For Class 8, 9 & 10

Master the basics - and everything after gets easier

Concept-first questions with clear model answers in Physics, Chemistry, Maths and Biology, all NCERT-aligned. Start early, build the habit, and walk into your boards, NEET and JEE already ahead.

Interactive lessons

learn by playing

Drag, slide and build - watch each concept come alive, then reveal the answer.

200 interactive lessons

Interactive

Ohm's law

Class 10 Physics

Slide V & R, watch the bulb glow

Open
Interactive

pH scale

Class 10 Chemistry

Slide across acids and bases

Open
Interactive

Atomic number and mass number

Class 9 Chemistry

Add protons & neutrons, build shells

Open
Interactive

Laws of reflection

Class 8 Physics

Change the angle, watch it bounce

Open
Interactive

Volume of a sphere

Class 9 Maths

Grow the radius, see the volume

Open
Interactive

Area of a trapezium

Class 8 Maths

Drag the sides, read the area

Open
Interactive

Power of a lens

Class 10 Physics

Move the object, trace the rays

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Interactive

Food chain and energy flow

Class 10 Biology

Follow the energy as it flows

Open
Interactive

Speed

Class 8 Physics

Slide distance & time, watch the speed

Open
Interactive

Density

Class 9 Physics

Pack mass into volume, float or sink

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Interactive

Work done

Class 9 Physics

Push harder or farther, watch work grow

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Interactive

Kinetic energy

Class 9 Physics

Speed it up - energy grows with the square

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Interactive

Power of a lens

Class 10 Physics

Shorten the focal length, boost the power

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Interactive

Mole concept

Class 9 Chemistry

Weigh out grams, count the moles

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Interactive

Avogadro's number

Class 9 Chemistry

Add moles, count the particles

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Interactive

Microscope magnification

Class 8 Biology

Grow the image, read the magnification

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Interactive

Population density

Class 10 Biology

Add individuals, shrink the land, see crowding

Open
Interactive

Simple interest

Class 8 Maths

Slide money, rate & time, watch interest

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Interactive

Pythagoras theorem

Class 9 Maths

Stretch the two sides, get the hypotenuse

Open
Interactive

Probability of an event

Class 10 Maths

Change the outcomes, watch the odds

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Interactive

Newton's second law

Class 9 Physics

Push a mass, pick an acceleration

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Interactive

Momentum

Class 9 Physics

Slide mass & velocity, build momentum

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Pressure

Class 8 Physics

Shrink the area, feel the pressure rise

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Interactive

Weight

Class 9 Physics

Change the planet's gravity, watch your weight

Open
Interactive

Refractive index

Class 10 Physics

Slow light in the medium, raise the index

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Interactive

Resistors in series

Class 10 Physics

Add two resistors in a line

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Mass percentage of a solution

Class 9 Chemistry

Dissolve solute, read the strength

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Concentration of a solution

Class 9 Chemistry

Pack solute into less liquid

Open
Interactive

Population change

Class 10 Biology

Balance births against deaths

Open
Interactive

Compound microscope

Class 8 Biology

Combine eyepiece & objective lenses

Open
Interactive

Area of a circle

Class 8 Maths

Grow the radius, watch the area square

Open
Interactive

Volume of a cuboid

Class 8 Maths

Stretch length, breadth & height

Open
Interactive

Electronic configuration and valency

Class 9 Chemistry

Slide the atomic number, build the atom

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Interactive

Homologous series (alkanes)

Class 10 Chemistry

Add carbons, name the compound

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Mass number

Class 9 Chemistry

Add protons & neutrons, get the mass number

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Power

Class 9 Physics

More work in less time = more power

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Potential energy

Class 9 Physics

Lift a mass higher, store energy

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Wave speed

Class 9 Physics

Tune frequency & wavelength, set the speed

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Electric current

Class 10 Physics

Push charge per second, get the current

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Percentage

Class 8 Maths

Compare part to whole as a %

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Electron dot structure

Class 9 Chemistry

Draw valence electrons as dots

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Acceleration

Class 9 Physics

Speed up over time, find acceleration

Open
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Distance, speed and time

