Case study (4 Marks)

Question 14 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. $A D=\frac{1}{10} C B$

View full question & answer→

Question 24 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.

View full question & answer→

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.

View full question & answer→

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^\circ $ 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.

View full question & answer→

Maths Case study (4 Marks)

Take a timed test