ESTIMATION FROM LINE GRAPHS

Problem 1 :

Use the temperature time graph to find

(a) the temperature at 10 am.

(b)  the time when the temperature was 25° C

(c)  The periods when the temperature was 

(i)  increasing  (ii)  decreasing

(d)  the maximum temperature and when it occurred.

Solution :

(a)  The temperature at 10 am was 30^oC. (point A)

(b) The temperature was 25^oC at 8 am, 6 pm and 10 pm.

(points B, C, D)

(c) The temperature was:

i) increasing from midnight to 2 pm and from 8 pm to 10 pm

ii) decreasing from 2 pm to 8 pm and from 10 pm to midnight.

(d) The maximum temperature was 35^oC at 2 pm.

Problem 2 :

a) What was the room temperature when the kettle was switched on?

b) How long did it take for the water to boil?

c) For how long did the water boil?

d) At what times was the water temperature 50^oC?

e) During what period was the temperature decreasing?

Solution :

(a)  The room temperature is 20^oC, when the kettle was switched on.

(b)  It is taking 2 minutes to boil.

(c)  Water is boiling for 1 minute.

(d)  At 1 minute the temperature is 50^oC

(e)  After 3 minutes the temperature is decreasing.

Problem 3 :

Managers of a retail store conduct a customer count to help them decide how to roster their sales staff. The results are shown in the line graph.

a) At what time was the number of people in the store greatest?

b) At what time was the number of people in the store least?

c) Describe what happened in the store between 3 pm and 4 pm.

d) Use the graph to estimate the number of people in the store at 9:30 am.

Solution :

(a)  At 11 am the greatest number of people are in the shop.

(b)  At 8 pm the number of people is least.

(c)  Between 3 pm to 4 pm, there is increase in number of shopper.

(d)  

At 9.30 am, there is 27 shoppers.

Problem 4 :

When a bottle of soft drink was placed in a refrigerator, its temperature was measure d at 5-minute intervals. The results are graphed alongside.

a) Determine the temperature of the liquid when it was first placed in the refrigerator.

b) Find the time taken for the temperature to drop to 20^oC.

c) Find the temperature after 10 minutes in the refrigerator.

d) Find the fall in temperature during:

i) the first 15 minutes

ii) the next 15 minutes.

Solution :

(a)  The temperature 40^oC, when the liquid is placed in the refrigerator.

(b)  By observing the picture the time is 16 minutes when it reaches 40^oC.

(c)  After 10 minutes the temperature is 25^oC.

(d)  (i)  Fall of temperature in first 15 minutes  =  40-22

=  18^oC

(ii)  Next 15 minutes  =  21 - 13

=  8^oC

Problem 5 :

The graph below shows the progress of the batting team in a game of cricket. It shows the runs accumulated at the times when the batsmen were given ‘out’.

Use the graph to estimate:

a) the total runs at the end of the innings

b) how many runs were achieved before the first batsman was out

c) during which over the third batsman got out

d) which batsman got out in the 38^th over

e) during which over the score reached 200.

Solution :

(a)  At the end of the innings, the score is 225.

(b)  He reached 30 runs, when he was out.

(c)  During the 19th over the third batsman got out.

(d)  During 38^th over, 7^th batsman got out.

(e)  At 45^th over 200 runs were reached.

Problem 6 :

The graph shows the temperature in Birmingham on one day.

a) What was the temperature at 1:00 pm?

b) What was the difference in temperature between 11:00 am and 1:00 pm?

c) Between which times was the temperature increasing?

d) How often was the temperature recorded?

Solution :

a) The temperature at 1 pm is 4 degree Celsius.

b) Temperature at 11 am = 2 degree Celsius

Temperature at 1 pm = 4 degree Celsius.

difference between these two temperatures = 4 - 2

= 2 degree Celsius.

c) The temperature is increasing in between the interval 11 am to 3 pm 

d) The temperature is recorded for every two hours.

Problem 7 :

The graph shows the values of two cars over time.

a) In which year was the recorded value of the cars the same?

b) In which two years was the difference in the recorded values of the two cars the same?

c) Which car’s value decreased the most between 1996 and 2020?

d) For approximately how many years was the value of car 2 greater than the value of car 1?

Solution :

a) In 2002 the value of cars is the same.

b) In 2012 and in 2020 the difference in the recorded values of the two cars  is the same.

c) The value of car is decreased in between 1996 and 2020 is car 1.

d) approximately 10 years.

Problem 8 :

Aisha goes for a walk. The graph shows the height above sea level during her walk.

a) What was the height above sea level where Aisha was walking at 2 pm? 

b) At what time in Aisha’s walk was she standing 200 m above sea level?

c) Part of the walk was along a beach. Between which times did Aisha walk along the beach? How do you know? Talk about it with a partner.

d) Did the walk start and finish in the same place? Explain how you know.

Solution :

a) At 2 pm, the height above the sea level is 175 m.

b) At 2.30 pm, she is standing 200 m above.

c)  At 11 am and noon.

d) No she was at the different height above sea level at the end compared to the start.

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