Class 8 Physics

Set speed & time, cover the distance

Open
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Frequency and time period

Class 9 Physics

Shorten the period, raise the frequency

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Interactive

Heating effect of current

Class 10 Physics

Raise the current, watch heating soar

Open
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Area of a triangle

Class 8 Maths

Set base & height, halve the rectangle

Open
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Area of a rectangle

Class 8 Maths

Set length & breadth, fill the area

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Mean (average)

Class 9 Maths

Share the total equally across items

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Interactive

Discount

Class 8 Maths

Slide price & % off, see the saving

Open
Interactive

Heart rate

Class 10 Biology

Set heart rate & time, count the beats

Open
Interactive

Resistors in parallel

Class 10 Physics

Wire two resistors side by side

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Interactive

Electric charge

Class 10 Physics

Flow current over time, collect charge

Open
Interactive

Electrical energy and units

Class 10 Physics

Run appliances, add up the units

Open
Interactive

Kelvin temperature scale

Class 9 Chemistry

Slide Celsius, read the Kelvin

Open
Interactive

Moles from number of particles

Class 9 Chemistry

Divide particles by Avogadro's number

Open
Interactive

Ten percent law

Class 10 Biology

See 10% of energy reach the next level

Open
Interactive

Area of a square

Class 8 Maths

Grow the side, square the area

Open
Interactive

Volume of a cube

Class 8 Maths

Grow the edge, cube the volume

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Interactive

Circumference of a circle

Class 8 Maths

Grow the radius, roll out the rim

Open
Interactive

Surface area of a cube

Class 9 Maths

Grow the edge, cover six faces

Open
Interactive

Potential difference

Class 10 Physics

Share work across charge, get volts

Open
Interactive

Resistance from Ohm's law

Class 10 Physics

Divide voltage by current, get resistance

Open
Interactive

Echo and SONAR

Class 9 Physics

Time the echo, find the distance

Open
Interactive

Mass from moles

Class 9 Chemistry

Multiply moles by molar mass

Open
Interactive

Breathing rate

Class 10 Biology

Set breathing rate & time

Open
Interactive

Volume of a cylinder

Class 10 Maths

Set radius & height, fill the can

Open
Interactive

Compound interest

Class 8 Maths

Compound money over years

Open
Interactive

Profit and loss percentage

Class 8 Maths

Set cost & selling price, see profit %

Open
Interactive

Perimeter of a rectangle

Class 8 Maths

Set length & breadth, walk the border

Open
Interactive

Surface area of a sphere

Class 10 Maths

Grow the radius, wrap the ball

Open
Interactive

Time period

Class 9 Physics

Raise the frequency, shrink the period

Open
Interactive

Relative velocity

Class 9 Physics

Two objects approach - add their speeds

Open
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Average velocity

Class 9 Physics

Average the start and end speeds

Open
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Equations of motion (v = u + at)

Class 9 Physics

Accelerate from u for a time t

Open
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Kelvin to Celsius

Class 9 Chemistry

Slide Kelvin, read the Celsius

Open
Interactive

Population growth rate

Class 10 Biology

Balance births vs deaths per population

Open
Interactive

Perimeter of a square

Class 8 Maths

Grow the side, walk four edges

Open
Interactive

Perimeter of a triangle

Class 8 Maths

Add the three sides

Open
Interactive

Area of a parallelogram

Class 8 Maths

Set base & height, slide the shape

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Area of a rhombus

Class 8 Maths

Set the two diagonals

Open
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Equations of motion (distance)

Class 9 Physics

Start, accelerate, cover ground

Open
Interactive

Joule's law of heating

Class 10 Physics

Raise current, resistance or time

Open
Interactive

Electric power (P = VI)

