Case study (4 Marks)

Question 14 Marks

2. Which of the following statements is true?
A. Every irrational number can be represented as a fraction.
B. Every irrational number can be represented with the help of decimals.
C. Every rational number can be represented as a terminating decimal.
D. Every rational number can be represented as an integer.

Answer

2. B. Every irrational number can be represented with the help of decimals.

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Question 24 Marks

Vasu represents √4.5 on the number line PW. The length of TS = 1 unit. His representation is shown below.

6. Which letter represent 0 of the number line?
A. P
B. R
C. X
D. S
7. Between which two points does 5.2 lie on this number line?
A. U and V
B. T and U
C. S and T
D. V and W
8. Screen size is deined by the distance between two diagonally opposite corners of a screen. A
manufacturer can make rectangular display screens as per clients’ demands.
A client purchased a display screen of size $\sqrt{70}$ units from the manufacturer last year. For an upgrade, he wants the same type of screen with a larger display.
What are the possible dimensions of the screen purchased by the client last year?
9. The new screen size must be more than double, but it should be less than three times that of the existing one.
Which of the following screen sizes meets the client’s requirement?
A. $\sqrt{145}$ units
B. $\sqrt{175}$ units
C. $2 \sqrt{70}$ units
D. $\sqrt{580}$ units
10. The new display screen is to be installed in a space measuring 3 m × 3 m. To make the desired screen for the client, what other information is required by the manufacturer?

Answer

6. D. S
7. A. U and V
8. Writes length and breadth, which are greater than zero and less than 70, with or without the word ‘Chapter(s)’
● Length 21 and breadth 7
● 21 units and 7 units
● 69 units and 1 Chapter
9. D. $\sqrt{580}$ units
10. Due consideration is given to factors including display dimensions and orientation (portrait/landscape) 2 x y z with or without the word ‘units’
● The manufacturer needs to know the space available for the screen installation along with the screen size.
● Length and breadth, along with orientation, is to be considered.

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Question 34 Marks

1. A number line consists of an ininite number of points. Points on it are associated with a rational
number.
Khushi says – ‘A point on the number line can represent different forms of a rational number.’
Akash says – ‘I think each point represents a unique rational number.’
Who is correct? Give an example to support your argument.

Answer

1. Names both Khushi and Akash and provides a valid explanation with examples
● Khushi is correct as numbers including 1/2, 2/4, 3/6, 4/8 and 0.5 can be represented by the same point on the number line. Akash is correct as each point on the number line represents a unique real number.

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Question 44 Marks

Deep draws the spiral of irrational numbers below on a paper.

4. What is the length of OE in the spiral?
5. Simplify:
A. -1
B. $\sqrt{3}-\sqrt{5}$
C. $-4+\sqrt{15}$
D. $4-2 \sqrt{ } 15$

Answer

4. Writes √5 with or without the word ‘units’
● √5 units
● √5
5. C. -4+√15

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Question 54 Marks

3. Irrational numbers can provide more precision on measuring scale.
What can be the possible arguments in favour and against this statement?

Answer

3. Uses the deinition of irrational numbers in the explanation and identiies the limitation of their placement on a measuring scale
● Irrational numbers are non-terminating with more number of decimals so precision on measuring scale can be more. But they are non-terminating, so ixing their exact location on a measuring scale is not possible.

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Maths Case study (4 Marks)

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