8 Math Graphs

Finish Line & Beyond

INTRODUCTION TO GRAPHS 1. Graphical presentation of data is easier to understand. 2. (i) Abar graph is used to show comparison among categories. (ii) A pie graph is used to compare parts of a whole. (iii) AHistogram is a bar graph that shows data in intervals. 3. Aline graph displays data that changes continuously over periods of time. 4. A line graph which is a whole unbroken line is called a linear graph. 5. For fixing a point on the graph sheet we need, x-coordinate and y-coordinate. 6. The relation between dependent variable and independent variable is shown through a graph. EXERCISE 1 1. The following graph shows the temperature of a patient in a hospital, recorded every hour. Temperature 40 39 38 37

Temperature

36 35 34 33 9:00 AM

10:00 AM

11:00 AM

12 NOON

1:00 PM

2:00 PM

3:00 PM

(a) What was the patient’s temperature at 1 p.m. ? (b) When was the patient’s temperature 38.5° C? (c) The patient’s temperature was the same two times during the period given. What were these two times? (d) What was the temperature at 1.30 p.m.? How did you arrive at your answer? (e) During which periods did the patients’ temperature showed an upward trend? Answer: (a) 36.5˚C (b) 12:00 Noon (c) at 1:00 PM and 2:00 PM (d) Data Insufficient (e) from 10:00 to 11:00 AM and from 2:00 to 3:00 PM

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Finish Line & Beyond 2. The following line graph shows the yearly sales figures for a manufacturing company.

12 10 Year 2002 2003 2004 2005 2006

8 6

Sale in Rs. Crores

4 2 0 2002

2003

2004

2005

2006

(a) What were the sales in (i) 2002 (ii) 2006? (b) What were the sales in (i) 2003 (ii) 2005? (c) Compute the difference between the sales in 2002 and 2006. (d) In which year was there the greatest difference between the sales as compared to its previous year? Answer: (a) (i) Rs. 4 crores (ii) Rs. 8 crores (b) (i) Rs. 7 Crores (ii) Rs. 10 crores (c) 8-4=4; Sales of 2006 is Rs. 4 crores more than that of 2002 (d) 2005 sees the greatest jump in sales which clear from the steepest angle between these years.

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Finish Line & Beyond 3. For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

12

Height(cm)

10 8 Plant A

6

Plant B

4 2 0 Start

Week 1 Week 2 Week 3 Period

(a) How high was Plant A after (i) 2 weeks (ii) 3 weeks? Answer: (i) 7 cm (ii) 9 cm (b) How high was Plant B after (i) 2 weeks (ii) 3 weeks? Answer: (i) 7 cm (ii) 10 cm (c) How much did Plant A grow during the 3rd week? Answer: 2 cm (d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week? Answer: 3 cm (e) During which week did Plant A grow most? Answer: from week 1 to week 2 by 5 cm (f) During which week did Plant B grow least? Answer: In the first week by 1 cm (g) Were the two plants of the same height during any week shown here? Specify.

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Finish Line & Beyond Answer: Second week both have a height of 7 cm 4. The following graph shows the temperature forecast and the actual temperature for each day of a week.

Temperature in celsius

40 35 30 25 Forecast

20

Actual

15 10 5 0 Mon

Tue

Wed

Thu

Fri

Sat

Sun

Days

(a) On which days was the forecast temperature the same as the actual temperature? Answer: Tuesday 20˚ c, Friday 15˚ c and Sunday 35˚ c (b) What was the maximum forecast temperature during the week? Answer: 35˚ c (c) What was the minimum actual temperature during the week? Answer: 35˚ c (d) On which day did the actual temperature differ the most from the forecast temperature? Answer: Thursday, by 7.5˚ c ( Notice the largest gap between two lines) 5. Use the tables below to draw linear graphs. (a) The number of days a hill side city received snow in different years. Year Days

