Question Paper 1
Section A: Very Short Answer Questions (1 Mark Each)
1. Simplify 45\sqrt{45} to its simplest radical form. (Chapter 1: Number Systems)
2. Find the zeroes of the polynomial x2+3x−4x^2 + 3x - 4. (Chapter 2: Polynomials)
3. What are the coordinates of the origin in the coordinate plane? (Chapter 3: Coordinate
Geometry)
4. Write the general form of a linear equation in two variables. (Chapter 4: Linear Equations in Two
Variables)
5. State Euclid’s first postulate. (Chapter 5: Introduction to Euclid's Geometry)
Section B: Short Answer Questions (2 Marks Each)
6. Find the measure of xx if two angles are supplementary and one angle is 4x4x while the other is
3x3x. (Chapter 6: Lines and Angles)
7. Prove that the sum of the angles of a triangle is 180∘180^\circ. (Chapter 7: Triangles)
8. Verify if the given points (1,2),(4,6),(7,10)(1, 2), (4, 6), (7, 10) lie on the same straight line.
(Chapter 8: Quadrilaterals)
9. Find the area of a triangle with base 6 cm6 \text{ cm} and height 4 cm4 \text{ cm}. (Chapter 9:
Areas of Parallelograms and Triangles)
10. Write the equation of a circle with radius 5 units5 \text{ units} and center at (0,0)(0, 0). (Chapter
10: Circles)
Section C: Short Answer Questions (3 Marks Each)
11. Construct a perpendicular bisector of a line segment of length 8 cm8 \text{ cm}. (Chapter 11:
Constructions)
12. Calculate the area of a triangle with sides 5 cm,12 cm,and 13 cm5 \text{ cm}, 12 \text{ cm},
\text{and } 13 \text{ cm} using Heron’s formula. (Chapter 12: Heron’s Formula)
13. A sphere has a radius of 7 cm7 \text{ cm}. Find its surface area. (Chapter 13: Surface Areas and
Volumes)
14. Find the mode of the following data set: 3,4,6,4,7,8,4,5,9,43, 4, 6, 4, 7, 8, 4, 5, 9, 4. (Chapter 14:
Statistics)
15. A coin is tossed. What is the probability of getting a head? (Chapter 15: Probability)
Section D: Long Answer Questions (4 Marks Each)
16. Solve: 2x+y=52x + y = 5 and 3x−y=43x - y = 4 using the substitution method. (Chapter 4: Linear
Equations in Two Variables)
17. Prove that the diagonals of a parallelogram bisect each other. (Chapter 9: Areas of
Parallelograms and Triangles)
Section E: Case-Based/Competency Questions (5 Marks Each)
18. A rectangular field is 50 m50 \text{ m} long and 30 m30 \text{ m} wide. A path of width 3 m3
\text{ m} runs around the field. Find the area of the path. (Chapters 9 & 13)
19. A cylindrical tank has a radius of 7 cm7 \text{ cm} and height 10 cm10 \text{ cm}. Find its
volume. (Chapter 13: Surface Areas and Volumes)
Question Paper 2
Section A: Very Short Answer Questions (1 Mark Each)
1. Express 50\sqrt{50} in its simplest radical form. (Chapter 1: Number Systems)
2. Find the zeroes of the polynomial x2−5x+6x^2 - 5x + 6. (Chapter 2: Polynomials)
3. What is the name of the quadrant in which x>0x > 0 and y<0y < 0? (Chapter 3: Coordinate
Geometry)
4. Write an example of a linear equation in two variables. (Chapter 4: Linear Equations in Two
Variables)
5. State Euclid’s fifth postulate. (Chapter 5: Introduction to Euclid's Geometry)
Section B: Short Answer Questions (2 Marks Each)
6. Find the value of xx if two angles are complementary and one angle is 3x3x and the other is
2x2x. (Chapter 6: Lines and Angles)
7. Prove that the diagonals of a parallelogram bisect each other. (Chapter 7: Triangles)
8. Find the fourth vertex of a parallelogram if three vertices are (0,0),(4,0),and (0,3).(0, 0), (4, 0),
\text{and } (0, 3). (Chapter 8: Quadrilaterals)
9. Find the area of a parallelogram with base 8 cm8 \text{ cm} and height 5 cm.5 \text{ cm}.
(Chapter 9: Areas of Parallelograms and Triangles)
10. Write the equation of a circle with center (2,−1)(2, -1) and radius 5 units.5 \text{ units}. (Chapter
10: Circles)
Section C: Short Answer Questions (3 Marks Each)
11. Construct a triangle with sides 6 cm,8 cm,and 10 cm.6 \text{ cm}, 8 \text{ cm}, \text{and } 10
\text{ cm}. (Chapter 11: Constructions)
12. Calculate the area of a triangle with sides 13 cm,14 cm,and 15 cm13 \text{ cm}, 14 \text{ cm},
\text{and } 15 \text{ cm} using Heron’s formula. (Chapter 12: Heron’s Formula)
13. A cone has a slant height of 13 cm13 \text{ cm} and a base radius of 5 cm.5 \text{ cm}. Find its
curved surface area. (Chapter 13: Surface Areas and Volumes)
14. The marks of students in a test are as follows: 12,15,14,18,10,20,18,16,14,19.12, 15, 14, 18, 10,
20, 18, 16, 14, 19. Find the mean and median of the marks. (Chapter 14: Statistics)
15. If two dice are rolled, find the probability of getting a sum of 8.8. (Chapter 15: Probability)
Section D: Long Answer Questions (4 Marks Each)
16. Solve: 4x−3y=64x - 3y = 6 and 2x+y=32x + y = 3 using the elimination method. (Chapter 4: Linear
Equations in Two Variables)
17. Prove that the sum of the exterior angles of a polygon is 360∘.360^\circ. (Chapter 9: Areas of
Parallelograms and Triangles)
Section E: Case-Based/Competency Questions (5 Marks Each)
18. A square park has side length 20 m.20 \text{ m}. A circular fountain of radius 7 m7 \text{ m} is
constructed in the middle of the park. Calculate the remaining area of the park after the
construction of the fountain. (Chapters 9 & 13)
19. A solid cylinder has a height of 10 cm10 \text{ cm} and a base radius of 7 cm.7 \text{ cm}. Find its
volume and total surface area. (Chapter 13: Surface Areas and Volumes)
