Linear Equations (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on linear equations in one variable for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on linear equations in one variable at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done on the blank space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Linear Equations (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The solution of 3x + 5 = 20 is x = _______.

   • A3
   • B5correct
   • C15
   • D25
   Solution: 3x + 5 = 20
   3x = 20 − 5 = 15
   x = 15 ÷ 3 = 5.
   Check: 3(5) + 5 = 20. ✓

2. 2. The sum of two consecutive natural numbers is 75. The smaller number is _______.

   • A36
   • B37correct
   • C38
   • D39
   Solution: Let the numbers be x and x + 1.
   x + (x + 1) = 75
   2x + 1 = 75, so 2x = 74 and x = 37.
   The two numbers are 37 and 38, and 37 + 38 = 75. ✓

3. 3. Consider the following statements.(i) A linear equation in one variable has exactly one solution.(ii) Adding the same number to both sides of an equation does not change its solution.(iii) The equation 2x + 3 = 2x + 5 has a solution.Which of the statements is/are correct?

   • A(i) and (ii) onlycorrect
   • B(ii) and (iii) only
   • C(i) and (iii) only
   • DAll three
   Solution: Statement (i) is true — an equation of the form ax + b = 0 with a ≠ 0 has the single solution x = −b ÷ a. Statement (ii) is true; this is the balancing rule used to solve equations. Statement (iii) is false; subtracting 2x from both sides leaves 3 = 5, which is impossible, so there is no solution. Hence (i) and (ii).