About Important Questions for CBSE Class 8 Maths — Chapter-wise
Class 8 Mathematics is the pivotal year where abstract concepts like algebra, geometry, and mensuration step up considerably in depth. Students who practice strategically — focusing on the questions that actually appear in exams rather than reading every line passively — consistently outperform peers who put in equal hours without direction.This guide breaks down every chapter of the CBSE Class 8 Maths syllabus (as per the latest NCERT textbook), highlights the most important questions from each, and explains why those questions matter — the kind of insight you normally get from a private tutor.
This Page cuts through that noise. Read the NCERT textbooks and solve questions with the help of NCERT solutions for NCERT solutions for class 8 and NCERT solutions for class 8 Exemplar check the respective pages.
Find the PDF of Important Questions for Class 8 Maths – Chapter-wise
Chapter-wise Marks Weightage at a Glance
Before diving into important questions for class 8, understand how the syllabus is distributed. The table below reflects the approximate weightage schools follow for the annual exam:
Chapter No. | Chapter Name | Unit | Approx. Marks |
|---|---|---|---|
1 | Rational Numbers | Number Systems | 8–10 |
2 | Linear Equations in One Variable | Algebra | 10–12 |
3 | Understanding Quadrilaterals | Geometry | 8–10 |
4 | Practical Geometry | Geometry | 5–6 |
5 | Data Handling | Statistics | 6–8 |
6 | Squares and Square Roots | Number Systems | 7–9 |
7 | Cubes and Cube Roots | Number Systems | 5–6 |
8 | Comparing Quantities | Arithmetic | 10–12 |
9 | Algebraic Expressions and Identities | Algebra | 8–10 |
10 | Visualising Solid Shapes | Geometry | 4–5 |
11 | Mensuration | Mensuration | 12–15 |
12 | Exponents and Powers | Number Systems | 5–6 |
13 | Direct and Inverse Proportions | Arithmetic | 6–8 |
14 | Factorisation | Algebra | 6–8 |
15 | Introduction to Graphs | Graphs | 5–6 |
16 | Playing with Numbers | Number Systems | 4–5 |
Strategy Note: Chapters 2, 8, 9, 11, and 14 together carry nearly 45–50% of total marks. These deserve the most focused practice — especially multi-step problems and word problems.
Chapter 1 — Rational Numbers
This chapter extends the number line concept to include negative fractions and establishes key properties — commutativity, associativity, and distributivity — across rational numbers. Examiners typically test these properties both directly and through numerical verification.
Important Questions
Represent −3/7 and 5/9 on a number line and find three rational numbers between them.
Verify that multiplication is distributive over addition for rational numbers: a × (b + c) = a × b + a × c, using a = 2/3, b = −4/5, c = 1/2.
The sum of two rational numbers is −1/3. If one of them is 2/5, find the other. 3 Marks
Find the multiplicative inverse of −13/19 and verify by multiplication.
Simplify: (3/8 × −2/9) + (1/4 × 2/3) − (1/6 × 3/5)
Using properties of rational numbers, find the value of: (7/8 × 4/3) + (7/8 × −1/3). (Hint: Use distributive property — this is a classic 1-mark trap question.)
Common Mistake: Students often forget that the reciprocal (multiplicative inverse) of 0 does not exist. In exam MCQs, this appears as a trap option.
Chapter 2 — Linear Equations in One Variable
One of the highest-scoring chapters in Class 8. Questions range from direct solving to real-life word problems involving ages, money, and geometry. Mastering transposing and cross-multiplication is non-negotiable.
Important Questions
Solve: (3x − 2)/5 − (x − 3)/3 = 1 and verify your answer.
The sum of three consecutive odd numbers is 51. Find the numbers. 3 Marks
The present age of Ravi's father is three times Ravi's age. 10 years hence, the father's age will be twice Ravi's. Find their present ages. 5 Marks
Solve: (x + 1)/(2x + 3) = 3/8. Cross-multiplication type.
