Homework on interpreting and drawing conversion graphs
1.
A speed limit in France is 100 kilometres per hour.
The speedometer shows the speed of a lorry.
80
100
140
60
160
40
180
20
0
(a)
100
120
km/h
200
How much slower than the speed limit is the lorry travelling?
.....................................................................................................................................
Answer ............................................................... km/h
(2)
(b)
(i)
Use the graph to convert 32 kilometres per hour into miles per hour.
20
miles 16
per
hour 12
8
4
0
0
4
8
12
16
20
24
kilometres per hour
28
32
Answer ............................................................... miles per hour
(1)
(ii)
Convert 96 kilometres per hour into miles per hour.
...........................................................................................................................
...........................................................................................................................
Answer ............................................................... miles per hour
(2)
(Total 5 marks)
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2.
This is a conversion graph for gallons and litres.
40
30
Litres
20
10
0
1
(a)
2
3
4
Gallons
5
6
7
8
Use the graph to convert
(i)
4 gallons to litres,
Answer ....................................................... litres
(ii)
30 litres to gallons.
Answer .................................................... gallons
(2)
(b)
50 gallons is approximately 225 litres.
Explain how you can use the graph to show this.
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(1)
(Total 3 marks)
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3.
This graph can be used to convert miles to kilometres.
11
10
9
8
7
Kilometres
6
5
4
3
2
1
0
0
(a)
1
2
3
4
5
Miles
6
7
8
1
miles from the Post Office.
2
How many kilometres is this?
Scott lives 3
Answer....................................................................................................................km
(1)
(b)
Jade goes for a training run of 7 kilometres.
How many miles is this?
Answer................................................................................................................miles
(1)
(c)
Jade is training to run a half marathon, which is a distance of 13 miles.
Use the graph to calculate this distance in kilometres.
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Answer....................................................................................................................km
(2)
(Total 4 marks)
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4.
A baby elephant is weighed at the end of each week.
The graph shows the weight of the elephant.
At the end of week 5 the elephant weighed 100 kg.
120
110
Weight (kg)
100
90
80
0
(a)
0
1
2
3
4
5
6
Week
7
8
9
10
At the end of week 6 the elephant weighed 104 kg.
At the end of week 10 the elephant weighed 120 kg.
(i)
Plot these points on the graph.
(2)
(ii)
Complete the graph with straight lines.
(1)
(b)
Use your graph to estimate the weight of the elephant at the end of week 8.
Answer ........................................................... kg
(1)
(Total 4 marks)
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5.
The table shows various temperatures measured on scales invented by Newton and Fahrenheit.
(a)
Freezing point of water
Boiling point of water
Newton (°N)
0
33
Fahrenheit (°F)
32
212
Draw a conversion graph on the grid.
°F
240
220
200
180
160
140
120
100
80
60
40
20
0
0
5
10
15
20
25
30
35
°N
(2)
(b)
Blood temperature is 96°F.
What is blood temperature in °N?
Answer …………………………………… °N
(1)
(Total 3 marks)
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6.
Sue knows that 8 kilometres is the same as 5 miles.
(a)
Plot this information on the grid to produce a conversion graph.
8
7
6
5
Miles
4
3
2
1
0
0
1
2
3
4
5
Kilometres
6
7
8
(2)
(b)
Use your graph to convert 4.6 miles into kilometres.
.....................................................................................................................................
Answer .................................................... km
(2)
(c)
Sue has to travel 40 km.
How many miles is this?
.....................................................................................................................................
Answer .................................................... miles
(2)
(Total 6 marks)
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7.
(a)
Change a speed of 72 kilometres per hour into miles per hour.
.....................................................................................................................................
.....................................................................................................................................
Answer .............................................. miles per hour
(2)
(b)
A car travels 200 kilometres in 3 hours 30 minutes.
Calculate its average speed in kilometres per hour.
Give your answer to an appropriate degree of accuracy.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ..................................... kilometres per hour
(4)
(Total 6 marks)
8.
Sharon travels from Leeds to London in her car. The distance she travels is 200 miles. The
journey takes her 4 hours. Find Sharon’s average speed.
.................................................................................................................................................
.................................................................................................................................................
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Answer .........................................................................
(Total 3 marks)
9.
A metal bar has a volume of 250 cm3.
It has a mass of 1.7 kg.
Calculate the density of the metal.
State the units of your answer.
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Answer .......................................................................
(Total 3 marks)
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1.
(a)
75
B1
Can be implied if final answer of 25 given
25
B1 ft
ft is for:
100 – (their seen answer in range 60 – 80)
(b)
(i)
20 (mph)
B1
(ii)
20 × 3
Or their (b) (i) × 3
oe
M1
60
A1ft
Note: If own graph used must have answer of 60 to score A1
[5]
2.
(a)
(b)
(i)
18
B1
(ii)
6.6 – 6.7 inclusive
B1
Read off value for 5 and multiply by 10
oe eg read off value for 1 and multiply by 50
B1
[3]
3.
(a)
5.6
(b)
4.4
(c)
attempt at 6 1 2 × 2 or 6 + 7 oe
relevant readings A1l  0.2
M1
20.8
A1
 0.2
 0.2
B1
B1
A1low 20 – 21 if evidence of an attempt at 1.3 × 10
[4]
4.
(a)
(i)
Point plotted at correct position
1
(6, 104)  square
2
Point plotted at (10, 120)
1
 square
2
(ii)
(b)
Straight lines joining their two plotted points and also to (5, 100)
Reading 
1
square from week 8 = “112”
2
ft their single straight line between their (6, 104) and their
(10, 120)
B1
B1
B1
B1 ft
[4]
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5.
(a)
Both points plotted
½ sq accuracy
Line drawn
B1
Blft
One plot must be correct
(b)
Any value between 11 and 12 inclusive
B1
[3]
6.
(a)
Line through (0, 0) and (8, 5)
B1 if through (8, 5) only
(b)
7.3 km to 7.4 km
B1 for 7.2 to 7.5.
f.t. their graph for B2 if straight. A1low B1 if poor accuracy
(c)
25 miles
B2
B2 ft.
M1,A1
M1 for 5 × their va1ue
A1 ft. their va1ue
[6]
7.
(a)
72 ×
5
8
M1
72 × 0.625, 72 ÷ 1.6
45
(b)
A1
3.5
B1
oe or 210
200
their3.5
M1
200
× 60
their210
57.1(4)
A1
Round their answer to 1dp or 0dp
57 or 57.1, or 60 with working
B1ft
[6]
8.
200 ÷ 4
M1
or 200 ÷ 240
50
A1
or
5
6
oe
miles per hour or mph
or miles per minute
units must be consistent
B1
[3]
9.
1.7 ÷ 250
M1
ie Digits ‘17’ ÷ digits ‘25’
eg 1700 ÷ 250
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0.0068
A1
6.8 accept answer with digits ‘68’ if consistent with units used.
eg 0.068 kg/cl
kg/cm3
B1
Units consistent with working
ie allow g/cm3 if working and answer
NB If M0 awarded all B1 for any units of
supports it
density.
[3]
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