Class 10 Mathematics
Final Exam Model – Full Solved Answers
These answers are written exactly in the manner a student should write in the Class 10 Board Examination to score full marks.
Section A – MCQs
1. HCF of 306 and 657 = 9
2. Zeroes are 2 and 3
3. sin 30° = 1/2
4. Distance = 5 units
5. Tangent intersects circle at one point
6. Depends on radius and height
7. Mean = 5.5
8. Probability = 1/2
9. Graph is a straight line
10. tan 45° = 1
Section B – Very Short Answers
11. HCF of 135 and 225 using Euclid’s Division Algorithm
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
∴ HCF = 45
12. Zeroes of x² − 7x + 10
(x − 5)(x − 2) = 0
Zeroes are 5 and 2
13. sin 60° + cos 30°
= √3/2 + √3/2 = √3
14. Distance between (1,2) and (4,6)
= √[(4−1)² + (6−2)²]
= √(9 + 16) = 5
15. Midpoint of (2,2) and (6,6)
= ((2+6)/2 , (2+6)/2) = (4,4)
16. Radius when circumference = 44 cm
2πr = 44 ⇒ r = 7 cm
17. tan 45° − sin 30°
= 1 − 1/2 = 1/2
18. Mean of first five natural numbers
Mean = (1+2+3+4+5)/5 = 3
19. Curved surface area of cone
πrl
20. Probability of even number on a die
= 3/6 = 1/2
Section C – Short Answers
21. Prove √5 is irrational
Assume √5 = a/b where a and b are co-prime.
5 = a²/b² ⇒ a² = 5b²
a divisible by 5 ⇒ let a = 5k
b also divisible by 5
Contradiction.
∴ √5 is irrational.
22. Quadratic equation with zeroes 4 and −1
Sum = 3, Product = −4
Equation: x² − 3x − 4 = 0
23. Solve: 2x + y = 7, x − y = 1
Adding equations: 3x = 8 ⇒ x = 8/3
y = 7 − 2x = 5/3
Section D – Long Answers
31. HCF and LCM of 26 and 91
26 = 2 × 13
91 = 7 × 13
HCF = 13
LCM = 182
LCM × HCF = 182 × 13 = 2366
26 × 91 = 2366
∴ Verified
32. Solve x² − 5x − 6 = 0
(x − 6)(x + 1) = 0
x = 6 or −1
33. Area of sector (r = 14 cm, θ = 90°)
Area = (θ/360) × πr²
= (90/360) × 22/7 × 14 × 14 = 154 cm²
34. Mean by step deviation method
Mean = 30
35. Probability of prime number on a die
Prime numbers: 2,3,5
Probability = 3/6 = 1/2
Shaktimatha CBSE Learning
Class 10 Mathematics – Final Exam Model Answers
⬅️ 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 ✨
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