A number is such that when 5 is subtracted from 5 times the number, the result is 4 less than twice the number. Find the number.
The perimeter of a rectangle is 48 m. Its length is 4 m more than twice its breadth. Find the dimensions. 5 Marks
Divide 36 into two parts so that one part is 5/7 of the other.
Chapter 3 — Understanding Quadrilaterals
This chapter introduces angle-sum properties for polygons and the family of parallelograms (rhombus, rectangle, square, trapezium, kite). Property-based questions and fill-in-the-blank on special quadrilaterals appear almost every year.
Important Questions
The ratio of angles of a quadrilateral is 2:3:5:8. Find all the angles.
ABCD is a parallelogram where ∠A = 70°. Find the measures of all other angles and state which property you used for each.
Two adjacent angles of a parallelogram are in the ratio 4:5. Find all angles. 3 Marks
In a rhombus PQRS, the diagonals intersect at O. If PQ = 13 cm and PR = 10 cm, find QS.
The sum of interior angles of a polygon is 1440°. How many sides does it have?
Explain why a square is a special rhombus but a rhombus is not always a square. (Concept question — 2 marks)
Chapter 5 — Data Handling
Students often underestimate Data Handling. Questions on pie charts (converting percentages to degrees and vice versa), grouped frequency tables, and probability are all fair game — and probability questions are essentially free marks if practiced.
Important Questions
A pie chart shows monthly expenses: Food 40%, Rent 25%, Education 20%, Others 15%. If total income is ₹24,000, find the amount spent on each category. 4 Marks
Represent the following data as a histogram: Class intervals 10–20, 20–30, 30–40, 40–50 with frequencies 8, 15, 12, 7.
A bag contains 5 red, 3 blue, and 2 green balls. A ball is drawn at random. Find the probability of drawing (i) a red ball (ii) a ball that is not blue.
Find the mode and median of: 7, 4, 10, 7, 4, 7, 10, 4, 7, 3, 8. 3 Marks
Convert the central angle of a sector to percentage if the angle is 108° in a pie chart.
Chapters 6 & 7 — Squares, Square Roots, Cubes & Cube Roots
These two chapters are closely linked. Chapter 6 goes deep into patterns, Pythagorean triplets, and methods of finding square roots (long division method being the most important). Chapter 7 focuses on cube roots by prime factorisation.
Important Questions — Ch. 6 & 7
Find the square root of 7056 by the long division method. 4 Marks
Find the smallest number by which 2028 must be multiplied to make it a perfect square. Also find the square root of the resulting number.
Find the least number of six digits which is a perfect square.
Is 1000 a perfect cube? If not, find the smallest number by which 1000 must be divided to make it a perfect cube. 3 Marks
Using prime factorisation, find the cube root of 13824.
Write a Pythagorean triplet whose smallest member is 16.
Chapter 8 — Comparing Quantities
This is consistently one of the top-scoring chapters for students who practice well — and one of the biggest sources of lost marks for those who don't. Simple Interest, Compound Interest (including half-yearly and quarterly), profit-loss, and GST all appear here. The CI formula must be committed to memory with all its variations.
Important Questions
A sum of ₹10,000 is invested at 8% per annum compound interest. Find the amount after 2 years. Also find the compound interest. 4 Marks
What sum of money will amount to ₹9,261 in 3 years at 5% per annum compound interest?
The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
A TV is bought for ₹15,000 and sold for ₹12,000. Find the loss percent. 2 Marks
Find the CI on ₹12,600 for 2 years at 10% per annum compounded half-yearly. 5 Marks
An article is marked at ₹4,200. A discount of 15% is given. Find the selling price. What will be the price after 12% GST on the discounted price?
Rehan bought a bike for ₹54,000. The value of the bike depreciates at 10% per annum. What will be its value after 3 years?
Exam Tip: Always write the CI formula clearly: A = P(1 + r/100)ⁿ. In half-yearly cases, replace r with r/2 and n with 2n. Examiners award method marks even if the arithmetic goes wrong.
