Cambridge Mathematics O Level Additional - Vectors and Calculus
Course

Cambridge Mathematics O Level Additional – Vectors and Calculus

5.1 Vectors
5.2 Vector Operations
5.3 Differentiation
5.4 Application of Differentiation
5.5 Integration
5.6 Exponential Functions
5.7 Logarithmic Functions
5.8 Application of Integration

58 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

VECTOR OPERATIONS

Operations with Plane Vectors

Vectors between Two Points

Vectors in Space

Operations with Vectors in Space

DIFFERENTIATION

Limits at Infinity

First Principles

First Principles at a Given x-Value

Basic Differentiation Rules

Chain Rule

Product Rule

Quotient Rule

Higher Derivatives

APPLICATION OF DIFFERENTIATION

Kinematics using Differentiation

Velocity and Acceleration

Differentiation and Displacement, Velocity and Acceleration

Rates of Change

Related Rates

Related Rates using Trigonometry

Optimisation

Application of Derivatives of Trigonometric Functions

Maxima and Minima with Trigonometry

INTEGRATION

Basic Integration Rules

Integration of Power Functions

Indefinite Integration by Recognition

Integration by Substitution

Particular Values

Definite Integration of Power Functions

Definite Integration by Substitution

EXPONENTIAL FUNCTIONS

Derivatives of Exponential Functions

Integration of Exponential Functions

Definite Integral of Exponential Functions

LOGARITHMIC FUNCTIONS

Derivatives of Logarithmic Functions

Integration of Rational Functions

Integrations Resulted in Natural Log Functions by Substitutions

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