Class 10 Compulsory Mathematicsकक्षा १० अनिवार्य गणित — SEE notes & solutions

Class 10 Compulsory Mathematics serves as a bridge between foundational arithmetic and higher secondary mathematical concepts, focusing on practical problem-solving, logical reasoning, and real-world quantitative analysis.

Represent multi-set relationships and extract unknown subsets using Venn diagrams and cardinality principles to resolve contextual survey scenarios.

Unit 1: Sets 

Sets forms the foundational unit of the curriculum. The chapter focuses primarily on cardinality of sets and solving practical word problems involving two or three intersecting subsets using Venn diagrams.

Unit 2: Compound Interest 

Compound Interest (CI) is a major commercial arithmetic unit. Unlike simple interest, where interest is earned only on the initial principal, compound interest adds accumulated interest back into the principal at fixed compounding intervals ("interest on interest").

Unit 3: Growth and Depreciation 

Compound Growth and Compound Depreciation directly extend the compound interest principle to real-world phenomena—such as population changes, plant growth, bacteria cultures, and the decline in value of machinery, vehicles, or physical assets over time.

Unit 4: Currency and Exchange Rate 

Currency and Exchange Rate is the final unit under Commercial Arithmetic. It deals with money conversions between different national currencies, bank transactions (buying vs. selling rates), bank service charges/commissions, and currency devaluation or revaluation.

Unit 5: Area and Volume 

Area and Volume covers plane figures, paths, walls/ceilings, prisms, cylinders, spheres/hemispheres, cones, pyramids, and combined solids.

Unit 6: Sequence and Series 

Sequence and Series introduces two primary algebraic progressions: Arithmetic Progression (AP) and Geometric Progression (GP), along with their general terms, arithmetic/geometric means, and sum formulae.

Unit 7: Quadratic Equation 

Quadratic Equation unit covers standard algebraic methods for solving degree-2 polynomial equations and applying them to solve practical word problems (numbers, age, geometry, and speed/time).

Unit 8: Algebraic Fraction 

Algebraic Fractions (Rational Expressions) is a core high-weightage topic within the Algebra unit. It tests proficiency in factoring polynomials, finding the Least Common Multiple (LCM) and Highest Common Factor (HCF), simplifying cyclic/symmetric fractions, and solving fractional algebraic equations.

Unit 9: Indices 

Indices is a standard high-scoring algebraic unit. It tests algebraic manipulation using exponent laws, simplifying multi-term fractional expressions, and solving exponential equations.

Unit 10: Circle 

Circle is one of the highest-weightage topics in Geometry. It encompasses angle properties subtended by arcs, cyclic quadrilaterals, tangent-secant properties, experimental verifications, and theoretical proofs.

Unit 11: Triangles and Quadrilaterals 

Triangles and Quadrilaterals is the foundational unit of Geometry. It focuses on the area relationships between triangles and parallelograms standing on the same base and between the same parallel lines, experimental verifications, and formal theoretical proofs.

Unit 12: Construction 

Construction is a guaranteed 4-mark long-answer question under the Geometry section. It assesses the practical application of theorems concerning triangles and parallelograms standing on the same base and between the same parallel lines, constructed strictly using a straightedge (ruler) and a pair of compasses.

Unit 13: Statistics 

Statistics carries a steady weightage (typically 5 to 7 marks total across short and long answer questions). The curriculum focuses on measures of central tendency (Mean, Median, Mode) and positional values (Quartiles) for continuous series (grouped frequency distributions), along with finding missing frequencies.

Unit 14: Probability 

Probability is the final unit, carrying around 4 to 5 marks across short and structured questions. It emphasizes basic definitions, event classifications, the addition and multiplication laws, and using tree diagrams to solve problems with or without replacement.