GCE AS and A-level Examination Specifications
Combinations of modules which we offer
Title |
Level |
Modules |
Mathematics |
AS |
MPC1 MPC2 MS1B or MM1B |
Mathematics |
A |
AS modules + MPC3 MPC4 MS2B or MM2B or MD01 |
Further Mathematics |
AS |
MFP1 MS1B (MM1B in maths) MD01 (not done in maths A2) |
Further Mathematics |
A |
AS modules + MFP2 MFP3 MM03 |
Statistics |
AS |
SS1B SS02 SS03 |
Statistics |
A |
AS modules + SS04 SS05 SS06 |
All modules carry equal weight.
Up to 4 AS modules can be taken for an A-level qualification.
Full details of the course specifications can be found on the AQA website: www.aqa.org.uk
Course outlines
Mathematics
MPC 1 and MPC 2
8 periods per week for the first half of the Michaelmas term followed by 4 periods per week until study leave begins in the summer term
Surds
Coordinate geometry of straight lines and circles
Quadratic functions and graphs
Factorising quadratics
Completing the square
Solving quadratic equations
Discriminant
Linear and quadratic inequalities
+ - x ÷ of polynomials
Remainder Theorem
Factor Theorem
Differentiation of polynomials
Applications of differentiation (gradient, tangent, normal, max and min stationary points, increasing and decreasing functions)
Second order derivatives
Integration of polynomials – indefinite and definite
Application to finding areas
Sine and Cosine Rules and Area of a triangle
Radian measure, arcs and sectors
Sine, cosine and tangent: graphs; equations; identities tan= sin/cos and sin^{2} + cos^{2} = 1
Sequences and series: iterative formulae; nth term; sigma notation; convergence and limits
Arithmetic series: nth term; sum of n terms
Geometric series: nth term; sum of n terms; sum to infinity
Binomial series (finite)
Indices
Differentiation of rational and negative powers of x and applications
Integration of rational and negative powers of x (except -1) and applications
Trapezium rule
Exponentials and logarithms
Transformations of graphs
MS1B
Numerical Measures
Probability
Binomial distribution
Correlation and Regression
Normal distribution
Estimation
MM1B
From start of November in Y12
Equations of motion & v-t graphs
Motion under gravity
Vectors
Resultant velocity
Forces: resolving; resultant; equilibrium
Friction
Newton’s Laws
Pulleys
Projectiles
Momentum
MPC3 and MPC4
The course starts when the students return from AS study leave in Y12. We use all available lessons to teach pure maths.
In Y13 we have 2 doubles a week pure maths, one double a week applied maths and one double a week which alternates between pure and applied. The students may continue with the applied subject they have studied in Y12 or change to decision maths, provided they have not done the latter as a further maths AS module.
Y12 Summer term
Trigonometry: sec, cosec and cot
Use of 1+tan^{2} = sec^{2} and 1 + cot^{2} = cosec^{2} in identities and equations
Numerical measures: location of roots; Iterative methods; Simpson’s rule; Mid-ordinate rule
Y13
Functions (including inverse trig fns)
Exponential and log functions
Differentiation of e^{x}, lnx, sinx, cosx , tanx and related functions
Chain rule, product rule, quotient rule
Integration of e^{x}, 1/x , sinx, cosx and related functions
Inspection, substitution and integration by parts
Volume of revolution
Rational functions: simplifying and expressing as partial fractions
Binomial series for any rational n incl. egs with partial fractions
Integration involving partial fractions
Trigonometry: addition theorems; double angle theorems; R,α form; identities; equations; use in integration.
Cartesian and parametric equations for curves and conversion between them
Differentiation of functions defined parametrically or implicitly and applications to tangents and normals.
Exponential growth and decay
Formation and solution of simple first order differential equations (variables separable)
Vectors
MS2B
Discrete random variables
Poisson distribution
Estimation
Hypothesis testing
Chi-squared contingency table tests
Continuous random variables
MM2B
Moments
Centre of mass
Energy
Hooke’s Law
EPE
Power
Variable acceleration
Horizontal circular motion
Circular motion with variable speed
Vertical circular motion
Differential equations (in conjunction with Pure)
MD01
Bubble sort & Shuttle sort
Shell sort & Quick sort, comparing sorts
Algorithms (flow diagrams, pseudo English instructions,
If then and for, stopping conditions)
Networks (minimum spanning tree, Kruskal’s and Prim’s)
Comparing Kruskal’s and Prim’s
Matrix formulation (Prim’s)
Shortest path & Dijkstra’s algorithm
Chinese postman
Traversable graphs, Eulerian trail
Pairing vertices & applying algorithm
Variations of Chinese postman
Problems from Dijkstra’s algorithm
Travelling salesman’s problem, tours and upper bounds
Travelling salesman best upper bound, nearest neighbour algorithm
Graph theory
Matchings: bipartite graphs. Maximum matching.
Linear programming
Further Mathematics
MFP1, MS1B and MD01 are each allocated 1 double or 2 singles per week throughout Y12.
MFP1
Complex numbers
Roots and coefficients of a quadratic equation
Differentiation from first principles
Series – sums of natural numbers, their squares and cubes
Algebra and graphs
Trigonometry
Matrices and transformations
Improper integrals
Numerical methods
The MS1B and MD01 courses are taught in the same order as they are to single maths candidates but at a faster speed.
MFP2
Roots of polynomials
Complex numbers
De Moivre’s Theorem
Proof by Induction
Finite series
The calculus of inverse trig functions
Hyperbolic functions
Arc length and area of the surface of revolution
MFP3
Series and limits
Polar Coordinates
Differential equations – first and second order
Statistics
Y12
SS01 As MS1B
SS02
Time series
Sampling
Discrete probability distributions
Interpretation of data
Applications of hypothesis testing
SS03
Significance testing – Chi-squared contingency table tests
- Sign test, Wilcoxon signed rank test, Mann-Whitney U-test, Kruskal-Wallis test
- Correlation – tests on product-moment and Spearman’s rank correlation coefficients
Y13
SS04
Continuous probability distributions – sums, differences and multiples of Normal variables
Distributional approximations
Estimation – confidence intervals for μ, p and λ
Hypothesis testing – t test on μ, tests on p and λ
SS05
Continuous probability distributions – uniform and exponential
Estimation – confidence interval for σ
Hypothesis testing – tests on σ. equality of means and variances. Chi-squared goodness of fit
SS06
Experimental design
Analysis of variance
Statistical process control
Acceptance sampling