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Class 10 Maths — Complete Formula Sheet (2026-27)

Every formula from all 14 chapters, memory tricks that actually stick, and the exact question patterns CBSE repeats every year.

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Option 1 (H1): Class 10 Maths Formula Sheet 2026-27 — All 14 Chapters in One Page
Meta: Free CBSE Class 10 Maths formula sheet covering all 14 chapters — quick revision cheatsheet, memory tricks, and most repeated board question patterns.

Option 2 (H1): CBSE Class 10 Maths All Formulas PDF-Style Cheatsheet (2026-27 Syllabus)
Meta: Every Class 10 Maths formula you need before the board exam — Algebra, Trigonometry, Mensuration, Statistics & Probability, with pro-tips for each chapter.

Option 3 (H1): Class 10 Maths Quick Revision Formulas — Back Bencher Class Edition
Meta: Struggling to remember Class 10 Maths formulas before the exam? Here's every formula, memory trick, and exam pattern from all 14 chapters in one simple page.

Formulas Bhool Jaate Ho? Chill, Hum Hain Na 🎸

Exam se ek raat pehle formula yaad karne ki tension har back bencher jaanta hai. Isliye ye page bana hai — Class 10 Maths ke saare 14 chapters ke formulas, ek hi jagah, bina kisi bhaari-bharkam jargon ke. Scroll karo, jo chapter revise karna hai wahan jump karo, aur exam hall mein confidently likho.

Quick Jump — All 14 Chapters

Ch 1: Real Numbers Ch 2: Polynomials Ch 3: Pair of Linear Equations in Two Variables Ch 4: Quadratic Equations Ch 5: Arithmetic Progressions Ch 6: Triangles Ch 7: Coordinate Geometry Ch 8: Introduction to Trigonometry Ch 9: Some Applications of Trigonometry Ch 10: Circles Ch 11: Areas Related to Circles Ch 12: Surface Areas and Volumes Ch 13: Statistics Ch 14: Probability

Chapter-Wise Formulas, Tricks & Exam Patterns

Chapter 1

Real Numbers — All Formulas

Euclid's Division Algorithm: a = bq + r, where 0 ≤ r < b

HCF × LCM = Product of the two numbers (for two positive integers)

If p is prime and p | a², then p | a

A rational number p/q has a terminating decimal expansion if q = 2^m × 5^n (m, n are non-negative integers)

💡 Pro-Tip / Memory Trick:

Remember 'HCF × LCM = Product' only works for TWO numbers, never for three or more — this trips up half the class every year.

📝 Most Repeated Board Question Pattern:

Find HCF/LCM using prime factorisation, or prove √2, √3, √5 etc. are irrational using contradiction method (2-3 marks).

Chapter 2

Polynomials — All Formulas

For quadratic ax² + bx + c: Sum of zeroes (α+β) = -b/a, Product of zeroes (αβ) = c/a

For cubic ax³ + bx² + cx + d: α+β+γ = -b/a, αβ+βγ+γα = c/a, αβγ = -d/a

Division Algorithm for polynomials: p(x) = g(x) × q(x) + r(x)

💡 Pro-Tip / Memory Trick:

Sign trick: the sign in front of b/a and d/a always flips (negative), but c/a stays positive. Say it out loud as '-b/a, +c/a, -d/a' while revising.

📝 Most Repeated Board Question Pattern:

Find a quadratic polynomial when sum and product of zeroes are given, or verify the relationship between zeroes and coefficients (2-3 marks).

Chapter 3

Pair of Linear Equations in Two Variables — All Formulas

a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

Unique solution (intersecting lines): a1/a2 ≠ b1/b2

No solution (parallel lines): a1/a2 = b1/b2 ≠ c1/c2

Infinite solutions (coincident lines): a1/a2 = b1/b2 = c1/c2

Cross-multiplication method: x/(b1c2-b2c1) = y/(c1a2-c2a1) = 1/(a1b2-a2b1)

💡 Pro-Tip / Memory Trick:

Memory line: 'Different slope = one point meet, same slope different height = never meet, same slope same height = always meet' — matches unique/no-solution/infinite-solutions in order.

