# NCERT solutions for Mathematics Exemplar Class 8 chapter 12 - Introduct To Graphs [Latest edition]

## Chapter 12: Introduct To Graphs

Exercise
Exercise [Pages 372 - 398]

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 12 Introduct To Graphs Exercise [Pages 372 - 398]

#### Choose the correct alternative:

Exercise | Q 1 | Page 372

Comparison of parts of a whole may be done by a ______.

• Bar graph

• Pie chart

• Linear graph

• Line graph

Exercise | Q 2 | Page 372

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

• Bar graph

• Pie chart

• Histogram

• Line graph

Exercise | Q 3 | Page 372

In the given graph the coordinates of point x are ______.

• (0, 2)

• (2, 3)

• (3, 2)

• (3, 0)

Exercise | Q 4 | Page 373

In the given graph the letter that indicates the point (0, 3) is ______.

• P

• Q

• R

• S

Exercise | Q 5 | Page 373

The point (3, 4) is at a distance of ______.

• 3 from both the axis

• 4 from both the axis

• 4 from the x-axis and 3 from y-axis

• 3 from x-axis and from y-axis

Exercise | Q 6 | Page 373

A point which lies on both the axis is ______.

• (0, 0)

• (0, 1)

• (1, 0)

• (1, 1)

Exercise | Q 7 | Page 373

The coordinates of a point at a distance of 3 units from the x axis and 6 units from the y axis is ______.

• (0, 3)

• (6, 0)

• (3, 6)

• (6, 3)

Exercise | Q 8 | Page 373

In the given figure the position of the book on the table may be given by ______.

• (7, 3)

• (3, 7)

• (3, 3)

• (7, 7)

Exercise | Q 9 | Page 374

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?

• 20

• 24

• 28

• 34

Exercise | Q 10 | Page 374

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

#### Fill in the blank:

Exercise | Q 11 | Page 375

______ displays data that changes continuously over periods of time.

Exercise | Q 12 | Page 375

The relation between dependent and independent variables is shown through a ______.

Exercise | Q 13 | Page 375

We need ______ coordinates for representing a point on the graph sheet.

Exercise | Q 14 | Page 375

A point in which the x-coordinate is zero and y-coordinate is nonzero will lie on the ______.

Exercise | Q 15 | Page 375

The horizontal and vertical line in a line graph are usually called ______ and ______.

Exercise | Q 16 | Page 375

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

Exercise | Q 17 | Page 375

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

Exercise | Q 18 | Page 375

All points with y-coordinate as zero lie on the ______.

Exercise | Q 19 | Page 375

For the point (5, 2), the distance from the x-axis is ______ units.

Exercise | Q 20 | Page 375

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

Exercise | Q 21 | Page 375

The y-coordinate of the point (2, 4) is ______.

Exercise | Q 22 | Page 375

In the point (4, 7), 4 denotes the ______.

Exercise | Q 23 | Page 376

A point has 5 as its x–coordinate and 4 as its y–coordinate. Then the coordinates of the point are given by ______.

Exercise | Q 24 | Page 376

In the coordinates of a point, the second number denotes the ______.

Exercise | Q 25 | Page 376

The point where the two axes intersect is called the ______.

#### State whether the following statement is True or False:

Exercise | Q 26 | Page 376

For fixing a point on the graph sheet we need two coordinates.

• True

• False

Exercise | Q 27 | Page 376

A line graph can also be a whole unbroken line.

• True

• False

Exercise | Q 28 | Page 376

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

• True

• False

Exercise | Q 29 | Page 376

The distance of the point (3, 5) from the y-axis is 5.

• True

• False

Exercise | Q 30 | Page 376

The ordinate of a point is its distance from the y-axis.

• True

• False

Exercise | Q 31 | Page 376

In the point (2, 3), 3 denotes the y-coordinate.

• True

• False

Exercise | Q 32 | Page 376

The coordinates of the origin are (0, 0).

• True

• False

Exercise | Q 33 | Page 376

The points (3, 5) and (5, 3) represent the same point.

• True

• False

Exercise | Q 34 | Page 376

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

• True

• False

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

Exercise | Q 35 | Page 377
 Column A Column B (i) (0, 5) (a) y coordinate is 2 × x - coordinate + 1. (ii) (2, 3) (b) Coordinates of origin. (iii) (4, 8) (c) Only y–coordinate is zero. (iv) (3, 7) (d) The distance from x –axis is 5. (v) (0, 0) (e) y coordinate is double of x –coordinate. (vi) (5, 0) (f) The distance from y–axis is 2.
Exercise | Q 36 | Page 377
 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.
Exercise | Q 37 | Page 378

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)

Exercise | Q 38 | Page 378

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

Exercise | Q 39 | Page 378

Plot the given points on a graph sheet.

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

Exercise | Q 40 | Page 379

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.

Exercise | Q 41.(a) | Page 379

Write the x -coordinate (abscissa) of the given points.

