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Page No 372:

Question 1:

In questions â€‹there are four options out of which one is correct.
Comparison of parts of a whole may be done by a
(a) bar graph
(b) pie chart
(c) linear graph
(d) line graph

Answer:

Pie charts are used to compare the parts of a whole represented as non-intersecting adjacent sectors of a circle.
Hence, the correct answer is option (b).

Page No 372:

Question 2:

In questions â€‹there are four options out of which one is correct.
A graph that displays data that changes continuously over periods of time is
(a) bar graph
(b) pie chart
(c) histogram
(d) line graph

Answer:

Line graph is an important way to represent and compare the data which varies continuously. By connecting all the points by a line segment, it displays the relation between two varying quantities over a period of time.

Hence, the correct answer is option (d).

Page No 372:

Question 3:

In questions â€‹there are four options out of which one is correct.
In the given graph the coordinates of point x are
(a) (0, 2)
(b) (2, 3)
(c) (3, 2)
(d) (3, 0)

Answer:

The foot of the perpendicular drawn from the indicated point on the X-axis is at a distance of 3 units from the origin.
The x-coordinate of the point is 3.
Again, the perpendicular drawn from the given point on Y-axis is at a distance of 2 units from the origin.
The y-coordinate of the point is 2.
Thus, the coordinates of the point are (3, 2).

Hence, the correct answer is option (c).



Page No 373:

Question 4:

In questions â€‹there are four options out of which one is correct.
In the given graph the letter that indicates the point (0, 3) is
(a) P
(b) Q
(c) R
(d) S



 

Answer:

The letter that represents the point (0, 3) is R.
Hence, the correct answer is option (c).

Page No 373:

Question 5:

In questions â€‹there are four options out of which one is correct.
The point (3, 4) is at a distance of
(a) 3 from both the axis
(b) 4 from both the axis
(c) 4 from the x axis and 3 from y axis   
(d) 3 from x axis and from y axis
                                               

Answer:

The x-coordinate of the point is its distance from the Y-axis and the y-coordinate is its distance from the X-axis.
Therefore, the point (3,4) is at a distance of 4 from the X-axis and 3 from Y-axis.

Hence, the correct answer is option (c).

Page No 373:

Question 6:

In questions â€‹there are four options out of which one is correct.
A point which lies on both the axis is __________
(a) (0, 0)
(b) (0, 1)
(c) (1, 0)
(d) (1, 1)

Answer:

Point (0, 0) known as origin, is at the intersection point of two mutually perpendicular axes X and Y.
Thus, the point which lies on both the axes is (0, 0).
Hence, the correct answer is option (a).

Page No 373:

Question 7:

In questions â€‹there are four options out of which one is correct.
The coordinates of a point at a distance of 3 units from the x axis and 6 units from the y axis is
(a) (0, 3)
(b) (6, 0)
(c) (3, 6)
(d) (6, 3)

Answer:

Distance from the x-axis represents the y-coordinate and distance from the y-axis represents the x-coordinate. So, the coordinates of the point are (6, 3).
Hence, the correct answer is option (d).

Page No 373:

Question 8:

In questions â€‹there are four options out of which one is correct.
In the given figure, the position of the book on the table may be given by

(a) (7, 3)
(b) (3, 7)
(c) (3, 3)
(d) (7, 7)

Answer:

The distance of the book from the X-axis = 7
The distance of the book from the Y-axis = 3

Therefore, the point is given by (3, 7).

Hence, the correct answer is option (b).



Page No 374:

Question 9:

In questions â€‹there are four options out of which one is correct.
Data was collected on a student’s typing rate and graph was drawn as shown below. Approximately how many words had this student typed in 30 seconds?



(a) 20
(b) 24
(c) 28
(d) 34

Answer:

From the graph, the line x = 30 lies just below the point (30, 30), which is the intersection of the lines x = 30 and y = 30.
Since the X-axis represents the time (in seconds) and the Y-axis represents the number of words typed.
Therefore we conclude that the students had typed approximately 28 words in 30 s.
Hence, the correct answer is option (c).

Page No 374:

Question 10:

In questions â€‹there are four options out of which one is correct.
Which graphs of the following represent the table below?
 

Length of Side of a Square 1 2 3 4 5
Perimeter    4 8 12 16 20

​

Answer:

Length of Side of a Square 1 2 3 4 5
Perimeter    4 8 12 16 20

The length of the side of the square is taken along the x-axis and the perimeter along the y-axis.
Therefore, the points should be (1, 4), (2, 8), (3, 12) and (4, 16).

Hence, the correct answer is option (d).



Page No 375:

Question 11:

Fill in the blanks to make the statements true.
__________ displays data that changes continuously over periods of time.

Answer:

A line graph displays data that changes continuously over periods of time.

Hence, the line graph displays data that changes continuously over periods of time.

Page No 375:

Question 12:

Fill in the blanks to make the statements true.
The relation between dependent and independent variables is shown through a __________.

Answer:

The graph depicts the relationship between two variables, one of them is independent and the other is dependent.

Hence, the relation between dependent and independent variables is shown through a graph.

Page No 375:

Question 13:

Fill in the blanks to make the statements true.
We need __________ coordinates for representing a point on the graph sheet.

Answer:

We need two coordinates for representing a point on the graph sheet i.e. x- coordinate and y-coordinate.

Page No 375:

Question 14:

Fill in the blanks to make the statements true.
A point in which the x-coordinate is zero and y-coordinate is non- zero will lie on the _________

Answer:

Since the x-coordinate is zero.
Therefore, the point will lie on the Y-axis.

Hence, a point in which the x-coordinate is zero and the y-coordinate is non-zero will lie on the Y-axis.

Page No 375:

Question 15:

Fill in the blanks to make the statements true.
The horizontal and vertical line in a line graph are usually called __________ and __________.

Answer:

To plot a point on a graph we require two mutually perpendicular axes, also known as the X-axis (horizontal line) and the Y-axis (vertical line).