Class 10 Physics

Multiply voltage by current

Open
Interactive

Average atomic mass of isotopes

Class 9 Chemistry

Mix two isotopes by abundance

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Seed germination percentage

Class 9 Biology

Count sprouted seeds out of the total

Open
Interactive

Volume of a cone

Class 9 Maths

Set radius & height, fill the cone

Open
Interactive

Surface area of a cylinder

Class 9 Maths

Wrap the side and both ends

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Surface area of a cuboid

Class 9 Maths

Cover all six rectangular faces

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nth term of an AP

Class 10 Maths

Step from the first term by d

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Interactive

Sum of an AP

Class 10 Maths

Add up the first n terms

Open
Interactive

Focal length of a mirror

Class 10 Physics

Halve the radius to find the focus

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Interactive

Speed of light in a medium

Class 10 Physics

Raise the index, slow the light

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Percentage purity

Class 9 Chemistry

Weigh the pure part of a sample

Open
Interactive

Slope of a line

Class 10 Maths

Rise over run gives the steepness

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Percentage change

Class 8 Maths

Compare a new value to the old

Open
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Volume of a hemisphere

Class 9 Maths

Grow the radius of half a ball

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Area of a sector

Class 10 Maths

Cut a slice of angle from a circle

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Length of an arc

Class 10 Maths

Measure the curved edge of a slice

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Slant height of a cone

Class 9 Maths

Combine radius & height for the slant

Open
Interactive

Unit conversion (km/h to m/s)

Class 9 Physics

Convert km/h into m/s

Open
Interactive

Equations of motion (v^2 = u^2 + 2as)

Class 9 Physics

Accelerate over a distance, find v

Open
Interactive

Impulse

Class 9 Physics

Hit harder or longer, change momentum

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Wavelength

Class 9 Physics

Speed over frequency gives wavelength

Open
Interactive

Oscillations

Class 9 Physics

Vibrate at a frequency for a time

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Cost of electricity

Class 10 Physics

Units times rate gives the bill

Open
Interactive

Number of neutrons

Class 9 Chemistry

Take protons away from the mass number

Open
Interactive

Curved surface area of a cone

Class 9 Maths

Wrap the slanted side of a cone

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Interactive

Total surface area of a cone

Class 9 Maths

Add the base circle to the cone's side

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Interactive

Curved surface area of a hemisphere

Class 9 Maths

Cover the dome of a hemisphere

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Diagonal of a square

Class 9 Maths

Cross a square corner to corner

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Unit conversion (m/s to km/h)

Class 9 Physics

Convert m/s into km/h

Open
Interactive

Distance from velocities

Class 9 Physics

From two speeds, find the distance

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Diagonal of a rectangle

Class 9 Maths

Cross a rectangle corner to corner

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Diagonal of a cuboid

Class 9 Maths

The longest rod that fits in a box

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Area by Heron's formula

Class 9 Maths

Area from just the three sides

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Interior angle sum of a polygon

Class 8 Maths

Add up a polygon's inside angles

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Exterior angle of a regular polygon

Class 8 Maths

Share 360 among a polygon's corners

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Number of diagonals of a polygon

Class 8 Maths

Count the diagonals of a polygon

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Discriminant

Class 10 Maths

Test how many roots a quadratic has

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Sum of roots

Class 10 Maths

Sum of a quadratic's roots

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Punnett square (monohybrid cross)

Class 10 Biology

Cross two parents, predict the offspring

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Balancing chemical equations

Class 10 Chemistry

Slide coefficients until atoms balance

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Writing chemical formulae (valency)

Class 9 Chemistry

Criss-cross valencies into a formula

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Interactive

Current from power

Class 10 Physics

Divide power by voltage for current

Open
Interactive

Power (P = V^2 / R)

Class 10 Physics

Voltage squared over resistance

Open
Interactive

Sine ratio

Class 10 Maths

Opposite over hypotenuse

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Cosine ratio

Class 10 Maths

Adjacent over hypotenuse

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Tangent ratio

Class 10 Maths

Opposite over adjacent

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Interactive

Area of an equilateral triangle

Class 9 Maths

Area of an equilateral triangle

Open
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Curved surface area of a cylinder

