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51 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Speed, distance and time
15 questions
Lesson
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A car travels
120
120
120
miles in
2
2
2
hours. Work out its average speed.
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Level 1
1 mark
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A cyclist rides at
15
15
15
km/h for
3
3
3
hours. How far does she travel?
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Level 1
1 mark
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A sprinter runs
200
200
200
m in
25
25
25
seconds.
Work out her average speed in m/s.
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Level 2
2 marks
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A coach travels
210
210
210
km at an average speed of
60
60
60
km/h.
(a)
How long does the journey take? Give your answer in hours and minutes. (2 marks)
On the return journey the coach takes
4
4
4
hours
12
12
12
minutes for the same
210
210
210
km.
(b)
Work out the average speed of the return journey. (1 mark)
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Level 2
3 marks
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A train travels
168
168
168
km in
1
1
1
hour
45
45
45
minutes.
(a)
Work out the average speed of the train, in km/h. (2 marks)
(b)
At this average speed, how long would the train take to travel
240
240
240
km? Give your answer in minutes. (1 mark)
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Level 2
3 marks
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A car travels 150 km in 2 hours 30 minutes. Work out its average speed in km/h.
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Level 3
3 marks
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A cyclist rides at an average speed of 24 km/h for 1 hour 45 minutes. Work out how far the cyclist rides.
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Level 3
3 marks
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A coach travels
87
87
87
km at an average speed of
60
60
60
km/h.
Work out how long the journey takes. Give your answer in hours and minutes.
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Level 3
3 marks
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The velocity–time graph shows the first
40
40
40
seconds of a train's journey.
10
20
30
40
2
4
6
8
10
12
14
Time (s)
Velocity (m/s)
(a)
Work out the acceleration of the train in the first
10
10
10
seconds. [2]
(b)
Work out the total distance travelled in the
40
40
40
seconds. [3]
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Level 3
5 marks
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A drone flies 27 km at an average speed of 36 km/h. Work out how long the flight takes. Give your answer in minutes.
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Level 4
3 marks
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A train travels for 40 minutes at an average speed of 90 km/h, and then for 20 minutes at an average speed of 120 km/h. Work out the average speed for the whole journey, in km/h.
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Level 4
4 marks
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Priya drives
90
90
90
km at an average speed of
72
72
72
km/h. She then stops at a service station for
15
15
15
minutes, and finally drives a further
30
30
30
km at an average speed of
60
60
60
km/h.
Work out her average speed for the whole journey,
including the stop
.
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Level 4
4 marks
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A lorry makes a delivery journey of
280
280
280
km in exactly
4
4
4
hours.
For the first
1.5
1.5
1.5
hours it travels at an average speed of
80
80
80
km/h.
Work out its average speed over the rest of the journey.
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Level 4
4 marks
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Amir drives 120 km at an average speed of 60 km/h, and then a further 120 km at an average speed of 40 km/h.
Meera says: "The average speed for the whole journey is 50 km/h, because the mean of 60 and 40 is 50."
(a)
Show that the whole journey takes 5 hours.
(b)
Work out the average speed for the whole journey, and explain why Meera is wrong.
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Level 5
5 marks
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Two trains are
180
180
180
km apart on the same line and travel towards each other, one at
70
70
70
km/h and the other at
50
50
50
km/h.
(a)
Work out how long it takes until they meet. Give your answer in hours and minutes.
(b)
Work out how far the faster train travels before they meet.
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Level 5
5 marks
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Density and pressure
19 questions
Lesson
Not started
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A block has mass
300
300
300
g and volume
50
50
50
cm
3
^3
3
. Work out its density in g/cm
3
^3
3
.
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Level 1
1 mark
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A force of
40
40
40
N acts on an area of
8
8
8
m
2
^2
2
. Work out the pressure.
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Level 1
1 mark
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A pebble has mass
322
322
322
g and volume
140
140
140
cm³.
Work out the density of the pebble.
