# Edexcel C4 Core Maths

### Algebra and Series

### Coordinate Geometry

### Differentiation

Exponential Functions

Parametric Functions

Implicit Functions

Connected Rates of Change

### Integration

(ax+b)^{n} types

The exponential functions : e^{x}, e^{ax} and e^{(ax+b)}

Reciprocal Functions : 1/x and 1/(ax+b)

Integrals of the form : f'(x)/f(x)

Integrals of the form : f'(x)e^{f(x)}

Trigonometric types

- sin x, cos x, sec² x
- sin(ax+b), cos(ax+b), sec² (ax+b) types
- Identity types
- sin² x and cos² x types
- Exam Questions

Partial fraction types

Substitution

- Integration by substitution
- square root types
- trigonometric types
- exponential types
- using limits (definite integration)
- Exam Questions

By Parts

- Integration by parts
- Natural log types (ln)
- e
^{ax}sin(bx) and e^{ax}cos(bx) types - Using limits (definite integration)
- Proof of the formula (not required for the exam)
- Exam Questions

Mixed examples

Applications

- Area
- Volume of Revolution about the x-axis

Differential equations

- Separating the variables

- Forming differential equations

### Numerical Methods

Trapezium Rule

### Vectors

- What is a vector and a scalar quantity?
- Notation
- Position vectors
- Equal and negative vectors
- Multiplying a vector by a scalar
- Addition and subtraction of vectors
- Magnitude of a 2 dimensional vector
- Magnitude of a 3 dimensional vector
- Unit vectors

Scalar Product (Dot Product)

Exam Questions

Lines

- Vector equation of a line
- Angle between two lines
- Parallel lines
- Intersecting and skew lines
- Exam Questions
- Closest point to a line and shortest distance from the origin
- Shortest distance of a point to a line

Exam Questions

### Exam Papers

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