Class 8 Maths questions with answers

210 NCERT Class 8 Maths questions with answers, chapter by chapter, from A Square and a Cube to Area.

How to teach Class 8 Maths · Class 8 Maths common misconceptions

• Chapter 1: A Square and a Cube

  15 questions, 1 with pictures · Factor pairs, and why only squares have an odd number of factors · Square roots: the inverse of squaring, and its two signs · What cubing a number means, and how cubes differ from squares · What squaring a number means, and the notation n squared · Building squares from consecutive odd numbers, and the gaps between them · Cube roots by prime factorisation, by last digits, and the odd-number pattern · What the last digits of a number can and cannot tell us about squareness · Deciding squareness and finding a square root by prime factorisation · Estimating a square root by bracketing it between known squares

• Chapter 2: Power Play

  15 questions · Exponential growth is multiplicative; linear growth is additive · Writing a number as a product of powers of its prime factors · (n^a)^b = n^(a x b), and the several ways to split one power · What n raised to the power a means, and what its sign is · Counting arrangements: independent choices multiply · Powers of 10: expanded form, decimals, and standard form · Comparing powers, adding like powers, and the two number-naming systems · m^a x n^a = (mn)^a, and m^a / n^a = (m/n)^a · n^(-a) = 1 / n^a · n^a / n^b = n^(a-b), and why n^0 = 1 · n^a x n^b = n^(a+b)

• Chapter 3: A Story of Numbers

  15 questions · Counting in groups of one fixed size, as the Gumulgal did · Place value, and reading a base-60 Mesopotamian numeral · Reading a numeral in another base as a sum of digit times power · Why adding and multiplying Roman numerals is awkward · Landmark numbers, and how a Roman numeral is built and read · A base-n system: the landmark numbers are the powers of n · A number system is a standard sequence in a fixed order · Grouping a number into the powers of the base · The Egyptian system: a base, but no place value · Two more place value systems, and what each is missing · Why a place value system needs a zero, twice over

• Chapter 4: Quadrilaterals

  15 questions, 3 with pictures · A quadrilateral is a closed figure with four straight sides · A rhombus has four equal sides and diagonals that cross at right angles · All four angles right is enough to make a rectangle · The diagonals of a rectangle are equal and bisect each other · The diagonals of a square are equal, perpendicular, and bisect its angles · The angles of any quadrilateral add up to 360 degrees · The special quadrilaterals nest inside one another · A parallelogram's diagonals bisect each other but are neither equal nor perpendicular · Adjacent angles of a parallelogram add to 180 and opposite angles are equal · A kite has two adjacent pairs of equal sides; a trapezium needs one parallel pair · A square is a rectangle with equal sides

• Chapter 5: Number Play

  15 questions · Every way of signing a ± b ± c ± d gives the same parity · Numbers leaving a fixed remainder, and how remainders add · Parity can be read off an expression without evaluating it · Two even numbers add to a multiple of 4 when their remainders match · Which pairs of factors may be used to test a composite divisor · How divisibility travels through sums, multiples and factors · Cryptarithms: recovering digits from letters by reasoning · Why the digit sum decides divisibility by 9 and by 3 · Writing a number as a sum of place values, and what that settles · Why the digits alternate in sign when testing for 11 · The digital root, and why it is the remainder on division by 9

• Chapter 6: We Distribute, Yet Things Multiply

  15 questions, 2 with pictures · How a product changes when one or both factors change · Expanding when a bracket has more than two terms, and collecting like terms · Identity 1: the product of two two-term expressions · Fast multiplication by 11, 101, 1001 and by 99, 999 · The distributive property of multiplication over addition · Identity 1A: the square of a sum · Pattern 1: twice a sum of two squares · Identity 1B: the square of a difference · Identity 1C: the difference of two squares · Mind the mistake, mend the mistake: judging a worked expansion · One arrangement, several expressions: showing they are the same

• Chapter 7: Proportional Reasoning

  15 questions, 2 with pictures · Adding the same number to both terms changes the ratio · Two pictures look alike when width and height change by the same factor · Quantities that move in opposite directions · Reducing a ratio by dividing both terms by their HCF · Testing two ratios: same simplest form, or ad = bc · What a ratio a : b says, and why its order matters · A proportion is only valid when matching terms carry the same unit · Finding the missing fourth term of a proportion · Deciding which of two offers or densities is greater · Dividing a quantity into parts in a given ratio

