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Maths & Science Formulas (Class 6-12)

Quick-reference formula sheets for Maths and Science, organised class-wise and chapter-wise to help you revise faster before exams.

Mensuration

  • Perimeter of square = 4 × side
  • Perimeter of rectangle = 2 × (l + b)
  • Area of square = side × side
  • Area of rectangle = l × b

Fractions & Ratio

  • Ratio a:b = a ÷ b
  • Equivalent fraction = (a×k)/(b×k)
  • Percentage = (Value/Total) × 100

Algebraic Expressions

  • (a+b)² = a² + 2ab + b²
  • (a−b)² = a² − 2ab + b²
  • a² − b² = (a+b)(a−b)

Perimeter & Area

  • Area of triangle = ½ × base × height
  • Area of parallelogram = base × height
  • Circumference of circle = 2πr

Algebraic Identities

  • (a+b)² = a² + 2ab + b²
  • (a−b)² = a² − 2ab + b²
  • (a+b)(a−b) = a² − b²
  • (x+a)(x+b) = x² + (a+b)x + ab

Mensuration

  • Surface area of cube = 6a²
  • Volume of cube = a³
  • Volume of cuboid = l × b × h
  • Area of trapezium = ½ × (a+b) × h

Polynomials & Algebra

  • (a+b)³ = a³ + 3a²b + 3ab² + b³
  • (a−b)³ = a³ − 3a²b + 3ab² − b³
  • a³+b³ = (a+b)(a²−ab+b²)
  • a³−b³ = (a−b)(a²+ab+b²)

Geometry & Circles

  • Heron's formula: Area = √[s(s−a)(s−b)(s−c)]
  • Angle in semicircle = 90°
  • Surface area of sphere = 4πr²
  • Volume of sphere = (4/3)πr³

Quadratic Equations

  • x = [−b ± √(b²−4ac)] / 2a
  • Sum of roots = −b/a, Product = c/a
  • Discriminant D = b² − 4ac

Trigonometry

  • sin²θ + cos²θ = 1
  • tanθ = sinθ/cosθ
  • 1 + tan²θ = sec²θ
  • 1 + cot²θ = cosec²θ

Trigonometric Functions

  • sin(A+B) = sinA cosB + cosA sinB
  • cos(A+B) = cosA cosB − sinA sinB
  • sin2A = 2 sinA cosA
  • cos2A = 1 − 2sin²A

Sequences, Sets & Binomial

  • nth term of AP: aₙ = a + (n−1)d
  • Sum of n terms of AP: Sₙ = n/2 [2a + (n−1)d]
  • (a+b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ

Calculus

  • d/dx(xⁿ) = nxⁿ⁻¹
  • ∫xⁿ dx = xⁿ⁺¹/(n+1) + C
  • d/dx(sinx) = cosx, d/dx(cosx) = −sinx
  • ∫eˣ dx = eˣ + C

Vectors & 3D Geometry

  • Direction cosines: l² + m² + n² = 1
  • Distance = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]

Measurement

  • 1 km = 1000 m
  • 1 m = 100 cm
  • 1 kg = 1000 g
  • Speed = Distance / Time

Basics of Living World

  • Components of food: carbs, proteins, fats, vitamins, minerals
  • Separation methods: sieving, filtration, evaporation

Heat & Electricity

  • °F = (°C × 9/5) + 32
  • Current flows from + to − terminal in a circuit

Physical & Chemical Changes

  • Acids turn blue litmus red
  • Bases turn red litmus blue
  • Neutralisation: Acid + Base → Salt + Water

Force & Pressure

  • Pressure = Force / Area
  • Thrust acts perpendicular to surface

Chemical Effects & Metals

  • Metal + Acid → Salt + Hydrogen gas
  • Electroplating uses electric current to coat metals

Motion & Force

  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as
  • Force = mass × acceleration

Gravitation & Work

  • Weight = mass × g
  • Work = Force × Displacement
  • Density = Mass / Volume

Electricity

  • V = IR (Ohm's Law)
  • P = VI = I²R
  • Series: R = R1+R2+R3
  • Parallel: 1/R = 1/R1+1/R2+1/R3

Light & Reflection

  • Mirror formula: 1/v + 1/u = 1/f
  • Magnification m = −v/u
  • Lens formula: 1/v − 1/u = 1/f

