# A-level Mathematics/Edexcel/Core 3

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[edit]

- 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_{e}x

- 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+tan
^{2}θ = sec^{2}θ and 1+cot^{2}θ = cosec^{2}θ - 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