Class 10 Maths Formula Sheet, Weightage & Board Guide 2026–27

Preparation Framework

The Preparation Framework That Actually Builds Score — Not Just Coverage

Maths is the one subject where effort and result diverge most dramatically from each other — and the reason is almost always the same. Students read solved examples. They think "I understand this." They move to the next chapter. And when the exam arrives, they discover that understanding a solved example and being able to solve a new problem independently under time pressure are completely different skills. Coverage is not preparation. Performance is preparation.

Study by weightage, not by chapter order

Don't start from Chapter 1 and work forward. Start from Algebra (20 marks), then Geometry (15 marks), then Trigonometry (12 marks). These three units carry nearly 60% of the paper — mastering them first means your highest-value marks are secured before you reach the lower-weightage units. Start with high-mark chapters: Algebra, Geometry, Trigonometry, Statistics. These chapters pull the most weight.

Produce answers — don't just read them

For every concept you study, attempt at least 3 questions without looking at solutions. Read the solution only after attempting. Then close the book and attempt again from memory. This production habit — not reading comprehension — is what builds the ability to solve problems under exam conditions in 3 hours. Step marking is usually used to give marks for correct steps, even if the final answer is wrong. Show every step. Always.

Treat every wrong answer as a data point

Every incorrect answer in a practice set or mock test contains specific information: which concept you misunderstood, which formula you confused, which step you skipped. That information is the most valuable study material you have. Log every wrong answer by unit and error type. Reattempt within 48 hours. Verify you can produce the correct solution independently. Then move on. Not before.

Build a rotation system — not a completion system

Don't study a unit until it feels "done" and then move on permanently. Build a weekly rotation: high-weightage units (Algebra, Geometry, Trigonometry) get 3 practice sessions per week each. Medium-weightage units (Statistics, Mensuration) get 2 sessions. Low-weightage units (Coordinate Geometry, Number Systems) get 1. This rotation means every unit is practised regularly — and high-value units compound across the full preparation period.

Practise under timed conditions from month 3 onwards

From October onwards, take at least one full Maths mock test per week under strict timed conditions — 3 hours, no interruptions, no open books. This builds two things simultaneously: pace (you discover which question types take too long) and confidence (you discover you can actually complete a paper). Both are necessary. Neither comes from untimed practice. Allocate 15 minutes for reading the paper, 2 hours 30 minutes for solving, and 15 minutes for revising answers.

Target case-based questions specifically

Case-based questions carry 12 marks in the 2025–26 paper (3 questions × 4 marks). The three Case-Based questions will be from Arithmetic Progressions, Coordinate Geometry, and Applications of Trigonometry. These chapters are fixed for case studies. Practise reading a scenario and identifying which formula or concept applies — this is a learnable pattern that rewards preparation and punishes last-minute cramming.

Common Score-Loss Patterns

Four Mistakes That Cost Class 10 Maths Students the Most Marks

These are not abstract mistakes. They are the specific, recurring patterns observed across thousands of Class 10 Maths board papers — the ones that separate students who score 68% from students who score 88% on the same paper.

01 Mistake 1

Skipping steps in long-answer questions

CBSE uses step marking — every correct step carries marks independently of the final answer. A student who writes the correct formula and correct substitution but makes a calculation error at the end typically earns 2 out of 3 marks. A student who writes only the final answer — even if correct — may earn just 1 mark.

Fix

Write every step. Formula → substitution → working → answer with units. No shortcuts in 3-mark and 5-mark questions.

02 Mistake 2

Memorising formulas without understanding when to use them

Students who memorise the quadratic formula without understanding what it does will apply it to every quadratic — including ones that factorise easily in 30 seconds. Students who understand the concept choose the fastest method. Understanding formula selection is a distinct skill from knowing the formulas.

Fix

For every formula, practise at least 5 questions of different types. Understand what conditions trigger each method.

03 Mistake 3

Ignoring Geometry proofs until the last week

Geometry proofs (Triangles, Circles) carry 15 marks and require a specific writing structure — Given, To Prove, Construction, Proof. Students who haven't practised writing full proofs with diagram and logical sequence consistently lose 4–6 marks in this section that are entirely preventable.

Fix

Write 2 full geometry proofs per week from July onwards. The format becomes automatic — and automatic is fast in the exam.

04 Mistake 4

Treating Statistics as easy and leaving it for last

Statistics carries 11 marks and the grouped data calculations (mean by all three methods, median, mode) are straightforward — but only if practised. Students who assume familiarity means readiness regularly lose 3–4 marks on calculation errors in mean, or by choosing the wrong method for the wrong question type.

