Real Numbers and Polynomials (Class 10)

What this worksheet covers

This is an eighteen-question practice worksheet on real numbers and polynomials for Class 10, 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 real numbers and polynomials at Class 10 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 Real Numbers and Polynomials (Class 10) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The HCF of 12 and 18 is _______.

   • A2
   • B3
   • C6correct
   • D36
   Solution: Writing the prime factorisations, 12 = 2² × 3 and 18 = 2 × 3². The HCF takes the lowest power of each common prime: 2 × 3 = 6. (36 is their LCM.)

2. 2. If the HCF of 96 and 404 is 4, then their LCM is _______.

   • A9696correct
   • B2424
   • C38 784
   • D404
   Solution: Since HCF × LCM = product of the numbers, LCM = {96 × 404/4} = {38784/4} = 9696.

3. 3. If α and β are the zeroes of x² − 6x + 8, then {1/α} + {1/β} equals _______.

   • A{3/4}correct
   • B{4/3}
   • C6
   • D{1/8}
   Solution: Here α + β = 6 and αβ = 8. Now {1/α} + {1/β} = {α + β/αβ} = {6/8} = {3/4}. Checking directly, the zeroes are 2 and 4, and {1/2} + {1/4} = {3/4}.