Hence, the horizontal and vertical lines in a line graph are usually called X-axis and Y-axis.

Page No 375:

Question 16:

Fill in the blanks to make the statements true.
The process of fixing a point with the help of the coordinates is known as __________ of the point.

Answer:

The process of fixing a point with the help of the coordinates is known as the plotting of the point.

Page No 375:

Question 17:

Fill in the blanks to make the statements true.
The distance of any point from the y-axis is the __________ coordinate.

Answer:

The distance of any point from the y-axis is the x-coordinate.

Page No 375:

Question 18:

Fill in the blanks to make the statements true.
All points with y-coordinate as zero lie on the __________.

Answer:

If a point lies on X-axis, the distance of the point from the X-axis is zero.
Thus, the y-coordinate is zero.
Hence, all points with y-coordinate as zero lie on the X-axis.

Page No 375:

Question 19:

Fill in the blanks to make the statements true.
For the point (5, 2), the distance from the x -axis is __________ units.

Answer:

The y-coordinate represents the distance of the point from the x-axis.

Hence, for the point (5, 2), the distance from the x-axis is 2 units.

Page No 375:

Question 20:

Fill in the blanks to make the statements true.
The x-coordinate of any point lying on the y-axis will be __________.

Answer:

The x-coordinate of any point lying on the y-axis will be zero.

Page No 375:

Question 21:

Fill in the blanks to make the statements true.
The y-coordinate of the point (2, 4) is __________.

Answer:

In ordered pair (2, 4), the second number 4 is called the y-coordinate of the point.

Hence, the y-coordinate of (2, 4) is 4.

Page No 375:

Question 22:

Fill in the blanks to make the statements true.
In the point (4, 7), 4 denotes the __________.

Answer:

In the point (4, 7), 4 denotes the x-coordinate or abscissa.



Page No 376:

Question 23:

Fill in the blanks to make the statements true.
A point has 5 as its x –coordinate and 4 as its y–coordinate. Then the coordinates of the point are given by __________.

Answer:

Given that, a point has 5 as its x-coordinate and 4 as its y-coordinate.

Hence, the coordinates of the point are given by (5, 4).

Page No 376:

Question 24:

Fill in the blanks to make the statements true.
In the coordinates of a point, the second number denotes the __________.

Answer:

In the ordered pair (x, y), the second number y is called the y-coordinate of the point.

Hence, in the coordinates of a point, the second number denotes the y-coordinate.

Page No 376:

Question 25:

Fill in the blanks to make the statements true.
The point where the two axes intersect is called the __________.

Answer:

The point where the two axes intersect is called the origin.
The coordinates of the origin are (0, 0).

Page No 376:

Question 26:

State whether the statements are true (T) or false (F).
For fixing a point on the graph sheet we need two coordinates.

Answer:

True

This is because for two axes, X and Y, the coordinates of the point on them will determine the position of the point.



Page No 377:

Question 27:

State whether the statements are true (T) or false (F).
A line graph can also be a whole unbroken line.

Answer:

True
A line graph, which represents the variation of a quantity with respect to the other, maybe an unbroken line.

Page No 377:

Question 28:

State whether the statements are true (T) or false (F).
The distance of any point from the x -axis is called the x-coordinate.

Answer:

False
The distance of any point from the x-axis is called the y-coordinate.

Page No 377:

Question 29:

State whether the statements are true (T) or false (F).
The distance of the point (3, 5) from the y-axis is 5.

Answer:

False

The x-coordinate of a point represents its distance from the Y-axis. Here, the x-coordinate is 3. Therefore, the distance of the point (3,5) from the Y-axis is 3.

Page No 377:

Question 30:

State whether the statements are true (T) or false (F).
The ordinate of a point is its distance from the y-axis.

Answer:

False

The ordinate of a point is the y-coordinate of the point and the y-coordinate denotes the distance of a point from the X-axis.

Page No 377:

Question 31:

State whether the statements are true (T) or false (F).
In the point (2, 3), 3 denotes the y-coordinate.

Answer:

True
The second number in the pair denotes the y-coordinate.

Page No 377:

Question 32:

State whether the statements are true (T) or false (F).
The coordinates of the origin are (0, 0).

Answer:

True

Origin is the point where both the axes meet. Thus, the coordinates of the origin are (0, 0).

Page No 377:

Question 33:

State whether the statements are true (T) or false (F).
The points (3, 5) and (5, 3) represent the same point.

Answer:

False

Two ordered pairs are equal, if they have the same numbers at the corresponding parts, i.e. x-coordinates are equal and y-coordinates are equal.
Here, 3 ≠ 5.
Hence, (3, 5) and (5, 3) are different points.

Page No 377:

Question 34:

State whether the statements are true (T) or false (F).
The y-coordinate of any point lying on the x -axis will be zero.

Answer:

True
The distance of the points which lie on x-axis, will be zero from the x-axis, i.e. y-coordinate is zero for the points lying on x-axis.

Page No 377:

Question 35:

Match the coordinates given in Column A with the items mentioned in Column B.

Column A Column B
(1) (0, 5) (a) y-coordinate is 2 × x-coordinate + 1.
(2) (2, 3) (b) Coordinates of origin.
(3) (4, 8) (c) Only y-coordinate is zero.
(4) (3, 7) (d) The distance from x-axis is 5.
(5) (0, 0) (e) y coordinate is double of x-coordinate.
(6) (5, 0) (f) The distance from y-axis is 2.

Answer:

(1) (0, 5)- The y-coordinate is known as the ordinate and it represents the distance of the point from X-axis, i.e. 5. Hence, it matches option (d).
(2) (2, 3)- The x-coordinate is known as the abscissa and it represents the distance of the point from Y-axis, i.e. 2. Hence, it matches option (f).
(3) (4, 8)- The x-coordinate is 4 and the y-coordinates is 8. Therefore, y-coordinate is double of x-coordinate. Hence, it matches option (e).
(4) (3, 7)- The y-coordinate = (2 × x-coordinate) + 1. Hence, it matches option (a).
(5) (0,0) are the coordinates of origin. Hence, it matches option (b).
(6) In the point (5,0), the y-coordinate is zero. Hence, it matches option (c).
 