Fix

Practise one complete Statistics set (mean + median + mode) every week. Each method has a distinct trigger — know which one to use when.

Performance Analysis

Your Mock Test Score Is Noise. This Is the Signal.

A Maths mock test score of 54 out of 80 tells you almost nothing useful. What you need is the breakdown underneath it — which units are costing you marks and which are already solid. Without this, the next study session goes to whichever chapter feels most comfortable, not the one actually losing you marks.

Noise

54 / 80

Your mock test score. Tells you 26 marks were lost. Tells you nothing about which units, which error types, or what to do next session.

Signal

Unit map

Algebra 71% · Geometry 43% · Trigonometry 58% · Statistics 88%. Now you know exactly where tomorrow's study session should go.

Genelis Performance Map

What a Genelis weak area map looks like after a Maths mock test

Statistics — grouped data

88%

Algebra — Quadratic Equations

71%

Trigonometry — identities

58%

Geometry — Triangles proofs

43%

Next session: Geometry — Triangles proofs (43%). Not Statistics (already 88%). Every session directed by data, not comfort.

Genelis is an AI-powered personalized learning platform built on Adaptive Personalized Intelligence. After every Maths mock test or practice session, Genelis builds this unit-level accuracy map automatically — tracking your performance separately across all 7 units, identifying which specific concepts are costing you marks, and directing your next session accordingly. Every wrong answer is logged to your wrong-question notebook, tagged by unit and question type, and queued for reattempt through the Genelis Learning Loop™.

Step 1 Attempt Maths mock

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Step 2 Unit-level gap detected

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Step 3 AI notes for weak concept

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Step 4 Wrong Qs auto-logged

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Step 5 Reattempt those questions

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Result Gap closed. Map updates. ✓

Start your personalised Class 10 Maths study plan on Genelis — free →

Complete Formula Reference

Complete Class 10 Maths Formula Sheet — All 7 Units, Every Formula You Need

This is your one-stop formula reference for every chapter in CBSE Class 10 Maths 2025–26. The right way to use this section: read it once carefully. Then close this page and reproduce every formula from memory on paper. Check what you missed. Return to those formulas specifically. Repeat daily in the final 6 weeks before boards. The formulas you can write from memory in under 10 seconds are the ones that won't cost you time or marks in February.

Read

Understand what each formula calculates and when it applies.

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Recall

Close the page and reproduce the formula from memory.

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Apply

Use it independently in different question types.

Algebra — Polynomials, Linear Equations, Quadratic Equations, Arithmetic Progressions

Highest-weightage unit in the Class 10 Maths theory paper

20 marks

Polynomials

Sum of roots (α+β)

α + β = −b/a For quadratic ax² + bx + c = 0

Product of roots (αβ)

α × β = c/a For quadratic ax² + bx + c = 0

Division algorithm

Dividend = Divisor × Quotient + Remainder

Pair of Linear Equations

Consistent system

a₁/a₂ ≠ b₁/b₂ Unique solution. Lines intersect at exactly one point.

Infinitely many solutions

a₁/a₂ = b₁/b₂ = c₁/c₂ Lines are coincident.

No solution

a₁/a₂ = b₁/b₂ ≠ c₁/c₂ Lines are parallel.

Quadratic Equations

Quadratic formula

x = [−b ± √(b²−4ac)] / 2a For ax² + bx + c = 0; use when factorisation is not straightforward.

Discriminant (D)

D = b² − 4ac D > 0: two real roots · D = 0: one repeated root · D < 0: no real roots

Arithmetic Progressions

nth term (aₙ)

aₙ = a + (n−1)d a = first term, d = common difference, n = term number

Sum of n terms (Sₙ)

Sₙ = n/2 × [2a + (n−1)d]

Sₙ when last term is known

Sₙ = n/2 × (a + l) l = last term

Common difference

d = aₙ − aₙ₋₁ Difference between any two consecutive terms

Geometry — Triangles & Circles

Proofs, theorem application and structured reasoning

15 marks

Triangles

Basic Proportionality Theorem

DE ∥ BC ⟹ AD/DB = AE/EC Also called Thales' theorem — appears in proof questions every year.

Pythagoras Theorem

AC² = AB² + BC² In right triangle ABC, right-angled at B. Converse: if AC² = AB² + BC², angle B = 90°.

Area similarity ratio

ar(△ABC) / ar(△DEF) = (AB/DE)² = (BC/EF)² = (AC/DF)² For similar triangles — ratio of areas equals square of ratio of corresponding sides.