(7, 3)

Exercise | Q 41.(b) | Page 379

Write the x -coordinate (abscissa) of the given points.

(5, 7)

Exercise | Q 41.(c) | Page 379

Write the x -coordinate (abscissa) of the given points.

(0, 5)

Exercise | Q 42.(a) | Page 379

Write the y-coordinate (ordinate) of the given points.

(3, 5)

Exercise | Q 42.(b) | Page 379

Write the y-coordinate (ordinate) of the given points.

(4, 0)

Exercise | Q 42.(c) | Page 379

Write the y-coordinate (ordinate) of the given points.

(2, 7)

Exercise | Q 43.(a) | Page 380

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.

(1, 2), (2, 4), (3, 6), (4, 8)

Exercise | Q 43..(b) | Page 380

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

(1, 1), (1, 2), (2, 1), (2, 2)

Exercise | Q 43.(c) | Page 380

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

(4, 2), (2, 4), (3, 3), (5, 4)

Exercise | Q 44 | Page 380

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

Exercise | Q 45 | Page 380

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?

Exercise | Q 46.(a) | Page 380

The cost of a notebook is Rs 10. Draw a graph after making a table showing cost of 2, 3, 4, .... notebooks. Use it to find the cost of 7 notebooks.

Exercise | Q 46.(b) | Page 380

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

Exercise | Q 47.(a) | Page 380

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

Exercise | Q 47.(b) | Page 380

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

Exercise | Q 47.(c) | Page 380

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

Exercise | Q 48.(a) | Page 380

Complete the given tables and draw a graph.

 x 0 1 2 3 y = 3x + 1 1 4 - -
Exercise | Q 48.(b) | Page 380

Complete the given tables and draw a graph.

 x 1 2 4 6 y = x – 1 0 - - -
Exercise | Q 49.(a) | Page 381

Study the given graphs and complete the corresponding tables below.

Exercise | Q 49.(b) | Page 381

Study the given graphs and complete the corresponding tables below.

Exercise | Q 50 | Page 381

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?

Exercise | Q 51 | Page 381

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?

Exercise | Q 52 | Page 382

The gra ph 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

Exercise | Q 53 | Page 383

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?

Exercise | Q 54 | Page 383

Find the coordinates of the vertices of the given figures.

Exercise | Q 55 | Page 384

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?

Exercise | Q 56.(a) | Page 384

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 the value of p when q = 3

Exercise | Q 56.(b) | Page 384

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 the value of q when p = 8

Exercise | Q 58 | Page 385

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?

Exercise | Q 59 | Page 386

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.

Exercise | Q 60 | Page 386

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.

Exercise | Q 61 | Page 386

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.

Exercise | Q 62 | Page 386

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 icecreams 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?

Exercise | Q 63 | Page 387

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?

Exercise | Q 64 | Page 387

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?

Exercise | Q 65 | Page 388

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.

Exercise | Q 66 | Page 388

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 (x, y) 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.

Exercise | Q 67 | Page 388

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?

Exercise | Q 68 | Page 389

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 0°C?
(d) What was the temperature after 25 seconds?
(e) What will be the temperature after 1.5 minutes? Justify your answer.

Exercise | Q 69 | Page 389

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?

Exercise | Q 70 | Page 390

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?

Exercise | Q 71 | Page 390

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?

Exercise | Q 72 | Page 391

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.

Exercise | Q 73 | Page 391

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
Exercise | Q 74 | Page 391

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 17 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)?

Exercise | Q 75 | Page 392

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?

Exercise | Q 76 | Page 392

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

 x 1 2 3 4 5 y

Exercise | Q 77 | Page 392

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

Exercise | Q 78 | Page 393

Observe the toothpick pattern given below:

(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.

Exercise | Q 79 | Page 394

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.

Exercise | Q 80 | Page 394

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.

Exercise | Q 81 | Page 395

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.

Exercise | Q 82 | Page 396

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?

Exercise | Q 83 | Page 396

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.

Exercise | Q 84 | Page 397

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.

Exercise | Q 85 | Page 397

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 Titles 1 2 3 4 5 10 100 Number of white Tilesin Border

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

Exercise | Q 86 | Page 398

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?

Exercise

## NCERT solutions for Mathematics Exemplar Class 8 chapter 12 - Introduct To Graphs

NCERT solutions for Mathematics Exemplar Class 8 chapter 12 (Introduct To Graphs) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 8 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 8 chapter 12 Introduct To Graphs are Concept of Bar Graph, Concept of Pie Graph (Or a Circle-graph), Graphical Representation of Data as Histograms, Concept of a Line Graph, Linear Graphs, Linear Graphs, Interpretation of Bar Graphs, Drawing a Bar Graph, Concept of Double Bar Graph, Some Application of Linear Graphs, Interpretation of a Double Bar Graph, Drawing a Double Bar Graph.

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