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

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

12

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

5

120 hours

Unit

Title

Estimated hours

Section A – Statistics

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

Section B – Mechanics

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