Class 8 ICSE Maths Sample Paper 2026 with Solutions

Step 1: A rational number is any number that can be written as a fraction p/q, where p and q are integers and q ≠ 0.

Step 2: 3/7 is already in the form p/q with p = 3, q = 7.

Step 3: √2, √5, and π are irrational numbers — they cannot be expressed as fractions.

Step 1: LHS: [2/3 × (4/5 + 1/5) = 2/3 × 5/5 = 2/3 × 1 = 2/3]

Step 2: RHS: [2/3 × 4/5 + 2/3 × 1/5 = 8/15 + 2/15 = 10/15 = 2/3]

Step 3: LHS = RHS = 2/3. Distributive property verified!

Step 1: Let x = a/b. Then: [x + 1/x = 25/12]

Step 2: Multiply by 12x: [12x² + 12 = 25x]

Step 3: Rearrange: [12x² - 25x + 12 = 0]

Step 4: Factor: [(3x - 4)(4x - 3) = 0, so x = 4/3 or x = 3/4]

Step 5: Since a/b > 1: [a/b = 4/3]

Step 1: Law of exponents: [a⁰ = 1 (for any a ≠ 0)]

Step 2: Therefore: [5⁰ = 1]

Step 1: Express 4 as 2²: [4² = (2²)² = 2⁴]

Step 2: Numerator: [2³ × 2⁴ = 2⁷]

Step 3: Divide: [2⁷ ÷ 2⁵ = 2² = 4]

Step 1: Factor: [2ˣ(2¹ + 1) = 48]

Step 2: Simplify: [2ˣ × 3 = 48]

Step 3: Solve: [2ˣ = 16 = 2⁴]

Step 4: Therefore: [x = 4]

Step 1: A quadrilateral has 4 sides, so n = 4.

Step 2: Sum of interior angles: [(n - 2) × 180° = (4 - 2) × 180° = 2 × 180° = 360°]

Step 1: Number of diagonals formula: [n(n - 3)/2]

Step 2: For a hexagon (n = 6): [6(6 - 3)/2 = 6 × 3/2 = 18/2 = 9]

Step 1: Let interior = 7k and exterior = 2k.

Step 2: They are supplementary: [7k + 2k = 180° → 9k = 180° → k = 20°]

Step 3: Exterior angle = 2 × 20° = 40°.

Step 4: Number of sides: [n = 360° ÷ 40° = 9]