A-level Mathematics/Edexcel/Core 4

Core 4 (C4)

This A2 module is the fourth and final core mathematics module in the series. C4 requires knowledge from previous core modules (such as differentials from C3), and is assessed in a single 90 minute paper consisting of approximately 7 questions. The module consists of 6 main topic areas:

•Partial Fractions

1. Addition and subtraction of algebraic fractions
2. Splitting of a fraction into partial fractions
3. Use/revision of algebraic division for improper fractions

•Binomial Expansion

1. Binomial Expansion when n is a fraction or a negative number
2. Binomial Expansion for (k+...) instead of (1+...) by taking out a factor of k
3. Use of partial fractions to produce the Binomial Expansion of more difficult expressions

In this topic, earlier C2 work on the Binomial Expansion is developed to include expansions involving fractions and negative numbers. Questions often require expressing problems in partial fraction form first.

•Co-ordinate Geometry

1. Use of parametric equations (using the parameter t) to define co-ordinates of points on a curve and solve related problems
2. Conversion of parametric equations to cartesian equations
3. Use of parametric equations to find the area under a curve

Parametric equations are introduced here, and finding relationships between x and y via a parameter t is studied.

•Vectors

•Differentiation

•Integration

${\displaystyle \int \sin {kx}\ dx=-{\frac {1}{k}}\cos {kx}+c}$

${\displaystyle \int \cos {kx}\ dx={\frac {1}{k}}\sin {kx}+c}$

${\displaystyle \int {\frac {1}{x}}\ dx=\ln {x}+c}$

${\displaystyle \int {\frac {f'(x)}{f(x)}}\ dx=\ln {f(x)}+c,\ {\mbox{provided}}\ f(x)>0}$ (this is usually resolved by taking the modulus of the f(x) result before we take the natural log of this)

Note: This book is so you can gain an alternative explanation for the concepts described and it should NOT replace your C4 textbook!