Class 10 Maths formulas: the complete chapter-wise list

Formulas are the quickest marks in Maths, but only if you can recall them without looking. Here is the list for the whole Class 10 course, in chapter order. Each chapter also has its own one-page formula bank you can download and print.

Algebra

Real Numbers: HCF × LCM = product of the two numbers. Every composite number has one and only one prime factorisation.
Polynomials: sum of zeroes = −b/a and product of zeroes = c/a, for ax² + bx + c.
Pair of linear equations: if a₁/a₂ ≠ b₁/b₂ there is one solution; if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ there is none; if all three ratios are equal there are infinitely many.
Quadratic equations: discriminant D = b² − 4ac. For D > 0 the roots are real and different, for D = 0 they are real and equal, for D < 0 there are no real roots. Roots: x = (−b ± √D) / 2a.
Arithmetic progression: nth term = a + (n − 1)d. Sum of n terms = n/2 [2a + (n − 1)d] = n/2 (a + l).

Geometry and coordinate geometry

Triangles: if DE ∥ BC then AD/DB = AE/EC. For similar triangles, the ratio of areas is the square of the ratio of corresponding sides.
Circles: the tangent is perpendicular to the radius at the point of contact, and the two tangents from an outside point are equal in length.
Distance between (x₁, y₁) and (x₂, y₂) = √[(x₂ − x₁)² + (y₂ − y₁)²].
Section formula (internal, ratio m : n) = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)). Mid-point is the case m = n.

Trigonometry

sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ.
Heights and distances: tan of the angle of elevation = height/horizontal distance.

Mensuration

Circle: circumference 2πr, area πr². Sector: area = (θ/360) × πr², arc length = (θ/360) × 2πr.
Cylinder: curved surface 2πrh, total surface 2πr(r + h), volume πr²h.
Cone: slant height l = √(r² + h²), curved surface πrl, volume ⅓πr²h.
Sphere: surface 4πr², volume ⁴⁄₃πr³. Hemisphere: curved surface 2πr², total surface 3πr², volume ⅔πr³.

Statistics and probability

Mean = Σfx / Σf. Median = l + [(n/2 − cf) / f] × h. Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h.
Empirical relation: mode = 3 × median − 2 × mean.
Probability of an event = favourable outcomes / total outcomes. P(E) + P(not E) = 1, and a probability is always between 0 and 1.

Extra for ICSE students

Remainder theorem: the remainder when f(x) is divided by (x − a) is f(a).
Slope of a line = (y₂ − y₁)/(x₂ − x₁). Equation of a line: y = mx + c.
Compound interest: A = P (1 + r/100)ⁿ. Recurring deposit interest = P × n(n + 1)/24 × r/100, where n is the number of months.

How to learn them

Do not try to memorise the whole list in one evening. Learn one chapter's formulas, then write them from memory the next day. The chapter notes show where each formula comes from, which makes it much easier to remember.