📝 Most Repeated Board Question Pattern:

Solve pairs by substitution/elimination, or determine the nature of solutions without solving (checking ratio of coefficients) — a very common 2-mark shortcut question.

Chapter 4

Quadratic Equations — All Formulas

Standard form: ax² + bx + c = 0 (a ≠ 0)

Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a

Discriminant: D = b² - 4ac

D > 0 → two distinct real roots; D = 0 → two equal real roots; D < 0 → no real roots

💡 Pro-Tip / Memory Trick:

D tells the 'drama' of the roots — Positive D = two different endings, Zero D = one repeated ending, Negative D = no real ending (imaginary). D for Drama.

📝 Most Repeated Board Question Pattern:

Solve word problems (ages, speed-distance-time, area) forming a quadratic equation, then find roots using the formula or factorisation (3-5 marks).

Chapter 5

Arithmetic Progressions — All Formulas

nth term: an = a + (n-1)d

Sum of n terms: Sn = n/2 [2a + (n-1)d]

Sum of n terms (alternate): Sn = n/2 (a + l), where l is the last term

Common difference: d = a(n) - a(n-1)

💡 Pro-Tip / Memory Trick:

If you're given the last term instead of 'd', always use Sn = n/2(a+l) directly — saves a full extra step of finding d first.

📝 Most Repeated Board Question Pattern:

Find the nth term or sum of n terms given some conditions (e.g., sum of first 14 terms, or which term equals a given value) — extremely common 3-mark numerical.

Chapter 6

Triangles — All Formulas

Basic Proportionality Theorem (Thales): if DE || BC, then AD/DB = AE/EC

Pythagoras Theorem: (Hypotenuse)² = (Base)² + (Perpendicular)²

Area of similar triangles ratio = (ratio of corresponding sides)² = (ratio of corresponding altitudes)² = (ratio of corresponding medians)²

AA, SSS, SAS similarity criteria for triangles

💡 Pro-Tip / Memory Trick:

For 'area of similar triangles' questions, always square the side ratio first — students forget the square and just carry forward the linear ratio, losing the answer.

📝 Most Repeated Board Question Pattern:

Prove two triangles similar using AA/SSS/SAS, then use the similarity to find a missing side or the ratio of areas (3 marks).

Chapter 7

Coordinate Geometry — All Formulas

Distance formula: d = √[(x2-x1)² + (y2-y1)²]

Section formula: (x,y) = [(m x2 + n x1)/(m+n), (m y2 + n y1)/(m+n)]

Midpoint formula: (x,y) = [(x1+x2)/2, (y1+y2)/2]

Area of triangle = ½ |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|

💡 Pro-Tip / Memory Trick:

Midpoint is just the section formula with m:n = 1:1 — don't memorise it separately, just plug m=n=1 into the section formula if you forget it under pressure.

📝 Most Repeated Board Question Pattern:

Find the distance between two points, or find a point dividing a line segment in a given ratio, or check if three points are collinear (area = 0) — 2-3 marks.

Chapter 8

Introduction to Trigonometry — All Formulas

sin θ = Perpendicular/Hypotenuse, cos θ = Base/Hypotenuse, tan θ = Perpendicular/Base

tan θ = sin θ / cos θ

Reciprocal ratios: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ

Identity 1: sin²θ + cos²θ = 1

Identity 2: 1 + tan²θ = sec²θ

Identity 3: 1 + cot²θ = cosec²θ

💡 Pro-Tip / Memory Trick:

Remember 'Pandit Badri Prasad Har Har Bole' for sin, cos, tan = Perpendicular/Hypotenuse, Base/Hypotenuse, Perpendicular/Base — a classic trick that never fails in the exam hall.

📝 Most Repeated Board Question Pattern:

Prove a trigonometric identity using the three Pythagorean identities, or evaluate an expression using standard angle values (0°, 30°, 45°, 60°, 90°) — 3 marks, very frequent.

Chapter 9

Some Applications of Trigonometry — All Formulas

Angle of elevation = angle formed looking UP from horizontal

Angle of depression = angle formed looking DOWN from horizontal

Height/distance found using tan θ = opposite/adjacent in a right triangle formed by the line of sight

💡 Pro-Tip / Memory Trick:

Angle of elevation and angle of depression between the same two points are always EQUAL (alternate angles) — this single fact solves half the height-and-distance problems instantly.

