Class 10 Mathematics Notes

The Fundamental Theorem of Arithmetic, HCF and LCM by prime factorisation, and irrationality proofs.

Zeroes of polynomials, their geometric meaning and the relation between zeroes and coefficients.

Graphical method, consistency conditions, and substitution and elimination methods.

Standard form, solving by factorisation and the quadratic formula, and nature of roots.

The nth term and the sum of the first n terms of an AP with applications.

Similar figures, the Basic Proportionality Theorem and the AAA, SSS and SAS similarity criteria.

The distance formula and the section formula with mid-point and collinearity problems.

Trigonometric ratios, values at standard angles and the identity sin²A + cos²A = 1.

Heights and distances using angles of elevation and depression.

Tangents to a circle, the radius–tangent theorem and equal tangents from an external point.

Area and arc length of sectors and areas of segments of a circle.

Surface area and volume of combinations of cuboids, cylinders, cones, spheres and hemispheres.

Mean, median and mode of grouped data and the empirical relationship between them.

Classical probability, equally likely outcomes, complementary events and problems on coins, dice and cards.