WJEC A-Level Further Mathematics Revision

Year 12

• Complex numbers
  • 1.1 ℂ the set of complex numbers
  • 1.2 = is equal to
  • 1.3 ≠ is not equal to
  • 1.4 ≡ is identical to or congruent to
  • 1.5 ≈ is approximately equal to
• Matrices
  • 2.1 M a matrix M
  • 2.2 0 zero matrix
  • 2.3 I identity matrix
  • 2.4 𝐌 −1 the inverse of the matrix M
  • 2.5 𝐌T the transpose of the matrix M
• Further algebra and functions
  • 3.1 Further Algebra and Functions
  • 3.2 Further Calculus
  • 3.3 Polar Coordinates
  • 3.4 Hyperbolic functions
  • 3.5 Differential equations
• Further calculus
  • 4.1 Further Calculus
  • 4.2 Polar Coordinates
  • 4.3 Hyperbolic functions
  • 4.4 Differential equations
  • 4.5 Samples and Populations
• Further vectors
  • 5.1 Further Vectors
  • 5.2 AS UNIT 2
  • 5.3 Random Variables and the Poisson Process
  • 5.4 Exploring relationships between variables and goodness
  • 5.5 Momentum and Impulse
• Polar coordinates
  • 6.1 Polar Coordinates
  • 6.2 Hyperbolic functions
  • 6.3 Differential equations
  • 6.4 Samples and Populations
  • 6.5 Statistical Distributions
• Differential equations
  • 7.1 Equilibrium of Rigid Bodies
  • 7.2 Differential Equations
  • 7.3 select and correctly carry out routine procedures; and
  • 7.4 accurately recall facts, terminology and definitions AO2 Reason, interpret and communicate mathematically
  • 7.5 construct rigorous mathematical arguments (including proofs)
• Discrete random variables
  • 8.1 Random Variables and the Poisson Process
  • 8.2 Exploring relationships between variables and goodness
  • 8.3 Momentum and Impulse
  • 8.4 Hooke's Law, Work, Energy and Power
  • 8.5 Circular Motion
• Statistical distributions
  • 9.1 the ability to compute summary statistics and access probabilities from standard statistical distributions Calculators must also meet the regulations set out below Calculators must be: Calculators must not
  • 9.2 of a size suitable for use on the desk; • be designed or adapted to offer any of these facilities: -
  • 9.3 either battery or solar powered
  • 9.4 text Formula Booklet A formula booklet will be required in all examinations. This will exclude any formulae Statistical Tables The following book of statistical tables is allowed in the examinations
  • 9.5 Elementary Statistical Tables (RND/WJEC Publications) GCE AS and A LEVEL FURTHER MATHEMATICS 33
• Hypothesis testing
  • 10.1 Hypothesis Testing
  • 10.2 Estimation
  • 10.3 A2 UNIT 6
  • 10.4 Rectilinear motion
  • 10.5 Momentum and Impulse
• Momentum and impulse
  • 11.1 Momentum and Impulse
  • 11.2 Hooke's Law, Work, Energy and Power
  • 11.3 Circular Motion
  • 11.4 Differentiation and Integration of Vectors
  • 11.5 Complex Numbers
• Work, energy and power
  • 12.1 Momentum and Impulse
  • 12.2 Hooke's Law, Work, Energy and Power
  • 12.3 Circular Motion
  • 12.4 Differentiation and Integration of Vectors
  • 12.5 A2 UNIT 4

