Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Class 9 Maths — Term 3 Unit Test
Time: 2.5 Hours | Marks: 60
Section A — 1 Mark (1 × 10 = 10)
1. Define sin θ in a right triangle. 2. What is the value of sin 30°? 3. What is the value of cos 60°? 4. State the identity: sin²θ + cos²θ = ? 5. Define mean of a data set. 6. What is the median? 7. Define mode. 8. What is the probability of an impossible event? 9. What is the sum of all probabilities in a sample space? 10. A die is rolled. What is P(getting 6)?
Section B — 3 Mark (3 × 6 = 18)
(Choose 6 of 7)
1. If sin θ = 3/5, find cos θ and tan θ. 2. Prove the identity: sec²θ − tan²θ = 1. 3. A ladder 10 m long leans against a wall. If the foot makes a 60° angle with the ground, find the height the ladder reaches. 4. Find the mean of: 5, 7, 9, 11, 13, 15. 5. Find the median of: 3, 7, 2, 9, 5, 8, 4. 6. A bag contains 3 red, 5 blue, and 2 green balls. Find the probability of drawing: (a) a red ball, (b) a blue ball, (c) a green ball. 7. Two coins are tossed. Write the sample space and find P(exactly one head).
Section C — 5 Mark (5 × 4 = 20)
(Choose 4 of 5)
1. Prove: tan²θ + 1 = sec²θ and cot²θ + 1 = cosec²θ. 2. A tower stands vertically. From a point 20 m away on the ground, the angle of elevation of the top is 45°. Find the height of the tower. 3. The following data shows marks scored by 20 students: 45, 52, 38, 61, 55, 48, 70, 42, 58, 63, 36, 51, 66, 47, 54, 69, 41, 57, 73, 44. Find the mean, median, and mode. 4. A die is thrown twice. Find the probability that: (a) both show the same number; (b) sum is 7; (c) sum is at least 10. 5. Construct a frequency distribution table and histogram for the data: scores of 30 students grouped in intervals 0-10, 10-20, 20-30, 30-40, 40-50.
Section D — Mixed Application (12 marks)
D1. Trigonometry (4 marks): If 3 sin θ = 4 cos θ, find sin θ, cos θ, and verify sin²θ + cos²θ = 1.
D2. Statistics (4 marks): The weights (in kg) of 10 students are: 42, 45, 48, 50, 52, 54, 55, 58, 60, 65. (a) Find the mean weight. (b) Find the median weight. (c) Is there a mode? Explain.
D3. Probability (4 marks): A pack of 52 playing cards is shuffled. (a) P(drawing an ace) = ? (b) P(drawing a red card) = ? (c) P(drawing a king of hearts) = ? (d) P(drawing a face card) = ?
Trigonometry Reference Table
| Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | ∞ |
End of Term 3 Unit Test