Vidaara.orgClass 8 · Mathematics
CodeVID-M08-02-RNL-01
The Real Number Line - Assignment
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.
Real numbers consist of:
- A.only integers
- B.rationals and irrationals
- C.only fractions
- D.only surds
2.
Every point on the number line is a:
- A.rational number
- B.real number
- C.whole number
- D.surd
3.
$\sqrt2$ is located using a right triangle with legs:
- A.$1$ and $1$
- B.$2$ and $2$
- C.$3$ and $4$
- D.$1$ and $2$
4.
Is every real number rational?
- A.Yes
- B.No
- C.Only positives
- D.Only integers
5.
Between any two real numbers there are:
- A.none
- B.one
- C.finitely many
- D.infinitely many
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Is every rational number a real number?
7.
Is every real number rational?
8.
A right triangle has legs $1$ and $1$. Find the hypotenuse.
9.
Between which integers does $\sqrt2$ lie?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Between which integers does $\sqrt{10}$ lie?
11.
Order on the number line: $-\sqrt2,\ 0,\ \sqrt3,\ 1$.
12.
A right triangle has legs $1$ and $2$. Which surd is the hypotenuse?
13.
Is $\pi$ to the left or right of $3$ on the number line?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Describe how to represent $\sqrt5$ on the number line using a right triangle.
15.
Arrange and place approximately on the number line: $-1.5,\ \sqrt2,\ -\sqrt3,\ 2.5$.
Answer Key
Section A — Multiple Choice Questions
- (B) rationals and irrationals
- (B) real number
- (A) $1$ and $1$
- (B) No
- (D) infinitely many
Section B — Short Answer (2 marks)
- Yes.
- No.
- $\sqrt2$.
- $1$ and $2$.
Section C — Short Answer (3 marks)
- $3$ and $4$.
- $-\sqrt2,\ 0,\ 1,\ \sqrt3$.
- $\sqrt5$.
- To the right.
Section D — Long Answer (5 marks)
- Draw a right triangle with legs $2$ and $1$; its hypotenuse is $\sqrt5$. With a compass, transfer this length from $0$ onto the line.
- $-\sqrt3,\ -1.5,\ \sqrt2,\ 2.5$.
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