Class 8 questions with answers

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

15 questions · What investigation means in Grade 8 · Science is everywhere: no fancy laboratory required · What we can change, and what we can observe or measure · Changing only one thing at a time · Keeping notes, and letting the results raise the next question · From electric current to the phases of the Moon: how this year's physical topics lead into one another · Roots and kites: grounded observation balanced with free thinking · From a drop of water to a planet that is just right for life

15 questions · Lenses, the microscope, and how the invisible world was found · The three basic parts of a cell and what each one does · What a plant cell carries that an animal cell does not · Why cells are shaped differently, and how the shape does the job · How cells build up into a whole organism · Unicellular and multicellular, and what a microbial cell has or lacks · What counts as a microorganism, the groups the chapter names, and where viruses sit · Fermentation, spoiling, and preserving: microbes in the kitchen · Microalgae: what they do for water, air and food · Rhizobium, root nodules, and why legumes are rotated with other crops · Decomposition: how microbes turn waste back into nutrients

15 questions · The habits that keep us healthy · What health means · Our surroundings and our health · How communicable diseases spread · Non-communicable diseases · Stopping the spread · What a disease is, and its two kinds · Signs and symptoms · Which pathogen causes which disease · Immunity and vaccines · Jenner and the first vaccine · Antibiotics and antibiotic resistance

15 questions · The heating effect of electric current · The magnetic effect of electric current · Where the magnetic effect is used · What makes a coil an electromagnet · What makes an electromagnet stronger · The poles of an electromagnet · Appliances that use the heating effect · When the heat is a problem · What the heat produced depends on · How a cell generates electricity · Dry cells and rechargeable batteries · Oersted and how the link was found

15 questions, 1 with pictures · A force needs two objects · What a force can do · What a force is · Muscular force · What friction depends on · What friction is · Magnetic force · Contact and non-contact forces · Electrostatic force · Gravitational force · Mass and weight · Reading a spring balance · Floating and sinking · Weight is a force

15 questions, 2 with pictures · Air exerts pressure · Making the area smaller on purpose · What pressure is · Working out a pressure · Pressure in a liquid column · A liquid presses in every direction · How large the atmospheric pressure is · Fast winds lower the pressure · How wind forms · Staying safe from lightning · Storms and thunderstorms · What causes lightning · How a cyclone forms

15 questions · Atoms and molecules · Matter is made of constituent particles · The word particle means different things in different places · Dissolving does not destroy the particles · The spaces between particles · Gases can be compressed, liquids practically cannot · How particles move in a gas · How particles move in a liquid · How the spacing is ordered across the three states · Interparticle attraction and what decides its strength · The gaseous state, and what a fluid is · The solid state · Dissolving changes the total volume · The liquid state · Melting and the melting point

15 questions, 1 with pictures · Heating sugar shows that it is a compound · Types of mixtures, and what counts as a component · What a mixture is · What pure means in science · Air is a uniform mixture · Alloys are uniform mixtures · Uniform and non-uniform mixtures · Dust is suspended in air, not part of it · Lime water shows carbon dioxide is in air · Elements and atoms · Metals, non-metals, and how many elements there are · Compounds combine elements in fixed ratios · How we use elements, compounds and mixtures · Passing electricity through water splits it into two gases · Minerals

15 questions, 6 with pictures · Saturated and unsaturated solutions · Uniform and non-uniform mixtures · What solute, solvent and solution are · Which component is the solvent · Concentration: dilute and concentrated · Solubility · Solubility of gases · Temperature and the solubility of solids · The volume of regular and irregular solids · Measuring mass, and how mass differs from weight · Choosing a measuring cylinder and its smallest reading · Measuring the volume of a liquid · Units of density and relative density · What density is · Temperature and density

15 questions, 2 with pictures · A concave mirror converges and a convex mirror diverges · How spherical mirrors differ from a plane mirror · Telling a concave mirror from a convex one · The laws hold for every kind of mirror · What spherical mirrors are · Where concave and convex mirrors are used · Images formed by a concave mirror · Images formed by a convex mirror · The angle of incidence equals the angle of reflection · The incident ray, the normal and the two angles · The incident ray, the normal and the reflected ray lie in one plane · Concentrating sunlight with a concave mirror · A convex lens converges and a concave lens diverges · What a lens is · Where lenses are used

15 questions · Locating the Moon in the sky · The Moon can be seen during the day · The Moon rises about fifty minutes later each day · The Sun's rising point shifts through the year · The day as a unit of time · The month and the year as units of time · The phases are not caused by the Earth's shadow · The phases of the Moon · The Moon shines by reflecting sunlight · Why the phases happen · Festivals and the calendars they follow · Solar calendars and leap years · Lunar calendars · Luni-solar calendars and the intercalary month · The Indian National Calendar

15 questions, 1 with pictures · Habitat and its biotic and abiotic components · How organisms meet their biotic and abiotic needs · Interactions between biotic and abiotic components · Community · Competition keeps populations in balance · Ecosystems and their types · Population · The nested levels from individual to ecosystem · Mutualism, commensalism and parasitism · Food chains and trophic levels · Producers, consumers and the feeding categories · Every organism matters: direct and indirect effects · Food webs · How one change leads to another · Decomposers and decomposition

15 questions · The habitable zone and liquid water · The planets of the solar system · Earth's magnetic field as a shield · Earth's size, its gravity and holding on to an atmosphere · The biosphere and the interdependence of living things · The ozone layer and shielding from ultraviolet rays · Earth as a unique life-bearing planet · Earth's nearly circular orbit and steady conditions through the year · Reproduction, genes and the continuity of life · The four spheres and the balance that keeps Earth habitable · The greenhouse effect · The Earth's crust, the thin layer where life exists · The geosphere: soil, rocks, minerals and geodiversity · Air, water and sunlight sustaining life · Asexual reproduction