Column A Column B
(1) (0, 5) (d) The distance from x-axis is 5.
(2) (2, 3) (f) The distance from y-axis is 2.
(3) (4, 8) (e) y coordinate is double of x-coordinate.
(4) (3, 7) (a) y-coordinate is 2 × x-coordinate + 1
(5) (0, 0) (b) Coordinates of origin.
(6) (5, 0) (c) Only y-coordinate is zero.

Page No 377:

Question 36:

Match the ordinates of the points given in Column A with the items mentioned in Column B.
 

Column A Column B
(a) (7, 0) (i) The ordinate is double the abscissa.
(b) (11, 11) (ii) The ordinate is zero.
(c) (4, 8) (iii) The ordinate is equal to the abscissa.
(d) (6, 2) (iv) The abscissa is double the ordinate.
(e) (0, 9) (v) The abscissa is triple the ordinate.
(f) (6, 3) (vi) The abscissa is zero.

Answer:

(a) The ordinate of the point (7, 0) is zero.
(b) In the point (11, 11), the ordinate is equal to the abscissa.
(c) In the point (4, 8), the ordinate is double of the abscissa.
(d) In the point (6, 2), the abscissa is triple of the ordinate.
(e) The abscissa of the point (0, 9) is zero.
(f) The abscissa of the point (0, 9) is double the ordinate.

Hence,
 

Column A Column B
(a) (7, 0) (ii) The ordinate is zero.
(b) (11, 11) (iii) The ordinate is equal to the abscissa.
(c) (4, 8) (i) The ordinate is double the abscissa.
(d) (6, 2) (v) The abscissa is triple the ordinate.
(e) (0, 9) (vi) The abscissa is zero.
(f) (6, 3) (iv) The abscissa is double the ordinate.



Page No 378:

Question 37:

From the given graph, choose the letters that indicate the location of the points given below.


(a) (2, 0)
(b) (0, 4)
(c) (5, 1)
(d) (2, 6)
(e) (3, 3)

Answer:

(a) (2, 0): F, because F is on X-axis, so its Y-coordinate will be zero and it is at a distance of 2 units from origin.
(b) (0, 4): A, because A is at a distance of 4 units from the X-axis from the origin.
(c) (5, 1): H, because B is at a distance of 1 unit from Y-axis and 5 units from X-axis.
(d) (2, 6): C, because C is at a distance of 2 units from Y-axis and 6 units from X-axis.
(e) (3, 3): E, because E is at a distance of 3 units from Y-axis and X-axis both.

Page No 378:

Question 38:

Find the coordinates of all letters in the graph given below.

Answer:

The coordinates of the points are given as:
A(0, 7.5), because A is on the Y-axis at a distance of 7.5 units from the origin.
B(4, 5), because B is at a distance of 4 units from Y-axis and 5 units from X-axis.
C(7.5, 2.5), because C is at a distance of 7.5 units from Y-axis and 2.5 units from X-axis.
D(11, 0), because D lies on X-axis at a distance of 11 units from the origin.
E(14.5, 6.5), because E is at a distance of 14.5 units from Y-axis and 6.5 units from X-axis.
F(18, 9.5), because F is at a distance of 18 units from Y-axis and 9.5 units from X-axis.

Page No 378:

Question 39:

Plot the given points on a graph sheet.
(a) (5, 4)
(b) (2, 0)
(c) (3, 1)
(d) (0, 4)
(e) (4,5)

Answer:




Page No 379:

Question 40:

Study the given map of a zoo and answer the following questions.



(a) Give the location of lions in the zoo.
(b) (D, f ) and (C, d) represent locations of which animals in the zoo?
(c) Where are the toilets located?
(d) Give the location of canteen.
 

Answer:

(a) (A, f), because lions are at a distance of A units from road Y and f units from road X.
(b) (D, f ): Monkeys, (C, d): Elephants
(c) (0, e), because toilets are located on road Y at a distance of e units from the origin.
(d) (C, c), because canteen is located at a distance of C units from road Y and c units from road X.

Page No 379:

Question 41:

Write the x -coordinate (abscissa) of each of the given points.
(a) (7, 3)
(b) (5, 7)
(c) (0, 5)

Answer:

(a) The x-coordinate or abscissa of the point (7, 3) is 7.
(b) The x-coordinate or abscissa of the point (5, 7) is 5.
(c) The x-coordinate or abscissa of the point (0, 5) is 0.

Page No 379:

Question 42:

Write the y-coordinate (ordinate) of each of the given points.
(a) (3, 5)
(b) (4, 0)
(c) (2, 7)

Answer:

(a) The y-coordinate of the point (3, 5) is 5.
(b) The y-coordinate of the point (4, 0) is 0.
(c) The y-coordinate of the point (2, 7) is 7.



Page No 380:

Question 43:

Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.
(a) (1, 2), (2, 4), (3, 6), (4, 8).
(b) (1, 1), (1, 2), (2, 1), (2, 2).
(c) (4, 2), (2, 4), (3, 3), (5, 4).

Answer:


(a)

The points form a straight line.

(b) 


The points do not form a straight line, they form a square.

(c) 


The points do not form a straight line, they form a triangle.

Page No 380:

Question 44:

If y-coordinate is 3 times x -coordinate, form a table for it and draw a graph.

Answer:

Given that, the y-coordinate is 3 times x -coordinate.

Thus,

x 0 1 2 3 4
y 0 3 6 9 12

Hence,

Page No 380:

Question 45:

Make a line graph for the area of a square as per the given table. 
 

Side (in cm) 1  2  3 4
Area (in cm2) 1 4 9 16

Is it a linear graph?