📝 Most Repeated Board Question Pattern:

Height of a tower/building/tree given the angle of elevation from a point on the ground, often combined with a second angle after moving closer — 3-5 marks word problem.

Chapter 10

Circles — All Formulas

A tangent to a circle is perpendicular to the radius at the point of contact

Lengths of tangents drawn from an external point to a circle are equal

Number of tangents from a point: 0 if inside circle, 1 if on circle, 2 if outside circle

💡 Pro-Tip / Memory Trick:

Whenever a tangent is mentioned in a question, immediately draw the radius to the point of contact and mark the 90° angle — this single step unlocks most circle proof questions.

📝 Most Repeated Board Question Pattern:

Prove tangent-related properties, or find the length of a tangent from an external point using the Pythagoras theorem (radius, tangent, and distance to centre form a right triangle) — 2-3 marks.

Chapter 11

Areas Related to Circles — All Formulas

Area of circle = πr²

Circumference of circle = 2πr

Area of sector = (θ/360) × πr²

Length of arc = (θ/360) × 2πr

Area of segment = Area of sector - Area of corresponding triangle

💡 Pro-Tip / Memory Trick:

θ/360 is the 'fraction of the pizza' — always figure out what fraction of the full circle the sector represents first, then multiply by the full circle's area or circumference.

📝 Most Repeated Board Question Pattern:

Find the area of a sector/segment given the radius and angle, or find the area of a combination of a triangle and a circle/semicircle (5 marks, high-value question).

Chapter 12

Surface Areas and Volumes — All Formulas

Cube: Surface Area = 6a², Volume = a³

Cuboid: Surface Area = 2(lb+bh+hl), Volume = lbh

Cylinder: Curved SA = 2πrh, Total SA = 2πr(h+r), Volume = πr²h

Cone: Curved SA = πrl, Total SA = πr(l+r), Volume = (1/3)πr²h, l = √(r²+h²)

Sphere: Surface Area = 4πr², Volume = (4/3)πr³

Hemisphere: Curved SA = 2πr², Total SA = 3πr², Volume = (2/3)πr³

💡 Pro-Tip / Memory Trick:

For 'combination of solids' questions (a cone on a hemisphere, a cylinder with hemispheres on both ends), NEVER add the flat circular faces where two solids join — only the curved/visible surfaces count. This is the single biggest mark-loser in this chapter.

📝 Most Repeated Board Question Pattern:

Find the surface area or volume of a combination of two or more solids (cone mounted on a cylinder or hemisphere is the most repeated 5-mark question in recent years).

Chapter 13

Statistics — All Formulas

Mean (Direct method): x̄ = Σfixi / Σfi

Mean (Assumed mean method): x̄ = a + (Σfidi / Σfi), where di = xi - a

Mode = l + [(f1-f0)/(2f1-f0-f2)] × h

Median = l + [(n/2 - cf)/f] × h

💡 Pro-Tip / Memory Trick:

For mode and median formulas, always identify the correct class FIRST (modal class = highest frequency, median class = where cumulative frequency crosses n/2) before plugging in numbers — most calculation errors come from picking the wrong class.

📝 Most Repeated Board Question Pattern:

Find mean, median, and mode of grouped data from a frequency distribution table — appears almost every year as a 3-5 mark question.

Chapter 14

Probability — All Formulas

Probability of an event: P(E) = Number of favourable outcomes / Total number of outcomes

P(E) + P(not E) = 1, so P(not E) = 1 - P(E)

0 ≤ P(E) ≤ 1

💡 Pro-Tip / Memory Trick:

Always list the total sample space carefully first (all outcomes of a die, coin, or deck of cards) before counting favourable outcomes — most probability mistakes come from miscounting the total, not the formula itself.

📝 Most Repeated Board Question Pattern:

Probability questions involving a single die, two dice, a deck of 52 cards, or coloured balls in a bag — 2-3 marks, direct application of the formula.

⚡ 5-Minute Quick Revision Cheatsheet

High-yield summary — scan this table one last time before you walk into the exam hall.

