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 |
Newton-Raphson method |
2 |
|
d |
Problem solving |
2 |
|
|
*See Integration (part 2) for the trapezium rule |
|
10 |
|
Integration (part 1) |
|
|
a |
Integrating xn (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 |