2003 8

2004 10

2005 5

2006 12

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Finish Line & Beyond Answer:

Number of Days of Snowfall

14 12 10 8

Year

6

Days

4 2 0 2003

2004

2005

2006

Year

(b) Population (in thousands) of men and women in a village in different years. Year Number of Men Number of Women

2003 12 11.3

2004 12.5 11.9

2005 13 13

2006 13.2 13.6

2007 13.5 12.8

Population in Thousands

16 14 12 10 Number of Men

8

Number of Women

6 4 2 0 2003

2004

2005

2006

2007

Year

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Finish Line & Beyond 6. A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph. Distance

Distance in Kms

25 20 15 Distance 10 5 0 8:00 AM

9:00 AM

10:00 AM 11:00 AM 12 NOON Time

(a) What is the scale taken for the time axis? Answer: Kilometres (b) How much time did the person take for the travel? Answer: 4 hours (c) How far is the place of the merchant from the town? Answer: 22 kms (d) Did the person stop on his way? Explain. Answer: Between 10:00 AM to 11:00 AM the line is horizontal, which explains that the person took rest between these timings (e) During which period did he ride fastest? Answer: Between 8:00 AM and 9:00 AM he traveled 10 kms, (look for the steepest angle made by the line)

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Finish Line & Beyond

EXERCISE 2 1. Plot the following points on a graph sheet. Verify if they lie on a line (a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

8 7 6 5 4

Series2

3 2 1 0 A

B

C

D

(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

6 5 4 3

Series2

2 1 0 P

Q

R

S

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Finish Line & Beyond (c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)

8 7 6 5 4

Series2

3 2 1 0 K

L

M

N

EXERCISE 3 1. Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples Number of apples Cost (in Rs)

1 5

2 10

3 15

4 20

5 25

30

Cost in Rupees

25 20 Number of apples

15

Cost (in Rs)

10 5 0 1

2

3

4

5

Number of Apples

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Finish Line & Beyond (b) Distance travelled by a car Time (in hours) Distances (in km)

6 am 40

7 am 80

8 am 120

9 am 160

180 160 Distance in km

140 120 100

Series1

80 60 40 20 0 6:00 AM

7:00 AM

8:00 AM

9:00 AM

Time in Hours

(i) How much distance did the car cover during the period 7.30 a.m. to 8 a.m? Answer: 20 km (ii) What was the time when the car had covered a distance of 100 km since it’s start? Answer: 7:30 AM (c) Interest on deposits for a year. Deposit (in Rs) Simple Interest (in Rs)

1000 80

2000 160

3000 240

4000 320

5000 400

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Finish Line & Beyond 450 Simple Interest in Rs

400 350 300 250

Series1

200 150 100 50 0 1000

2000

3000

4000

5000

Deposit in Rs

(i) Does the graph pass through the origin? Answer: Yes (ii) Use the graph to find the interest on Rs 2500 for a year. Answer: The mid point between 2000 and 3000 is near Rs. 200, so the interest for Rs. 2500 is Rs. 200 (iii) To get an interest of Rs 280 per year, how much money should be deposited?

 to get Rs. 80 per year one needs to deposit Rs. 1000 1000 ∴ to get Re. 1 per year one needs to deposit Rs. 80 1000 ∴ to get Rs. 280 per year one needs to deposit Rs. × 280 = 3500 80 Answer:

2. Draw a graph for the following. (i)

Side of square (in cm) Perimeter (in cm)

2 8

3 12

3.5 14

5 20

6 24

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Finish Line & Beyond 30

Perimeter (in cm)

25 20 15

Series1

10 5 0 2

3

3.5

5

6

Side of Square (in cm)

(ii) Side of square (in cm) Area (in sqcm)

2 4

3 9

4 16

5 25

6 36

40

Area (in sq cm)

35 30 25 Series1

20 15 10 5 0 2

3

4

5

6

Side of Square (in cm)

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