Algebraic Expressions (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on algebraic expressions, identities and factorisation 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 algebraic expressions, identities and factorisation 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 Algebraic Expressions (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. How many terms are there in the expression 4x2y − 3xy + 7?

   • A1
   • B2
   • C3correct
   • D4
   Solution: Terms are the parts separated by + and − signs. Here they are 4x²y, −3xy and 7, so there are 3 terms. Such an expression is called a trinomial.

2. 2. The factors of x2 − 7x + 12 are _______.

   • A(x − 3)(x − 4)correct
   • B(x + 3)(x + 4)
   • C(x − 2)(x − 6)
   • D(x − 1)(x − 12)
   Solution: We need two numbers whose product is +12 and whose sum is −7. These are −3 and −4.
   x² − 7x + 12 = x² − 3x − 4x + 12 = x(x − 3) − 4(x − 3) = (x − 3)(x − 4).

3. 3. Consider the following statements.(i) (a + b)2 = a2 + b2 for all values of a and b.(ii) Every polynomial of degree 2 can be written as the product of two linear factors with integer coefficients.(iii) 3x and 3x2 are unlike terms.Which of the statements is/are correct?

   • A(iii) onlycorrect
   • B(i) and (iii) only
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is false — the middle term 2ab is missing; it is true only when ab = 0. Statement (ii) is false; for example x² + 1 cannot be factorised into linear factors with integer coefficients. Statement (iii) is true; like terms must have exactly the same variables raised to the same powers, and x ≠ x². Hence (iii) only.