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Level 2
2 marks
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A block of metal has mass
540
540
540
g and volume
200
200
200
cm
3
^3
3
.
(a)
Work out the density of the metal, in g/cm
3
^3
3
. (2 marks)
Water has density
1
1
1
g/cm
3
^3
3
. An object floats in water if its density is less than the density of water.
(b)
Will the block float in water? Give a reason. (1 mark)
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Level 2
3 marks
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A solid metal cylinder has radius
4
4
4
cm and height
9
9
9
cm.
The metal has a density of
7.8
7.8
7.8
g/cm
3
^3
3
.
Work out the mass of the cylinder.
Give your answer correct to 3 significant figures. (3 marks)
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Level 2
3 marks
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A solid block has mass
2.4
2.4
2.4
kg and volume
800
800
800
cm
3
^3
3
.
Work out the density of the block in g/cm
3
^3
3
. [3]
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Level 2
3 marks
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The density of aluminium is 2.7 g/cm³. A solid aluminium block has volume 250 cm³. Work out the mass of the block, in grams.
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Level 3
2 marks
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Gold has a density of 19.3 g/cm³. A gold bar has mass 579 g. Work out the volume of the bar, in cm³.
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Level 3
2 marks
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A solid metal cuboid measures
8
8
8
cm by
5
5
5
cm by
4
4
4
cm. Its mass is
1.28
1.28
1.28
kg.
(a)
Work out the volume of the cuboid.
(b)
Work out the density of the metal in g/cm³.
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Level 3
3 marks
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A box exerts a force of
600
600
600
N on the ground. The area of the base of the box is
0.4
0.4
0.4
m
2
^2
2
.
(a)
Work out the pressure exerted, in N/m
2
^2
2
. [2]
(b)
Convert your answer to N/cm
2
^2
2
. [2]
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Level 3
4 marks
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The diagram shows a solid prism on a horizontal floor.
25 cm
pressure
=
force
area
\text{pressure} = \frac{\text{force}}{\text{area}}
pressure
=
area
force
The prism has
a volume of
4500
4500
4500
cm³
a height of
25
25
25
cm.
The force of the prism on the floor is
540
540
540
newtons.
Work out the pressure the prism exerts on the floor.
Give your answer in newtons/cm².
(3 marks)
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Level 3
3 marks
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Nadia has two identical jars.
She puts
720
720
720
grams of lentils into one of the jars.
The lentils fill the jar completely.
The density of the lentils is
0.8
0.8
0.8
g/cm³
Nadia puts
720
720
720
grams of sugar into the other jar.
This time the jar is not full. There is
300
300
300
cm³ of empty space left in the jar.
Work out the density of the sugar.
You must show all your working.
(4 marks)
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Level 3
4 marks
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Paving slabs are made from concrete with density
2.4
2.4
2.4
g/cm³
Each paving slab has a volume of
12
500
12\,500
12
500
cm³
The maximum mass of paving slabs that a van can carry is
850
850
850
kg.
Work out the greatest number of paving slabs that the van can carry.
(3 marks)
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Level 3
3 marks
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A crate weighs 480 N and rests on horizontal ground on a rectangular base measuring 0.6 m by 0.5 m.
0.6 m
0.5 m
Diagram NOT accurately drawn
Work out the pressure the crate exerts on the ground, in N/m².
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Level 4
3 marks
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A force of
F
F
F
newtons acting on an area of 0.4 m² produces a pressure of 250 N/m².
(a)
Work out the value of
F
F
F
.
(b)
The same force now acts on an area of 0.2 m². Write down the new pressure, in N/m².
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Level 4
3 marks
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A force of
60
60
60
N acts on an area of
400
400
400
cm².
Work out the pressure in N/m².
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Level 4
3 marks
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Two crates stand on horizontal ground.
Crate
A
A
A
weighs
300
300
300
N and its base measures
0.5
0.5
0.5
m by
0.4
0.4
0.4
m.
Crate
B
B
B
weighs
360
360
360
N and its base measures
0.6
0.6
0.6
m by
0.5
0.5
0.5
m.
