Class 10 Mathematics
Comprehensive chapter-wise formula banks, NCERT exemplar proofs, previous years' board questions (PYQs), and high-yield video lectures for CBSE Class 10 aspirants.
CBSE Class 10 Chapters
All Class 10 content is organized inside this /class10/ folder. Click any chapter to view comprehensive notes, formula banks, and board exam solutions.
Real Numbers
Fundamental Theorem of Arithmetic, HCF & LCM relation [HCF(a,b) × LCM(a,b) = a × b], and proving irrationality of √2, √3, √5.
Polynomials
Geometrical meaning of zeroes of a polynomial, relationship between zeroes and coefficients of quadratic polynomials (α + β and α·β).
Pair of Linear Equations in Two Variables
Graphical method, algebraic methods (Substitution, Elimination), and consistency conditions (a₁/a₂ vs b₁/b₂ vs c₁/c₂).
Quadratic Equations
Standard form ax² + bx + c = 0, solution by factorisation and quadratic formula, discriminant (D = b² - 4ac), and nature of roots.
Arithmetic Progressions (AP)
nth term formula aₙ = a + (n - 1)d, sum of first n terms Sₙ = n/2[2a + (n - 1)d], and practical daily-life word applications.
Triangles
Basic Proportionality Theorem (Thales' Theorem) with complete proof, converse of BPT, and AAA, SAS, SSS similarity criteria.
Coordinate Geometry
Distance formula √[(x₂ - x₁)² + (y₂ - y₁)²], Section formula for internal division, and Midpoint formula with collinearity problems.
Introduction to Trigonometry
Trigonometric ratios (sin, cos, tan, cot, sec, cosec), values at 0°, 30°, 45°, 60°, 90°, and proof of sin²A + cos²A = 1.
Some Applications of Trigonometry
Angles of elevation and depression, line of sight, heights of towers, width of rivers, and multi-observer board problems.
Circles
Tangent to a circle, tangent is perpendicular to the radius at point of contact, lengths of tangents drawn from external point are equal.
Areas Related to Circles
Area of sector of a circle (θ/360° × πr²), length of an arc of a sector, and area of major and minor segments of a circle.
Surface Areas and Volumes
Surface areas and volumes of combinations of solids: cubes, cuboids, spheres, hemispheres, and right circular cylinders or cones.
Statistics
Mean of grouped data (Direct, Assumed Mean methods), Mode of grouped data formula, and Median of grouped data using cumulative frequency.
Probability
Classical definition of probability P(E) = n(E)/n(S), impossible & sure events, complementary events P(Ē) = 1 - P(E), and card/coin problems.
Copy templates/chapter-template.html into this class10/ folder, rename it (e.g. ch02-polynomials.html), and link it above.