Year 13

• Roots of polynomials
  • 1.1 Matrices
  • 1.2 linear and non-linear transformations in 2-D, involving 2 x 2 using 2 x 2 and/or 3 x 3 matrices and 3 x 3 matrices, Knowledge that the transformation represented by AB is the
  • 1.3 successive transformations, transformation represented by B followed by the transformation
  • 1.4 single transformations in 3-D (3-D transformations confined represented by A to reflection in one of x = 0, y = 0, z = 0 or rotation about one of the coordinate axes). Knowledge of 3-D vectors is assumed
  • 1.5 Further Algebra and Functions
• Advanced complex numbers
  • 2.1 ℂ the set of complex numbers
  • 2.2 = is equal to
  • 2.3 ≠ is not equal to
  • 2.4 ≡ is identical to or congruent to
  • 2.5 ≈ is approximately equal to
• Advanced matrices and linear transformations
  • 3.1 Matrices
  • 3.2 linear and non-linear transformations in 2-D, involving 2 x 2 using 2 x 2 and/or 3 x 3 matrices and 3 x 3 matrices, Knowledge that the transformation represented by AB is the
  • 3.3 successive transformations, transformation represented by B followed by the transformation
  • 3.4 single transformations in 3-D (3-D transformations confined represented by A to reflection in one of x = 0, y = 0, z = 0 or rotation about one of the coordinate axes). Knowledge of 3-D vectors is assumed
  • 3.5 Further Algebra and Functions
• Hyperbolic functions
  • 4.1 } the inverse trigonometric functions
  • 4.2 } the hyperbolic functions
  • 4.3 the inverse hyperbolic functions
  • 4.4 i,j square root of -1
  • 4.5 r(cos 𝜃+ isin𝜃) number with modulus 𝑟 and argument
• Advanced differential equations
  • 5.1 Equilibrium of Rigid Bodies
  • 5.2 Differential Equations
  • 5.3 select and correctly carry out routine procedures; and
  • 5.4 accurately recall facts, terminology and definitions AO2 Reason, interpret and communicate mathematically
  • 5.5 construct rigorous mathematical arguments (including proofs)
• Series and limits
  • 6.1 ∫𝑎 𝑦 dx 𝑥 between the limits 𝑥 = 𝑎 and 𝑥 = b
  • 6.2 e base of natural logarithms
  • 6.3 e, exp x exponential function of 𝑥
  • 6.4 log 𝑎 𝑥 logarithm to the base 𝑎 of 𝑥
  • 6.5 ln 𝑥, loge 𝑥 natural logarithm of 𝑥
• Continuous random variables
  • 7.1 Random Variables and the Poisson Process
  • 7.2 Exploring relationships between variables and goodness
  • 7.3 Momentum and Impulse
  • 7.4 Hooke's Law, Work, Energy and Power
  • 7.5 Circular Motion
• Further statistical inference
  • 8.1 an iterative function
  • 8.2 the ability to compute summary statistics and access probabilities from standard statistical distributions Calculators must also meet the regulations set out below Calculators must be: Calculators must not
  • 8.3 of a size suitable for use on the desk; • be designed or adapted to offer any of these facilities: -
  • 8.4 text Formula Booklet A formula booklet will be required in all examinations. This will exclude any formulae Statistical Tables The following book of statistical tables is allowed in the examinations
  • 8.5 Elementary Statistical Tables (RND/WJEC Publications) GCE AS and A LEVEL FURTHER MATHEMATICS 33
• Circular motion
  • 9.1 Circular Motion
  • 9.2 Differentiation and Integration of Vectors
  • 9.3 A2 UNIT 4
  • 9.4 Complex Numbers
  • 9.5 Further Trigonometry
• Centres of mass
  • 10.1 Equilibrium of Rigid Bodies
  • 10.2 Differential Equations
  • 10.3 select and correctly carry out routine procedures; and
  • 10.4 accurately recall facts, terminology and definitions AO2 Reason, interpret and communicate mathematically
  • 10.5 construct rigorous mathematical arguments (including proofs)
• Further dynamics
  • 11.1 Aims and objectives
  • 11.2 develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
  • 11.3 develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs
  • 11.4 extend their range of mathematical skills and techniques and use them in more difficult, unstructured problems
  • 11.5 develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected
• Optional pure, statistics or mechanics content
  • 12.1 Grading, awarding and reporting
  • 12.2 ∈ is an element of
  • 12.3 ∉ is not an element of
  • 12.4 ⊆ is a subset of
  • 12.5 ⊂ is a proper subset of