Physics: Laws of Motion

  • F = ma (Newton's Second Law)
  • Momentum p = mv
  • Impulse = Force × time = Δp

Chemistry: Mole Concept

  • Moles = Given mass / Molar mass
  • PV = nRT (Ideal Gas Equation)
  • Molarity = Moles of solute / Volume (L)

Physics: Electrostatics & Current

  • Coulomb's Law: F = kq₁q₂/r²
  • Electric field E = F/q
  • Capacitance C = Q/V

Chemistry & Biology Essentials

  • pH = −log[H⁺]
  • Rate of reaction = Δ[Concentration] / Δt
  • Mendel's Law of Segregation & Independent Assortment

Maths Sample Papers (Class 6-12)

Practice with model and previous years' sample papers for every class to build speed and accuracy before your exams.

Maths Sample Paper 1

Class 6 · Full Syllabus

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Maths Sample Paper 2

Class 6 · Full Syllabus

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Science Sample Paper 1

Class 6 · Full Syllabus

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Science Sample Paper 2

Class 6 · Full Syllabus

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Maths Sample Paper 1

Class 7 · Full Syllabus

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Maths Sample Paper 2

Class 7 · Full Syllabus

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Science Sample Paper 1

Class 7 · Full Syllabus

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Science Sample Paper 2

Class 7 · Full Syllabus

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Maths Sample Paper 1

Class 8 · Full Syllabus

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Maths Sample Paper 2

Class 8 · Full Syllabus

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Science Sample Paper 1

Class 8 · Full Syllabus

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Science Sample Paper 2

Class 8 · Full Syllabus

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Maths Sample Paper 1

Class 9 · Full Syllabus

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Maths Sample Paper 2

Class 9 · Full Syllabus

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Science Sample Paper 1

Class 9 · Full Syllabus

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Science Sample Paper 2

Class 9 · Full Syllabus

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Maths Sample Paper 1

Class 10 · Full Syllabus

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Maths Sample Paper 2

Class 10 · Full Syllabus

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Science Sample Paper 1

Class 10 · Full Syllabus

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Science Sample Paper 2

Class 10 · Full Syllabus

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Maths Sample Paper 1

Class 11 · Full Syllabus

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Maths Sample Paper 2

Class 11 · Full Syllabus

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Science Sample Paper 1

Class 11 · Full Syllabus

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Science Sample Paper 2

Class 11 · Full Syllabus

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Maths Sample Paper 1

Class 12 · Full Syllabus

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Maths Sample Paper 2

Class 12 · Full Syllabus

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Science Sample Paper 1

Class 12 · Full Syllabus

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Science Sample Paper 2

Class 12 · Full Syllabus

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CBSE / ICSE / BSEB Updates

Direct links to official CBSE, CISCE (ICSE/ISC) and BSEB (Bihar Board) resources for syllabus, datesheets, circulars, sample papers, previous year question papers and results.

Note: Always cross-check exam dates, syllabus changes and paper formats on the official board websites linked above, as schedules are updated periodically by CBSE, CISCE and BSEB.

Latest Blogs

Study tips, exam strategies and academic guidance written by our faculty to help students prepare smarter.

Study Tips

5 Effective Ways to Memorise Maths Formulas Before Exams

Struggling to remember formulas during exams is one of the most common problems students face. Flashcards, grouping and daily micro-revision can fix this fast...

Struggling to remember formulas during exams is one of the most common problems students face. The truth is, memorising a formula without understanding where it comes from rarely lasts beyond a few days. Start by writing every formula on small flashcards and revising them for just 10 minutes daily instead of cramming the night before. Group similar formulas together — for example, all algebraic identities in one card and all mensuration formulas in another — so your brain builds patterns rather than isolated facts. Solving 3-4 practice questions immediately after learning a formula helps convert short-term memory into long-term recall. Teaching the formula out loud to a friend or even to yourself is another underrated trick, as explaining forces you to actually understand the logic. Finally, revise your complete formula sheet once a week, even after the topic is over, so it stays fresh right up to exam day.
Faculty, ConceptLab Academy 5 min read
Exam Strategy

How to Attempt a Maths Board Exam Paper for Maximum Marks

Scoring well is not just about knowing the syllabus — it's about how you manage the paper. Here's a time-tested attempt strategy...

