Class 10 · Mathematics (Basic)

Fundamental Theorem of Arithmetic, HCF and LCM by prime factorisation, and the irrationality of numbers like $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$.

Zeroes of a polynomial and their relationship with coefficients; division algorithm for polynomials.

Graphical and algebraic methods (substitution, elimination) to solve two linear equations in two variables.

Standard form, factorisation, completing the square, quadratic formula, nature of roots and word problems.

Sequences where each term differs from the previous by a fixed common difference; formulas for the $n$-th term and sum of the first $n$ terms.

Similar triangles, criteria for similarity (AAA, SAS, SSS), Basic Proportionality Theorem (Thales) and Pythagoras theorem.

Distance formula, section formula, area of a triangle from coordinates.

Trigonometric ratios (sin, cos, tan and reciprocals), values at standard angles, and fundamental identities.

Real-life problems on heights and distances using angles of elevation and depression.

Tangents to a circle, number of tangents from a point, tangent-radius property.

Circumference and area of a circle, area of a sector and segment, combined figures.

Formulas for combinations of solids: cube, cuboid, cylinder, cone, sphere and hemisphere.

Measures of central tendency for grouped data: mean, median, mode and their empirical relationship.

Classical (theoretical) probability, sample space, favourable outcomes, complementary events.