Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
How to Use This Question Bank
- Attempt questions chapter by chapter in your notebook.
- Check answers with your textbook notes.
- Mark questions you cannot answer and revisit them after two days.
Chapter 1 — Rational Numbers
One Mark 1. Write the standard form of 14/−21. 2. Identify the rational number: −3/0, 5/7, 0/4. 3. What is the additive identity for rational numbers? 4. Is the set of rational numbers closed under division? 5. Find the product of 2/3 and its multiplicative inverse.
Short Answer (3 marks) 6. Verify the commutative property of multiplication for 3/4 and −2/5. 7. Find three rational numbers between −1/2 and 1/3. 8. Simplify: (2/3 + 1/6) ÷ (5/9).
Long Answer (5 marks) 9. Verify the distributive property of multiplication over addition for a = 1/2, b = 2/3, c = −1/4. 10. Arrange in descending order and represent on a number line: 2/3, −1/2, 1/4, −3/4.
Chapter 2 — Measurements
One Mark 1. The formula for the area of a rhombus using diagonals is ________. 2. A cube has side 5 cm. Its lateral surface area is ________. 3. What is the total surface area of a cuboid with l = 3, b = 2, h = 1? 4. The area of a trapezium with a = 8, b = 4, h = 3 is ________. 5. 1 m³ = ________ litres.
Short Answer (3 marks) 6. Find the area of a trapezium with parallel sides 12 cm and 8 cm and height 6 cm. 7. The TSA of a cube is 294 cm². Find its side and volume. 8. Find the side of a rhombus with diagonals 24 cm and 10 cm.
Long Answer (5 marks) 9. A godown is 12 m long, 8 m wide, and 5 m high. Find the cost of whitewashing the walls and ceiling at ₹15 per m². 10. A cuboidal swimming pool is 25 m × 10 m × 2 m. Find the volume in litres. How many hours to fill it at 500 litres per minute?
Chapter 3 — Algebra
One Mark 1. Expand (y + 7)². 2. Factorise 16x² − 9. 3. Evaluate 105² using an identity. 4. What is the middle term in (a + b)²? 5. Factorise: 3y² + 6y.
Short Answer (3 marks) 6. Expand and simplify (5m + 3)(5m − 3) − (2m)². 7. Factorise: x² − 14x + 49. 8. Find 48 × 52 using the identity (50 − 2)(50 + 2).
Long Answer (5 marks) 9. Factorise completely: 2a² + 8ab + 8b². Show all steps. 10. If x + 1/x = 5, find x² + 1/x² using the identity (a − b)².
Chapter 4 — Geometry
One Mark 1. State the RHS congruence criterion. 2. An exterior angle of a triangle is 120°. One opposite interior angle is 55°. Find the other. 3. In a rhombus, what is the angle between the diagonals? 4. The diagonal of a rectangle are always ________. 5. How many congruence criteria are there for triangles?
Short Answer (3 marks) 6. In △ABC, AB = AC and angle A = 40°. Find angle B and angle C. 7. In parallelogram ABCD, angle B = 115°. Find all four angles. 8. Name and state the criterion used when two angles and the included side are equal.
Long Answer (5 marks) 9. Prove: If two sides of a triangle are equal, the angles opposite them are also equal.
| 10. In quadrilateral ABCD, AB | CD and AB = CD. Prove ABCD is a parallelogram. |
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Chapters 5–8 — Coordinate Geometry, Statistics, Graphs, Information Processing
Short Answer 1. Find the distance between (2, −1) and (−2, 2). 2. Plot A(3, 0), B(0, 4), and find AB. 3. Draw y = 3x − 1 for x = 0, 1, 2. 4. Find the mean of: 12, 15, 18, 20, 25. 5. The mode of 3, 5, 3, 7, 5, 3, 8 is ________.
Long Answer 6. Two lines y = 2x and y = x + 3 are drawn. Find their intersection point graphically and verify algebraically. 7. The marks of 10 students are 45, 60, 55, 70, 65, 50, 80, 75, 90, 85. Find mean, median, and mode.