Cambridge Mathematics IGCSE Additional - Calculus and Vectors
Course

Cambridge Mathematics IGCSE Additional – Calculus and Vectors

5.1 Vectors
5.2 Differentiation
5.3 Application of Differentiation
5.4 Differentiation of Trigonometric Functions
5.5 Integration
5.6 Application of Integration

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55 Lessons

Course Materials

VECTORS

Vectors and Scalars

Vector Equality

Position Vector

Vector Addition

Vector Subtraction

Basic Vector Equations

Scalar Multiplication

Vectors in the Plane

Length of a Vector

Operations with Plane Vectors

Vectors between Two Points

Vectors in Space

Operations with Vectors in Space

Parallelism

Scalar Product of Two Vectors

DIFFERENTIATION

Basic Integration Rules

Chain Rule

Product Rule

Quotient Rule

Higher Derivatives

APPLICATION OF DIFFERENTIATION

Tangents

Normals

Increasing and Decreasing Functions

Turning Points

Points of Inflection and Concavity

Curves of Rational Functions

Sketching Graphs Containing Stationary Points

Gradient Functions

Kinematics using Differentiation

Velocity and Acceleration

Differentiation and Displacement, Velocity and Acceleration

Rates of Change

Related Rates

Optimisation

DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS

Derivative of Sine Functions

Derivatives of Cosine Functions

Derivatives of Tangent Functions

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

INTEGRATION

Basic Integration Rules

Integration of Power Functions

Particular Values

Indefinite Integration by Recognition

Integration of Sine and Cosine

Integrating Trigonometric Functions by Recognition

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