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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-01-CT
Number Systems — Full Chapter Test
Chapter: Number Systems
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Every real number corresponds to ___ on the number line.
  • A.two points
  • B.a unique point
  • C.no point
  • D.many points
2.
A rational number's decimal is terminating or:
  • A.non-recurring
  • B.recurring
  • C.irrational
  • D.random
3.
Rational $+$ irrational $=$
  • A.rational
  • B.irrational
  • C.zero
  • D.integer
4.
$\sqrt2$ is:
  • A.rational
  • B.irrational
  • C.an integer
  • D.zero
5.
Rationalizing $\dfrac{1}{\sqrt2}$ gives:
  • A.$\tfrac{\sqrt2}{2}$
  • B.$\sqrt2$
  • C.$2$
  • D.$\tfrac12$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Which is greater: $-3$ or $-5$?
7.
Express $0.6$ as a fraction.
8.
Is $2+\sqrt3$ rational or irrational?
9.
Is $\sqrt7$ rational or irrational?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find three rational numbers between $\tfrac13$ and $\tfrac12$.
11.
Express $0.\overline{7}$ as a fraction.
12.
Simplify $\sqrt8+\sqrt{18}$.
13.
Describe how to represent $\sqrt2$ on the number line.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find six rational numbers between $3$ and $4$.
15.
Express $0.\overline{123}$ as a fraction in lowest terms.

Answer Key

Section A — Multiple Choice Questions
  1. (B) a unique point
  2. (B) recurring
  3. (B) irrational
  4. (B) irrational
  5. (A) $\tfrac{\sqrt2}{2}$
Section B — Short Answer (2 marks)
  1. $-3$.
  2. $\tfrac35$.
  3. Irrational.
  4. Irrational.
Section C — Short Answer (3 marks)
  1. e.g. $\tfrac{2}{5},\ \tfrac{9}{20},\ \tfrac{7}{18}$.
  2. $\tfrac79$.
  3. $5\sqrt2$.
  4. Right triangle with legs $1,1$ gives hypotenuse $\sqrt2$; transfer it with a compass.
Section D — Long Answer (5 marks)
  1. e.g. $3.1,3.2,3.3,3.4,3.5,3.6$.
  2. $\tfrac{41}{333}$.
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