For Class 8, 9 & 10

Foundation - a strong base in Physics, Chemistry, Maths & Biology

Concept-first questions with clear model answers across all four subjects, aligned to NCERT. Start early, build the habit, and walk into your board exams, NEET and JEE already ahead.

Showing 6 questions in Mathematics for Class 8. Tap a card to reveal the answer.

MathematicsLinear Equations in One Variableeasy

Solve the linear equation 3x + 5 = 20.

Reveal answer ↓

What it is

Solving an equation means undoing the operations to leave the unknown by itself.

Answer

Subtract 5 from both sides: 3x = 20 - 5 = 15. Divide both sides by 3: x = 15/3 = 5. So x = 5. Check: 3(5) + 5 = 15 + 5 = 20, which is correct.

Isolate the variable using inverse operations

  • 3x = 20 - 5 = 15
  • x = 15/3 = 5
  • Check: 3(5) + 5 = 20

Why learn this

Every 'find the missing value' problem - money, coding, physics - is a hidden equation.

💡 Memory trick

Do the opposite, in reverse order: undo the +5 first, then the x3.

MathematicsSquares and Square Rootsmedium

Find the square root of 1225 by prime factorisation.

Reveal answer ↓

What it is

A square root asks: which number multiplied by itself gives this number?

Answer

Factorise: 1225 = 5 x 5 x 7 x 7 = 5^2 x 7^2. Pair the equal factors and take one from each pair: sqrt(1225) = 5 x 7 = 35. So the square root of 1225 is 35.

sqrt(a^2 x b^2) = a x b

  • 1225 = 5^2 x 7^2
  • Take one factor from each pair
  • sqrt(1225) = 5 x 7 = 35

Why learn this

Square roots power areas, geometry and, later, all of trigonometry.

💡 Memory trick

Prime-factorise, pair them up, take one factor from each pair.

MathematicsExponents and Powersmedium

Express 0.0000073 in standard (scientific) form.

Reveal answer ↓

What it is

Standard form writes very large or very small numbers as a x 10^n.

Answer

Move the decimal point to just after the first non-zero digit to get 7.3. The point moved 6 places to the right, so we multiply by 10 raised to the power -6. Therefore 0.0000073 = 7.3 x 10^-6.

Standard form: a x 10^n, where 1 <= a < 10

  • Bring one non-zero digit before the decimal
  • Count places moved = 6 (moving right -> negative power)
  • = 7.3 x 10^-6

Why learn this

Scientists write an atom's mass or a galaxy's size this way - it kills long strings of zeros.

💡 Memory trick

Move the point, count the hops; hopping right gives a negative power.

MathematicsComparing Quantitieseasy

A shopkeeper buys a bag for 500 rupees and sells it for 575 rupees. Find the profit percent.

Reveal answer ↓

What it is

Profit percent measures your gain compared with the cost price, not the selling price.

Answer

Profit = selling price - cost price = 575 - 500 = 75 rupees. Profit percent = (profit / cost price) x 100 = (75 / 500) x 100 = 15 percent. So the shopkeeper makes a 15 percent profit.

Profit% = (Profit / Cost Price) x 100

  • Profit = SP - CP = 75
  • Profit% = (Profit / CP) x 100
  • = (75/500) x 100 = 15%

Why learn this

It's the number every shop, startup and investor lives and dies by.

💡 Memory trick

Always divide by CP - the Cost Price is your 'Compare Point'.

MathematicsAlgebraic Expressions and Identitiesmedium

Use a standard identity to expand (x + 5)^2.

Reveal answer ↓

What it is

Algebraic identities are shortcuts that expand or factor expressions instantly.

Answer

Use the identity (a + b)^2 = a^2 + 2ab + b^2 with a = x and b = 5. So (x + 5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25.

(a + b)^2 = a^2 + 2ab + b^2

  • (a + b)^2 = a^2 + 2ab + b^2
  • Here a = x, b = 5
  • = x^2 + 10x + 25

Why learn this

They save time in almost every algebra, physics and competitive-exam problem.

💡 Memory trick

Square the first, twice the product, square the last: a^2 + 2ab + b^2.

MathematicsMensurationmedium

Find the area of a trapezium whose parallel sides are 12 cm and 8 cm and whose height is 5 cm.

Reveal answer ↓

What it is

A trapezium's area is the average of its two parallel sides times the height.

Answer

Area of a trapezium = (1/2) x (sum of parallel sides) x height = (1/2) x (12 + 8) x 5 = (1/2) x 20 x 5 = 50 square cm.

Area = (1/2)(a + b) x h

  • Area = (1/2)(a + b) h
  • = (1/2)(12 + 8)(5)
  • = 50 cm^2

Why learn this

It measures real shapes - fields, plots and cross-sections that are not perfect rectangles.

💡 Memory trick

Half the sum of the parallel sides, times the height: (1/2)(a + b) h.