AA similarity criterion

∠A = ∠D and ∠B = ∠E ⟹ △ABC ∼ △DEF

Circles

Tangent-radius

Tangent ⊥ radius at point of contact Angle between tangent and radius = 90° — foundational for all circle proofs.

Equal tangents

PA = PB Tangents drawn from an external point P to a circle are equal in length.

Angle in alternate segment

∠BAT = ∠ACB Angle between tangent and chord = angle in alternate segment.

⚠️ Geometry proof structure — non-negotiable: Every proof must follow the format: Given → To Prove → Construction (if needed) → Proof (step by step with reasons). Missing the "reason" for each step in a proof costs 1 mark per step. Write reasons in every line.

Trigonometry — Ratios, Identities & Applications (Heights and Distances)

Most formula-dense unit in Class 10 Mathematics.

12 Marks

The Six Ratios — Defined for Angle θ in a Right Triangle

sin θ / cos θ / tan θ

sin θ = Opposite/Hypotenuse · cos θ = Adjacent/Hypotenuse · tan θ = Opposite/Adjacent

cosec θ / sec θ / cot θ

cosec θ = 1/sin θ · sec θ = 1/cos θ · cot θ = 1/tan θ

Standard Angle Values — Memorise This Table Cold

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

Memory trick for sin: 0, 1/2, 1/√2, √3/2, 1 = √0/2, √1/2, √2/2, √3/2, √4/2. cos is sin in reverse. tan = sin/cos.

Pythagorean Identities — The Three You Must Know

Identity 1

sin²θ + cos²θ = 1 Derived from: sin²θ = 1−cos²θ · cos²θ = 1−sin²θ

Identity 2

1 + tan²θ = sec²θ Derived from: tan²θ = sec²θ−1 · sec²θ−tan²θ = 1

Identity 3

1 + cot²θ = cosec²θ Derived from: cot²θ = cosec²θ−1 · cosec²θ−cot²θ = 1

Heights & Distances

tan θ application

tan θ = height / horizontal distance Angles of elevation/depression should be only 30°, 45° and 60°. Always draw a diagram first — it prevents setup errors.

Coordinate Geometry

Formula-direct and high-scoring

6 marks

Distance formula

d = √[(x₂−x₁)² + (y₂−y₁)²] Distance between points (x₁, y₁) and (x₂, y₂)

Section formula

P = [(mx₂ + nx₁)/(m+n) , (my₂ + ny₁)/(m+n)] Point P dividing (x₁,y₁) to (x₂,y₂) in ratio m:n internally

Midpoint formula

M = [(x₁+x₂)/2 , (y₁+y₂)/2] Special case of section formula with m:n = 1:1

Area of triangle

Area = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| For vertices (x₁,y₁), (x₂,y₂), (x₃,y₃). If area = 0, points are collinear.

Coordinate Geometry is an easy and scoring topic, as questions are about using formulas, which is quick. These 4 formulas cover the entire unit — master them.

Application-heavy and formula-based

10 marks

Areas Related to Circles

Area of circle

A = πr²

Circumference

C = 2πr

Area of sector

A = (θ/360°) × πr² θ = angle at centre in degrees

Length of arc

l = (θ/360°) × 2πr

Area of segment

Area of segment = Area of sector − Area of triangle Most common Mensuration question type in boards

Surface Areas & Volumes — All Solids

Cylinder

CSA = 2πrh · TSA = 2πr(r+h) · Volume = πr²h

Cone

CSA = πrl · TSA = πr(r+l) · Volume = ⅓πr²h · l = √(r²+h²)

Sphere

SA = 4πr² · Volume = (4/3)πr³

Hemisphere

CSA = 2πr² · TSA = 3πr² · Volume = (2/3)πr³

Frustum of cone

CSA = πl(r₁+r₂) · Volume = (πh/3)(r₁²+r₂²+r₁r₂) · l = √[h²+(r₁−r₂)²]

Statistics & Probability

Formulaic and learnable

11 marks

Mean — Three Methods (Know When to Use Each)

Direct method

x̄ = Σfᵢxᵢ / Σfᵢ Use when class midpoints (xᵢ) are small and calculations are manageable

Assumed mean method

x̄ = a + (Σfᵢdᵢ / Σfᵢ) where dᵢ = xᵢ − a Use when class midpoints are large numbers. Choose a = midpoint of middle class as assumed mean.

Step deviation method

x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h where uᵢ = (xᵢ−a)/h Most efficient for equal class intervals. h = class width.