Answer:



Yes, it is a linear graph.

Page No 380:

Question 46:

The cost of a note book is Rs 10. Draw a graph after making a table showing cost of 2, 3, 4, .... note books. Use it to find
(a) the cost of 7 notebooks.
(b) The number of note books that can be purchased with Rs 50.

Answer:

Let x be the number of notebooks and y be the cost of a notebook.

x 1 2 3 4 5 6 7 8
y 10 20 30 40 50 60 70 80

Graph of the above data:


(a) According to the graph, the cost of 7 notebooks = â‚¹70
(b) According to the graph, the number of notebooks that can be purchased with â‚¹50 = 5

Page No 380:

Question 47:

Explain the situations represented by the following distance-time graphs.

Answer:

In the given graphs, the X-axis represents time and Y-axis represents the distance covered.

(a) In the first graph, as the time changes, distance also varies with the same rate. Hence, the object is moving at a uniform speed.

(b) In the graph (b), the graph initially increases steadily, i.e., at uniform speed. After a certain period of time, it comes to rest position, i.e., it remains constant.

(c) In the graph (c), the graph increases strictly with non-uniform speed and then slowly comes to the rest position.

Page No 380:

Question 48:

Complete the given tables and draw a graph for each.

(a) 

x 0 1 2 3
y = 3x + 1 1 4 - -

(b)
x 1 2 4 6
y = – 1 0 - - -
​

Answer:


(a)

x 0 1 2 3
y = 3x + 1 1 4 7 10



(b)
x 1 2 4 6
y = – 1 0 1 3 5



Page No 381:

Question 49:

Study the given graphs (a) and (b) and complete the corresponding tables below.

 
(a)

x 0 1 2 3
y        

(b)
x 0 1 2 3 4
y          

Answer:

(a)
At x = 0, y = 0
At 
x = 1, y = 1
At 
x = 2, y = 2
At 
x = 3, y = 3
 

x 0 1 2 3
y 0 1 2 3

(b)
At x = 0, y = 2
At 
x = 1, y = 4
At 
x = 2, y = 6
At 
x = 3, y = 8
At x = 4, y = 10

 
x 0 1 2 3 4
y 2 4 6 8 10

Page No 381:

Question 50:

Draw a graph for the radius and circumference of circle using a suitable scale.
(Hint : Take radius = 7, 14, 21 units and so on)
From the graph,
(a) Find the circumference of the circle when radius is 42 units.
(b) At what radius will the circumference of the circle be 220 units?

Answer:

The circumference of a circle with radius r is given as:
Circumference of a circle = 2πr

Now, for r = 7 cm,
Circumference of circle = 2πr=2×227×7=44 cm

For r = 14 cm,
Circumference of circle = 2πr=2×227×14=88 cm

For r = 21 cm,
Circumference of circle = 2πr=2×227×21=132 cm

For r = 28 cm,
Circumference of circle = 2πr=2×227×28=176 cm

For r = 35 cm,
Circumference of circle = 2πr=2×227×35=220 cm

For r = 42 cm,
Circumference of circle = 2πr=2×227×42=264 cm
Thus,

r 7 14 21 28 35 42
Circumference 44 88 132 176 220 264
 


(a) When r = 42 cm,
Circumference of circle = 264 cm

(b) From the table, it can be concluded that for r = 35 cm, the circumference of the circle is 220 cm.

Page No 381:

Question 51:

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.



(a) What information is given by the two axes?
(b) In which week was the temperature higher on most of the days?
(c) On which day was the temperature same in both the weeks?
(d) On which day was the difference in temperatures the maximum for both the weeks?
(e) What were the temperatures for both the weeks on Thursday?
(f) On which day was the temperature 35°C for the first week?
(g) On which day was the temperature highest for the second week?
 

Answer:

(a) On the graph, the X-axis represents the days of a particular week and the Y-axis represents the maximum temperatures (in °C) recorded on those days.
(b) Yes; in the first week, the temperature was higher on most of the days.
(c) The temperature was the same on Wednesday in both the weeks, i.e., 36°C.
(d) From the graph, it can be observed that the difference in temperatures of the two weeks was maximum on Friday, i.e. 5°C.
(e) On Thursday, the temperature for the first week was 37°C and for the second week was 34°C.
(f) For the first week, the temperature was 35°C on Sunday.
(g) On Wednesday, the temperature was the highest for second week, i.e., 36°C.



Page No 382:

Question 52:

The graph given below gives the actual and expected sales of cars of a company for 6 months. Study the graph and answer the questions that follow.

 

(a) In which month was the actual sales same as the expected sales?
(b) For which month(s) was (were) the difference in actual and expected sales the maximum?
(c) For which month(s) was (were) the difference in actual and expected sales the least?
(d) What was the total sales of cars in the months–Jan, Feb. and March?
(e) What is the average sales of cars in the last three months?
(f) Find the ratio of sales in the first three months to the last three months.

Answer:

(a) April; the actual sales was the same as the expected sales.
(b) March; the difference in actual and expected sales was the maximum i.e., 75.
(c) April; the difference in actual and expected sales was the least i.e., 0.
(d) The total sales of cars in the months Jan, Feb and March = 75 + 100 + 75 = 250
(e) The average sales of cars in the last three months = 125+100+1503=125
(f) Sale in first three months = 75 + 100 + 75 = 250
Sale of last three months = 125 + 100 + 150 = 375
Ratio = 250375=23 = 2 : 3.



Page No 383:

Question 53:

The graph given below shows the marks obtained out of 10 by Sonia in two different tests. Study the graph and answer the questions that follow.



(a) What information is represented by the axes?
(b) In which subject did she score the highest in Test I?
(c) In which subject did she score the least in Test II?
(d) In which subject did she score the same marks in both the Tests?
(e) What are the marks scored by her in English in Test II?
(f) In which test was the performance better?
(g) In which subject and which test did she score full marks?
 

Answer:

(a) The X-axis represents subjects and the Y-axis represents the marks obtained by Sonia.

