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
• Choose EITHER major + minor OR three minors
• Major: Mechanics or Statistics
• Minor: Mechanics, Statistics, Modelling with algorithms,
Numerical methods, Extra pure, Further pure with
technology
A level Further Mathematics
OCR 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 Statistics, Mechanics, Discrete
Mathematics, Additional Pure Mathematics
Deciding on a
specification
Looking at SAMs
• In your handout there are some AS and A level
questions on matrices from each awarding body
together with the mark schemes
• Look at the questions and discuss
– In what ways are they similar to current
papers?
– In what way are they different?
– Do the marks allocated reflect the degree of
difficulty in your view?
Points to consider
• There is no longer any advantage in choosing
the same awarding body for both Maths and
Further Maths
Consider choosing the awarding body which
looks:
• the best match for your department’s skills
• the most useful for your students’ likely career
path
• like it offers the best support
• the most fun to teach
… rather than the easiest or most familiar
Discussion Points
• What are the implications for planning and
staffing?
• Will you enter all students for AS at the end of
year 12? Is there a whole school policy?
• Will you offer AS Further Maths as a stand alone
qualification (possibly over 2 years)?
• What obsticles do you face?
Choosing a specification
On the FMSP
website there
is a Guide to
choosing a
new
specification
Further support
• Dedicated MEI website for the 2017 developments
mei.org.uk/2017
• MEI provides expert advice on the latest developments,
and supports you and your department as the changes
approach
• Support for all specifications is given
Further support - PD
‘Get Set for 2017’ courses:
mei.org.uk/2017-pd
A series of 4 one-day courses in an area near you coming
during the 2016-17
- Principles of the new mathematics A levels
- Statistics
- Mechanics
- Effective use of technology
Further support - PD Sustained PD courses for teachers looking to develop subject
knowledge & pedagogy for AS/A level Maths or Further Maths.
Teaching Advanced Maths (TAM) course mei.org.uk/tam
Teaching Further Mathematics (TFM) course mei.org.uk/tfm
TAM and TFM cover the pure mathematics content of A level
Maths and Further Maths respectively. For Mechanics and
Statistics PD we run the following:
Teaching Mechanics (TM) furthermaths.org.uk/teaching-mechanics
Teaching Statistics (TS) furthermaths.org.uk/teaching-statistics
Further support - FMSP
• Dedicated FMSP website for the 2017 developments
furthermaths.org.uk/2017
• A wealth of advice, guidance and support form the FMSP
team on the latest developments as the changes approach
• Support for all specifications is given
About MEI
• Registered charity committed to improving
mathematics education
• Independent UK curriculum development body
• We offer continuing professional development
courses, provide specialist tuition for students
and work with industry to enhance mathematical
skills in the workplace
• We also pioneer the development of innovative
teaching and learning resources