CBSE Class 10 Maths Syllabus 2026-27 Study Material

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS

• Fundamental Theorem of Arithmetic- statements after reviewing work done earlier and after illustrating and motivating through examples

• Proofs of irrationality of √2, √3, √5

• Develops understanding of numbers, including the set of real numbers and its properties.

• Extends the understanding of powers (radical powers) and exponents.

• Applies Fundamental Theorem of Arithmetic to solve problems related to real life contexts.

• Describes Fundamental Theorem of Arithmetic with examples

• Prove algebraically the Irrationality of numbers like √2, √3, √5, 3 + 2√5 etc.

UNIT II: ALGEBRA

1. POLYNOMIALS

• Zeros of a polynomial

• Relationship between zeros and coefficients of quadratic polynomials

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

• Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency

• Algebraic conditions for number of solutions

• Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination

• Simple situational problems

3. QUADRATIC EQUATIONS

• Standard form of a quadratic equation ax2+bx+c=0,(a≠0)ax^2 + bx + c = 0, (a ≠ 0)ax2+bx+c=0,(a=0)

• Solutions of quadratic equations (only real roots) by factorization and by using quadratic formula

• Relationship between discriminant and nature of roots

• Situational problems based on quadratic equations related to day-to-day activities

4. ARITHMETIC PROGRESSIONS

• Motivation for studying Arithmetic Progression

• Derivation of the nth term and sum of the first n terms of AP and their application in solving daily life problems

UNIT III: COORDINATE GEOMETRY

1. Coordinate Geometry

• Review: Concepts of coordinate geometry
• Distance formula
• Section formula (internal division)

UNIT IV: GEOMETRY

1. TRIANGLES

• Definitions, examples, counter-examples of similar triangles

• (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

• (State) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side

• (State) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar

• (State) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the triangles are similar

• (State) 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

2. CIRCLES

• Tangent to a circle at the point of contact

• (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact

• (Prove) The lengths of tangents drawn from an external point to a circle are equal

UNIT V: TRIGONOMETRY

1. Introduction to Trigonometry

• Trigonometric ratios of an acute angle of a right-angled triangle.

• Proof of their existence (well defined).

• Motivate the ratios whichever are defined at 0° and 90°.

• Values of the trigonometric ratios of 30°, 45°, and 60°.

• Relationships between the ratios.

2. Trigonometric Identities

• Proof and applications of the identity:

• sin⁡2A+cos⁡2A=1

• Only simple identities to be given.

3. Heights and Distances

• Angle of elevation, angle of depression.

• 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°.

UNIT VI: MENSURATION

1. Areas Related to Circles

• Area of sectors and segments of a circle.
• Problems based on areas and perimeter/circumference of the above said plane figures.
• In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90°, and 120° only.

2. Surface Areas and Volumes

Surface areas and volumes of combinations of any two of the following:

• Cubes
• Cuboids
• Spheres
• Hemispheres
• Right circular cylinders/cones

UNIT VII: STATISTICS AND PROBABILITY

1. Statistics

• Mean, median and mode of grouped data (Bimodal situation to be avoided)

2. Probability

• Classical definition of probability
• Simple problems on finding the probability of an event