(b) In Test-I, she scored the highest marks in Maths.

(c) In Test-II, she scored the least in two subjects namely, English and Hindi.

(d) In none of the subjects did she obtain the same marks in both tests.

(e) She scored 6 marks in English in Test II.

(f) Total score in Test-I = 7 + 8 + 10 + 7 + 5 = 37
Total score in Test-II = 6 + 6 + 8 + 9 + 8 = 37
Hence, the performance in both the tests is the same.

(g) In the first test, she scored full marks in Maths subject, i.e., 10 marks.

Page No 383:

Question 54:

Find the coordinates of the vertices of the given figures.

Answer:



The coordinates of the vertices of the given figures are as follows:

Figure I: A(1, 1), B(3, 0), C(4, 2) and D(2, 3)

Figure II: P(1, 2), O(2, 4) and Q(0, 5)

Figure III: E(5, 1), F(6, 3), G(5,5) and H(4, 3)

Figure IV: I(4,4), J(4, 5), K(3, 6), L(2, 6), M(1, 5), N(2, 5) and O(2, 4)


 



Page No 384:

Question 55:

Study the graph given below of a person who started from his home and returned at the end of the day. Answer the questions that follow.


(a) At what time did the person start from his home?
(b) How much distance did he travel in the first four hours of his journey?
(c) What was he doing from 3 pm to 5 pm?
(d) What was the total distance travelled by him throughout the day?
(e) Calculate the distance covered by him in the first 8 hours of his journey.
(f) At what time did he cover 16 km of his journey?
(g) Calculate the average speed of the man from (a) A to B (b) B to C 
(h) At what time did he return home?
 

Answer:

(a) 10 am
(b) For 4 hours, he travelled till 2 pm, he travelled 16 km.
(c) He was at rest.
(d) Total distance covered by him is 20 + 20 = 40 km
(e) 8 hours of his journey is till 6 pm. Till 6 pm he travelled 24 km.
(f) 2 pm
(g): 
       (a) Total distance covered from A to B = 20 km
            Time taken to travel from A to B = 5 h
            Average speed = 205=4 km/h
       (b) Total distance covered from B to C = 0 km
             Time taken to travel from B to C = 2 h
             Average speed = 02=0 km/h
            He was at rest.
(c) 10 pm

Page No 384:

Question 56:

Plot a line graph for the variables p and q where p is two times q i.e, the equation is p = 2q. Then find.
(a) the value of p when q = 3
(b) the value of q when p = 8

Answer:

Given that, the equation is p = 2q.

Thus,

p 2 4 6 8
q 1 2 3 4



According to the graph,
(a) When q = 3, then p = 6.
(b) When p = 8, then q = 4.

Page No 384:

Question 57:

Study the graph and answer the questions that follow.


(a) What information does the graph give?
(b) On which day was the temperature the least?
(c) On which day was the temperature 31°C?
(d) Which was the hottest day?
 

Answer:

(a) The graph represents the maximum temperature on various days of a week.
(b) The least temperature in the week was on Sunday, i.e. 25°C.
(c) The temperature was 31°C on Saturday.
(d) On Friday, the temperature was maximum, i.e., 34°C. Hence, it was the hottest day of the week.



Page No 385:

Question 58:

Study the distance-time graph given below for a car to travel to certain places and answer the questions that follow.

 

(a) How far does the car travel in 2 hours?
(b) How much time does the car take to reach R?
(c) How long does the car take to cover 80 km?
(d) How far is Q from the starting point?
(e) When does the car reach the place S after starting?

 

Answer:

(a) 80 km; the car travels 80 km in 2 hours.
(b) 5 hours; car took 5 hours to reach R.
(c) 2 hours; car took 2 hours to cover 80 km.
(d) 120 km; Q is 120 km from the starting point.
(e) 6 hours; after starting car took 6 hours to reach the place S.



Page No 386:

Question 59:

Locate the points A (1,2), B (4,2) and C (1,4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D to complete the rectangle ABCD.

Answer:

Given that, the points A (1,2), B (4,2) and C (1,4) are three vertices of a rectangle and the fourth one is D.

Now, plotting these three points on the graph,


To complete the rectangle, draw point D.


Hence, the fourth vertex of the rectangle ABCD is D(4, 4).

Page No 386:

Question 60:

Locate the points A(1, 2), B(3, 4) and C(5, 2) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D to complete the rhombus ABCD. Measure the diagonals of this rhombus and find whether they are equal or not.

Answer:

Given that, the three points of a rhombus are A(1, 2), B(3,4) and C(5,2).

Completing the rhombus, the fourth point is D(3, 0).


Now, the diagonals of the rhombus are AC and BD.
According to the graph,
AC = 4 units
BD = 4 units

Hence, the diagonals measure 4 units and are equal to each other.

Page No 386:

Question 61:

Locate the points P (3,4), Q (1,0), R (0,4), S (4,1) on a graph sheet and write the coordinates of the point of intersection of line segments PQ and RS.

Answer:




Line segments PQ and RS intersect at point T(2, 2).

Page No 386:

Question 62:

The graph given below compares the sales of ice creams of two vendors for a week.



Observe the graph and answer the following questions.
(a) Which vendor has sold more ice creams on Friday?
(b) For which day was the sales same for both the vendors?
(c) On which day did the sale of vendor A increase the most as compared to the previous day?
(d) On which day was the difference in sales the maximum?
(e) On which two days was the sales same for vendor B?
 

Answer:

(a) According to the graph, vendor A has sold more ice-creams on Friday.

(b) On Sunday, the sales was the same for vendor A and vendor B.

(c) On Sunday, the sale of vendor A increased the most as compared to the previous day i.e., Saturday.

(d) The difference in sales was the maximum on Thursday, i.e., 20 (= 40 − 20).

(e) On Tuesday and Wednesday, the sales was the same for vendor B, i.e., 30.



