Class 10 Maths Formula Sheet — All 14 Chapters

September 24, 2026 Pandey Sir

Class 10 Maths Formula Sheet — All 14 Chapters (CBSE 2026-27)

Everything you need to revise: every formula for the 14 chapters of the CBSE Class 10 Mathematics syllabus, on one printable sheet — algebra, trigonometry, coordinate geometry, mensuration, statistics and probability. Deleted topics are left out, and every formula is checked before publishing.

Aligned to the CBSE Class 10 Mathematics syllabus 2026-27 · Last updated 24 September 2026

1 Real Numbers 2 Polynomials 3 Linear Equations 4 Quadratic Equations 5 AP 6 Coordinate Geometry 7 Triangles 8 Circles 9 Trigonometry 10 Applications 11 Areas of Circles 12 Surface Area & Volume 13 Statistics 14 Probability

How the marks are spread (unit-wise)

Unit	Name	Marks
I	Number Systems	06
II	Algebra	20
III	Coordinate Geometry	06
IV	Geometry	15
V	Trigonometry	12
VI	Mensuration	10
VII	Statistics and Probability	11
Theory total		80
Internal assessment		20
Grand total		100

Algebra carries the biggest share. If your time is short, start there and with Geometry.

1 · Real Numbers

What it does	Formula
Links HCF and LCM of two positive integers	HCF(a, b) × LCM(a, b) = a × b
Fundamental Theorem of Arithmetic	Every composite number can be written as a product of primes, and this factorisation is unique apart from the order of the factors.
Testing for irrationality	√p is irrational for every prime p. So √2, √3, √5, √7 are all irrational.
Irrationality proof pattern (contradiction)	Assume it is rational = ab with HCF(a, b) = 1, square both sides, and show p divides both a and b — which contradicts HCF = 1.

Out of scope — do not revise: Euclid’s Division Lemma, and decimal expansions of rational numbers. Both were removed from the syllabus.

2 · Polynomials

What it does	Formula
Sum of zeroes, quadratic ax² + bx + c	α + β = −ba
Product of zeroes, quadratic	αβ = ca
Building the polynomial from its zeroes	p(x) = x² − (α + β)x + αβ
Geometric meaning	The zeroes are the x-coordinates where the graph cuts the x-axis. A quadratic cuts it at 2, 1 or 0 points.

3 · Pair of Linear Equations in Two Variables

Condition	Ratio test	Result
Lines intersect at one point	a₁a₂ ≠ b₁b₂	Unique solution · consistent
Lines are the same	a₁a₂ = b₁b₂ = c₁c₂	Infinitely many solutions · consistent
Lines are parallel	a₁a₂ = b₁b₂ ≠ c₁c₂	No solution · inconsistent

Methods you can use: substitution, elimination, and graphical. If a question asks for the number of solutions, use the ratio test above — it is faster and safer than solving.

4 · Quadratic Equations

What it does	Formula
Standard form	ax² + bx + c = 0, with a ≠ 0
Quadratic formula (used for every solvable quadratic)	x = −b ± √(b² − 4ac)2a
Discriminant — decides the nature of roots	D = b² − 4ac
D > 0	Two distinct real roots
D = 0	Two equal real roots, each = −b2a
D < 0	No real roots

Method not required: “completing the square” is no longer a separate method in the current syllabus. Factorisation and the quadratic formula cover everything you need.

5 · Arithmetic Progressions

What it does	Formula
General term (nth term)	a_n = a + (n − 1)d
Sum of the first n terms, using a and d	S_n = n2[2a + (n − 1)d]
Sum when the last term is known	S_n = n2[a + a_n]
Finding a term from two sums	a_n = S_n − S_n−1
Common difference	d = a₂ − a₁ = a₃ − a₂

6 · Coordinate Geometry

What it finds	Formula
Distance between two points	PQ = √[(x₂ − x₁)² + (y₂ − y₁)²]
Distance from the origin	√(x² + y²)
Section formula (divides in ratio m₁ : m₂)	( m₁x₂ + m₂x₁m₁ + m₂ , m₁y₂ + m₂y₁m₁ + m₂ )
Midpoint	( x₁ + x₂2 , y₁ + y₂2 )
Area of a triangle	12\|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)\|

Collinear points: if the area comes to 0, the three points lie on a straight line. That is the fastest collinearity test.

7 · Triangles

Result	Statement
Basic Proportionality Theorem (Thales)	DE ∥ BC in △ABC ⟹ ADDB = AEEC
Converse of BPT	If ADDB = AEEC, then DE ∥ BC
Similarity — AA	Two equal angles ⟹ triangles are similar
Similarity — SSS	All three pairs of sides in the same ratio
Similarity — SAS	One equal angle between two pairs of sides in the same ratio
Areas of similar triangles	area △ABCarea △PQR = ( ABPQ )²
Pythagoras theorem	In a right triangle, hypotenuse² = base² + perpendicular²
Converse of Pythagoras	If a² + b² = c², the triangle is right-angled

8 · Circles

Result	Statement
Tangent and radius	A tangent is perpendicular to the radius at the point of contact, so ∠OPT = 90°
Tangents from an external point	The two tangent lengths are equal: PA = PB
Number of tangents	From an internal point: 0. On the circle: 1. From an external point: 2.

