## Course content

**AS LEVEL**

** Unit 1** –

**(Code: FMP1)**

__Mathematics Further Pure 1__- Algebra and Graphs
- Complex Numbers
- Roots and Coefficients of a quadratic equation
- Series
- Calculus
- Numerical Methods
- Trigonometry
- Matrices and Transformations

** Unit 2 **–

**(Code: MDO1)**

__Mathematics Decision 1__- Simple Ideas of Algorithms
- Graphs and Networks
- Spanning Tree Problems
- Matchings
- Shortest Paths in Networks
- Route Inspection Problem
- Travelling Salesperson Problem
- Linear Programming
- Mathematical Modelling

** Unit 3 **–

**(Code: MS1B)**

__Mathematics Statistics 1__- Numerical Measures
- Probability
- Binomial Distribution
- Normal Distribution
- Estimation
- Correlation and Regression

**A2 LEVEL**

** Unit 4** –

**(Code: MFP3)**

__Mathematics Further Pure 3__- Series and Limits
- Polar Coordinates
- Differential Equations
- Differential Equations . First Order
- Differential Equations . Second Order

** Unit 5** –

**(Code: MFP4)**

__Mathematics Further Pure 4__- Vectors and Three-Dimensional Coordinate Geometry
- Matrix Algebra
- Solution of Linear Equations
- Determinants
- Linear Independence

**AS Optional Modules Unit 6 (Choose one unit)**

** Mathematics Further Pure 2 **(Code: MFP2)

- Roots of Polynomials
- Complex Numbers
- De Moivre’s Theorem
- Proof by Induction
- Finite Series
- The Calculus of Inverse Trigonometrical Functions
- Hyperbolic Functions
- Arc Length and Area of surface of revolution about the x-axis

** Mathematics Decision 2** (Code: MDO2)

- Critical Path Analysis
- Allocation
- Dynamic Programming
- Network Flows
- Linear Programming
- Game Theory for Zero Sum Games
- Mathematical Modelling

** Mathematics Statistics 2** (Code: MS2B)

- Discrete Random Variables
- Poisson Distribution
- Continuous Random Variables
- Estimation
- Hypothesis Testing
- Chi-Square Contingency Table Tests

** Mathematics Mechanics 3** (Code: MM03)

- Relative Motion
- Dimensional Analysis
- Collisions in one dimension
- Collisions in two dimensions
- Further Projectiles
- Projectiles on Inclined Planes

** Mathematics Mechanics 4** (Code: MM04)

- Moments
- Frameworks
- Vector Product and Moments
- Centres of mass by Integration for Uniform Bodies
- Moments of Inertia
- Motion of a Rigid Body about a Fixed Axis

** Mathematics Mechanics 5** (Code: MM05)

- Simple Harmonic Motion
- Forced and Damped Harmonic Motion
- Stability
- Variable Mass Problems
- Motion in a Plane using Polar Coordinates

## Entry requirements

GCSE Higher Tier – Grade A at Higher Tier

GCSE APS of 43

## Assessment

A written paper for each of the 3 units lasting 1 hour 30 minutes

__Maximum Marks available: __

Each unit has 75 marks in total which is scaled to a UMS mark of 100.

__Information regarding Assessment:__

All questions are compulsory.

A scientific or graphics calculator can be used.

Weighted at 16.7% of an A Level.

## How to apply

If you want to apply for this course, you will need to contact S. Peter's Collegiate School - A CofE Academy directly.