Page No 387:

Question 63:

The table given below shows the temperatures recorded on a day at different times.



Observe the table and answer the following questions.
(a) What is the temperature at 8 am?
(b) At what time is the temperature 3°C?
(c) During which hour did the temperature fall?
(d) What is the change in temperature between 7 am and 10 am?
(e) During which hour was there a constant temperature?
 

Answer:

(a) According to the graph, at 8 am, the temperature is 7°C.
(b) At 6 am, the temperature is 3°C.
(c) The temperature fell in the first hour of the day, i.e., from 5 am to 6 am.
(d) At 7 am, the temperature is 5°C and at 10 am, the temperature is 8°C. Thus, the change in temperature is 3°C between this time.
(e) The temperature was constant from 8 am to 9 am.

Page No 387:

Question 64:

The following table gives the growth chart of a child.
​

 Height (in cm) 75 90 110 120 130
 Age (in years) 2 4 6 8 10

Draw a line graph for the table and answer the questions that follow.
(a) What is the height at the age of 5 years?
(b) How much taller was the child at the age of 10 than at the age of 6?
(c) Between which two consecutive periods did the child grow more faster?

Answer:

Line graph for the table is:           


(a) 100 years
(b) At the age of 6, the child was 110 cm tall.
At the age of 10, the child was 130 cm tall.
Difference = 20 cm
(c) 2-4 years and 4-6 years



Page No 388:

Question 65:

The following is the time-distance graph of Sneha’s walking.

(a) When does Sneha make the least progress? Explain your reasoning.
(b) Find her average speed in km/hour.

Answer:

(a) In the first 15 mins, Sneha travels 0.75 km.
In the next 10 mins, she travels 1.25 − 0.75 = 0.5 km.
In the next 15 mins, she travels 1.5 − 1.25 = 0.5 km.
In the next 5 mins, she travels 1.75 − 1.5 = 0.5 km.
In the next 10 mins, she travels 2 − 1.75 = 0.25 km.

Hence, she makes the least progress in the last 10 minutes of the journey, i.e., 45-55 minutes.

(b) According to the graph, in 1 hour or 60 mins, Sneha walks 55 km.
Now,
Average speed=Total distanceTotal time taken=25560=255×60=2.19 km/h
Hence, the average speed is 2.19 km/h.

Page No 388:

Question 66:

Draw a parallelogram ABCD on a graph paper with the coordinates given in Table I. Use this table to complete Tables II and III to get the coordinates of E, F, G, H and J, K, L, M.​
 

Point  (xy)
A (1, 1)
B (4, 4)
C (8, 4)
D (5, 1)
Table I
 
Point (0.5x, 0.5y)
E (0.5, 0.5)
F  
G  
H  
Table II
 
Point (2x, 1.5y)
J (2, 1.5)
K  
L  
M  
Table III

Draw parallelograms EFGH and JKLM on the same graph paper. Plot the points (2, 4) and (4, 2) on a graph paper, then draw a line segment joining these two points.

Answer:

Completing the two tables,

Point  (xy)
A (1, 1)
B (4, 4)
C (8, 4)
D (5, 1)
Table I
 
Point (0.5x, 0.5y)
E (0.5, 0.5)
F (2, 2)
G (4, 2)
H (2.5, 0.5)
Table II
 
Point (2x, 1.5y)
J (2, 1.5)
K (8, 6)
L (16, 6)
M (10, 1.5)
Table III
 


Now, 

 

Page No 388:

Question 67:

Extend the line segment on both sides to meet the coordinate axes. What are the coordinates of the points where this line meets the x -axis and the y-axis?

Answer:




The extended line segment meets the x-axis at point (6, 0) and the y-axis at (0, 6).



Page No 389:

Question 68:

The following graph shows the change in temperature of a block of ice when heated. Use the graph to answer the following questions:


(a) For how many seconds did the ice block have no change in temperature?
(b) For how long was there a change in temperature?
(c) After how many seconds of heating did the temperature become constant at 100°C?
(d) What was the temperature after 25 seconds?
(e) What will be the temperature after 1.5 minutes? Justify your answer.

Answer:

(a) In the first 20 seconds of observation, the ice block showed no change in its temperature.

(b) There was a change in temperature from 20 secs to 50 secs, i.e., 50 − 20 = 30 secs. Thus, the change in temperature could be seen for 30 seconds.

(c) After 50 seconds of heating, the temperature became constant at 100°C.

(d) The temperature was 20°C after 25 seconds.

(e) Since, the temperature becomes constant at 100°C after 50 seconds of heating.
Therefore, the temperature will be 100°C even after 1.5 minutes.

Disclaimer: The answers in the NCERT Exemplar are incorrect. The correct answers are as per the calculations above.

Page No 389:

Question 69:

The following graph shows the number of people present at a certain shop at different times. Observe the graph and answer the following questions.

(a) What type of a graph is this?
(b) What information does the graph give?
(c) What is the busiest time of day at the shop?
(d) How many people enter the shop when it opens?
(e) About how many people are there in the shop at 1:30 pm?
 

Answer:

(a) The given graph is a line graph.
(b) The graph represents the number of people who visited the shop at a particular time.
(c) The busiest time of day at the shop is 1 pm. It has the maximum number of people, i.e., 25.
(d) When the shop opens, less than 5 people enter the shop.
(e) There are 20 people in the shop at 1:30 pm.



Page No 390:

Question 70:

A man started his journey on his car from location A and came back. The given graph shows his position at different times during the whole journey.


(a) At what time did he start and end his journey?
(b) What was the total duration of journey?
(c) Which journey, forward or return, was of longer duration?
(d) For how many hours did he not move?
(e) At what time did he have the fastest speed?

Answer:

(a) He started his journey at 5:30 am and ended it at 6 pm.
(b) 12:30 hours
(c) His forward journey is of duration 8:30 hours and return journey is of duration 4 hours. Forward journey was of longer duration.
(d) He did not move from 6 am to 9 am (approx.) and 10 am to 1 pm so 6 hours total.
(e) He had the fastest speed at 1 pm as that is the highest slope.

