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 =
 * 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=ax
 * 2. Graphs of exponential functions and modelling using y=ex
 * 3. Using ex and the inverse of the exponential function logex


 * 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