Class 9 Maths

Wrap only the curved side

Open
Interactive

Loss percentage

Class 8 Maths

Sell below cost, find the loss %

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Interactive

Amount with simple interest

Class 8 Maths

Principal plus its simple interest

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Distance formula

Class 10 Maths

Straight distance between two points

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Interactive

States of matter

Class 9 Chemistry

Heat particles solid → liquid → gas

Open
Interactive

Parts of a plant cell

Class 8 Biology

Tap a cell part to see its job

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Diagonal of a cube

Class 9 Maths

Longest diagonal through a cube

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Total surface area of a hemisphere

Class 9 Maths

Dome plus its flat circle

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Interactive

Sum of first n natural numbers

Class 10 Maths

Add 1 + 2 + ... + n instantly

Open
Interactive

Range of data

Class 9 Maths

Spread from smallest to largest

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Class mark

Class 9 Maths

Midpoint of a class interval

Open
Interactive

Selling price from profit percent

Class 8 Maths

Mark up cost by a profit %

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Interactive

Perimeter of a sector

Class 10 Maths

Two radii plus the curved arc

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Interactive

Circumference from diameter

Class 8 Maths

Circumference straight from diameter

Open
Interactive

Power (P = F x v)

Class 9 Physics

Force times velocity gives power

Open
Interactive

Percentage of a number

Class 8 Maths

Find a percentage of a number

Open
Interactive

Series and parallel circuits

Class 10 Physics

Break a bulb in series vs parallel

Open
Interactive

Symbols of elements

Class 9 Chemistry

Match each element to its symbol

Open
Interactive

Free fall (velocity)

Class 9 Physics

Drop from a height, hit this speed

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Free fall (time)

Class 9 Physics

How long a drop takes

Open
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Free fall (distance)

Class 9 Physics

Distance fallen in a given time

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Complement of an event

Class 10 Maths

Chance an event does NOT happen

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Product of roots

Class 10 Maths

Product of a quadratic's roots

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Exterior angle theorem

Class 9 Maths

Exterior angle = sum of remote interiors

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Complementary angles

Class 10 Maths

What adds to 90 degrees

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Supplementary angles

Class 9 Maths

What adds to 180 degrees

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Perimeter of a semicircle

Class 10 Maths

Curved half plus the diameter

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Interactive

Area of a semicircle

Class 10 Maths

Half the area of a circle

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Turning effect (moments)

Class 9 Physics

Balance the see-saw with moments

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Interactive

Reflex arc

Class 10 Biology

Step through a reflex, stimulus to action

Open
Interactive

Buoyant force (upthrust)

Class 9 Physics

Displace liquid, feel the upthrust

Open
Interactive

Relative density

Class 9 Physics

Compare a density to water's

Open
Interactive

Power in lifting a load

Class 9 Physics

Lift a load, faster needs more power

Open
Interactive

Cosecant ratio

Class 10 Maths

Hypotenuse over opposite

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Secant ratio

Class 10 Maths

Hypotenuse over adjacent

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Interactive

Cotangent ratio

Class 10 Maths

Adjacent over opposite

Open
Interactive

Height from angle of elevation

Class 10 Maths

Height from an angle of elevation

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Area of a quadrant

Class 10 Maths

A quarter of a circle's area

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Interior angle of a regular polygon

Class 8 Maths

One inside angle of a regular polygon

Open
Interactive

Sum of first n odd numbers

Class 10 Maths

Add the first n odd numbers

Open
Interactive

Sum of first n even numbers

Class 10 Maths

Add the first n even numbers

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Interactive

Quadratic formula (a root)

Class 10 Maths

Larger root of a quadratic

Open
Interactive

LCM from HCF

Class 10 Maths

LCM from the product and HCF

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Interactive

Depreciation

Class 8 Maths

Value drops by a % each year

Open
Interactive

Cost price from selling price

Class 8 Maths

Work back to the cost price

Open
Interactive

Downstream speed

Class 8 Maths

Row with the current

Open
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Upstream speed

Class 8 Maths

Row against the current

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Average speed for a round trip

Class 8 Maths

Average speed there and back

Open
Interactive

Sales tax / GST

Class 8 Maths

Tax added on a price

Open
Interactive

Area of a ring (annulus)

