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Important Questions

Linear Equations in one Variable

ICSE · Class 8 · Mathematics

Most important questions from Linear Equations in one Variable for ICSE Class 8 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

47 questions24 flashcards5 concepts

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47 Questions·
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Sample Questions

1multiple choice
3 marks

Solve the equation and then find y from 1/x + 1/y = 3, where x is the solution of (2x + 1)/10 - (3 - 2x)/15 = (x - 2)/6. What is the value of y?

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7/26

First solve (2x + 1)/10 - (3 - 2x)/15 = (x - 2)/6. LCM of 10, 15, and 6 is 30. Multiply each term by 30: 3(2x + 1) - 2(3 - 2x) = 5(x - 2). 6x + 3 - 6 + 4x = 5x - 10. 10x - 3 = 5x - 10. 5x = -7. x = -7/5. Now use 1/x + 1/y = 3. 1/x = -5/7. So, -5/7 + 1/y = 3. 1/y = 3 + 5/7 = 26/7. y = 7/26.

2multiple choice
3 marks

A rectangle is 8 cm long and 5 cm wide. Its perimeter becomes double when each side is increased by x cm. What is the new length of the rectangle?

Show answer

14.5 cm

Original perimeter = 2(length + width) = 2(8 + 5) = 26 cm. After increasing each side by x cm, new length = 8 + x and new width = 5 + x. New perimeter = 2(8 + x + 5 + x) = 26 + 4x. Given: new perimeter is double the original perimeter. So, 26 + 4x = 2 × 26 = 52. 4x = 26. x = 6.5 cm. New length = 8 + 6.5 = 14.5 cm.

3multiple choice
3 marks

Solve 21 - 3(a - 7) = a + 20. What is the value of a?

Show answer

11/2

Expand the bracket: 21 - 3a + 21 = a + 20. So, 42 - 3a = a + 20. 42 - 20 = a + 3a. 22 = 4a. a = 22/4 = 11/2.

4multiple choice
3 marks

Solve (y + 2)/4 - (y - 3)/3 = 1/2. What is the value of y?

Show answer

12

LCM of 4, 3, and 2 is 12. Multiply each term by 12: 3(y + 2) - 4(y - 3) = 6. 3y + 6 - 4y + 12 = 6. -y + 18 = 6. -y = -12. y = 12.

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Frequently Asked Questions

What are the important topics in Linear Equations in one Variable for ICSE Class 8 Mathematics?
Linear Equations in one Variable covers several key topics that are frequently asked in ICSE Class 8 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Linear Equations in one Variable — ICSE Class 8 Mathematics?
Understand the core concepts first, then work through the 47 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Linear Equations in one Variable?
There are 47 practice questions available for Linear Equations in one Variable. These cover multiple question types including MCQs, short answer, and long answer questions.

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