Course Description

Course Content

Unit 1: Real Numbers

• Natural, Whole, Integers, Rational and Irrational Numbers
• Prime Factorization and HCF–LCM
• Laws of Indices
• Surds and Simplification
• Rationalization of Denominators

Unit 2: Algebraic Expressions

• Addition and Subtraction of Algebraic Expressions
• Multiplication and Division of Algebraic Expressions
• Factorization by Common Factors
• Factorization by Grouping Terms
• Factorization by Using Identities

Unit 3: Algebraic Identities and Factorization

• Identities: (a + b)², (a – b)², (a + b)(a – b)
• (a + b + c)² and Related Forms
• Factorization Using Identities
• Perfect Squares and Differences of Squares
• Cubic Identities and Factorization

Unit 4: Linear Equations

• Linear Equations in One Variable
• Word Problems on Linear Equations
• Linear Equations in Two Variables
• Elimination and Substitution Methods
• Applications of Linear Equations

Unit 5: Quadratic Equations

• Standard Form and Roots of a Quadratic Equation
• Factorization Method
• Completing the Square Method
• Quadratic Formula
• Nature of Roots and Real-life Applications

Unit 6: Polynomials and Remainder Theorem

• Concept of Polynomials
• Division of Polynomials
• Remainder and Factor Theorems
• Relation Between Coefficients and Roots
• Graphical Representation of Polynomials

Unit 7: Ratio, Proportion, and Variation

• Ratio and Its Properties
• Proportion and Its Types
• Continued Proportion
• Direct and Inverse Variation
• Joint and Compound Variation

Unit 8: Exponents and Logarithms

• Laws of Exponents
• Concept of Logarithm
• Laws of Logarithm
• Use of Logarithm Tables
• Applications in Calculation

Unit 9: Sets and Venn Diagrams

• Concept of Sets
• Representation of Sets
• Operations on Sets (Union, Intersection, Difference)
• Complement of a Set
• Venn Diagrams and Word Problems

Unit 10: Geometry – Basics and Angles

• Basic Geometric Terms and Figures
• Types of Angles and Their Relations
• Properties of Parallel Lines and Transversals
• Construction of Angles
• Angle Sum Property of a Triangle

Unit 11: Triangles

• Types and Properties of Triangles
• Congruence of Triangles
• Similarity of Triangles
• Basic Proportionality Theorem
• Pythagoras Theorem and Its Converse

Unit 12: Circle Geometry

• Circle and Its Components
• Chord and Its Properties
• Tangent to a Circle
• Angle Subtended by an Arc
• Cyclic Quadrilaterals

Unit 13: Geometry of Quadrilaterals

• Types of Quadrilaterals
• Properties of Parallelogram, Rectangle, Rhombus, and Square
• Midpoint Theorem
• Diagonals and Their Relations
• Application in Geometry

Unit 14: Trigonometry

• Concept of Trigonometric Ratios
• Trigonometric Ratios of Standard Angles
• Complementary Angles
• Trigonometric Identities
• Height and Distance Problems

Unit 15: Mensuration (Plane Figures)

• Perimeter and Area of Triangle
• Area of Quadrilateral and Polygon
• Circle: Circumference and Area
• Sector and Segment of a Circle
• Application in Daily Life

Unit 16: Mensuration (Solid Figures)

• Volume and Surface Area of Cuboid and Cube
• Cylinder and Cone
• Sphere and Hemisphere
• Frustum of a Cone
• Conversion of Solid Units

Unit 17: Coordinate Geometry

• Cartesian Plane and Coordinates
• Distance Between Two Points
• Section Formula (Internal and External)
• Area of a Triangle Using Coordinates
• Equation of a Line (Slope and Intercept Form)

Unit 18: Statistics

• Collection and Classification of Data
• Frequency Distribution Table
• Graphical Representation (Bar, Histogram, Frequency Polygon)
• Mean, Median, and Mode
• Interpretation of Data

Unit 19: Probability

• Basic Concepts of Probability
• Sample Space and Events
• Classical Definition of Probability
• Simple Problems on Probability
• Real-life Applications

Unit 20: Practical Geometry and Constructions

• Construction of Triangles
• Construction of Quadrilaterals
• Construction Using Locus
• Tangents to a Circle from an External Point
• Division of a Line Segment in Given Ratio

Learning Objectives

• Algebraic Fluency — Manipulate algebraic expressions; solve linear and quadratic equations and simple systems with clear steps.
• Geometric Reasoning — Apply properties of triangles, quadrilaterals and circles; construct basic figures with accuracy; justify steps where required.
• Measurement — Compute perimeter, area, surface area and volume for standard shapes and solids; handle unit conversions and composite figures.
• Analytic Geometry — Use coordinate formulas for distance, section and area; model and interpret straight-line relationships.
• Trigonometry — Use right-triangle ratios and basic identities to solve heights-and-distances and numerical problems.
• Data & Chance — Summarize data (mean/median/mode) and interpret charts; compute simple probabilities and reason about likelihood.
• Real-life Application — Solve routine finance problems (interest, discount, VAT) and translate word problems into equations.
• Exam Preparedness — Show neat workings, label figures correctly, manage time by section, and avoid common errors per SSC marking criteria.