Case study (4 Marks)

Question 14 Marks

The map shows three cities Conlen ©, Stratford (S), and Texhoma (T) on a straight highway.

4. Which of the following is true for the length of the highway between them?
A. The length of the highway between C and S is equal to the length of the highway between S and T.
B. The length of the highway between C and S is three-fourth of the length of the highway between S and T.
C. The length of the highway between S and T is the sum of the lengths of the highway between CT and CS.
D. The length of the highway between C and T is the sum of the lengths of the highway between CS and ST.
5. A number Y is greater than a number X and another number Z < 0.
Which of the following relations can be true for a unique value of Z?
A. X × Z = Y × Z
B. X ÷ Z = Y ÷ Z
C. X – Z = Y
D. X + Z = Y
6. The area of a triangle is equal to the area of a rectangle.
The area of the rectangle is equal to the area of a parallelogram.
What is the relation between the area of the triangle and the area of the parallelogram?

Answer

4. D. The length of the highway between C and T is the sum of the lengths of the highway between CS and ST
5. C. X – Z = Y
6. Explanation states equality in the area of the triangle and the parallelogram.
● Both have equal area.
● The area of the triangle is equal to the area of the parallelogram.

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Question 24 Marks

Raghvan claims that the magnitude of the angle ABC is greater than the magnitude of the area of the right triangle PQR.

7. Is his claim correct? Why?
8. Two lines intersect at a point P.
Which of the following is true for the distance between the two lines as they travel beyond point P?
A. The distance becomes constant.
B. The distance increases continuously.
C. The distance decreases continuously.
D. The distance increases and decreases depending upon the intersection point.
9. Balan says, ‘The measure of all right angles cannot be equal as their arms can be of different lengths.’
Why is Balan’s statement not true?
A. The measure of an angle depends upon its orientation.
B. The measure of an angle depends upon the instrument used to measure it.
C. The measure of an angle depends on the length of its angle arms.
D. The measure of an angle depends upon the rotation of one arm on another.
10. TAB is a straight line. C is the mid-point of AB. D is the mid-point of AC.
Which of the following shows the relation between the line segments?
A. $AD =\frac{1}{2} AB$
B. $AD =\frac{1}{2} CB$
C. $AD =2 AC$
D. $AD =2 DC$

Answer

7. No, with an explanation involving reasoning about magnitudes.
● No, the measure of an angle cannot be compared to the area of a triangle.
8. B. The distance increases continuously.
9. D. The measure of an angle depends upon the rotation of one arm with respect to the other.
10. B. $A D=\frac{1}{10} C B$

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Question 34 Marks

Karan marks his city on the map as point A.

2. Savita says, ‘A dot is dimensionless, so your city is also dimensionless.’ Why is Savita wrong? Justify your answer.
3. Which of the following is not true?
A. A line has one dimension.
B. A plane has two dimensions.
C. A circle can be drawn with any radius and at any point.
D. Two distinct lines can pass through a point in the same direction.

Answer

2. Answer demonstrates understanding of geometrical axioms and their relation with real-world.
● A dot in the map is for representational purpose.
● Dot is used only to show the location of the city, not its area.
3. D. Two distinct lines can pass through a point in the same direction.

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Question 44 Marks

1. Highways 20A and 56C run parallel to each other for 20 km in a state.
Which of the following statements is most likely to be true regarding them?
A. Both highways are of the same length.
B. There can be no link road between them.
C. The highways make an angle 90° with each other.
D. The distance between the two highways remains almost the same in the state.

Answer

1. D. The distance between the two highways remains almost the same in the state.

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MATHS Case study (4 Marks)

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