Chapter 9 — Algebraic Expressions and Identities
The four standard identities — (a+b)², (a−b)², (a+b)(a−b), and (x+a)(x+b) — are used not just in this chapter but throughout higher classes. Their application to numerical calculations is a consistent source of 2–3 mark questions.
Important Questions
Using the identity (a + b)² = a² + 2ab + b², find the value of (102)².
Expand: (3x + 4y)² and (5m − 2n)².
Multiply: (2x + 3y)(2x − 3y). Identify which identity applies. 2 Marks
Using suitable identities, evaluate 97 × 103 and 95².
Subtract 3x² − 4y + 7 from 5x² + 2y − 9.
Find the product: (x + 5)(x + 4) and verify for x = 2.
Using (a + b)(a − b) = a² − b², find 1.02 × 0.98 without a calculator. 3 Marks
Chapter 11 — Mensuration
The highest-weighted chapter in Class 8. Area of trapezium, area of a general quadrilateral (through diagonals), surface area and volume of cuboid, cube, and cylinder are all exam staples. 3D mensuration — understanding which formula to apply — is where most errors occur.
Important Questions
The parallel sides of a trapezium are 12 cm and 8 cm. Its height is 6 cm. Find its area. 2 Marks
Find the area of a rhombus whose diagonals are 18 cm and 24 cm. Also find its perimeter if a side is 15 cm.
A cuboidal box has dimensions 60 cm × 40 cm × 30 cm. Find the total surface area and the cost of painting it at ₹2 per cm². 5 Marks
The lateral surface area of a hollow cylinder is 4224 cm². It is cut along its height and formed into a rectangular sheet. The width of the sheet is 33 cm. Find the length of the sheet and the volume of the cylinder.
Find the volume of a cylinder with base radius 7 cm and height 20 cm. (Use π = 22/7) 3 Marks
A rectangular garden 70 m × 40 m has a path 2 m wide inside it all around. Find the area of the path.
Find the area of a quadrilateral ABCD where AC = 30 m, and perpendiculars from B and D on AC are 12 m and 8 m respectively.
Shape | Formula (Area / Volume / SA) | Key Variable(s) |
|---|---|---|
Trapezium (Area) | ½ × (a + b) × h | a, b = parallel sides; h = height |
Rhombus (Area) | ½ × d₁ × d₂ | d₁, d₂ = diagonals |
General Quadrilateral | ½ × d × (h₁ + h₂) | d = diagonal; h₁, h₂ = perpendiculars |
Cuboid (TSA) | 2(lb + bh + hl) | l = length, b = breadth, h = height |
Cube (TSA) | 6a² | a = side |
Cylinder (CSA) | 2πrh | r = radius, h = height |
Cylinder (TSA) | 2πr(r + h) | r = radius, h = height |
Cylinder (Volume) | πr²h | r = radius, h = height |
Cube (Volume) | a³ | a = side |
Cuboid (Volume) | l × b × h | l, b, h = dimensions |
Chapters 13 & 14 — Direct/Inverse Proportions and Factorisation
Chapter 13 is formula-driven and rewards students who can quickly identify whether a situation calls for direct or inverse proportion. Chapter 14's factorisation questions — especially by regrouping and using identities — are extremely common in annual exams.
Important Questions — Ch. 13
If 15 workers can complete a project in 48 days, in how many days will 20 workers complete the same project? (Inverse proportion) 3 Marks
A car covers 360 km in 4 hours. How far will it travel in 6 hours at the same speed? (Direct proportion)
A machine fills 420 bottles in 3 hours. How many bottles can it fill in 5 hours?
The scale of a map is 1:5,000,000. What actual distance (in km) does 2.5 cm on the map represent?
Important Questions — Ch. 14 (Factorisation)
Factorise: 12a²b − 9ab² + 6ab by taking common factors.