Class 10 Maths

Area of a ring between two circles

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Edge of a cube from volume

Class 9 Maths

Edge back from the volume

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Radius from area

Class 10 Maths

Radius back from a circle's area

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Side from area of a square

Class 8 Maths

Side back from a square's area

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Interactive

Height of a triangle from area

Class 9 Maths

Height back from area and base

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Interactive

Rate from simple interest

Class 8 Maths

Rate back from the interest

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Interactive

Time from simple interest

Class 8 Maths

Time back from the interest

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Principal from simple interest

Class 8 Maths

Principal back from the interest

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Mean proportional

Class 10 Maths

Geometric mean of two numbers

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Interactive

Fourth proportional

Class 8 Maths

Complete the proportion a : b = c : ?

Open
Interactive

Marked price from selling price

Class 8 Maths

Marked price back from the sale price

Open
Interactive

Chambers of the human heart

Class 10 Biology

Tap a heart chamber to see its job

Open
Interactive

Equation of a line (y = mx + c)

Class 9 Maths

Read y off a straight line

Open
Interactive

Average term of an AP

Class 10 Maths

Average of first and last term

Open
Interactive

Number of terms in an AP

Class 10 Maths

How many terms in an AP

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Midpoint of two points

Class 10 Maths

x-coordinate of a midpoint

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Empirical mode

Class 10 Maths

Estimate the mode from mean & median

Open
Interactive

Length of a shadow

Class 10 Maths

Shadow from height and sun angle

Open
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Train crossing a pole

Class 8 Maths

Speed to cross a pole

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Time and work

Class 8 Maths

More workers, fewer days

Open
Interactive

Dividing in a ratio

Class 8 Maths

Split a total in a ratio

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Interactive

Unitary method

Class 8 Maths

Cost of a single item

Open

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Showing 17 questions for Class 9. Tap a card to reveal the answer.

PhysicsMotionmedium

A car starting from rest accelerates uniformly at 2 m/s^2 for 5 seconds. Find its final velocity and the distance travelled.

Reveal answer ↓

What it is

The three equations of motion connect initial velocity, acceleration, time, distance and final velocity for steady acceleration.

Answer

Given u = 0, a = 2 m/s^2, t = 5 s. Final velocity v = u + at = 0 + 2 x 5 = 10 m/s. Distance s = ut + (1/2)at^2 = 0 + (1/2)(2)(5^2) = 25 m. So the car reaches 10 m/s and covers 25 m.

v = u + at ; s = ut + (1/2)at^2

  • v = u + at = 10 m/s
  • s = ut + (1/2)at^2 = 25 m
  • u = 0 (starts from rest)

Why learn this

They let engineers predict a rocket's speed, a car's braking distance and a ball's flight - the maths of all moving things.

💡 Memory trick

Use 'v = u + at' first (no distance), then 's = ut + 1/2 at^2'. Velocity gets a time-boost 'at'.

PhysicsMotionmedium

A body speeds up from 0 to 20 m/s in 5 s. Find its acceleration. Slide the values to explore.

Reveal answer ↓

What it is

Acceleration is the rate at which velocity changes with time.

Acceleration = (v − u) ÷ time
Acceleration4.0 m/s²

Answer

Acceleration = (final velocity - initial velocity) / time = (20 - 0) / 5 = 4 m/s^2. If the final velocity is less than the initial velocity the acceleration is negative, which means the body is decelerating (slowing down).

a = (v - u) / t

  • a = (v - u) / t
  • Unit: m/s^2
  • Negative acceleration = deceleration

Why learn this

It tells us how quickly vehicles speed up or slow down.

💡 Memory trick

a = (v - u) / t. A negative answer means slowing down.

PhysicsMotionmedium

Two cars approach each other at 20 m/s and 10 m/s. How fast do they close in? Slide to explore.

Reveal answer ↓

What it is

When two bodies move directly towards each other, their relative speed is the sum of their individual speeds.

