# Further Mathematics

### SPECIFIC AIMS OF THE DEPARTMENT

#### EXAM BOARD

CCEA

#### OVERVIEW OF KEY STAGE 3 CURRICULUM

#### OVERVIEW OF KEY STAGE 4 CURRICULUM

https://ccea.org.uk/key-stage-4/gcse/subjects/gcse-further-mathematics-2017

The Key Stage 4 Further Mathematics curriculum is based on the CCEA GCSE Further Mathematics course.

**Aims and Key Features**

This specification aims to encourage students to:

• develop further their mathematical knowledge, skills and understanding;

• select and apply mathematical techniques and methods to mathematical, everyday and real-world situations;

• reason mathematically, interpret and communicate mathematical information, make deductions and inferences, and draw conclusions;

• extend their base in mathematics from which they can progress to:

o higher studies in mathematics;

o studies such as science, geography, technology or business, which contain a significant requirement in mathematics beyond Higher Tier GCSE Mathematics;

• design and develop mathematical models that allow them to use problem-solving strategies and apply a broader range of mathematics to a variety of situations.

**The following are important features of this specification.**

• It is designed to broaden the experience of students whose mathematical ability is above average and who would like to:

o study mathematical courses at AS/A level;

o study other courses at AS/A level that require mathematics beyond GCSE Higher Tier;

o extend their knowledge of mathematics.

• It gives students the appropriate mathematical skills, knowledge and understanding to help them progress to further academic and vocational study and to employment.

**Course Structure**

This specification comprises three units. All units are assessed through an external written examination in the form of a single question-and-answer booklet that includes a formula sheet.

**Unit 1 Pure Mathematics - 50% - 2 hours**

Unit 2 Mechanics - 25% - 1 hour

Unit 3 Statistics - 25% - 1 hour

**The units address the three assessment objectives for this specification:**

• AO1: Use and apply standard techniques;

• AO2: Reason, interpret and communicate mathematically;

• AO3: Solve problems in mathematics and other contexts

**Subject Content**

Some of the content associated with each unit appears below.

**Unit 1 Pure Mathematics**

Algebraic Fractions, Algebraic Manipulation, Completing the Square, Simultaneous Equations, Quadratic Inequalities, Trigonometric Equations, Differentiation, Integration, Logarithms, Matrices

**Unit 2 Mechanics**

Kinematics, Vectors, Forces, Newton’s Laws of Motion, Moments

**Unit 3 Statistics**

Central Tendency and Dispersion, Probability, Binomial Distribution, Normal Distribution, Bivariate Analysis

#### OVERVIEW OF KEY STAGE 5 CURRICULUM

https://ccea.org.uk/post-16/gce/subjects/gce-further-mathematics-2018

The Key Stage 5 Further Mathematics curriculum is based on the CCEA GCE Advanced Subsidiary (AS) and Advanced (A level) GCE courses in Further Mathematics.

**Aims**

This specification aims to encourage students to:

• understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study;

• extend their range of mathematical skills and techniques;

• understand coherence and progression in mathematics and how different areas of mathematics are connected;

• apply mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general;

• use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly;

• reason logically and recognise incorrect reasoning;

• generalise mathematically;

• construct mathematical proofs;

• use their mathematical skills and techniques to solve challenging problems that require them to decide on the solution strategy;

• recognise when they can use mathematics to analyse and solve a problem in context;

• represent situations mathematically and understand the relationship between problems in context and mathematical models that they may apply to solve these;

• draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions;

• make deductions and inferences and draw conclusions by using mathematical reasoning;

• interpret solutions and communicate their interpretation effectively in the context of the problem;

• read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding;

• read and comprehend articles concerning applications of mathematics and communicate their understanding;

• use technology such as calculators and computers effectively, and recognise when such use may be inappropriate;

• take increasing responsibility for their own learning and the evaluation of their own mathematical development.

**Course Structure **

The course has been divided into four units: two units at AS and two units at A2. All units are assessed through external written examinations

AS 1: Pure Mathematics - 1hr 30mins - 50% of AS (20% of A level)

AS 2: Applied Mathematics - 1hr 30mins - 50% of AS (20% of A level)

A2 1: Pure Mathematics - 2hrs 15mins - 30% of A level

A2 2: Applied Mathematics – 2hrs 15mins - 30% of A level

**Content**

This section sets out the content and some of the learning outcomes for each unit.

### Year 13

**Unit AS 1 Pure Mathematics**

Algebra and Functions - Roots of Quadratic Equations

Complex Numbers - Cartesian and Modulus-Argument Forms, Argand Diagrams, Solving Quadratic, Cubic, Quartic Equations

Matrices - Linear Transformations, Systems of Simultaneous Linear Equations

Vectors - Equation of Line, Scalar and Vector Products, Equation of Plane, Area and Volum

**Unit AS 2 Applied Mathematics Section A: Mechanics 1**

Hooke’s Law - Elastic Strings and Springs

Work and Energy - Work Done by Force, Principle of Conservation of Mechanical Energy, Work-Energy Principle

Power - Vehicles in Motion, Pumps

Circular Motion - Motion in Horizontal Circle, Conical Pendulum, Banked Corners

**Unit AS 2 Applied Mathematics Section C: Statistics**

Sampling - Simple Random, Stratified, Quota, Cluster, Opportunity

Probability - Permutations and Combinations

Statistical Distributions - Geometric Distribution, Poisson Distribution, Discrete and Continuous Probability Distributions, Coding

Bivariate Distributions - Product Moment Correlation Coefficient, Least Squares Regression Analysis

### Year 14

**Unit A2 1 Pure Mathematics**

Proof - Mathematical Induction

Further Algebra and Functions - Partial Fractions, Summation of Series, Maclaurin Series

Complex Numbers - De Moivre’s Theorem, Complex Roots of Unity

Further Calculus - Improper Integrals, Integration using Partial Fractions, Repeated Integration by Parts, Simple Reduction Formulae

Polar Coordinates - Curve Sketching, Area Enclosed by Polar Curve

Hyperbolic Functions - Differentiation and Integration of, Logarithmic Forms of Inverse Hyperbolic Functions

Differential Equations - Integrating Factor Method, First and Second Order Differential Equations

**Unit A2 2 Applied Mathematics Section A: Mechanics 1**

Simple Harmonic Motion - Simple Pendulum, Elastic Strings and Springs

Damped Oscillations - Model using Second Order Differential Equations

Centre of Mass - Systems of Particles and Rods, Laminae

Frameworks - Problems involving Tension and Thrust

Further Circular Motion - Banked Corners including Sliding and Overturning

**Unit A2 2 Applied Mathematics Section B: Mechanics 2**

Further Kinematics - Kinematics in 3D, Variable Acceleration

Further Centre of Mass - Laminae and Solids, Suspended Bodies, Sliding/Toppling Problems

Force Systems - System of Coplanar Forces, Couples

Restitution - Elastic Collisions

**The A2 assessment units include some synoptic assessment, which encourages candidates to develop their understanding of the subject as a whole.**

The A2 assessment units provide opportunities to demonstrate higher order thinking skills by incorporating:

• more demanding unstructured questions;

• questions that require candidates to make more connections between sections of the specification.