CBSE · Class 10
Maths Formulas for Class 10
All important Maths formulas chapter-wise for CBSE Class 10 (2026-27) — quick-revision tables covering every chapter from Real Numbers to Probability.
For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.
Ch 1.Real Numbers
| Formula / Relation | Expression |
|---|---|
| Euclid's Division Lemma | a = bq + r, where 0 ≤ r < b |
| HCF × LCM | HCF(a,b) × LCM(a,b) = a × b |
| Rational decimal rule | p/q is terminating if q = 2^m × 5^n |
Ch 2.Polynomials
| Formula / Relation | Expression |
|---|---|
| Sum of zeroes (quadratic) | α + β = −b/a |
| Product of zeroes (quadratic) | αβ = c/a |
| Sum of zeroes (cubic) | α + β + γ = −b/a |
| Product of zeroes (cubic) | αβγ = −d/a |
| Sum of products of pairs (cubic) | αβ + βγ + γα = c/a |
Ch 3.Pair of Linear Equations
| Formula / Relation | Expression |
|---|---|
| Consistent (unique solution) | a₁/a₂ ≠ b₁/b₂ |
| Consistent (infinite solutions) | a₁/a₂ = b₁/b₂ = c₁/c₂ |
| Inconsistent (no solution) | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ |
| Cross-multiplication method | x/(b₁c₂−b₂c₁) = y/(c₁a₂−c₂a₁) = 1/(a₁b₂−a₂b₁) |
Ch 4.Quadratic Equations
| Formula / Relation | Expression |
|---|---|
| Quadratic Formula | x = [−b ± √(b²−4ac)] / 2a |
| Discriminant (D) | D = b² − 4ac |
| Nature of roots | D > 0 → distinct; D = 0 → equal; D < 0 → imaginary |
Ch 5.Arithmetic Progressions (AP)
| Formula / Relation | Expression |
|---|---|
| nth term | aₙ = a + (n−1)d |
| Sum of n terms | Sₙ = n/2 [2a + (n−1)d] = n/2 (a + l) |
| Common difference | d = aₙ − aₙ₋₁ |
Ch 6.Triangles (Similarity)
| Formula / Relation | Expression |
|---|---|
| Basic Proportionality Theorem | DE ∥ BC ⇒ AD/DB = AE/EC |
| Area ratio (similar triangles) | ar(△ABC)/ar(△DEF) = (AB/DE)² = (BC/EF)² = (AC/DF)² |
| Pythagoras Theorem | AC² = AB² + BC² |
| Converse of Pythagoras | If AC² = AB² + BC², then ∠B = 90° |
Ch 7.Coordinate Geometry
| Formula / Relation | Expression |
|---|---|
| Distance Formula | d = √[(x₂−x₁)² + (y₂−y₁)²] |
| Section Formula (internal) | P = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)] |
| Midpoint Formula | M = [(x₁+x₂)/2, (y₁+y₂)/2] |
| Area of Triangle | Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| |
Ch 8.Introduction to Trigonometry
| Formula / Relation | Expression |
|---|---|
| sin θ | Opposite / Hypotenuse |
| cos θ | Adjacent / Hypotenuse |
| tan θ | Opposite / Adjacent = sin θ / cos θ |
| Pythagorean Identity 1 | sin²θ + cos²θ = 1 |
| Pythagorean Identity 2 | 1 + tan²θ = sec²θ |
| Pythagorean Identity 3 | 1 + cot²θ = cosec²θ |
| Reciprocal: cosec | cosec θ = 1/sin θ |
| Reciprocal: sec | sec θ = 1/cos θ |
| Reciprocal: cot | cot θ = 1/tan θ = cos θ/sin θ |
Ch 9.Heights and Distances
| Formula / Relation | Expression |
|---|---|
| Angle of Elevation | tan θ = height / horizontal distance |
| Angle of Depression | tan θ = drop / horizontal distance |
Ch 10.Circles
| Formula / Relation | Expression |
|---|---|
| Tangent ⊥ radius | OT ⊥ PT (O = centre, T = point of tangency) |
| Tangents from external point | PA = PB (equal length) |
| Angle in alternate segment | ∠between tangent and chord = inscribed angle in alternate segment |
Ch 11.Areas Related to Circles
| Formula / Relation | Expression |
|---|---|
| Area of Circle | A = πr² |
| Circumference | C = 2πr |
| Area of Sector | A = (θ/360°) × πr² |
| Length of Arc | l = (θ/360°) × 2πr |
| Area of Segment | A = Area of sector − Area of triangle |
Ch 12.Surface Areas and Volumes
| Formula / Relation | Expression |
|---|---|
| Cuboid: TSA | 2(lb + bh + hl) |
| Cuboid: Volume | l × b × h |
| Cube: TSA | 6a² |
| Cube: Volume | a³ |
| Cylinder: CSA | 2πrh |
| Cylinder: TSA | 2πr(h+r) |
| Cylinder: Volume | πr²h |
| Cone: Slant height | l = √(r²+h²) |
| Cone: CSA | πrl |
| Cone: TSA | πr(l+r) |
| Cone: Volume | (1/3)πr²h |
| Sphere: SA | 4πr² |
| Sphere: Volume | (4/3)πr³ |
| Hemisphere: CSA | 2πr² |
| Hemisphere: TSA | 3πr² |
| Hemisphere: Volume | (2/3)πr³ |
Ch 13.Statistics
| Formula / Relation | Expression |
|---|---|
| Mean (Direct Method) | x̄ = Σfᵢxᵢ / Σfᵢ |
| Mean (Assumed Mean) | x̄ = a + (Σfᵢdᵢ / Σfᵢ) |
| Median (grouped data) | M = l + [(n/2 − cf) / f] × h |
| Mode (grouped data) | Mode = l + [(f₁−f₀) / (2f₁−f₀−f₂)] × h |
Ch 14.Probability
| Formula / Relation | Expression |
|---|---|
| Probability of event E | P(E) = number of favourable outcomes / total outcomes |
| Complementary event | P(Ē) = 1 − P(E) |
| Sure event | P(S) = 1 |
| Impossible event | P(∅) = 0 |
Frequently Asked Questions
Which formulas are most important in Class 10 Maths for board exams?
Trigonometric identities (sin²θ + cos²θ = 1 and derived forms), Quadratic formula, AP sum formula, Surface area and volume formulas, and the Distance/Section formula from Coordinate Geometry carry the most marks. These appear in almost every CBSE Class 10 board paper.
How many formulas should I memorise for Class 10 Maths?
Focus on 30–40 core formulas rather than memorising everything. Prioritise: all trig identities, AP nth term and sum, quadratic formula, coordinate geometry formulas, and all surface area/volume formulas. Understand the derivation of each — it helps remember them under exam pressure.
What is the section formula in Class 10 Maths?
The section formula gives the coordinates of a point P dividing line segment AB (with A(x₁,y₁) and B(x₂,y₂)) in ratio m:n internally as P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). For midpoint (m=n=1) it simplifies to ((x₁+x₂)/2, (y₁+y₂)/2).
Is Euclid's division lemma important for Class 10 boards?
Yes — it is asked directly as a 2-mark proof question or used in HCF problems. Know the statement: a = bq + r (0 ≤ r < b) and be able to apply it step-by-step to find HCF using the algorithm.
Related resources
Need help with Class 10 Maths?
Learnizo tutors help you master every formula with solved board-pattern questions.
Find a Maths Tutor