Class 10 Maths Chapter-wise Notes & Formulas

Fundamental Theorem of Arithmetic, HCF & LCM properties, and formal contradiction proofs of irrationality.

Geometrical meaning of zeroes, zeroes-coefficients relationships, forming quadratics, and symmetric expressions.

Consistency conditions, Graphical Method, Substitution & Elimination algebraic methods, and upstream/downstream word problems.

Standard form $ax^2+bx+c=0$, factorisation with roots, quadratic formula, discriminant $D=b^2-4ac$, and equal root parameter problems.

General term $a_n = a + (n-1)d$, sum of $n$ terms $S_n$, relation $a_n = S_n - S_{n-1}$, and board real-life word problems.

Compulsory Basic Proportionality Theorem (BPT) full proof, Converse of BPT, and similarity criteria (AA, SSS, SAS).

Distance Formula, Collinearity, Section Formula for internal division, Midpoint formula, and types of geometric shapes.

Trigonometric ratios, values table ($0^\circ$ to $90^\circ$), fundamental identities ($\sin^2\theta+\cos^2\theta=1$), and step-by-step proofs.

Line of sight, Angle of Elevation and Depression, single & two-triangle geometric formulations for towers, hills, and balloons.

Theorem 10.1 (Radius $\perp$ Tangent), Theorem 10.2 (Lengths of Tangents from External Point are equal) with full board proof and standard riders.

Perimeter and area of circle, area of sector, arc length, area of minor/major segment ($\theta = 60^\circ, 90^\circ, 120^\circ$), and clock problems.

Surface areas and volumes of combinations of solids (cone on hemisphere, cylinder with hemispheres, tent), and TSA vs Volume rules.

Mean (Direct & Assumed Mean Method), Mode and Median of grouped data, finding missing frequencies ($x$ and $y$), and empirical formula.

Classical probability definition, impossible vs sure events, complete 52-card deck distribution, 2-dice 36 outcome grid, and leap year problems.