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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-19-NLN-01
Number-Line Representation — Assignment
Chapter: Linear Inequations
Topic: Graphical Representation on Number Line
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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.
$x>3$ is shown by:
  • A.closed circle at $3$
  • B.open circle at $3$, arrow right
  • C.closed circle, arrow left
  • D.a solid line
2.
A closed circle means the endpoint is:
  • A.excluded
  • B.included
  • C.infinite
  • D.negative
3.
An open circle means the endpoint is:
  • A.included
  • B.excluded
  • C.doubled
  • D.zero
4.
$x\le5$ is shown by:
  • A.open circle at $5$
  • B.closed circle at $5$, arrow left
  • C.closed circle, arrow right
  • D.no mark
5.
$x\ge0$ is shown by:
  • A.open circle at $0$
  • B.closed circle at $0$, arrow right
  • C.closed circle, arrow left
  • D.open, arrow left
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
How is $x>2$ marked at $2$?
7.
How is $x\le4$ marked at $4$?
8.
Does $x<5$ include $5$?
9.
Describe the graph of $x\ge1$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Describe the number-line graph of $x\le3$ ($x\in\mathbb{R}$).
11.
Describe the graph of $-1
12.
Describe the graph of the solution set $\{1,2,3\}$ ($x\in\mathbb{N},\ x<4$).
13.
Describe the graph of $x>0$ ($x\in\mathbb{R}$).
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Solve $-3\le 2x-1<5$ for $x\in\mathbb{R}$ and represent the solution on a number line.
15.
Solve $\dfrac{x}{2}-1\le2$ together with $x\ge-2$ for $x\in\mathbb{R}$ and represent the common solution.

Answer Key

Section A — Multiple Choice Questions
  1. (B) open circle at $3$, arrow right
  2. (B) included
  3. (B) excluded
  4. (B) closed circle at $5$, arrow left
  5. (B) closed circle at $0$, arrow right
Section B — Short Answer (2 marks)
  1. An open circle.
  2. A closed circle.
  3. No.
  4. A filled dot at $1$ with an arrow to the right.
Section C — Short Answer (3 marks)
  1. A closed dot at $3$ with an arrow to the left.
  2. Open dot at $-1$, closed dot at $2$, segment joined.
  3. Dots at $1,2$ and $3$.
  4. Open dot at $0$ with an arrow to the right.
Section D — Long Answer (5 marks)
  1. $-1\le x<3$ (closed at $-1$, open at $3$).
  2. $-2\le x\le6$ (closed dots at both ends).
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