Approach speed = u + v
Relative speed30 m/s

Answer

Moving towards each other, the relative speed = u + v = 20 + 10 = 30 m/s. The gap between them shrinks at 30 metres every second - faster than either car alone.

relative speed (approaching) = u + v

  • Towards each other: relative speed = u + v
  • Same direction: relative speed = difference
  • Unit: m/s

Why learn this

It explains how quickly two approaching vehicles or trains actually close in.

💡 Memory trick

Towards each other -> add: relative speed = u + v.

PhysicsMotioneasy

A body speeds up from 10 m/s to 30 m/s uniformly. Find its average velocity. Slide to explore.

Reveal answer ↓

What it is

For uniformly accelerated motion, the average velocity is the mean of the initial and final velocities.

Average velocity = (u + v) ÷ 2
Average velocity20.0 m/s

Answer

Average velocity = (u + v) / 2 = (10 + 30) / 2 = 20 m/s. This midpoint value works because, under uniform acceleration, the velocity increases at a steady rate.

average velocity = (u + v) / 2

  • Average velocity = (u + v) / 2
  • Valid for uniform acceleration
  • Unit: m/s

Why learn this

It lets us use a single steady speed to work out the distance covered.

💡 Memory trick

Average velocity = (u + v) / 2 - the midpoint speed.

PhysicsMotionmedium

A body starts at 5 m/s and accelerates at 2 m/s^2 for 5 s. Find its final velocity. Slide to explore.

Reveal answer ↓

What it is

The first equation of motion gives the final velocity as the initial velocity plus acceleration times time.

Final velocity = u + a × t
Final velocity15.0 m/s

Answer

Final velocity v = u + a t = 5 + 2 x 5 = 5 + 10 = 15 m/s. The term a t is the extra velocity gained during the time t at constant acceleration.

v = u + a t

  • v = u + a t
  • a t is the velocity gained
  • Valid for constant acceleration

Why learn this

It predicts how fast something is going after accelerating for a while.

💡 Memory trick

v = u + a t. Start speed plus the speed gained.

PhysicsMotionmedium

A body starts at 10 m/s and accelerates at 2 m/s^2 for 5 s. How far does it go? Slide to explore.

Reveal answer ↓

What it is

The second equation of motion gives the distance covered under uniform acceleration.

Distance = u t + ½ a t²
Distance75.0 m

Answer

Distance s = u t + 1/2 a t^2 = 10 x 5 + 1/2 x 2 x 5^2 = 50 + 25 = 75 metres. The first term (u t) is the distance at the starting speed; the second term is the extra distance from accelerating.

s = u t + 1/2 a t^2

  • s = u t + 1/2 a t^2
  • u t is steady travel, 1/2 a t^2 is the extra
  • Valid for uniform acceleration

Why learn this

It predicts how far a body travels while it is speeding up.

💡 Memory trick

s = u t + 1/2 a t^2. Steady part plus the accelerating part.

PhysicsMotioneasy

Convert 72 km/h into metres per second. Slide the speed to explore.

Reveal answer ↓

What it is

To convert a speed from kilometres per hour to metres per second, multiply by 5 and divide by 18.

m/s = km/h × 5 ÷ 18
Speed20.0 m/s

Answer

m/s = km/h x 5 / 18 = 72 x 5 / 18 = 360 / 18 = 20 m/s. The factor 5/18 comes from 1000 metres in a kilometre divided by 3600 seconds in an hour.

m/s = km/h x 5 / 18

  • m/s = km/h x 5 / 18
  • 5/18 = 1000 / 3600
  • To go back, multiply m/s by 18/5

Why learn this

Physics numericals use m/s, but everyday speeds are quoted in km/h.

💡 Memory trick

m/s = km/h x 5 / 18. (1000 m in 3600 s.)

PhysicsMotionmedium

A body starts at 10 m/s and accelerates at 2 m/s^2 over 100 m. Find its final velocity. Slide to explore.

