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15 Drawing and using graphs 15

15 Drawing and using graphsYou should know how to

plot coordinates

work out expressions like 3 + 4n when n = 2

This work will help you draw and interpret straight-line graphs for real-life situations.

A1 Aluna is filling a fish tank.

(a) How deep will the water be after 2 minutes?

(b) Copy and completethis table.

(c) On graph paper draw and label axes like these.Then plot the points from your table(the first two are shown already plotted).

(d) Join the points you have plotted.Extend the line they make.

(e) Use your graph to say how deepthe water will be after 7 minutes.

(f) How deep will the water be after 32 minutes?(g) How many minutes will it take

until the water is 10cm deep?

(h) Aluna starts filling the tankat exactly quarter past 3.At what time is the water 17cm deep?

Time in minutes 0 1 2 3 4 5Depth of water in cm 5 7

9

8

7

6

5

43

2

1

00 1 2 3

Depth

ofwaterincm

Time in minutes

The tank starts with5 cm of water in it.

Each minute her hose-pipeadds 2 cm.

So after 1 minute, there is 7cmof water in the tank.

5cm 5cm

2cm

7cm

A Tables and graphs (answers p 00)

Go up to 20

Stop at 7

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16 15 Drawing and using graphs

After it is lit,it gets shorterby 4cm eachhour.

A2

(a) How tall will the candle be after 2 hours?

(b) Copy and complete this table.

(c) On graph paper, draw and label axes like these.Then plot the points from your table.

(d) Join the points you have plotted.Extend the line they make.

(e) Use your graph to say how tallthe candle will be after 6 hours.

(f) How tall will it be after 42 hours?

(g) How many hours will it takeuntil the candle is 12 cm tall?

(h) How long will the candlelast until it goes out?

(i) If the candle was lit at half past one,at what time will it go out?

Time in hours 0 1 2 3 4

Height of candle in cm 26 22

Heightof

candleincm

Time in hours

0 1 2 3 4 5 6 7

12

11

10

9

8

7

6

5

4

3

2

1

0

4cm

Stop at 7

Go up to 26

26 cm

This candle is26cm tall whenit is first lit.

So after 1 hour it isonly 22cm tall.

22 cm

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15 Drawing and using graphs 17

A3 Labib is slowly heating up a liquid in a science experiment.The liquid starts at 20C, and heats up by 8 degreesevery 5 minutes.

(a) Copy and complete this table.

(b) Plot the points from your table on axes likethe ones below.

(c) Join your points and extend the line.

(d) Use the graph to find out what the temperature will be after 40 minutes.

(e) About how long will it take for the liquid to get to 30C?

(f ) Labib needs to get the liquid to 70C.He starts the experiment at a quarter past 4.At about what time does the liquid get to 70 C?

Time in minutes 0 5 10 15 20 25

Temperature in C 20 28

50

40

30

20

0 10 20 30 40

Temperatur

einC

Time in minutes

Go up to 90

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18 15 Drawing and using graphs

A4 Chemico make anti-freeze for car radiators.

They test each batch of anti-freezeby cooling a sample.

At the start of the test, the anti-freeze is at 15C.

Then the temperature of the anti-freezedrops by 4 degrees each hour.

(a) What will the temperature of the anti-freeze be after 1 hour?

(b) After 5 hours, by how many degrees will the temperature have dropped?What will the temperature of the anti-freeze be after 5 hours?

(c) Copy and complete this table.

(d)Draw axes like these and plot the points from your table.

Join the points with a line, and extend it.

(e) Use your graph to find out what the temperatureof the anti-freeze will be after 22 hours.

(f ) What will the temperature be after 6 hours?

(g) How long will it take for the temperatureof the anti-freeze to drop to 3C?

(h) If Chemico start testing the anti-freeze at 10 a.m.at what time will the temperature be 7C?

Number of hours 0 1 2 3 4 5

Temperature in C 15

TemperatureinC5

4

3

2

1

0

1

2

3

4

0 1 2 3 4 5 6

Number of hours

Radiator

Up to 15

Down to 10

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15 Drawing and using graphs 19

B1 You can use this rule to change miles into kilometres.

number of kilometres = number of miles98 5

(a) Use the rule to check that 10 miles is the same as 16 kilometres.

(b) Work out how many kilometres there are in(i) 20 miles (ii) 30 miles (iii) 50 miles

(c) Copy and complete this table.

(d) Plot the points from your table using axes like these.Join the points with a line and extend it.

