Revision of GCSE Specifications Draft Proposals Further Mathematics

Draft Proposals for Consultation 2016

Draft Proposals for Consultation 2016

Content Page Introduction ................................................................................................................ 3 A. Specification at a Glance ..................................................................................... 4 B. Subject Content for each Unit .............................................................................. 5 C. Summary of Changes .......................................................................................... 9 New Content ........................................................................................................... 9 Content Remaining ................................................................................................. 9 D. External Assessment ......................................................................................... 10 E. Progression from Key Stage 3 ........................................................................... 10 F. Progression to GCE ........................................................................................... 12 G. Additional Comments......................................................................................... 12 H. Support .............................................................................................................. 13

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Draft Proposals for Consultation 2016

Introduction Awarding Bodies are revising their GCSE and GCE specifications to ensure that both content and assessment continue to reflect the needs of learners and the society, economy and environment in which they live and work.

The revision programme is now underway to review our GCSE and produce revised specifications for first teaching from September 2017.

The new specification should provide opportunities for students to build upon the knowledge, understanding and skills developed at Key Stage 3, and the relevant requirements of the Northern Ireland Curriculum at Key Stage 4.

This document has been designed to provide you with an outline of our draft proposals for the revised GCSE specification. For further information on the revision of GCSE Specifications go to: http://www.ccea.org.uk/the-revision/

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Draft Proposals for Consultation 2016

A. Specification at a Glance The table below summarises the structure of this GCSE course: Relevant information in relation to course content, assessment, weighting and availability is inserted below. Content

Unit 1 Pure Maths

Unit 2 Applications (Choice of 2 sections out of 4)

Assessment

Weighting

Availability

External exam with calculator 2 hours 15 minutes

55%

January and Summer sittings starting Summer 2018

External exam with calculator 1 hour 45 minutes

45%

January and Summer sittings starting Summer 2018

At least 40% of the assessment (based on unit weightings) must be taken at the end of the course as terminal assessment.

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Draft Proposals for Consultation 2016

B. Subject Content for each Unit We have divided the course into two units. A brief description of each unit is provided below. Unit 1 Pure Maths Content

Description

PURE MATHS Algebraic Fractions

Add, subtract, multiply and divide rational algebraic fractions with linear and quadratic numerators and/or denominators;

Algebraic Manipulation

Manipulation of algebraic expressions and including expansion of 3 linear brackets;

Completing the square

The coefficient of x2 will always be 1. Applying this to solving quadratic equations, identifying minimum turning point

Simultaneous Equations

Formation and solution of three equations in three unknowns

Equation of a circle

Centred on the origin. Including finding the equation of a tangent at a given point on the circle;

Transformation of functions

f(x)±a, -f(x), f(x±a), f(-x)

Quadratic Inequalities

Restricted to quadratic expressions that factorise. Including using set notation to represent the solution set.

Trigonometric Equations

Solve simple trigonometric equations leading to a maximum of 2 solutions in a given range

Differentiation

Restricted to integer powers of x and includes the application of differentiation to gradient; finding equations of tangents and normal to points on a curve; simple optimisation problems and elementary curve sketching of a quadratic or cubic function

Integration

Restricted to integer powers of x and including definite integration and finding the area under a curve;

Logarithms

Laws of logs and including the use of log/log graphs in context. The solution of indicial equations. 5

Draft Proposals for Consultation 2016

Vectors

Vector concept, sum of 2 vectors and scalar multiples of a vector, simple geometrical problems. (Proofs using vector geometry included);

Matrices

Performing addition, subtraction and multiplication on matrices, finding inverses and solving matrix equations and using matrices to solve 2x2 simultaneous equations;

Unit 2 Applications Content

Description

Section 1 Mechanics Kinematics

Displacement/time graphs and velocity/time graphs and their applications (excluding interception problems); Use of constant acceleration formulae;

Vectors

Use of i/j notation including the magnitude and direction of a vector and the application of i/j vectors in calculations

Forces

Resolving forces into components and finding the resultant of a set of forces. Apply the concept of equilibrium;

Newton’s Laws of Motion

Apply F = ma including the scenarios: Inclined plane (applied forces parallel to the plane) Two connected particles in rectilinear motion; Friction will be given as a value or ratio to mass; (F = µR will not be tested)

Moments

Restricted to a horizontal uniform rod supported by 1 or 2 pivots

Section 2 Statistics Measures of Central Calculation of mean and standard deviation. Tendency and Dispersion Including combining sets of data. Transformation of data sets; (Excluding the calculation of median.)

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Draft Proposals for Consultation 2016

Probability

Calculation of combined probabilities using the addition rule. Calculate and interpret conditional probabilities through representation using expected frequencies, two-way tables, tree diagrams and Venn diagrams; Including construction of Venn diagrams;

Binomial Probabilities

Calculate binomial probabilities in context using Pascal’s triangle and the expansion of (p+q)n where n