Reveal answer ↓

What it is

The third equation of motion links the final velocity to the distance travelled under uniform acceleration.

v = √(u² + 2as)
Final velocity22.4 m/s

Answer

Using v^2 = u^2 + 2as = 10^2 + 2 x 2 x 100 = 100 + 400 = 500, so v = sqrt(500) = 22.36 m/s. This equation is handy because it connects velocity and distance directly, without the time.

v^2 = u^2 + 2as

  • v^2 = u^2 + 2as
  • Uses distance, not time
  • v = sqrt(u^2 + 2as)

Why learn this

It finds the final speed when the time is not known - only the distance.

💡 Memory trick

v^2 = u^2 + 2as. No time needed - it uses distance instead.

PhysicsMotioneasy

Convert 20 m/s into kilometres per hour. Slide the speed to explore.

Reveal answer ↓

What it is

To convert a speed from metres per second to kilometres per hour, multiply by 18 and divide by 5.

km/h = m/s × 18 ÷ 5
Speed72.0 km/h

Answer

km/h = m/s x 18 / 5 = 20 x 18 / 5 = 360 / 5 = 72 km/h. This is the reverse of the km/h to m/s rule, which multiplies by 5/18.

km/h = m/s x 18 / 5

  • km/h = m/s x 18 / 5
  • Reverse of x 5/18
  • 20 m/s = 72 km/h

Why learn this

It turns a physics answer in m/s back into the km/h we see on road signs.

💡 Memory trick

km/h = m/s x 18 / 5 (the reverse of x 5/18).

PhysicsMotionmedium

A body goes from 10 m/s to 30 m/s at 2 m/s^2. Find the distance covered. Slide to explore.

Reveal answer ↓

What it is

The distance covered can be found from the initial and final velocities and the acceleration.

Distance = (v² − u²) ÷ (2a)
Distance200.0 m

Answer

Distance s = (v^2 - u^2) / (2a) = (30^2 - 10^2) / (2 x 2) = (900 - 100) / 4 = 800 / 4 = 200 m. This is the third equation of motion rearranged to make the distance the subject.

s = (v^2 - u^2) / (2a)

  • s = (v^2 - u^2) / (2a)
  • Rearranged from v^2 = u^2 + 2as
  • No time needed

Why learn this

It gives the stopping or run-up distance when only the speeds and acceleration are known.

💡 Memory trick

s = (v^2 - u^2) / (2a), from v^2 = u^2 + 2as.

PhysicsMotioneasy

Differentiate between distance and displacement.

Reveal answer ↓

What it is

Distance is the total path length covered; displacement is the shortest straight-line distance from start to finish, with direction.

Answer

Distance is the actual length of the path travelled by a body, irrespective of direction; it is a scalar quantity and is always positive. Displacement is the shortest distance measured from the initial to the final position of the body in a particular direction; it is a vector quantity and can be positive, negative or zero. Distance is always greater than or equal to the magnitude of displacement.

Displacement = shortest distance (with direction)

  • Distance: total path length, scalar
  • Displacement: shortest path with direction, vector
  • Displacement can be zero
  • Distance >= magnitude of displacement

Why learn this

It explains why an athlete running one full round of a track covers distance but has zero displacement.

💡 Memory trick

Distance = scalar (only size). Displacement = vector (size + direction), can be zero.

PhysicsMotioneasy

Define speed and velocity. State their SI unit.

Reveal answer ↓

What it is

Speed is the rate of change of distance; velocity is the rate of change of displacement, so it has direction.

Answer

Speed is the distance travelled by a body per unit time; it is a scalar quantity. Velocity is the displacement of a body per unit time in a given direction; it is a vector quantity. The SI unit of both speed and velocity is the metre per second (m/s).

Speed = distance/time ; Velocity = displacement/time

  • Speed = distance / time (scalar)
  • Velocity = displacement / time (vector)
  • SI unit m/s
  • Velocity has direction

Why learn this

Velocity, not just speed, is needed to describe motion fully (e.g. a car turning).

💡 Memory trick

Speed = scalar (how fast). Velocity = vector (how fast AND which way).

PhysicsMotionmedium

A car's velocity increases from 10 m/s to 30 m/s in 5 s. Find its acceleration.