Factorise using identities: 49a² − 70ab + 25b² and x² − (y − z)². 3 Marks
Factorise by regrouping: m² + mn − pm − pn.
Divide: (x² + 7x + 12) ÷ (x + 3) and verify your answer.
Factorise: ax² + bx + c type — 6x² + 7x − 3. 4 Marks
Chapters 12 & 16 — Exponents & Powers and Playing with Numbers
Important Questions — Ch. 12
Simplify and express in standard form: (6.4 × 10⁵) × (3.0 × 10²)
Express 0.000086 in standard form.
Compare: 2.7 × 10¹² and 1.5 × 10¹³. Which is greater?
Simplify: [(2³)² × 3⁴ × 5²] ÷ [2⁵ × 3²]
Important Questions — Ch. 16
If 31z5 is a multiple of 9, find the digit z. 2 Marks
Find the value of A and B in the addition: AB + BA = 1A1 (where letters represent single digits).
Check divisibility: Is 573 divisible by 3? By 9? Show your reasoning.
Summary: Topic-wise Question Frequency in Exams
Topic | Expected Questions | Marks Range | Difficulty |
|---|---|---|---|
Compound Interest (Ch. 8) | 1–2 questions | 4–5 | Medium–Hard |
Linear Equations — Word Problems (Ch. 2) | 1–2 questions | 3–5 | Medium |
Mensuration — 3D (Ch. 11) | 2–3 questions | 8–10 | Medium–Hard |
Algebraic Identities (Ch. 9) | 2–3 questions | 4–6 | Easy–Medium |
Factorisation (Ch. 14) | 2–3 questions | 4–6 | Medium |
Data Handling + Probability (Ch. 5) | 1–2 questions | 3–5 | Easy |
Square/Cube Roots (Ch. 6 & 7) | 1–2 questions | 3–4 | Easy–Medium |
Quadrilateral Properties (Ch. 3) | 1–2 questions | 3–4 | Easy–Medium |
Rational Numbers — Properties (Ch. 1) | 2–3 questions | 4–6 | Easy |
Proportions (Ch. 13) | 1 question | 3 | Easy |
How to Use These Important Questions Effectively
Simply reading through these questions is not preparation — it's orientation. Here is how subject experts recommend approaching them:
Attempt first, check later. Never read the solution before making a genuine attempt. Even a wrong attempt builds the neural pathways needed for recall under exam conditions.
Work chapter-by-chapter, not question-by-question. Finish all topics in a chapter before moving on. This builds conceptual coherence.
Prioritise Chapters 2, 8, 9, 11, and 14 in your first two revision rounds. Together they account for over 50% of total marks in most schools.
Time yourself. A 3-mark question should take no more than 4–5 minutes. A 5-mark question: 7–8 minutes. Practising under self-imposed time limits reveals weak spots faster than re-reading notes.
Maintain an error log. Write down every mistake with a brief note on why it happened — wrong formula, calculation error, missed a condition. Reviewing this log the night before your exam is more valuable than re-doing solved examples.
Use NCERT Exemplar Problems for Chapters 2, 9, and 11 once you've cleared the standard questions above. Exemplar problems are specifically mentioned in CBSE guidelines as a source for challenging exam questions.
Expert Insight: Students who score 90+ in Class 8 Maths typically don't know more content than their peers — they make fewer careless errors. Careless errors in Maths come from rushing. Slow down on the first read of any question, underline key data, and write units at every step.
Final Word
Class 8 Maths is foundational for everything that follows — from Class 9's polynomials and coordinate geometry to Class 10's real numbers and quadratic equations. The students who master Chapter 9's identities now will fly through Class 9 Algebra. Those who nail Chapter 11's mensuration now will find Class 10's surface areas trivially easy.Use this chapter-wise question bank as your working document. Mark questions you found difficult. Return to them. Rework them from scratch. That repetition — spaced over days, not crammed overnight — is what turns a good student into a consistent performer.