HW4 – Grade C
Homework on interpreting and drawing distance time graphs,
working out average speed and other real life graphs
1.
(a)
Liquid is poured at a steady rate into the bottle shown in the diagram.
As the bottle is filled, the height, h, of the liquid in the bottle changes.
Which of the five graphs below shows this change?
Give a reason for your choice.
Graph A
Graph B
h
h
Time
Time
Graph C
Graph D
h
h
Time
Time
Graph E
h
Time
Graph ..………………………………………………………………………………
Reason .………………………………………………………………………………
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(2)
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(b)
Liquid is poured at a steady rate into another container.
The graph shows how the height, h, of the liquid in this container changes.
h
Time
Sketch a picture of this container.
(1) (Total 3 marks)
2.
Mr Smith leaves the home at 10 am to go to the shopping mall.
He walks to the station where he catches a train.
He gets off the train at the mall.
The travel graph shows his journey.
15
10
Distance
from home
(km)
5
0
10 am
11 am
12 am
1pm
2 pm
Time
After shopping Mr Smith goes home by taxi.
The taxi leaves the mall at 1 pm and arrives at his home at 1.45 pm.
(a)
Complete the travel graph.
(b)
Calculate the average speed of the taxi.
(2)
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Answer .......................................................km per hour
(2)
(Total 4 marks)
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2
3.
The graph shows Amy’s progress on a sponsored walk.
20
15
10
Distance (km)
5
0
1000
(a)
1100
1200
1300
Time of day
1400
1500
How many times does Amy stop during her walk?
Answer...............................................................................
(1)
(b)
Between which times does Amy walk the fastest?
Explain your answer.
Answer ................................................................
Explanation .................................................................................................................
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(2)
(c)
Bill sponsors Amy for 20 pence per kilometre.
Kate sponsors Amy for 30 pence per kilometre.
How much should Amy collect altogether from Bill and Kate after her walk?
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Answer...............................................................................
(3)
(Total 6 marks)
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3
4.
Wayne cycles from Newcastle to Ashington, a distance of 20 miles.
The diagram shows the distance-time graph of his journey.
20
16
Distance
from
Newcastle 12
(miles)
8
4
0
10.00
(a)
11.00
12.00
13.00
14.00 Time
How far from Newcastle is Wayne at 11.00?
Answer .......................................... miles
(1)
(b)
Describe what is happening between 12.00 and 13.00
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(1)
(c)
How far does Wayne travel in the first 2 hours of his journey?
Answer .......................................... miles
(1)
(d)
What is Wayne’s average speed over the first 2 hours of his journey?
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Answer ........................................... mph
(2)
(e)
Darren travels from Ashington to Newcastle by bus.
He leaves Ashington at 10.00 and arrives in Newcastle at 11.00
On the diagram draw a possible distance-time graph of Darren’s journey.
(1)
(Total 6 marks)
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4
5.
Mrs Murphy drives from Pyeton (P) to Queenswell (Q).
The graph shows her journey.
50
R
40
Distance
in km
30
Q
20
10
P
0
1000
1020
1040
1100
1120
1140
Time
(a)
How far is it from Pyeton to Queenswell?
.....................................................................................................................................
Answer ………………………………….. km
(1)
(b)
At what time does she arrive at Queenswell?
.....................................................................................................................................
Answer ………………………………………
(1)
(c)
Mrs Murphy stays at Queenswell for 20 minutes.
Then she drives on to Rokeby (R) at the same speed as before.
(i)
Show the rest of her journey on the grid.
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(3)
(ii)
At what time does she arrive at Rokeby?
Answer ………………………………………
(1)
(Total 6 marks)
The Robert Smyth School
5
6.
The graph shows a train journey.
D
E
100
75
Distance
from start
(km)
B
50
C
25
A
F
0
0
1
2
3
4
5
Time (hours)
(a)
What is happening from B to C?
.....................................................................................................................................
(1)
(b)
Which part of the journey is faster, from A to B or from C to D?
Explain your answer.
.....................................................................................................................................
.....................................................................................................................................
(1)
(c)
How far did the train travel altogether?
.....................................................................................................................................
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Answer ................................................................ km
(2)
(Total 4 marks)
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6
7.
The distance-time graph shows the journey of a train between two stations.
The stations are 6 kilometres apart.
6
5
4
Distance
(kilometres)
3
2
1
0
0
(a)
1
2
3
4
5
6
Time (minutes)
7
8
9
10
During the journey the train stopped at a signal. For how long was the train stopped?
........................….........................................................................................................
