Chapter Summaries›Class 10 Mathematics
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Class 10 MathematicsChapter Summaries

14 chapters · Quick revision in under 3 minutes per chapter

Ch 1

Real Numbers

Covers Euclid's division algorithm and the fundamental theorem of arithmetic. Students learn to find HCF and LCM using prime factorisation. Irrational numbers and their decimal expansions are explored in depth.

Topics covered

Euclid's Division LemmaFundamental Theorem of ArithmeticHCF and LCM by prime factorisationRational and irrational numbersDecimal expansions

⚠️ Removed from 2025-26 syllabus

Euclid's division algorithm (proof of lemma only, application retained)

Ch 2

Polynomials

Introduces the relationship between zeros and coefficients of polynomials. Students explore graphical representation of polynomials and learn to divide one polynomial by another. Division algorithm for polynomials is a key topic.

Topics covered

Zeros of a polynomialRelationship between zeros and coefficientsDivision algorithm for polynomialsGraphical meaning of zeros
Ch 3

Pair of Linear Equations in Two Variables

Explores methods to solve simultaneous linear equations — graphical, substitution, elimination, and cross-multiplication. Consistency of equations and conditions for unique, infinite, or no solutions are covered.

Topics covered

Graphical methodSubstitution methodElimination methodCross-multiplication methodConsistent and inconsistent equations
Ch 4

Quadratic Equations

Covers solving quadratic equations by factorisation and using the quadratic formula. The discriminant and nature of roots is an important concept. Word problems involving quadratic equations are frequently asked in exams.

Topics covered

Factorisation methodCompleting the squareQuadratic formulaDiscriminant and nature of rootsWord problems
Ch 5

Arithmetic Progressions

Introduces sequences where the difference between consecutive terms is constant. Students learn to find the nth term and the sum of n terms. AP-based word problems about savings, seating arrangements, etc., are exam favourites.

Topics covered

nth term of an AP: aₙ = a + (n−1)dSum of n terms: Sₙ = n/2[2a + (n−1)d]Finding missing termsWord problems on AP
Ch 6

Triangles

Focuses on similarity of triangles and the conditions for two triangles to be similar (AA, SSS, SAS). Pythagoras theorem and its converse are proven and applied. This chapter carries high marks in board exams.

Topics covered

Basic Proportionality Theorem (BPT)Criteria for similar triangles: AA, SSS, SASAreas of similar trianglesPythagoras theoremConverse of Pythagoras theorem
Ch 7

Coordinate Geometry

Extends the coordinate plane to include distance, section formulas, and area of triangles. Students apply these formulas to real-world and abstract problems. The section formula (internal division) is especially important.

Topics covered

Distance formulaSection formula (internal and external division)Midpoint formulaArea of a triangle using coordinatesCollinearity of three points
Ch 8

Introduction to Trigonometry

Defines trigonometric ratios for acute angles and establishes fundamental identities. Students memorise values for standard angles and apply identities to simplify expressions. Complementary angles are also covered.

Topics covered

Trigonometric ratios (sin, cos, tan, cosec, sec, cot)Trigonometric ratios of standard angles (0°, 30°, 45°, 60°, 90°)Complementary anglesTrigonometric identities: sin²θ + cos²θ = 1
Ch 9

Some Applications of Trigonometry

Applies trigonometry to find heights and distances of objects using angles of elevation and depression. This chapter is almost entirely word-problem based and is a consistent 4-5 mark question in board exams.

Topics covered

Angle of elevationAngle of depressionHeight and distance word problemsLine of sight
Ch 10

Circles

Covers tangents to a circle from an external point, proving that the tangent is perpendicular to the radius at the point of tangency. Proof-based questions from this chapter appear consistently in board exams.

Topics covered

Tangent to a circleNumber of tangents from an external pointTheorem: tangent perpendicular to radiusLength of tangents from external point
Ch 11

Areas Related to Circles

Introduces arc length, area of sector, area of segment, and combinations of plane figures involving circles. Questions involving shaded regions (circle + square or triangle combinations) are common in exams.

Topics covered

Area and circumference of a circleArea of sectorArea of segmentAreas of combinations of plane figures

⚠️ Removed from 2025-26 syllabus

Problems on plane figures other than circles (rectangles, triangles) — only circle-based combinations retained

Ch 12

Surface Areas and Volumes

Covers surface areas and volumes of combinations of solids (cone + hemisphere, cylinder + cone etc.) and conversion of one solid to another. Frustum of a cone is also included.

Topics covered

Surface area of combined solidsVolume of combined solidsConversion of solidsFrustum of a cone
Ch 13

Statistics

Covers mean, median, and mode of grouped data with different methods — direct, assumed mean, and step deviation for mean. Ogive curves for median are also included.

Topics covered

Mean by direct method, assumed mean method, step deviation methodMode of grouped dataMedian of grouped dataOgive (cumulative frequency graph)
Ch 14

Probability

Introduces classical probability — theoretical probability of equally likely outcomes. Students solve problems involving cards, dice, coins, and bags of coloured balls.

Topics covered

Classical definition of probabilitySimple probability problemsComplementary eventsProbability using playing cards and dice

⚠️ Removed from 2025-26 syllabus

Problems based on geometrical probability

More resources for Class 10 Mathematics

NCERT Solutions →Important Questions →Deleted Topics →Revision Checklist →