Page No 390:

Question 71:

The following graph shows the journey made by two cyclists, one from town A to B and the other from town B to A.


(a) At what time did cyclist II rest? How long did the cyclist rest?
(b) Was cyclist II cycling faster or slower after the rest?
(c) At what time did the two cyclists meet?
(d) How far had cyclist II travelled when he met cyclist I?
(e) When cyclist II reached town A, how far was cyclist I from town B?

Answer:

(a) The cyclist II took rest for 15 minutes from 8:45 AM to 9:00 AM.

(b)  Before the rest, he travelled 10 km in 1 hour.
After the rest, he travelled 20 km (= 30 − 10) in 1 hour.
Hence, he travelled faster after rest.

(c) Since, the two lines intersect at the point where the time is 9:00 AM. Therefore, both the cyclists meet at 9:00 AM.

(d) They meet at 9:00 AM. Till that time, the second cyclist has travelled 10 km.

(e) When cyclist I reached town A, the cyclist II was 10 km (= 30 − 20) for from town B.

Disclaimer: The question should be- "(e) When cyclist I reached town A, how far was cyclist II from town B?"



Page No 391:

Question 72:

Ajita starts off from home at 07.00 hours with her father on a scooter that goes at a uniform speed of 30 km/h and drops her at her school after half an hour. She stays in the school till 13.30 hours and takes an auto rickshaw to return home. The rickshaw has a uniform speed of 10 km/h. Draw the graph for the above situation and also determine the distance of Ajita’s school from her house.

Answer:

According to the given information, the graph obtained is as follows:

The speed of the scooter is 30 km/h and it takes 30 minutes to reach the school.
Thus,
Distance of the school from the home = speed × time
                                                             = 30 × 12
                                                             = 15 km

Hence, the distance of her house from the school is 15 km.

Page No 391:

Question 73:

Draw the line graph using suitable scale to show the annual gross profit of a company for a period of five years.

Year 1st 2nd 3rd  4th  5th
Gross Profit     
(in Rs)
17,00,000 15,50,000 11,40,000 12,10,000 14,90,000

Answer:


Page No 391:

Question 74:

The following chart gives the growth in height in terms of percentage of full height of boys and girls with their respective ages.
 

Age (in years) 8 9 10 11 12 13 14 15 16 17 18
Boys 72% 75% 78% 81% 84% 88% 92% 95% 98% 99% 100%
Girls            77% 81% 84% 88% 91% 95% 98% 99% 99.5% 100% 100%

Draw the line graph of above data on the same sheet and answer the following questions.
(a) In which year both the boys and the girls achieve their maximum height?
(b) Who grows faster at puberty (14 years to 16 years of age)?

Answer:

(a) In the 18th year, both of them attain their maximum height.
(b) Between 14 years to 16 years of age,
Increase in boy's height = 98% − 92% = 6%
Increase in girl's height = 99.5% − 98% = 1.5%
Hence, boys grow faster the girls during puberty.



Page No 392:

Question 75:

The table shows the data collected for Dhruv’s walking on a road.
 

Time  
(in minutes)
0 5 10 15 20 25
Distance 
(in km)
0  0.5 1 1.25 1.5 1.75

(a) Plot a line graph for the given data using a suitable scale.
(b) In what time periods did Dhruv make the most progress?

Answer:

(a) According to the given data, the graph is as follows:


(b)
In the first 5 minutes, he covered 0.5 km.
In the next 5 minutes, he covered 0.5 km.
In the next 5 minutes, he covered 0.25 km.
In the next 5 minutes, he covered 0.25 km.
In the next 5 minutes, he covered 0.25 km.
Hence, he made the maximum progress in the first 10 minutes of his journey.

Page No 392:

Question 76:

Observe the given graph carefully and complete the table given below.
 

x 1 5
y          

Answer:

x 1 5
y   5 10 15 20


**DISCLAIMER: The graph is ambiguous without the grid thus, it is difficult to find the exact value of y corresponding to x = 1.

Page No 392:

Question 77:

This graph shows the per cent of students who dropped out of school after completing High School. The point labelled A shows that, in 1996, about 4.7% of students dropped out.



(a) In which year was the dropout rate the highest? In which year was it the lowest?
(b) When did the per cent of students who dropped out of high school first fall below 5%?
(c) About what per cent of students dropped out of high school in 2007? About what per cent of students stayed in high school in 2008?
 

Answer:

(a) From the graph, it can be observed that the drop out rate was the highest in the year 1990 and the least in the year 2000.

(b) In the year 1996, the percentage of students who dropped out of high school first fall below 5%.

(c) About 4.7% of the students dropped out of high school in the year 2007.



Page No 393:

Question 78:

Observe the toothpick pattern given below:

                                                               Pattern 1Pattern 2Pattern 3Pattern 4

(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
 

Pattern  1 2 3 4 5 6
Toothpicks 4     13    

(b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.
(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.
(d) Would it make sense to join the points on this graph? Explain.

Answer:

(a) Continuing the given pattern, following table is obtained:

Pattern  1 2 3 4 5 6
Toothpicks 4 7 10 13 16 19

(b) The following graph can be obtained by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis:


(c) The graph follows the pattern y = 3x + 1.
When x = 7,
y = 3 × 7 + 1 = 21 + 1 = 22
When x = 8,
y = 3 × 8 + 1 = 24 + 1 = 25

(d) Joining the points on the graph, a line can be obtained showing the relation y = 3+ 1.



Page No 394:

Question 79:

Consider this input/output table.

Input 1 2 4 5 7
Output 2 5 11 14 20

(a) Graph the values from the table by taking Input along horizontal axis from 0 to 8 and Output along vertical axis from 0 to 24.
(b) Use your graph to predict the outputs for inputs of 3 and 8.

