MEI Conference 2016 Preparing to teach forces Sue de Pomerai MEI Conference 2016 Preparing to teach

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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