Course Description
This course follows the NCTB syllabus for SSC Higher Mathematics (Subject Code: 126). It extends core mathematics with deeper algebra, trigonometry, coordinate geometry and introductory calculus, plus matrices, vectors, combinatorics and probability. Emphasis is on proof ideas, multi-step problem solving, graphical reasoning and exam-oriented presentation (MCQ & CQ). Students develop fluency with identities, transformations and standard techniques alongside real-world applications.
Course Content
Chapter 1: Sets and Functions
- Operations on Sets
- Relations between Sets
- Cartesian Product of Sets
- Concept of Functions and Domain–Range
Chapter 2: Real Numbers and Inequalities
- Real Numbers and Their Properties
- Absolute Value and Intervals
- Inequalities and Their Graphs
- Solving Linear and Quadratic Inequalities
Chapter 3: Polynomials
- Definition and Types of Polynomials
- Degree and Coefficients
- Remainder and Factor Theorems
- Roots and Relations between Roots and Coefficients
- Graphical Representation of Polynomials
Chapter 4: Coordinate Geometry
- Coordinate System and Distance Formula
- Section Formula and Area of Triangle
- Straight Line Equation (Point-Slope, Two-Point, Intercept Form)
- Angle between Two Lines
- Perpendicular and Parallel Lines
- Equation of Line in General Form
Chapter 5: Circle
- Standard Equation of Circle
- Equation of Tangent and Normal to a Circle
- Chord, Diameter, and Radius Relations
- Intersection of Line and Circle
- Pair of Tangents from an External Point
Chapter 6: Trigonometric Ratios and Identities
- Definition of Trigonometric Ratios
- Trigonometric Ratios of Special Angles
- Fundamental Trigonometric Identities
- Allied Angles and Related Formulas
- Transformation and Simplification of Expressions
Chapter 7: Trigonometric Equations and Applications
- General Solutions of Trigonometric Equations
- Height and Distance Problems
- Use of Trigonometry in Real Life
Chapter 8: Matrices and Determinants
- Concept and Types of Matrices
- Matrix Addition, Subtraction, and Multiplication
- Determinant of a 2×2 and 3×3 Matrix
- Properties and Application of Determinants
- Inverse of a Matrix and Its Use in Solving Equations
Chapter 9: Vectors
- Concept and Representation of Vectors
- Addition and Subtraction of Vectors
- Scalar Multiplication and Dot Product
- Geometrical Interpretation and Applications
Chapter 10: Differentiation
- Concept of Limit and Continuity
- Definition of Derivative
- Basic Rules of Differentiation
- Derivatives of Algebraic, Trigonometric, and Exponential Functions
- Applications of Differentiation (Slope, Tangent, Rate of Change)
Chapter 11: Integration
- Concept of Anti-Derivative
- Basic Formulas of Integration
- Integration by Substitution
- Geometrical Meaning of Integration (Area under Curve)
- Simple Applications in Real Life Problems
Chapter 12: Statistics and Probability
- Data Collection and Classification
- Frequency Distribution and Graphical Representation
- Measures of Central Tendency (Mean, Median, Mode)
- Basic Probability Concepts and Laws
- Application of Probability in Real-Life Situations
