1.1 Relations

Inverse Relations and Graphs

1.2 Functions

Function Definitions & Notation

1.3 Types of Functions

One-to-One, Onto, and More

1.4 Composition of Functions

Combining Multiple Functions

1.5 Inverse Functions

Finding Inverse Function f⁻¹(x)

2.1 Simplification

Simplifying Rational Expressions

2.2 Equations

Equations and Inequalities

2.3 Rational Functions

Graphs, Asymptotes & Holes

2.4 Applications

Modeling and Work Problems

3.1 Concepts of Matrix

Definition, Order & Entries

3.2 Operations

Addition & Scalar Multiplication

3.3 Matrix Multiplication

Properties of Matrix Product

3.4 Row Operations

Elementary Row Operations (ERO)

3.5 Special Types of matrix

types of matrix

4.1 Determinants Order 2

2x2 Matrix Determinants

4.2 Minors and Cofactors

Cofactor Expansion Method

4.3 Determinants Order 3

3x3 Matrix Determinants

4.4 Properties

Basic Determinant Properties

4.5 Inverse Matrix

Finding Inverse using Adjoint

4.6 Cramer's Rule

Solving Systems via Determinant

4.7 Applications

Area of Triangle & Collinearity

5.1 Vector Concepts

Magnitude and Direction

5.2 Vector Addition

Geometrical and Algebra Sum

5.3 Scalar Product

The Dot Product Properties

5.4 Components

Standard Basis Vectors i, j

5.5 Vector Applications

Physics and Engineering

6.1 Translation

Mapping and Shifting Points

6.2 Reflection

Across x-axis, y-axis & Lines

6.3 Rotation

Turning points about Origin

6.4 Dilation

Enlargement and Contraction

7.1 Frequency Tables

Data for Grouped Statistics

7.2 Mean of Groups

Calculating Average for Data

7.3 Median & Mode

Mid-point and Frequent Values

7.4 Measures of Central Tendency

Comprehensive Data Analysis

7.5 Applications

Real-life Statistics Models

8.1 Introduction

Basic Probability Concepts

8.2 Counting Principle

Fundamental Rules of Counting

8.3 Permutation & Combination

Selection and Arrangement

8.4 Binomial Theorem

Expansion and Pascal Triangle

8.5 Random Experiments

Outcomes and Sample Spaces

8.6 Events

Defining Mathematical Events

8.7 Probability of Events

P(A) Calculations & Laws

8.8 Applications

Probability in Daily Life