Year 10: CBSE Class X Mathematics

Listed Mathematics syllabus topics at Class X, in the words of the Central Board of Secondary Education (CBSE), with the practice on this site that covers it. Checked against the source on 3 September 2026.

The 2026-27 syllabus (subject codes 041 and 241), redesigned against NEP 2020 and NCF-SE 2023.

15syllabus topics
91skills mapped
100%have practice

Coverage is the percentage of listed syllabus topics with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one syllabus topic, so some appear more than once below.

Number systems

I.1Real numbers1. Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples. 2. Proofs of irrationality of √2, √3, √5.

Algebra

II.1Polynomials1. Zeros of a polynomial. 2. Relationship between zeros and coefficients of quadratic polynomials.
II.2Pair of linear equations in two variables1. Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. 2. Algebraic conditions for number of solutions. 3. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.
II.3Quadratic equations1. Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). 2. Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. 3. Situational problems based on quadratic equations related to day-to-day activities to be incorporated.
II.4Arithmetic progressions1. Motivation for studying Arithmetic Progression. 2. Derivation of the nth term and sum of the first n terms of AP and their application in solving daily life problems.

Coordinate geometry

III.1Coordinate geometry1. Review: Concepts of coordinate geometry. Distance formula. Section formula (internal division).

Geometry

IV.1TrianglesDefinitions, examples, counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. State (without proof) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. State (without proof) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4. State (without proof) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5. State (without proof) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
IV.2CirclesTangent to a circle at point of contact. 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

Trigonometry

V.1Introduction to trigonometry1. Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). 2. Motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45° and 60°. 3. Relationships between the ratios.
V.2Trigonometric identities1. Proof and applications of the identity sin²A + cos²A = 1. 2. Only simple identities to be given.
V.3Heights and distancesAngle of elevation, angle of depression. 1. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

Mensuration

VI.1Areas related to circles1. Area of sectors and segments of a circle. 2. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.)
VI.2Surface areas and volumes1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Statistics and probability

VII.1Statistics1. Mean, median and mode of grouped data (bimodal situation to be avoided).
VII.2Probability1. Classical definition of probability. 2. Simple problems on finding the probability of an event.

Other Year 10 skills

Year 10 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.