Tamil Nadu Class 9 Maths Model Paper 2 — Samacheer Kalvi

Instructions

• Time: 2 hours 30 minutes | Maximum Marks: 75
• Part A: 15 × 1 = 15 marks | Part B: 5 × 3 = 15 | Part C: 5 × 5 = 25 | Part D: 1 × 20 = 20

Part A — 1 Mark Questions

1. Write the power set of {3, 7}. 2. State whether 0.121121112... is rational or irrational. 3. Find the zero of p(x) = 5x − 10. 4. What is the exterior angle of a triangle if the two non-adjacent interior angles are 60° and 75°? 5. In which quadrant does (−4, 5) lie? 6. What is the value of cos 0°? 7. Find the volume of a sphere with radius 3 cm. (Take π = 22/7) 8. Define cumulative frequency. 9. A card is drawn from a deck. Find P(ace). 10. If n(U) = 20 and n(A) = 12, find n(A'). 11. Simplify: (5√3)(2√3). 12. Find the remainder when x³ + 2 is divided by (x + 1). 13. State the condition for two triangles to be similar by AA criterion. 14. Find the centroid of triangle with vertices (0,0), (6,0), (0,6). 15. State Heron's formula.

Part B — 3 Mark Questions (Answer any 5)

1. In a class of 50 students, 30 study Tamil and 25 study Hindi. If 15 study both, find those studying neither. 2. Simplify: (√5 + √3)² − (√5 − √3)². 3. Using Factor Theorem, check if (x + 3) is a factor of x³ + 27. 4. Prove that the diagonals of a rectangle are equal. 5. Find the coordinates of the point that divides the segment joining (1,−3) and (4,3) in the ratio 1:2. 6. If sin A = 8/17, find cos A and tan A. 7. The diameter of a hemisphere is 28 cm. Find its TSA. 8. Find the mode and median for: 12, 15, 20, 25, 15, 30, 15, 28.

Part C — 5 Mark Questions (Answer any 5)

1. Verify De Morgan's Law for U = {1-12}, A = {even numbers}, B = {multiples of 3}. 2. Simplify: [2^(n+2) − 4 × 2^n] / [2 × 2^(n+3)] and express as a power of 2. 3. If (x − 3) is a factor of x³ − kx² + 11x − 6, find k. Then factorise the polynomial completely. 4. Prove: The perpendicular from the centre of a circle to a chord bisects the chord. 5. Prove that the points A(4, 3), B(6, 4), C(5, 6), D(3, 5) form a rhombus. 6. Prove the identity: (tan A + sin A)/(tan A − sin A) = (sec A + 1)/(sec A − 1). 7. A solid consists of a cone on top of a cylinder, both with r = 6 cm. If the cone height = 8 cm and cylinder height = 12 cm, find the total surface area. 8. The scores of 60 students in a test are given. Using the grouped frequency table (0–10: 4, 10–20: 10, 20–30: 18, 30–40: 15, 40–50: 10, 50–60: 3), find mean using assumed mean method.

Part D — 20 Marks

Graph (8 marks): Draw a histogram and frequency polygon for the following data: (0–10: 5), (10–20: 10), (20–30: 18), (30–40: 12), (40–50: 5)

Construction (6 marks): Construct a right triangle with hypotenuse 10 cm and one leg 6 cm. Verify using Pythagoras.

Computation (6 marks): The rainfall data for 7 days: 12, 8, 15, 20, 12, 18, 25 (in mm). Find mean, median, and mode.

Answer Key Hints