Class 8 Maths — Important Questions with Answers

6 concept-first Class 8 Maths questions across 6 chapters — each with a clear model answer, the why behind it, and a memory trick to make it stick. NCERT-aligned and free. Build the base now, and your board exams, NEET and JEE feel a whole lot easier later.

6 questions•6 chapters•Concept-first•NCERT-aligned•For boards, NEET & JEE

Linear Equations in One Variable (1)Squares and Square Roots (1)Exponents and Powers (1)Comparing Quantities (1)Algebraic Expressions and Identities (1)Mensuration (1)

Linear Equations in One Variable1 question

MathematicsSolving a linear equationeasy

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.

Squares and Square Roots1 question

MathematicsSquare root by prime factorisationmedium

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.

Exponents and Powers1 question

MathematicsStandard formmedium

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.

Comparing Quantities1 question

MathematicsProfit percenteasy

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'.

Algebraic Expressions and Identities1 question

MathematicsStandard identitymedium

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.

Mensuration1 question

MathematicsArea of a trapeziummedium

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.

Top a = 8Base b = 12Height h = 5

Area = ½ (a + b) h = ½ (8 + 12) × 5 = 50 cm²

Trapezium — change the sides and height; the area follows ½ (a + b) h

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.

Start early. Stay ahead.

A few Class 8 Maths questions a day and the concepts become second nature. Explore every subject for Class 8 in the interactive Foundation bank, or ask the AI tutor any doubt the moment it shows up.

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