Class 10 Mathematics
Model Answers – How to Write in Board Exam
These answers are written exactly in the way a student should write in the Class 10 public examination.
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Section A – MCQs (Model)
Q1. The HCF of 306 and 657 is:
Answer: 9
Q2. If α and β are the zeroes of 2x² − 5x + 3, then α + β is:
Answer: 5/2
Q3. The value of sin 30° is:
Answer: 1/2
Section B – Very Short Answers (2 Marks)
Q11. Use Euclid’s Division Algorithm to find the HCF of 135 and 225.
Answer:
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
Since the remainder becomes zero, the HCF of 135 and 225 is 45.
Q12. Find the zeroes of the polynomial x² − 7x + 10.
Answer:
x² − 7x + 10 = 0
(x − 5)(x − 2) = 0
∴ x = 5, 2
So, the zeroes are 5 and 2.
Section C – Short Answers (3 Marks)
Q21. Prove that √3 is irrational.
Answer:
Assume that √3 is a rational number.
Then √3 = a/b, where a and b are co-prime integers.
Squaring both sides:
3 = a² / b²
⇒ a² = 3b²
So, a² is divisible by 3 ⇒ a is divisible by 3.
Let a = 3k.
Substituting:
9k² = 3b² ⇒ b² = 3k²
So, b is also divisible by 3.
This contradicts the assumption that a and b are co-prime.
∴ √3 is irrational.
Section D – Long Answer (4 Marks)
Q31. Find the HCF and LCM of 26 and 91 and verify that:
LCM × HCF = Product of numbers.
Answer:
26 = 2 × 13
91 = 7 × 13
HCF = 13
LCM = 2 × 7 × 13 = 182
LCM × HCF = 182 × 13 = 2366
Product of numbers = 26 × 91 = 2366
∴ LCM × HCF = Product of the numbers.
Important Exam Writing Tips
- Write step-by-step
- Use proper mathematical symbols
- Underline final answer
- Do not skip steps
- Neat handwriting gives extra advantage
Shaktimatha CBSE Learning
Class 10 Mathematics – Model Answers (Student Writing Style)
⬅️ 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
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