Answer ................................................... minutes
(1)
(b)
What was the average speed of the train for the whole journey? Give your answer in
kilometres per hour.
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Answer .............................. kilometres per hour
(2)
(Total 3 marks)
8.
The graph illustrates a 1000 metre race between Nina and Polly.
(a) Who was in the lead 10
seconds after the start of the
race ?
1000
Distance
(metre)
Answer ......................................................
(1)
Nina
Polly
(b) Who won the race?
500
Answer ....................................................
(1)
(c) Describe what happened
20 seconds after the start of
0
0
20
40
60
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80
100 120 140
Time (seconds)
160
180
200
7
the race.
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(1)
(d)
Describe what happened to Nina 90 seconds after the start of the race.
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(1)
(Total 4 marks)
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8
9.
Two gas supply companies have different ways of charging for the gas they supply.
Alpha gasCO
Fixed Charge
Price per kilowatt hour of gas
£9.60
First 5 kilowatt hours free then
£1.30 for every kilowatt hour over 5.
Beta gasCO
Fixed Charge
Price per kilowatt hour of gas
No fixed charge
£1.50 for every kilowatt hour.
Find the number of kilowatt hours after which Alpha gasCo becomes cheaper than Beta gasCo.
You might want to use some graph paper.
You must show your method clearly.
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Answer ................................... kilowatt hours
(Total 4 marks)
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9
10.
The graphs show two parts of a train journey.
Describe in words what is happening in each part.
(a)
Speed
Time
......................................................................................................................................
......................................................................................................................................
(1)
(b)
Speed
Time
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(2)
(Total 3 marks)
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10
1.
(a)
Graph D
B1
Slow, steady, faster steady
Steady rate and an indication why quicker at top.
(b)
Any container with uniform vertical cross-section
Allow 2-D, e.g. Rectangle, and/or substantially uniform Xsection
DB1
B1
[3]
2.
(a)
Line from (11:15,12) to (13:00,12)
± 1mm
‘Line’ from (13:00,12) to (13:45,0)
ft their (13:00,12) ± 1mm
(b)
‘Their 12’ ÷ ‘Their 45mins’
oe 12 ÷ 0:45, 1200 ÷ 45 etc
Allow ft from the ‘distance’ and ‘time’ on their graph
16
B1
B1ft
M1
A1ft
ft if Ml awarded rounded  3sf.
[4]
3.
(a)
2
B1
(b)
1130 and 1230
Steepest (or steeper) line
oe, e.g. covers greater distance in same time
B1
B1
(c)
19
B1
20 × (their 19) +30 × (their 19)
oe
M1
9.50
A1ft
[6]
4.
(a)
8
B1
(b)
Not moving
B1
Same distance from Newcastle oe
(c)
16
B1
(d)
Their 16/2
M1
8
(e)
A1ft
Line or curve from (10.00, 20) to (11.00,0)
B1
[6]
5.
(a)
27
B1
(b)
1036
B1
(c)
(i)
Horizontal line to 1056
or line up from 1056
Bl
Line leaving Q after 1040 and
arriving at R 24 min later
Tolerance on 24 min = ± 2 min
M1
Correct line from 1056 to 1120
A1
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11
(ii)
1120
Blft
ft where their line arrives at R
Tolerance ± 1 min
[6]
6.
(a)
Not moving
B1
(b)
oe
A to B and acceptable reason
Accept:
Steeper
B1
Because it only takes
1
hour
2
Longer from C to D
Note: ignore incorrect times (further working) if implication is
correct
(c)
100 × 2
M1
oe
200
A1
[4]
7.
(a)
2
B1
(b)
6 km in 10 minutes
6/10 oe
M1
36 kph
A1
[3]
8.
(a)
Nina
B1
(b)
Nina
B1
(c)
Polly overtook Nina
B1
(d)
Stopped, fell etc
B1
[4]
9.
9.60 + (x – 5) × 1.30
Alt: M1 for graph of Alpha parcels
M1
= 1.50x
M1
M1 for graph of Beta
3.10 = 0.20x
A1
A1 accuracy
x = 15.5
A1
A1 answer. Accept 16 but not 15.
T&I gets M1 iff taken as far as 15.
A1 for both schemes at 15
A1 for both schemes at 16
A1 conclusion
[4]
10.
(a)
Moving at constant speed
Same time and same speed B0
B1
(b)
Slowing down
B1
(then) speeding up
eg
Variable speed B1
Down then up B0
B1
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12
Slows down, stops, speeds up B1
[3]
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13