Tamil Nadu Class 9 Maths Model Paper 1 — Samacheer Kalvi

Instructions

• Time: 2 hours 30 minutes | Maximum Marks: 75
• Part A: 15 × 1 = 15 marks (Answer all)
• Part B: 5 × 3 = 15 marks (Answer any 5 from 8)
• Part C: 5 × 5 = 25 marks (Answer any 5 from 8)
• Part D: 1 × 20 = 20 marks (Answer all sub-questions)

Part A — 1 Mark Questions (Answer All)

1. If A = {1, 2, 3} and B = {2, 3, 4}, find n(A ∩ B). 2. Classify √16 as rational or irrational. 3. State the Remainder Theorem. 4. The sum of angles in a triangle is ______. 5. Find the distance between (0,0) and (5, 12). 6. Write the value of sin 90°. 7. What is the TSA of a cube with side 4 cm? 8. Find the class mark of the interval 40–50. 9. P(E) + P(E') = ______. 10. If n(A) = 6, n(B) = 4, n(A ∩ B) = 2, find n(A ∪ B). 11. Simplify: √12 + √27. 12. Is (x − 1) a factor of x² − 3x + 2? Verify. 13. Name the congruence rule: two angles and included side equal. 14. Simplify: sin 30° + cos 60°. 15. A die is rolled. Find P(prime number).

Part B — 3 Mark Questions (Answer any 5)

1. If A = {1,3,5,7,9} and B = {3,6,9}, draw a Venn diagram and find A − B and B − A. 2. Rationalise the denominator: 3/(2 − √3). 3. Find the remainder when p(x) = 3x³ − 4x² + x − 7 is divided by (x − 2). 4. ABCD is a parallelogram with ∠A = 65°. Find all angles. 5. Find the midpoint and distance between the points (−2, 3) and (4, −1). 6. A cone has r = 7 cm and h = 24 cm. Find its slant height and LSA. 7. Find the mean of: (0–10: 3), (10–20: 7), (20–30: 10), (30–40: 5). 8. Two coins are tossed. Find P(at least one head) and P(no head).

Part C — 5 Mark Questions (Answer any 5)

1. In a survey of 100 students: 60 like cricket, 50 like football, 30 like both. Find those liking neither, only cricket, and only football. Draw a Venn diagram. 2. Prove that √3 is irrational. Hence, show that (2 + √3) is also irrational. 3. Factorise: x³ + 13x² + 32x + 20 using Factor Theorem. 4. Prove: The angle subtended at the centre is twice the angle at the circumference. 5. The vertices of a triangle are (2,1), (4,5), (−3,3). Find all side lengths and determine the type of triangle. 6. Prove: (cosec θ − cot θ)² = (1 − cos θ)/(1 + cos θ). 7. A cylindrical tank has radius 14 m and depth 5 m. How many litres does it hold? (1 m³ = 1000 L) 8. The following are the weekly wages (₹) of 30 workers. Find mean, median, and mode for the grouped data: (100–200: 5), (200–300: 8), (300–400: 10), (400–500: 4), (500–600: 3).

Part D — 20 Marks (Answer All)

Graph Question (8 marks): Draw a less-than ogive for the following data and estimate the median: (10–20: 5), (20–30: 8), (30–40: 12), (40–50: 10), (50–60: 5)

Construction (6 marks): Construct a triangle with sides 5 cm, 6 cm, and 7 cm. Construct the centroid.

Computation (6 marks): A metallic solid consists of a cylinder (r = 3 cm, h = 8 cm) with a hemisphere on top (r = 3 cm). Find total volume and TSA.

Answer Key Hints