Mathematics • 12th Grade / Senior Year /WASSCE / O Level.

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Relations And Functions

Introduction

Introduction
Notes PPT MCQs

Types Of Relations

Types Of Relations
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Types Of Functions

Types Of Functions
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Composition Of Functions And Invertible Functions

Composition Of Functions And Invertible Functions
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Binary Operations

Binary Operations
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Inverse Trigonometric Functions

Introduction

Introduction
Notes PPT MCQs

Basic Concepts

Basic Concepts
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Properties Of Inverse Trigonometric Functions

Properties Of Inverse Trigonometric Functions
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Examples
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Matrices

Introduction

Introduction
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Matrix

Matrix
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Order Of A Matrix
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Types Of Matrices

Types Of Matrices
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Equality Of Matrices
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Operation On Matrices

Addition Of Matrices
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Multiplication Of A Matrix By A Scalar
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Properties Of Matrix Addition
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Properties Of Scalar Multiplication Of A Matrix
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Multiplication Of Matrices
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Properties Of Multiplication Of Matrices
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Transpose Of A Matrix

Properties Of Transpose Of The Matrices
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Symmetric And Skew Symmetric Matrices

Symmetric And Skew Symmetric Matrices
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Elementary Operations Of A Matrix

Elementary Operations Of A Matrix
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Invertible Matrices

Invertible Matrices
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Inverse Of A Matrix By Elementary Operations
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Determinants

Introduction

Introduction
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Determinant

Determinant Of A Matrix Of Order One
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Determinant Of A Matrix Of Order Two
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Determinant Of A Matrix Of Order 3 X 3
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Properties Of Determinants

Properties Of Determinants
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Area Of A Triangle

Area Of A Triangle
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Minors And Cofactors

Minors And Cofactors
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Adjoint And Inverse Of A Matrix

Adjoint Of A Matrix
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Application Of Determinants And Matrices

Solution Of System Of Linear Equations Using Inverse Of A Matrix
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Continuity And Differentiability

Introduction

Introduction
Notes PPT MCQs

Continuity

Continuity
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Algebra Of Continuous Functions
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Differentiability

Differentiability
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Derivatives Of Composite Functions
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Derivatives Of Implicit Functions
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Derivatives Of Inverse Trigonometric Functions
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Exponent And Logarithmic Functions

Exponent And Logarithmic Functions
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Logarithmic Differentiation

Logarithmic Differentiation
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Derivatives Of Functions In Parametric Forms

Derivatives Of Functions In Parametric Forms
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Second Order Derivative

Second Order Derivative
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Mean Value Theorem

Mean Value Theorem
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Application Of Derivatives

Introduction

Introduction
Notes PPT MCQs

Rate Of Change Of Quantities

Rate Of Change Of Quantities
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Increasing And Decreasing Functions

Increasing And Decreasing Functions
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Tangents And Normals

Tangents And Normals
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Approximations

Approximations
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Maxima And Minima

Maxima And Minima
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Maximum And Minimum Values Of A Function In A Closed Interval
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Integrals

Introduction

Introduction
Notes PPT MCQs

Integration As An Inverse Process Of Differentiation

Integration As An Inverse Process Of Differentiation
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Geometrical Interpretation Of Indefinite Integral
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Some Properties Of Indefinite Integral
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Comparison Between Differentiation And Integration
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Methods Of Integration

Integration By Substitution
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Integration Using Trigonometric Identities
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Integrals Of Some Particular Functions

Integrals Of Some Particular Functions
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Integration By Partial Fractions

Integration By Partial Fractions
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Integration By Parts

Integration By Parts
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Integral Of The Type
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Integrals Of Some More Types
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Definite Integral

Definite Integral As The Limit Of Sum
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Fundamental Theorem Of Calculus

Area Function
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First Fundamental Theorem Of Integral Calculus
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Second Fundamental Theorem Of Integral Calculus
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Evaluation Of Definite Integrals By Substitution

Evaluation Of Definite Integrals By Substitution
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Some Properties Of Definite Integrals

Some Properties Of Definite Integrals
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Application Of Integrals

Introduction

Introduction
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Area Under Simple Curve

Area Under Simple Curve
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The Area Of The Region Bounded By A Curve And A Line
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Area Between Two Curves

Area Between Two Curves
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Differential Equations

Introduction

Introduction
Notes PPT MCQs

Basic Concepts

Basic Concepts
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Order Of A Differential Equation
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Degree Of Differential Equation
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Procedure To Form A Differential Equation That Will Represent A Given Family Of Curves
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General And Particular Solutions Of A Differential Equations

General And Particular Solutions Of A Differential Equations
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Formation Of A Differential Equation Whose General Solution Is Given

Formation Of A Differential Equation Whose General Solution Is Given
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Methods Of Solving First Order, First Degree Differential Equations

Differential Equation With Variable Separable
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Homogeneous Differential Equations
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Linear Differential Equations
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Vector Algebra

Introduction

Introduction
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Some Basic Concepts

Types of vectors
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Types Of Curves

Types Of Curves
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Addition Of Vectors

Addition Of Vectors
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Multiplication Of A Vector By A Scalar

Multiplication Of A Vector By A Scalar
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Vector joining two points
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Section Formula
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Section Formula
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Product Of Two Vectors

Scalar Product Of Two Vectors
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Projection Of A Vector On A Line
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Vector/cross product
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Three Dimensional Geometry

Introduction

Introduction
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Direction Cosines And Direction Ratios Of A Line

Direction Cosines And Direction Ratios Of A Line
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Relation Between The Direction Cosines Of A Line
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Direction Cosines Of A Line Passing Through Two Points
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Equation Of A Line Space

Equation Of A Line Through A Given Point And Parallel To A Given Vector
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Equation Of A Line Passing Through Two Given Points
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Angle Between Two Lines

Angle Between Two Lines
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Shortest Distance Between Two Lines

Shortest Distance Between Two Lines
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Distance Between Two Skew Lines
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Distance Between Two Parallel Lines
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Plane

Equation Of A Plane In Normal Form
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Equation Of A Plane Perpendicular To A Given Vector And Passing Through A Given Point
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Equation Of A Plane Passing Through Three Non Collinear Points
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Intercept Form Of The Equation Of A Plane
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Plane Passing Through The Intersection Of Two Given Planes
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Coplanarity Of Two Lines

Coplanarity Of Two Lines
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Angle Between Two Planes

Angle Between Two Planes
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Distance Of A Point From A Plane

Distance Of A Point From A Plane
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Angle Between A Line And A Plane

Angle Between A Line And A Plane
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Linear Programming

Introduction

Introduction
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Linear Programming Problem And Its Mathematical Formulation

Mathematical Formulation Of The Problem
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Graphical Method Of Solving Linear Programming Problems
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Different Types Of Linear Programming Problems

Different Types Of Linear Programming Problems
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Probability

Introduction

Introduction
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Conditional Probability

Conditional Probability
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Properties Of Conditional Probability
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Multiplication Theorem On Probability

Multiplication Theorem On Probability
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Independent Events

Independent Events
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Bayes' Theorem

Partition Of A Sample Space
Notes PPT MCQs

Theorem Of Total Probability
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Random Variables And Its Probability Distributions

Random Variables And Its Probability Distributions
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Probability Distribution Of A Random Variable
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Mean Of A Random Variable
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Variance Of A Random Variable
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Bernoulli Trials And Binomial Distribution

Bernoulli Trials
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Binomial Distribution
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