Reveal answer ↓

What it is

Acceleration is the rate of change of velocity with time.

Answer

Acceleration a = (final velocity - initial velocity) / time = (v - u)/t = (30 - 10)/5 = 20/5 = 4 m/s^2. So the car accelerates at 4 metres per second squared.

a = (v - u) / t

  • a = (v - u)/t
  • (30 - 10)/5 = 4
  • SI unit m/s^2
  • Negative value means retardation

Why learn this

It tells how quickly a vehicle speeds up or slows down.

💡 Memory trick

Acceleration = change in velocity / time. Negative acceleration = retardation.

PhysicsMotionmedium

Write the three equations of motion and state what each symbol means.

Reveal answer ↓

What it is

For uniform acceleration, the three equations of motion relate u, v, a, t and s.

Answer

The three equations of motion for uniform acceleration are: v = u + at; s = ut + (1/2)a t^2; and v^2 = u^2 + 2as. Here u is the initial velocity, v is the final velocity, a is the acceleration, t is the time and s is the displacement. They are valid only when the acceleration is uniform (constant).

v = u + at ; s = ut + 1/2 a t^2 ; v^2 = u^2 + 2as

  • v = u + at
  • s = ut + 1/2 a t^2
  • v^2 = u^2 + 2as
  • Valid only for uniform acceleration

Why learn this

They let us predict the position and velocity of a body at any time.

💡 Memory trick

v = u + at ; s = ut + 1/2 a t^2 ; v^2 = u^2 + 2as.

PhysicsMotionmedium

A body starting from rest accelerates at 2 m/s^2 for 5 s. Find the distance covered.

Reveal answer ↓

What it is

The equations of motion solve problems where a body moves with uniform acceleration.

Answer

Given u = 0 (starts from rest), a = 2 m/s^2, t = 5 s. Using s = ut + (1/2)a t^2 = 0 x 5 + (1/2)(2)(5^2) = 0 + (1/2)(2)(25) = 25 m. So the body covers 25 metres.

s = ut + 1/2 a t^2

  • u = 0, a = 2, t = 5
  • s = ut + 1/2 a t^2
  • s = 0 + 1/2 x 2 x 25
  • Distance = 25 m

Why learn this

It is how we calculate braking distances and launch speeds.

💡 Memory trick

Pick the equation that has the three known quantities and the one you want to find.

PhysicsMotionmedium

Why is uniform circular motion called accelerated motion?

Reveal answer ↓

What it is

A body moving in a circle at constant speed is accelerating because its direction keeps changing.

Answer

In uniform circular motion, a body moves along a circular path with a constant speed. However, its direction of motion changes continuously at every point. Since velocity depends on both speed and direction, the velocity is changing even though the speed is constant. A changing velocity means the body is accelerating, so uniform circular motion is an accelerated motion.

v = 2 pi r / t (speed in a circle)

  • Constant speed along a circle
  • Direction changes continuously
  • Velocity changes -> acceleration
  • Example: stone tied to a string

Why learn this

It explains why a stone on a string or a satellite keeps turning inward.

💡 Memory trick

Constant speed but changing direction -> velocity changes -> it is accelerated motion.

PhysicsMotionmedium

What do the slope and the area under a velocity-time graph represent?

Reveal answer ↓

What it is

On a velocity-time graph, the slope gives acceleration and the area under the graph gives displacement.

Answer

On a velocity-time graph, the slope of the line represents the acceleration of the body, since acceleration is the change in velocity per unit time. The area enclosed between the graph line and the time axis represents the distance (displacement) travelled by the body. A straight, slanting line indicates uniform acceleration, while a horizontal line indicates uniform velocity.

Acceleration = slope ; Distance = area under v-t graph

  • Slope of v-t graph = acceleration
  • Area under v-t graph = distance
  • Horizontal line = uniform velocity
  • Slanting line = uniform acceleration

Why learn this

Graphs let us read motion information quickly without formulae.

💡 Memory trick

Slope of v-t graph = acceleration; area under v-t graph = distance travelled.

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