The old NCERT Class 10 Mathematics syllabus (prior to the rationalization/reduction of content) comprises 15 chapters across 6 core units.
Detailed Chapter-Wise Syllabus
Unit 1: Number Systems
- Chapter 1: Real Numbers
- Euclid’s Division Lemma
- Fundamental Theorem of Arithmetic (Prime factorization, HCF, LCM)
- Proofs of irrationality of numbers (e.g., \sqrt{2}, \sqrt{3}, \sqrt{5})
- Decimal expansions of rational numbers (Terminating and non-terminating repeating decimals)
Unit 2: Algebra - Chapter 2: Polynomials
- Geometrical meaning of zeros of a polynomial
- Relationship between zeros and coefficients of a quadratic polynomial
- Statement and simple problems on division algorithm for polynomials
- Chapter 3: Pair of Linear Equations in Two Variables
- Graphical method of solution
- Algebraic methods: Substitution Method, Elimination Method, Cross-Multiplication Method
- Equations reducible to a pair of linear equations in two variables
- Chapter 4: Quadratic Equations
- Standard form of a quadratic equation: ax^2 + bx + c = 0
- Solution methods: Factorisation, Completing the Square, Quadratic Formula
- Nature of roots (Discriminant b^2 – 4ac)
- Chapter 5: Arithmetic Progressions (AP)
- Introduction to AP, common difference
- Derivation of the n^{\text{th}} term (a_n = a + (n-1)d)
- Sum of the first n terms (S_n = \frac{n}{2}[2a + (n-1)d]) and application to daily life problems
Unit 3: Coordinate Geometry - Chapter 7: Coordinate Geometry
- Review of concepts of coordinate geometry
- Distance Formula
- Section Formula (Internal division)
- Area of a Triangle using coordinates
Unit 4: Geometry - Chapter 6: Triangles
- Definitions, examples, and counter-examples of similar triangles
- Basic Proportionality Theorem (Thales Theorem) and its converse
- Criteria for similarity of triangles (AAA, SSS, SAS)
- Ratio of areas of two similar triangles
- Pythagoras Theorem and its converse
- Chapter 10: Circles
- Tangent to a circle at a point of contact
- Theorems:
- Tangent is perpendicular to the radius at the point of contact.
- Lengths of tangents drawn from an external point to a circle are equal.
- Chapter 11: Constructions
- Division of a line segment in a given ratio (internally)
- Construction of a triangle similar to a given triangle
- Construction of tangents to a circle from a point outside it
Unit 5: Trigonometry - Chapter 8: Introduction to Trigonometry
- Trigonometric ratios of an acute angle of a right-angled triangle
- Trigonometric ratios of specific angles (0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ)
- Relationships between the ratios
- Trigonometric identities (\sin^2\theta + \cos^2\theta = 1, 1 + \tan^2\theta = \sec^2\theta, 1 + \cot^2\theta = \csc^2\theta)
- Trigonometric ratios of complementary angles
- Chapter 9: Some Applications of Trigonometry
- Heights and Distances
- Angles of elevation and depression
- Simple problems involving two right-angled triangles (30^\circ, 45^\circ, 60^\circ)
Unit 6: Mensuration - Chapter 12: Areas Related to Circles
- Perimeter (circumference) and area of a circle
- Area of sector and segment of a circle
- Problems on areas and perimeter/circumference of plane figures involving combinations of triangles, simple quadrilaterals, and circle parts
- Chapter 13: Surface Areas and Volumes
- Surface areas and volumes of combinations of solids (cubes, cuboids, spheres, hemispheres, right circular cylinders/cones)
- Conversion of solid from one shape to another
- Frustum of a cone
Unit 7: Statistics & Probability - Chapter 14: Statistics
- Mean, Median, and Mode of grouped data (Direct, Assumed Mean, and Step-Deviation methods)
- Cumulative frequency graph (Ogives – less than and more than types)
- Chapter 15: Probability
- Classical definition of probability
- Simple problems on finding the probability of an event