Chapter	Key Formula	Quick Trick
1. Real Numbers	Euclid's Division Algorithm: a = bq + r, where 0 ≤ r < b	Remember 'HCF × LCM = Product' only works for TWO numbers, never for t...
2. Polynomials	For quadratic ax² + bx + c: Sum of zeroes (α+β) = -b/a, Product of zeroes (αβ) = c/a	Sign trick: the sign in front of b/a and d/a always flips (negative), ...
3. Pair of Linear Equations in Two Variables	a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0	Memory line: 'Different slope = one point meet, same slope different h...
4. Quadratic Equations	Standard form: ax² + bx + c = 0 (a ≠ 0)	D tells the 'drama' of the roots — Positive D = two different endings,...
5. Arithmetic Progressions	nth term: an = a + (n-1)d	If you're given the last term instead of 'd', always use Sn = n/2(a+l)...
6. Triangles	Basic Proportionality Theorem (Thales): if DE \|\| BC, then AD/DB = AE/EC	For 'area of similar triangles' questions, always square the side rati...
7. Coordinate Geometry	Distance formula: d = √[(x2-x1)² + (y2-y1)²]	Midpoint is just the section formula with m:n = 1:1 — don't memorise i...
8. Introduction to Trigonometry	sin θ = Perpendicular/Hypotenuse, cos θ = Base/Hypotenuse, tan θ = Perpendicular/Base	Remember 'Pandit Badri Prasad Har Har Bole' for sin, cos, tan = Perpen...
9. Some Applications of Trigonometry	Angle of elevation = angle formed looking UP from horizontal	Angle of elevation and angle of depression between the same two points...
10. Circles	A tangent to a circle is perpendicular to the radius at the point of contact	Whenever a tangent is mentioned in a question, immediately draw the ra...
11. Areas Related to Circles	Area of circle = πr²	θ/360 is the 'fraction of the pizza' — always figure out what fraction...
12. Surface Areas and Volumes	Cube: Surface Area = 6a², Volume = a³	For 'combination of solids' questions (a cone on a hemisphere, a cylin...
13. Statistics	Mean (Direct method): x̄ = Σfixi / Σfi	For mode and median formulas, always identify the correct class FIRST ...
14. Probability	Probability of an event: P(E) = Number of favourable outcomes / Total number of outcomes	Always list the total sample space carefully first (all outcomes of a ...

⚠️ Common Mistakes to Avoid in the Exam Hall

Sign errors in coefficient formulas — forgetting the negative sign in α+β = -b/a or α+β+γ = -b/a costs easy marks in Polynomials.
Forgetting to square the ratio in similar triangles' area questions — area ratio is (side ratio)², not the side ratio itself.
Adding extra circular faces in combination-of-solids surface area questions — joined flat faces are hidden, not counted.
Mixing up modal class and median class in Statistics — modal class has the highest frequency, median class is where cumulative frequency crosses n/2. These are usually NOT the same class.
Using degrees and radians interchangeably without converting — always double check whether a trigonometry/mensuration question expects degrees before plugging into θ/360.

❓ FAQs — Class 10 Maths Formulas

How many chapters are there in CBSE Class 10 Maths for 2026-27?

There are 14 chapters in the current CBSE Class 10 Maths syllabus, after the Constructions chapter was removed in the latest rationalisation.

Which chapter has the highest weightage in Class 10 Maths board exam?

Algebra (Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions) generally carries the highest combined weightage, followed closely by Geometry and Trigonometry.

How to memorise Class 10 Maths formulas fast before the exam?

Use short memory tricks and mnemonics (like "Pandit Badri Prasad Har Har Bole" for trigonometric ratios) instead of rote memorisation, and practise writing formulas by hand rather than only reading them.

Is Class 10 Maths formula sheet enough to score well, or do I need to solve problems too?

A formula sheet is a strong revision tool, but scoring well requires practising NCERT problems and previous year questions so you know exactly how each formula gets applied in different question patterns.

Are Class 10 Maths formulas the same for Standard and Basic Maths papers?

Yes, both Standard (Code 041) and Basic (Code 241) papers follow the same syllabus and formulas — the difference lies in the difficulty level and question pattern, not the formulas themselves.

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