Class 10 Mathematics
Final Exam Model Question Paper
Time: 3 Hours Maximum Marks: 80
General Instructions:
- All questions are compulsory.
- The question paper consists of 5 Sections A, B, C, D and E.
- Use of calculator is not permitted.
- Draw neat diagrams wherever required.
Section A – MCQs
(1 × 10 = 10 Marks)
1. The HCF of 306 and 657 is:
a) 3 b) 6 c) 9 d) 18
2. The zeroes of the polynomial x² − 5x + 6 are:
a) 2, 3 b) −2, −3 c) 1, 6 d) 3, 4
3. The value of sin 30° is:
a) 1 b) √3/2 c) 1/2 d) 0
4. Distance between (0,0) and (3,4) is:
a) 4 b) 5 c) 6 d) 7
5. A tangent to a circle intersects it in:
a) Two points b) One point c) No point d) Infinite points
6. The curved surface area of a cylinder depends on:
a) Radius only b) Height only c) Radius and height d) Diameter
7. Mean of first 10 natural numbers is:
a) 4.5 b) 5 c) 5.5 d) 6
8. Probability of getting a head when a coin is tossed is:
a) 0 b) 1 c) 1/2 d) 2
9. The graph of a linear equation is:
a) Curve b) Circle c) Straight line d) Parabola
10. The value of tan 45° is:
a) 0 b) 1 c) √3 d) 1/√3
Section B – Very Short Answer
(2 × 10 = 20 Marks)
11. Use Euclid’s Division Algorithm to find the HCF of 135 and 225.
12. Find the zeroes of the polynomial x² − 7x + 10.
13. Find the value of sin 60° + cos 30°.
14. Find the distance between the points (1, 2) and (4, 6).
15. Find the midpoint of the line joining (2, 2) and (6, 6).
16. Find the radius of a circle whose circumference is 44 cm.
17. Find the value of tan 45° − sin 30°.
18. Find the mean of first five natural numbers.
19. Write the formula for curved surface area of a cone.
20. Find the probability of getting an even number when a die is thrown.
Section C – Short Answer
(3 × 10 = 30 Marks)
21. Prove that √5 is irrational.
22. Find the quadratic equation whose zeroes are 4 and −1.
23. Solve the pair of linear equations:
2x + y = 7, x − y = 1
24. Find the area of a triangle whose vertices are (1,1), (4,1) and (2,5).
25. Find the ratio in which the point (2, −2) divides the line joining A(4, −6) and B(−2, 2).
26. Find the radius of a sphere whose surface area is 616 cm².
27. Evaluate: sin 30° / cos 60°.
28. Find the mode of the data: 3, 5, 7, 5, 9, 5, 11.
29. Find the probability of getting a multiple of 3 from numbers 1 to 10.
30. Find the sum of first 30 natural numbers.
Section D – Long Answer
(4 × 5 = 20 Marks)
31. Find the HCF and LCM of 26 and 91 and verify that:
LCM × HCF = Product of the numbers.
32. Solve the quadratic equation by factorisation:
x² − 5x − 6 = 0.
33. Find the area of a sector of a circle of radius 14 cm and angle 90°.
34. Find the mean using step deviation method:
| x | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| f | 3 | 7 | 12 | 8 | 5 |
35. Find the probability of getting a prime number when a die is thrown.
Shaktimatha CBSE Learning
Class 10 Mathematics – Final Exam Model Paper
⬅️ Back to Class 10 Mathematics Library
📘 Class 10 Mathematics – Previous Board Question Papers & Model Answers
This library is specially prepared for Class 10 Board Exam students to understand question patterns, answer-writing style, step-by-step solutions, and examiner expectations.
🧠 How to Write Maths Answers in Exam
📝 Previous Board Question Papers
- Previous Board Question Paper – Set 1
- Question Paper – Set 2
- Question Paper – Set 3
- Question Paper – Set 4
- Question Paper – Set 5
- Question Paper – Set 6
✍️ Full Board Exam Answers (Student Writing Style)
- Full Answers – Set 1
- Full Answers – Set 2
- Full Answers – Set 3
- Full Answers – Set 5
- Full Answers – Set 6
📊 Model Papers & Practice Sets
✔ First read the Question Paper
✔ Try writing answers yourself
✔ Compare with Full Model Answers
✔ Observe steps, diagrams, and presentation
✔ Practice again to score full marks
Prepared with dedication by Shaktimatha Learning ✨
Concept clarity • Exam confidence • Board success
.png)
No comments:
Post a Comment