9 · Introduction to Trigonometry

Ratio	Formula	Reciprocal
sine	sin θ = perpendicularhypotenuse	cosec θ
cosine	cos θ = basehypotenuse	sec θ
tangent	tan θ = perpendicularbase	cot θ

Standard angles — learn this table

Angle θ	0°	30°	45°	60°	90°
sin θ	0	12	1√2	√32	1
cos θ	1	√32	1√2	12	0
tan θ	0	1√3	1	√3	Not defined

The three identities (and their rearrangements)

Identity	Rearranged forms you will actually use
sin²θ + cos²θ = 1	sin²θ = 1 − cos²θ · cos²θ = 1 − sin²θ
1 + tan²θ = sec²θ	sec²θ − tan²θ = 1 · tan²θ = sec²θ − 1
1 + cot²θ = cosec²θ	cosec²θ − cot²θ = 1 · cot²θ = cosec²θ − 1

Complementary angles — (90° − θ)

Given	Equals
sin(90° − θ)	cos θ
cos(90° − θ)	sin θ
tan(90° − θ)	cot θ
cosec(90° − θ)	sec θ
sec(90° − θ)	cosec θ
cot(90° − θ)	tan θ

10 · Some Applications of Trigonometry

Term	Meaning and formula
Angle of elevation	Measured upwards from the horizontal, to an object above eye level.
Angle of depression	Measured downwards from the horizontal, to an object below eye level.
Standard right-triangle setup	tan θ = height of objecthorizontal distance
When the angle is 45°	Height = horizontal distance (because tan 45° = 1)
Angle of elevation = angle of depression	When measured between the same two parallel horizontals (alternate angles)

11 · Areas Related to Circles

What it finds	Formula
Circumference	2πr
Area of a circle	πr²
Length of an arc (angle θ in degrees)	θ360 × 2πr
Area of a sector	θ360 × πr²
Area of a minor segment	area of sector − area of the triangle formed by the two radii
Perimeter of a sector	arc length + 2r

Use π = 227 when the radius is a multiple of 7, and π = 3.14 otherwise — unless the question tells you which to use.

12 · Surface Areas and Volumes

Solid	Curved / Lateral surface	Total surface area	Volume
Cube (edge a)	4a²	6a²	a³
Cuboid (l, b, h)	2h(l + b)	2(lb + bh + hl)	l × b × h
Cylinder (r, h)	2πrh	2πr(r + h)	πr²h
Cone (r, h, slant l)	πrl	πr(l + r)	13πr²h
Sphere (r)	4πr²	4πr²	43πr³
Hemisphere (r)	2πr²	3πr²	23πr³
Frustum (radii r₁, r₂; slant l)	πl(r₁ + r₂)	πl(r₁ + r₂) + πr₁² + πr₂²	13πh(r₁² + r₂² + r₁r₂)

Slant height of a cone: l = √(r² + h²) — this is the most common missing step in cone questions.

13 · Statistics

Measure	Formula (grouped data)
Mean — direct method	x̄ = Σf_ix_iΣf_i
Mean — assumed mean method	x̄ = a + Σf_id_iΣf_i, where d_i = x_i − a
Mean — step-deviation method	x̄ = a + h × Σf_iu_iΣf_i, where u_i = x_i − ah
Median	Median = l + (n/2) − cff × h
Mode	Mode = l + f₁ − f₀2f₁ − f₀ − f₂ × h
Empirical relationship	3 Median = Mode + 2 Mean

Reading the letters: l = lower limit of the median/modal class · n = total frequency · cf = cumulative frequency of the class before the median class · f = frequency of the median class · h = class size · f₁ = frequency of the modal class · f₀ and f₂ = frequencies of the classes before and after it.

14 · Probability

Result	Formula
Classical (theoretical) probability	P(E) = number of outcomes favourable to Etotal number of equally likely outcomes
Range of any probability	0 ≤ P(E) ≤ 1
Sure event / impossible event	P(sure) = 1 · P(impossible) = 0
Complement rule	P(E) + P(not E) = 1, so P(not E) = 1 − P(E)
Sum of probabilities of all outcomes	= 1

Know your sample spaces: one die = 6 outcomes · two dice = 36 outcomes · one coin = 2 · two coins = 4 · a standard deck = 52 cards (26 red, 26 black; 4 suits of 13; 12 face cards; 4 aces).

How to use this sheet properly

Do not just read it. Cover the right-hand column and try to recall each formula from the description.
Write the identity you are using before substituting numbers. Most lost marks in trigonometry come from substituting first and rearranging later.
Check the unit. Area answers are in square units, volume in cubic units, and lengths in units.
Print it and keep it with your revision notes. The print button below gives a clean black-and-white sheet.

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Written and checked by Pandey Sir · Pandey Sir’s BEST Classes, Dammaiguda, Hyderabad. Every formula on this page is verified before publishing, and deleted syllabus topics are deliberately left out.

Curriculum scope checked against the CBSE Class 10 Mathematics syllabus 2026-27 and the NCERT rationalised textbook. cbseacademic.nic.in · ncert.nic.in

Spotted a mistake? Tell us here — corrections are welcome and get fixed quickly.

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Class 10 Maths Formula Sheet — All 14 Chapters

Class 10 Maths Formula Sheet — All 14 Chapters (CBSE 2026-27)

How the marks are spread (unit-wise)

1 · Real Numbers

2 · Polynomials

3 · Pair of Linear Equations in Two Variables

4 · Quadratic Equations

5 · Arithmetic Progressions

6 · Coordinate Geometry

7 · Triangles

8 · Circles

9 · Introduction to Trigonometry

Standard angles — learn this table

The three identities (and their rearrangements)

Complementary angles — (90° − θ)

10 · Some Applications of Trigonometry

11 · Areas Related to Circles

12 · Surface Areas and Volumes

13 · Statistics

14 · Probability

How to use this sheet properly

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