Equations and Algebraic Expressions (Class 7)

What this worksheet covers

This is an eighteen-question practice worksheet on simple equations and algebraic expressions for Class 7, 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 simple equations and algebraic expressions at Class 7 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 in the space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Equations and Algebraic Expressions (Class 7) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The solution of 5x − 8 = 3x + 12 is x = _______.

   • A2
   • B6
   • C10correct
   • D20
   Solution: 5x − 3x = 12 + 8
   2x = 20, so x = 10.
   Check: LHS = 5(10) − 8 = 42 and RHS = 3(10) + 12 = 42. ✓

2. 2. The sum of three consecutive integers is 78. What is the largest of them?

   • A25
   • B26
   • C27correct
   • D28
   Solution: Let the integers be x, x + 1 and x + 2.
   3x + 3 = 78
   3x = 75, so x = 25.
   The integers are 25, 26 and 27, so the largest is 27.

3. 3. Consider the following statements.(i) 5x and 5x² are like terms.(ii) An equation remains balanced if both sides are multiplied by the same non-zero number.(iii) The equation 3x + 4 = 3x + 9 has no solution.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(ii) and (iii) onlycorrect
   • C(i) and (iii) only
   • DAll three
   Solution: Statement (i) is false — like terms must have exactly the same variables raised to the same powers, and x ≠ x². Statement (ii) is true. Statement (iii) is true; subtracting 3x from both sides leaves 4 = 9, which is impossible. Hence (ii) and (iii).