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MEI Conference 2016

Preparing to teach forces

Sue de Pomerai Sue.depomerai@mei.org.uk

AS level Further Mathematics

A level Further Mathematics

Sample assessment materials

MEI AS level

MEI A level

AQA AS level

AQA A level

Edexcel AS level

Edexcel A level

OCR AS level

OCR A level

Get set for September 2017

Further Mathematics

Session description

• In this session we will explore the main features of the new

Further Mathematics AS and A levels and discuss the

implications for teaching and learning

• This session is one of a series of 4 which are designed to

inform teachers of upcoming changes to A level. It is

therefore suitable to any teachers of A level and may be of

particular interest to heads of department or KS5

coordinators. The resources accompanying this conference

session will be suitable for using with departmental

colleagues in order to help teams prepare for the changes.

Structure of

FM

Further Mathematics

• 50% content specified, all pure

• Awarding bodies can decide on

the other 50% so they may (or

may not) be significant

differences

• There may be some element of

choice retained in FM

• All exam boards should be

producing at least one

specification that can run

alongside Mathematics

Awarding

bodies

choose,

may be

pure or

applied

Prescribed

content, all

pure.

AS FM

• This is designed to be a

separate, valuable

qualification

• It must be able to be co-

taught with the full A

level in Further

Mathematics

• AS Further Mathematics

must be at least 30%

Pure Mathematics

Awarding

bodies

choose,

may be

pure or

applied

Prescribed

content, all

pure.

Specifically

prescribed

content

Optional

prescribed

content

A level FM

AS FM

AS FM • The 30% Pure Mathematics

content of AS Further Maths

has to be constructed from

some compulsory content:

– Matrices

– Complex Numbers

• together with some

additional Pure Maths

content chosen from the

compulsory content for A

Level Further Maths

Awarding

bodies

choose,

may be

pure or

applied

Prescribed

content, all

pure.

Specifically

prescribed

content

Optional

prescribed

content

A level FM

AS FM

Compulsory AS FM Complex

Numbers

Solve any quadratic, cubic or quartic equations with

real coefficients

Add, subtract, multiply and divide complex numbers

Complex conjugate; know that non-real roots of

polynomial equations with real coefficients occur in

conjugate pairs

Argand diagram

Evaluate the modulus and argument

Modulus-argument form (use of radians)

Multiply and divide complex numbers in modulus-

argument form

Simple loci

Compulsory AS FM Matrices Add, subtract, multiply, multiply by a scalar

Zero, identity

Linear transformations 2D, successive transformations

Simple linear transformations in 3D

Invariant points and lines

Determinant of a 2 2 matrix

Add, subtract, multiply, multiply by a scalar

Zero, identity

Linear transformations 2D, successive transformations

Simple linear transformations in 3D

Invariant points and lines

Determinant and inverse of a 2 2 matrix

Content and

structure of the

AS FP

examinations

AS Further Mathematics AQA

Paper

Length

(mins)

Raw

Marks

AS Further Maths 1 90 80

AS Further Maths 2 90 80

TOTAL 180 160

• Paper 1: Pure

• Paper 2: Applied – enter for two of Discrete, Mechanics,

Statistics

Optional prescribed pure content for AS level

AQA

Vectors Vector and Cartesian forms of equation of a

line

Scalar product

Angle between two lines

Distance between two lines

Distance of point from a line

Vector product

Algebra, sequences and proof Roots of polynomials

Summations of finite series

Method of differences

Hyperbolic functions Hyperbolic and inverse hyperbolic functions

Logarithmic form

calculus Volumes of revolution

Mean value function

Optional prescribed content for AS level

AQA

Polar coordinates Polar and Cartesian coordinates

Curve sketching

Area enclosed by a polar curve

Algebra, Graphs and inequalities Inequalities involving polynomials

Modulus functions and their graphs

Conics Simple loci

AS Further Mathematics

Edexcel

Paper

Length

(mins)

Raw

Marks

AS Further Maths 1 90 75

AS Further Maths option 90 75

TOTAL 180 150

• Paper 1: Pure compulsory

• Paper 2: Option – enter for one of Decision, Mechanics,

Statistics, Further Pure

Optional prescribed pure content for AS level

Edexcel

Complex Numbers Solving simultaneous linear equations

using matrices

Vectors Vector and Cartesian forms of equation

of a line and a plane

Scalar product

Angle between two lines

Distance between two lines

Distance of point from a line

Vector product

Algebra, sequences and proof Roots of polynomials

Summations of finite series

Proof by induction

calculus Volumes of revolution

AS Further Mathematics MEI

Paper

Length

(mins)

Raw

Marks

AS Further Maths compulsory 75 60

AS Further Maths option 1 75 60

AS Further Maths option 2 75 60

TOTAL 225 180

• Paper 1: Pure compulsory

• Options – enter for two of Mechanics a, Statistics a,

Modelling with algorithms, Numerical methods,

Mechanics b, Statistics b

Optional prescribed pure content for AS level

MEI

Complex Numbers Solving simultaneous linear equations using

matrices

Vectors Vector and Cartesian forms of equation of a

line and a plane

Scalar product

Algebra, sequences and proof Roots of polynomials

Summations of finite series

Method of differences

Proof by induction

AS Further Mathematics OCR

Paper

Length

(mins)

Raw

Marks

AS Further Maths compulsory 70 60

AS Further Maths option 1 70 60

AS Further Maths option 2 70 60

TOTAL 210 180

• Paper 1: Pure compulsory

• Options – enter for two of Mechanics, Statistics,

Discrete, Additional Pure

Optional prescribed pure content for AS level

OCR

Matrices Determinant and inverse of a 3X3 matrix

Solving simultaneous linear equations using

matrices

Vectors Vector and Cartesian forms of equation of a

line

Scalar product

Angle between two lines

Vector product

Algebra, sequences and proof Roots of polynomials

Proof by induction

Structure of the

Further Maths

A levels

A level Further Mathematics

AQA

Paper Length (mins) Raw Marks

Further Maths 1 120 100

Further Maths 2 120 100

Options 120 100

TOTAL 360 300

• Paper 1: Pure (compulsory)

• Paper 2: Pure (compulsory)

• Applied options– enter for two of Discrete, Mechanics,

Statistics

A level Further Mathematics

Edexcel Paper Length (mins) Raw Marks

Further Maths 1 90 75

Further Maths 2 90 75

Option 1 90 75

Option 2 90 75

TOTAL 360 300

• Paper 1: Pure (compulsory)

• Paper 2: Pure (compulsory)

• Options – enter for two of Further Pure 3, Further Pure 4,

Mechanics 1, Mechanics 2, Statistics 1, Statistics 2,

Decision 1, Decision 2

A level Further Mathematics MEI Paper Length (mins) Raw Marks

Compulsory Pure 160 144 (scales to 180)

Major 135 120

Minor 75* 60

TOTAL varies 360

* 105 minutes for Further Pure with Technology

• Choos