• Chapter 8: Fractions in Disguise

  15 questions, 15 with pictures · Estimating and comparing percentages · Fractions and percentages · Percentage of a target · Percentages and multiples · Reading and completing bar models · Finding a percentage of a quantity · Percentage shares sum to100 · Ratios as parts of a whole · Compare proportions using percentages · Proportions and absolute amounts · Recovering the whole · Compounding successive changes · Percentage area of a region · Peaceful Knights · Grouped bar chart readings

• Chapter 9: The Baudhāyana-pythagoras Theorem

  15 questions, 12 with pictures · Bounding the square root of 2 by squaring · Doubling a square · Doubling a square by rearranging four congruent triangles · Halving the area of a square · Finding a missing leg from the hypotenuse · Finding the hypotenuse from the two legs · Hypotenuse of an isosceles right triangle · Hypotenuse of the unit isosceles right triangle · Baudhāyana triples and their scaled versions · Constructing a square of triple, five-times or difference area · Fermat's Last Theorem · Combining two different squares · Squares with corners on a dot grid · The Baudhayana-Pythagoras theorem from squares on the sides · The lotus problem: depth of the lake

• Chapter 10: Proportional Reasoning-2

  15 questions, 9 with pictures · Map scale as a Representative Fraction · Testing proportion by cross-multiplication · Scaling a ratio with more than two terms · Simplest form of a ratio with many terms · Triangles with sidelengths in a given ratio · Angles of a triangle in a given ratio · Dividing a whole in a given ratio · Pie-chart angles from counts or percentages · Constructing a pie chart with a protractor · Reading a labelled pie chart · Time taken together · Direct and inverse proportion · Direct proportion at a constant rate · Inverse-proportion applications · Reading a ring chart of the day

• Chapter 11: Exploring Some Geometric Themes

  15 questions, 15 with pictures · Area remaining in the Sierpinski fractals · Counting the squares and holes of the Sierpinski carpet · Counting the triangles and holes of the Sierpinski gasket · Fractals in nature and human-made art · Changing cube projection outlines · Different objects can share one projection · Identify basic solids · Profiles of solids · Reconstructing solids and hidden edges · Tracing a boundary after corner cuts · Unroll curved surfaces · Counting the sides and perimeter of the Koch snowflake · Counts from polygonal bases · Cube nets · Dimensioned cuboid nets

• Chapter 12: Tales by Dots and Lines

  15 questions, 15 with pictures · Combined changes and the mean · Mean and median with frequencies · Mean as the unique balance point · Mean grids · Uniform scaling of the mean · Means on dot plots · Verify and complete a dot plot · Adding or subtracting the same amount · Mean after including or removing one value · Choosing a graph representation · Interpreting published graphs · Median positions and changes · Read line series and changes · Reading sun and moon clock graphs · Tables and line-graph values

• Chapter 13: Algebra Play

  15 questions, 6 with pictures · Changing the date trick · Reversing the digits of a 2-digit number · Solving a pyramid with a letter-number · Sum of a number and its reversal · The date trick · Think of a number tricks · Tricks with a constant result · Filling a pyramid downward · Filling a pyramid upward · Pyramids built on the Virahāṅka-Fibonacci numbers · Pyramids with scattered givens · The top of a pyramid as an expression · Top of a pyramid from its bottom row · Calendar magic with a 2 x 2 grid · Shape values from row sums in a grid

• Chapter 14: Area

  15 questions, 15 with pictures · Area comparisons within figures · Area of a rectangle by counting unit squares · Area of a tube of constant width · Crosspath area · Dividing a square into four parts of equal area · Doubling the sidelength multiplies area by four · Length and area unit conversions · Missing sides in connected rectangles · Perimeter is not a measure of area · Shaded regions inside rectangles · A second altitude of a triangle from its area · Area of a triangle from its base and height · Parallelogram area from matching base and height · Triangle with the opposite vertex on the far side is half the rectangle · Numeric equal-area relations