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Showing 6 questions in Mathematics for Class 8. Tap a card to reveal the answer.
MathematicsLinear Equations in One VariableeasySolve 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 RootsmediumFind 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 PowersmediumExpress 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 QuantitieseasyA 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 IdentitiesmediumUse 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.
MathematicsMensurationmediumFind 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.