Answer:


(a)


(b) The graph uses the pattern y = 3x − 1 pattern.
Putting x = 3, y = 8
Putting x = 8, y = 23

Page No 394:

Question 80:

This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km.

Point A represents a resort that is located 5 km East and 3 km North of Point B. The values 5 and 3 are the coordinates of Point A. The coordinates can be given as the ordered pair (5, 3), where 5 is the horizontal coordinate and 3 is the vertical coordinate.
(i) On a copy of the map, mark the point that is 3 km East and 5 km North of Point B and label it S. Is Point S in the water or on the island? Is Point S in the same place as Point A?
(ii) Mark the point that is 7 km east and 5 km north of Point B and label it C. Then mark the point that is 5 km east and 7 km north of Point B and label it D. Are Points C and D in the same place? Give the coordinates of Points C and D.
(iii) Which point is in the water, (2, 7) or (7, 2)? Mark the point which is in water on your map and label it E.
(iv) Give the coordinates of two points on the island that are exactly 2 km from Point A.
(v) Give the coordinates of the point that is halfway between Points L and P.
(vi) List three points on the island with their x-coordinates greater than 8.
(vii) List three points on the island with a y-coordinate less than 4.

Answer:

(i) The point S(3, 5) is in the water. Also, No, point S is not in the same place as point A.

(ii) The coordinate of the point C is (7, 5) and that of D is (5, 7). The pints C and D are not in the same place.
(iii) Out of the two points, the point (2, 7) is in the water.
(iv) The coordinate of point A is (5, 3). Two points which are at a distance of 2 km from A are (7, 3) and (5, 5).
(v) The coordinates of the point that is halfway between Points L and P is (8.5, 3).
(vi) Three points on the island with their x-coordinates greater than 8 are (9, 4), (10, 4) and (10, 7).
(vii) Three points on the island with a y-coordinate less than 4 are (5, 3), (7, 2) and (7, 3).
Note that the answer for parts (vi) and (vii) may vary from student to student.



Page No 395:

Question 81:

As part of his science project, Prithvi was supposed to record the temperature every hour one Saturday from 6 am to midnight. At noon, he was taking lunch and forgot to record the temperature. At 8:00 pm, his favourite show came on and so forgot again. He recorded the data so collected on a graph sheet as shown below.

(a) Why does it make sense to connect the points in this situation?
(b) Describe the overall trend, or pattern, in the way the temperature changes over the time period shown on the graph.
(c) Estimate the temperature at noon and 8 pm.

Answer:

(a) Connected points will ease the study of the change in temperature overtime.
(b) The temperature was 8°C at 6 am and it started increasing strictly till 1 pm. After that, it decreased to 8°C till 12 pm.
(c) At noon, the temperature is 19°C and at 8pm, it is 10°C.



Page No 396:

Question 82:

The graph given below compares the price (in Rs) and weight of 6 bags (in kg) of sugar of different brands A, B, C, D, E, F.


(a) Which brand(s) costs/cost more than Brand D?
(b) Bag of which brand of sugar is the heaviest?
(c) Which brands weigh the same?
(d) Which brands are heavier than brand B?
(e) Which bag is the lightest?
(f) Which bags are of the same price?
 

Answer:

(a) E and F
(b) D
(c) B and F, C and E
(d) C, D, E
(e) A
(f) A and C

Page No 396:

Question 83:

The points on the graph below represent the height and weight of the donkey, dog, crocodile and ostrich shown in the drawing.


(a) What are the two variables represented in the graph?
(b) Which point represents each animals? Explain.

Answer:

(a) The two variables used in the graph are: height and weight.
(b) In the graph, we observe that the points A represents a crocodile as it has least height and greatest weight among all animals.
A- Crocodile It has the least height but the greatest weight)
B- Donkey (Its height and weight are more than that of a dog)
C- Dog
D- Ostrich (It has the greatest height)



Page No 397:

Question 84:

The two graphs below compare Car A and Car B. The left graph shows the relationship between age and value. The right graph shows the relationship between size and maximum speed.

Use the graphs to determine whether each statement is true or false, and explain your answer.
(a) The older car is less valuable.
(b) The faster car is larger.
(c) The larger car is older.
(d) The faster car is older.
(e) The more valuable car is slower.
 

Answer:

(a) False; in the first graph, the older car is B and it is more valuable more than car A.
(b) True; in the second graph, car B is larger and has greater speed.
(c) True; in the second graph, the larger car is B and it is older than A.
(d) True; the faster car is B and it is faster than A.
(e) False, the more valuable car is B and it is faster than A.

Page No 397:

Question 85:

Sonal and Anmol made a sequence of tile designs from square white tiles surrounding one square purple tile. The purple tiles come in many sizes. Three of the designs are shown below.
(a) Copy and complete the table
 

Side Length of Purple  Tiles 10  100
Number of white Tiles in Border              

        
(b) Draw a graph using the first five pairs of numbers in your table.
(c) Do the points lie on a line?
 

Answer:

(a)

Side Length of Purple  Tiles 10  100
Number of white Tiles in Border 4 8 12 16 20 40 400

(b)

(c) After the plotting and joining the points, the points form a line.



Page No 398:

Question 86:

Sonal and Anmol then made another sequence of the designs. Three of the designs are shown below.


(a) Complete the table.

Rows, r 4 6 8
Number of white Tiles, w 9    
Number of Purple Tiles, p 1    
(b) Draw a graph of rows and number of white tiles. Draw another graph of the number of rows and the number of purple tiles. Put the number of rows on the horizontal axis.
(c) Which graph is linear?
 

Answer:

(a) Complete the table.

Rows, r 4 6 8
Number of white Tiles, w 9 15 21
Number of Purple Tiles, p 1 6 15

(b) The graph of rows and number of white tiles is given as:


The graph of the number of rows and the number of purple tiles is given below:


(c) The graph of the number of rows and number of white tiles is a linear graph.



View NCERT Solutions for all chapters of Class 8