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Mathematics Curriculum Overview - A Level

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 sin2 + cos2 = 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+tan2 = sec2 and 1 + cot2 = cosec2 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 ex, lnx, sinx, cosx , tanx and related functions

Chain rule, product rule, quotient rule

Integration of ex, 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