Year 13 Curriculum  Maths
A Level Pure Maths
Unit 
Title 
Estimated hours 

1 

Proof: Examples including proof by deduction* and proof by contradiction 
3 
2 

Algebraic and partial fractions 


a 
Simplifying algebraic fractions 
2 

b 
Partial fractions 
3 
3 

Functions and modelling 


a 
Modulus function 
2 

b 
Composite and inverse functions 
3 

c 
Transformations 
3 

d 
Modelling with functions* 
2 


*examples may be Trigonometric, exponential, reciprocal etc. 

4 

Series and sequences 


a 
Arithmetic and geometric progressions (proofs of ‘sum formulae’) 
4 

b 
Sigma notation 
2 

c 
Recurrence and iterations 
3 
5 

The binomial theorem 


a 
Expanding (a + bx)^{n} for rational n; knowledge of range of validity 
4 

b 
Expansion of functions by first using partial fractions 
3 
6 

Trigonometry 


a 
Radians (exact values), arcs and sectors 
4 

b 
Small angles 
2 

c 
Secant, cosecant and cotangent (definitions, identities and graphs); Inverse trigonometrical functions; Inverse trigonometrical functions 
3 

d 
Compound* and double (and half) angle formulae 
6 


*geometric proofs expected 


e 
R cos (x ± α) or R sin (x ± α) 
3 

f 
Proving trigonometric identities 
4 

g 
Solving problems in context (e.g. mechanics) 
2 
7 

Parametric equations 


a 
Definition and converting between parametric and Cartesian forms 
3 

b 
Curve sketching and modelling 
2 
Unit 
Title 
Estimated hours 

8 

Differentiation 


a 
Differentiating sin x and cos x from first principles 
2 

b 
Differentiating exponentials and logarithms 
3 

c 
Differentiating products, quotients, implicit and parametric functions. 
6 

d 
Second derivatives (rates of change of gradient, inflections) 
2 

e 
Rates of change problems* (including growth and kinematics) 
3 


*see Integration (part 2) – Differential equations 

9 

Numerical methods* 


a 
Location of roots 
1 

b 
Solving by iterative methods (knowledge of ‘staircase and cobweb’ diagrams) 
3 

c 
NewtonRaphson method 
2 

d 
Problem solving 
2 


*See Integration (part 2) for the trapezium rule 

10 

Integration (part 1) 


a 
Integrating x^{n} (including when n = –1), exponentials and trigonometric functions. Integrating functions defined parametrically. 
4 

b 
Using the reverse of differentiation, and using trigonometric identities to manipulate integrals 
5 
11 

Integration (part 2) 


a 
Integration by substitution 
4 

b 
Integration by parts 
3 

c 
Use of partial fractions 
2 

d 
Areas under graphs or between two curves, including understanding the area is the limit of a sum (using sigma notation). Areas under curves expressed parametrically 
4 

e 
The trapezium rule 
2 

f 
Differential equations (including knowledge of the family of solution curves) 
4 

Vectors (3D): Use of vectors in three dimensions; knowledge of column vectors and i, j and k unit vectors 
5 


120 hours 
A Level Applied Content
Unit 
Title 
Estimated hours 

1 

Regression and correlation 

a 
Change of variable 
2 

b 
Correlation coefficients Statistical hypothesis testing for zero correlation 
5 

2 

Probability 

a 
Using set notation for probability Conditional probability 
5 

b 
Questioning assumptions in probability 
2 

3 

The Normal distribution 

a 
Understand and use the Normal distribution 
5 

b 
Use the Normal distribution as an approximation to the binomial distribution Selecting the appropriate distribution 
5 

c 
Statistical hypothesis testing for the mean of the Normal distribution 
6 



30 hours 

4 

Moments: Forces’ turning effect 
5 
5


Forces at any angle 

a 
Resolving forces 
3 

b 
Friction forces (including coefficient of friction µ) 
3 

6 

Applications of kinematics: Projectiles 
5 
7 

Applications of forces 

a 
Equilibrium and statics of a particle (including ladder problems) 
4 

b 
Dynamics of a particle 
4 

8 

Further kinematics 

a 
Constant acceleration (equations of motion in 2D; the i, j system) 
3 

b 
Variable acceleration (use of calculus and finding vectors and at a given time) 
3 



30 hours 