The Core Mathematics 3 (C3) module builds further on the mathematics which you have learnt in both your Core Mathematics 1 and 2. The examination consists of a 1½ hour paper in which calculators are allowed.

Core Content

Algebraic Fractions

1. Simplifying algebraic fractions by cancelling down common factors

2. Multiplying and dividing algebraic fractions

3. Dividing algebraic fractions and the remainder theorem

Functions

1. Mapping diagrams and graphs of operations

2. Functions and function notation

3. Range, mapping diagrams, graphs and definitions of functions

4. Using composite functions

5. Finding and using inverse functions

The exponential and log functions

1. Introducing exponential functions of the form y=a^x

2. Graphs of exponential functions and modelling using y=e^x

3. Using e^x and the inverse of the exponential function log_ex

Numerical methods

1. Finding approximate root of f(x)=0 graphically

2. Using iterative and algebraic methods to find approximate roots of f(x)=0

Transforming graphs of functions

1. Sketching graphs of the modulus function y=|f(x)|

2. Sketching graphs of the function y=f(|x|)

3. Solving equations using a modulus

4. Applying a combination of transformations to sketch curves

5. Sketching transformations and labelling the coordinates of a given point

Trigonometry

1. The functions secantθ, cosecantθ and cotangentθ

2. The graphs of secantθ, cosecantθ and cotangentθ

3. Simplifying expressions, proving identities and solving equations using secθ, cosecθ and cotθ

4. Using the identities 1+tan²θ = sec²θ and 1+cot²θ = cosec²θ

5. Using inverse trigonometrical functions and their graphs

Further trigonometric identities and their applications

1. Using addition trigonometrical formulae

2. Using double angle trigonometrical formulae

3. Solving equations and proving identities using double angle formulae

4. Using the form a cosθ+b sinθ in solving trigonometrical problems

5. The factor formulae

Differentiation

1. Differentiating using the chain rule

2. Differentiating using the product rule

3. Differentiating using the quotient rule

4. Differentiating the exponential function

5. Finding the differential of logarithmic functions

6. Differentiating sinθ

7. Differentiating cosθ

8. Differentiating tanθ

9. Differentiating further trigonometrical functions

10. Differentiating functions formed by combining trigonometrical, exponential, logarithmic and polynomial functions