ICSE Class 10 Maths: Predicted Paper 2

• The question paper is for ICSE Class 10 Mathematics.
• The paper is predicted question paper 2.
• The time allowed is 2½ hours.
• The maximum marks is 80.
• All working, including rough work, must be clearly shown on the answer sheet.
• The intended marks for questions are given in brackets.
• Logarithm tables or calculators should be used for calculations, as appropriate.
• Section A is compulsory and contains 40 marks.
• Section B contains 40 marks, and any four questions must be attempted.

Section A, Question 1

• Solve the quadratic equation: 2x² - 5x + 3 = 0.
• Find the value of k if the point (3, k) lies on the line 2x - 3y = 5.
• Calculate the mean of the data set: 12, 15, 20, 25, 30.

Section A, Question 2

• In a geometric progression, the first term is 5, and the common ratio is 2. Find the 5th term.
• A sum of ₹5000 is invested at a compound interest rate of 10% per annum. Calculate the amount after 2 years.
• Prove that the diagonals of a rhombus bisect each other at right angles.

Section A, Question 3

• If sin θ = 3/5, find the values of cos θ and tan θ.
• Solve for x: log(x - 1) + log(x + 1) = log 6.
• Calculate the area of a sector with a radius of 7 cm and a central angle of 60°.

Section A, Question 4

• Find the equation of the line passing through the points (2, 3) and (4, 7).
• Evaluate: ∫(2x + 3) dx.
• In a triangle ABC, if angle A = 45°, angle B = 60°, and side a = 10 cm, find the length of side b.

Section B, Question 5

• A bag contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, the probability that it is either red or green needs to be determined.
• Prove that the opposite angles of a cyclic quadrilateral are supplementary using the properties of circles.
• Solve the system of equations using the substitution method: 2x + 3y = 12 and x - y = 3.

Section B, Question 6

• Find the sum of the first 15 terms of an arithmetic progression where the first term is 7 and the common difference is 3.
• If the coordinates of the midpoint of the line segment joining (2, -3) and (x, 5) are (4, 1), find the value of x.
• A cylindrical tank has a radius of 2 meters and a height of 5 meters. Calculate its volume.

Section B, Question 7

• Simplify: (x² - 9)/(x² - 6x + 9).
• If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the product of the roots, show that b² = 4ac.
• In a right-angled triangle, if the length of the hypotenuse is 13 cm and one of the legs is 5 cm, find the length of the other leg.

Section B, Question 8

• Find the value of k for which the lines 3x + 4y = 7 and 6x + 8y = k are parallel.
• Calculate the standard deviation of the data set: 4, 8, 6, 5, 3.
• Prove that the sum of the angles in a triangle is 180°.

Section B, Question 9

• If the function f(x) = 2x² - 3x + 5, find f(2).
• Solve the inequality: 2x - 5 > 3x + 1.
• In a parallelogram, prove that opposite sides are equal.

Section B, Question 10

• A cone has a base radius of 3 cm and a height of 4 cm. Calculate its slant height.
• If the arithmetic mean of two numbers is 8 and their geometric mean is 6, find the numbers.
• Using the binomial theorem, expand (1 + x)⁵.