(e) About how many kilometres are there in

(i) 42 miles (ii) 55 miles(f ) About how many miles is

(i) 20 kilometres (ii) 75 kilometres

(g) On the road-signs below, the distances are in kilometres.Sketch each sign with the distances written in miles.

Miles 0 10 20 30 40 50

Kilometres 0 16

Kilom

etres

Miles0 10 20 30

30

20

10

0

Paris 85

Versailles 78

Aroport dOrly 65

Fontainebleau 36

Gare TGV 15

Dunkerque 28

Boulogne 34

St Omer 45

Centre ville 8

B Graphs and rules (answers p 00)

Up to 100

Across to 60

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20 15 Drawing and using graphs

B2 Z car taxis have meters in their taxis to work outthe charge for each trip.The meters use the formula c= 4m + 1

c is the charge in pounds; m is the number of miles the trip takes.

For example, if a customer travels 2 miles,

c = 492 + 1 = 9so the charge on the meter will be 9.00.

(a) Copy and complete this table showingthe charge for different lengths of journey.

(b) Draw a graph to show the values in your table.Draw and label your axes like this.

Plot the points from your table and join themwith a line. Extend your line backwards.

Label the line Z car taxis.

(c) Use your graph to find the missing numbers on these meters.

miles

charge

2 0

9 0 0

Z car taxis

Costin

(c)

Distance travelled in miles (m)0 1 2 3

5

4

3

2

1

0

Miles travelled (m) 1 2 3 4 5 6

Charge in (c) 9

Go up to 28

Stop at 7

miles

charge

1 8

9 0 0

Z car taxis(i)

miles

charge

5 5

9 0 0

Z car taxis(ii)

miles

charge

0 7

9 0 0

Z car taxis(iii)

miles

charge

1 8

5 0 0

Z car taxis(iv)

miles

charge

1 8

3 4 0

Z car taxis(v)

miles

charge

1 8

3 8 0

Z car taxis(vi)

1 2 1

? ? ?

? ? ?

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15 Drawing and using graphs 21

For this question, you need the graph you drew in question B2.

*B3 Aardvark taxis use a different formula.Their formula is c = 4.5 + 3m.

So for a trip of 2 miles, c= 4.5 + 392 = 10.5

The charge will be 10.50

(a) Copy and complete this table for Aardvark taxis.

(b) Use the values in your table to plot a graphfor the charges Aardvark taxis make.Plot the graph on the same axes as for Z car taxis.

Label the line Aardvark taxis.

Use your graphs to answer these questions.

(c) (i) How much do Z cars charge for a trip of 1.5 miles?

(ii) How much do Aardvark charge for the same distance?

(d) Which is cheaper, Z cars or Aardvark, for a trip of 1.5 miles?

(e) Which is cheaper, Z cars or Aardvark, for a trip of 4.5 miles?

(f ) For one distance, Z cars and Aardvark charge the same.What distance is that?

(g) Copy and complete this advice.

Z car taxis 01979 345 123Aardvark taxis 01979 387 395

Phone for journeys over miles as they are cheaper.

Miles travelled (m) 1 2 3 4 5 6

Charge in (c) 10.50

miles

charge

2 0

0 5 0

Aardvark taxis

1

? ?

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22 15 Drawing and using graphs

Test yourself(answers p 00)

T1 Computer Helpline give help to computer users over the phone.They use a formula to work out the charge.The charge is based on how many minutes long the phone call is.

charge in pounds = number of minutes9

3 + 5So if a call is 2 minutes long, the charge is 293 + 5 = 11.

(a) Copy and complete this table.

(b) Draw a graph to show the values in your table.Draw and label your axes like this.

Plot the points from your table andjoin them with a line.

Extend your line backwards.

(c) Use the graph to say how much ComputerHelpline charge for a 32 minute call.

(d) Alix makes a call. The charge is 21.50How long was her call?

(e) Use your graph to find the missing numbers on these bills.

(i) (ii) (iii)ComputerHelpline

Length of call

minutes

Our charge 6.50

Helplinefor

Happy Help

Number of minutes 1 2 3 4 5 6

Charge in 11

6

5

43

2

1

0

Chargein

Time in minutes0 1 2 3

ComputerHelpline

Length of call

minutes

Our charge 18.50

Helplinefor

Happy Help

ComputerHelpline

Length of call

62 minutes

Our charge 6.50

Helplinefor

Happy Help

Go up to 28

Stop at 7

?

??

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