Median & Mode from Grouped Data

Median

Median = l + [(n/2 − cf) / f] × h l = lower boundary of median class · cf = cumulative frequency before median class · f = frequency of median class · h = class width · n = Σf

Mode

Mode = l + [(f₁−f₀) / (2f₁−f₀−f₂)] × h l = lower boundary of modal class · f₁ = freq of modal class · f₀ = freq of preceding class · f₂ = freq of succeeding class

Empirical relationship

3 Median = Mode + 2 Mean Useful for verification and for finding one measure when the other two are known

Probability

Basic probability

P(E) = Number of favourable outcomes / Total number of outcomes

Complementary event

P(not E) = 1 − P(E) P(E) + P(not E) = 1 always. Both values lie between 0 and 1 inclusive.

Number Systems — Real Numbers

Conceptual and direct

6 marks

Fundamental Theorem

Every composite number can be expressed as a unique product of prime numbers Used in HCF and LCM questions — always show the prime factorisation step

HCF × LCM

HCF(a,b) × LCM(a,b) = a × b Only valid for two numbers. This relationship is directly tested in 2-mark questions.

Euclid's Division Lemma

a = bq + r where 0 ≤ r < b a = dividend, b = divisor, q = quotient, r = remainder. Apply repeatedly to find HCF.

Rational decimal condition

p/q is a terminating decimal if and only if q = 2ᵐ × 5ⁿ (m, n ≥ 0) If denominator has any other prime factor, the decimal is non-terminating repeating.

Number Systems questions are typically direct — 1-mark or 2-mark. Secure all 6 marks here before boards. These are the most time-efficient marks in the paper.

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How to use this formula sheet for maximum retention

Don't read it passively. After reading each unit's formulas, close this page and write every formula from memory on a blank sheet. Check what you missed. Return to only those formulas. Repeat this process weekly from September onwards. By January, the formulas should write themselves — with no hesitation, no checking, no lost seconds in the exam.

Frequently Asked Questions

Which is the most important chapter in Class 10 Maths CBSE 2026–27?

Highest weightage units: Algebra (20 marks) and Geometry (15 marks). Within the 2025–26 blueprint, Triangles and Introduction to Trigonometry have the highest individual weightage at 8 marks each. For overall unit priority: Algebra (20), Geometry (15), and Trigonometry (12) together account for 59% of the paper — master these three units before investing heavily in others.

What is the chapter-wise marks distribution for Class 10 Maths CBSE 2025–26?

The curriculum distributes 80 marks across various units, with Algebra receiving 20 marks, Geometry 15 marks, Trigonometry 12 marks, Mensuration 10 marks, and Statistics and Probability 11 marks. Coordinate Geometry carries 6 marks and Number Systems 6 marks. Chapter-wise distribution within units can vary slightly paper to paper — unit-wise weightage is fixed by CBSE and more reliable for planning.

How do I prepare for Class 10 Maths boards effectively?

Study by unit weightage — prioritise Algebra, Geometry, and Trigonometry before lower-weightage units. Produce answers independently rather than reading solved examples. Take weekly timed mock tests from October. Categorise every wrong answer by error type and reattempt within 48 hours. Build a formula sheet and reproduce it from memory daily in the final 6 weeks. Start with high-mark chapters: Algebra, Geometry, Trigonometry, Statistics. These chapters pull the most weight.

What are the most important formulas for Class 10 Maths CBSE?

The must-know formulas span all 7 units: Algebra — quadratic formula, discriminant, AP nth term and sum; Geometry — BPT, Pythagoras, area ratio for similar triangles; Trigonometry — all 6 ratios, standard angle table, three Pythagorean identities; Coordinate Geometry — distance, section, and area formulas; Mensuration — sector area, arc length, all solid surface areas and volumes; Statistics — mean by all three methods, median and mode from grouped data formula; Number Systems — HCF×LCM relationship, Euclid's lemma. All formulas are in the complete formula sheet above.

How should I use mock tests for Class 10 Maths preparation?

Use mock tests as diagnostic tools, not practice runs. After every test: categorise every wrong answer into conceptual gap, formula error, or careless mistake — before reading the solution. Reattempt all wrong questions within 48 hours without looking at the solution. Log unresolved gaps. Use the results to direct next week's revision to your lowest-accuracy unit — not the most comfortable one. Solve PYQs and sample papers — not once, not twice, multiple times. Track your mistakes. Each error is a clue. Fix it.

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Class 10 Maths 2026–27: The Only Guide You Need — Strategy, Weightage & Complete Formula Sheet