PYQs
Practise questions grouped by chapter and source year.
Practice questions are organised using the years and labels in our source collection. Work through the solutions with your teacher; these are not a complete official examination paper.
Practice question 1
Source year: 20253 marksSolve using quadratic formula: 2x² + x - 4 = 0. [CBSE 2025]
Practice question 2
Source year: 20242 marksFind the nature of roots of equation 2x² - 4x + 3 = 0 without actually finding them. [CBSE 2024]
Practice question 3
Source year: 20232 marksFind value of k for which x² + 5kx + 16 = 0 has equal roots. [CBSE 2023]
Practice question 4
Source year: 20223 marksA train travels 360 km at a uniform speed. If speed had been 5 km/h more, it would have taken 1 hour less. Find original speed. [CBSE 2022]
Practice question 5
Source year: 20212 marksSolve by factorization: x² - 3x - 10 = 0. [CBSE 2021]
Formulae
Revisit important relationships and quick revision formulae.
Standard Form
ax² + bx + c = 0, where a ≠ 0
Quadratic Formula
x = [-b ± √(b²-4ac)] / 2a
Discriminant
D = b² - 4ac\nD > 0: Two distinct real roots\nD = 0: Two equal real roots\nD < 0: No real roots
Sum and Product of Roots
If α and β are roots:\nSum: α + β = -b/a\nProduct: αβ = c/a
Derivations
Work through the reasoning behind key concepts.
Deriving Quadratic Formula
From ax² + bx + c = 0, divide by a: x² + (b/a)x + c/a = 0. Complete the square: [x + b/(2a)]² - b²/(4a²) + c/a = 0. Simplify: [x + b/(2a)]² = (b²-4ac)/(4a²). Taking square root: x = [-b ± √(b²-4ac)] / (2a).
Nature of Roots
Discriminant D = b²-4ac determines roots: If D > 0, two distinct real roots. If D = 0, two equal real roots (perfect square). If D < 0, no real roots (complex roots).
Deriving Quadratic Formula
From ax² + bx + c = 0:\nDivide by a: x² + (b/a)x + c/a = 0\nComplete the square: [x + b/(2a)]² = (b²-4ac)/(4a²)\nTaking square root: x = [-b ± √(b²-4ac)] / 2a
Condition for Equal Roots
Roots are equal when discriminant D = 0, i.e., b² - 4ac = 0
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