Scoring well in a maths board exam is not just about knowing the syllabus — it's about how you manage the paper. In the first 5 minutes, quickly scan the entire question paper and mark the questions you're most confident about. Attempt those first to build momentum and secure easy marks early. For long-answer questions, always show your steps clearly, since CBSE and ICSE both award step-marking even if the final answer is wrong. Never leave a question blank — attempting a formula or a partial method can still fetch you marks. Keep 10-15 minutes at the end purely for revision, checking silly calculation errors and units. Time yourself while practising sample papers at home so that pacing becomes second nature by the time you sit for the real exam.
Faculty, ConceptLab Academy 4 min read
CBSE Updates

What Changed in the CBSE Maths Syllabus This Year

CBSE has shifted focus from rote learning to competency-based, application-driven questions in line with NEP 2020...

CBSE reviews its curriculum periodically to align with NCF 2005 and NEP 2020, shifting the focus from rote memorisation towards competency-based and application-based questions. For maths, this means more case-study and real-life application questions instead of purely formula-based ones. Students are now expected to explain the reasoning behind a solution, not just arrive at the right number. It's important to prepare from the latest NCERT textbook edition, as older editions may not match the current chapter numbering or exercises. We recommend checking the official CBSE Academic website every few months for updated circulars, since minor syllabus revisions are announced there directly rather than through news articles. Staying updated early in the academic year avoids last-minute surprises closer to board exams.
Faculty, ConceptLab Academy 4 min read
ICSE Updates

ICSE vs CBSE Maths: Key Differences Students Should Know

Both boards share a similar core syllabus, but question framing, internal weightage and paper length differ quite a bit...

While both boards cover a similar core of algebra, geometry, and mensuration, the way questions are framed differs quite a bit. ICSE papers tend to be more detailed and lengthy, often requiring longer step-by-step derivations, while CBSE questions are generally more direct and increasingly application-based. ICSE also follows an 80:20 split between the written board exam and internal school assessment, so consistent classwork genuinely affects your final percentage. CBSE, on the other hand, weighs periodic tests and the final board exam differently depending on the class. If you're switching boards midway through school, focus first on practice papers from your new board rather than assuming your old preparation method will transfer directly — the presentation style matters as much as the concept itself.
Faculty, ConceptLab Academy 5 min read
Study Tips

Building a Daily Maths Practice Routine That Actually Works

Maths can't be learned by reading alone. A simple daily routine with an "error log" can transform your problem-solving speed...

Maths is a subject you cannot learn by reading alone — it has to be practised daily, even if only for 30 minutes. Start each session by redoing 2-3 problems from the previous day before moving to new material; this reinforces memory far better than jumping straight to something new. Keep a separate notebook exclusively for mistakes, where you rewrite any question you got wrong along with the correct method — this "error log" becomes one of the most powerful revision tools closer to exams. Avoid practising the same type of question repeatedly in one sitting; instead, mix topics so your brain learns to identify which method to apply, just like in an actual exam. Consistency matters more than intensity — a focused 30-minute daily routine will outperform an occasional 4-hour cramming session every time.
Faculty, ConceptLab Academy 4 min read
BSEB Updates

BSEB Matric & Inter Exam: Preparation Tips That Really Help

Bihar Board papers reward students who follow the official model paper pattern closely. Here's how to prepare smartly for BSEB...

BSEB (Bihar School Examination Board) exams follow their own paper pattern, and students who practise directly from the official model papers usually perform noticeably better than those who rely only on generic guides. Start by downloading the latest model papers from the BSEB website and solving them under exam-like time limits, since BSEB papers often include a mix of objective and subjective questions with strict time management needs. Focus heavily on NCERT and BSEB-prescribed textbooks rather than assuming other state board books will fully match the syllabus. Keep your admit card, previous mark sheets and required documents ready well in advance, as BSEB deadlines for form corrections and admit card downloads are strict and rarely extended. Finally, revise objective-type questions from previous year papers regularly, since a good chunk of BSEB's Matric and Inter papers are objective-based and can significantly boost your overall score if practised consistently.
Faculty, ConceptLab Academy 5 min read
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