Class 9 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 is not zero.

Step 2: 3/4 is already in the form p/q, so it is rational.

Step 3: sqrt(2), sqrt(3), sqrt(5) are all irrational numbers as they cannot be expressed as fractions.

Step 1: To rationalise, multiply numerator and denominator by sqrt(5):

Step 2: Calculate: [1/sqrt(5) x sqrt(5)/sqrt(5) = sqrt(5)/5]

Step 1: Multiply by the conjugate:

Step 2: Numerator: [sqrt(7) + sqrt(5)]

Step 3: Denominator: [(sqrt(7))^2 - (sqrt(5))^2 = 7 - 5 = 2]

Step 4: Result: [(sqrt(7) + sqrt(5))/2]

Step 1: The compound interest formula is: [A = P(1 + r/100)^n]

Step 2: Where A = Amount, P = Principal, r = rate per annum, n = number of years.

Step 1: Amount: [A = 20000(1 + 8/100)^3]

Step 2: Step by step: [A = 20000 x 1.08 x 1.08 x 1.08]

Step 3: Calculate: [A = 20000 x 1.259712 = Rs 25194.24]

Step 1: After year 1: [20000 x 1.12 = 22400. After payment: 22400 - 8000 = 14400]

Step 2: After year 2: [14400 x 1.12 = 16128. After payment: 16128 - 9000 = 7128]

Step 3: After year 3: [7128 x 1.12 = 7983.36]

Step 1: The angle sum property states that the sum of all interior angles of any triangle is always 180°.

Step 2: This can be proven by drawing a line parallel to the base through the opposite vertex. [∠A + ∠B + ∠C = 180°]

Step 1: Using angle sum property: [∠A + ∠B + ∠C = 180°]

Step 2: Substitute: [(2x + 10) + 3x + (x + 20) = 180]

Step 3: Combine like terms: [6x + 30 = 180]

Step 4: Solve: [6x = 150 → x = 25°]

Step 1: Sum of angles: [(3x-5) + (2x+15) + (x+20) = 180]

Step 2: Simplify: [6x + 30 = 180 → x = 25]

Step 3: ∠P = 3(25)-5 = 70°, ∠Q = 2(25)+15 = 65°, ∠R = 25+20 = 45°

Step 4: All angles < 90°, so it's an acute triangle.