Which crate exerts the greater pressure on the ground? You must show your working.
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Level 4
3 marks
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An alloy is made by mixing 150 cm³ of metal A, which has density 4.2 g/cm³, with 100 cm³ of metal B, which has density 6.7 g/cm³.
Work out the density of the alloy.
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Level 5
4 marks
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An alloy is made by melting together
400
400
400
g of metal
P
P
P
and
270
270
270
g of metal
Q
Q
Q
.
Metal
P
P
P
has density
8
8
8
g/cm³. Metal
Q
Q
Q
has density
4.5
4.5
4.5
g/cm³.
Work out the density of the alloy. Give your answer correct to 3 significant figures.
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Level 5
4 marks
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Converting compound units and rates of flow
19 questions
Lesson
Not started
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Convert
3.5
3.5
3.5
km to metres.
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Level 1
1 mark
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Amelia is paid £
8.40
8.40
8.40
per hour.
Work out her rate of pay in pence per minute.
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Level 2
2 marks
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A car uses
6
6
6
litres of fuel for every
100
100
100
km it travels.
How far can the car travel on
27
27
27
litres of fuel? (2 marks)
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Level 2
2 marks
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A solid block has mass
2.4
2.4
2.4
kg and volume
800
800
800
cm
3
^3
3
.
Work out the density of the block in g/cm
3
^3
3
. [3]
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Level 2
3 marks
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A box is a cuboid measuring
40
40
40
cm by
25
25
25
cm by
30
30
30
cm.
(a)
Work out the volume of the box in m
3
^3
3
. [2]
Packets of rice are cuboids of volume
250
250
250
cm
3
^3
3
.
(b)
Work out the greatest number of packets that could fit in the box, by volume. [2]
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Level 2
4 marks
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Convert 54 km/h into m/s.
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Level 3
3 marks
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Convert 8 m/s into km/h.
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Level 3
2 marks
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The speed limit on a UK motorway is
65
65
65
mph on a stretch with roadworks.
Using
5
5
5
miles
=
8
= 8
=
8
km, convert
65
65
65
mph into km/h.
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Level 3
2 marks
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Concrete has a density of
2400
2400
2400
kg/m³.
Convert this density into g/cm³.
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Level 3
2 marks
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A box exerts a force of
600
600
600
N on the ground. The area of the base of the box is
0.4
0.4
0.4
m
2
^2
2
.
(a)
Work out the pressure exerted, in N/m
2
^2
2
. [2]
(b)
Convert your answer to N/cm
2
^2
2
. [2]
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Level 3
4 marks
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A water butt is in the shape of a cylinder.
35 cm
90 cm
The water butt has radius
35
35
35
cm.
The water butt has height
90
90
90
cm.
The water butt is empty.
Water from a hose then flows into the water butt at a rate of
40
40
40
cm³ per second.
Work out how many minutes it takes to fill the water butt completely.
Give your answer correct to the nearest minute.
You must show all your working.
(4 marks)
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Level 3
4 marks
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Water is pumped out of a flooded quarry at a constant rate of
0.35
0.35
0.35
m³/s
How many days does it take to pump
1
250
000
1\,250\,000
1
250
000
m³ of water out of the quarry?
Give your answer correct to the nearest day.
(3 marks)
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Level 3
3 marks
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In Edinburgh,
2.5
2.5
2.5
kg of potatoes cost £1.95
In Toronto,
4
4
4
lbs of potatoes cost
2.55
2.55
2.55
Canadian dollars.
£1
=
1.85
= 1.85
=
1.85
Canadian dollars
1
1
1
kg
=
2.2
= 2.2
=
2.2
lbs
In which city are potatoes better value for money, Edinburgh or Toronto?
You must show how you get your answer.
(4 marks)
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Level 3
4 marks
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The density of a liquid is 1.05 g/cm³. Convert this density into kg/m³.
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Level 4
3 marks
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A car travels at 90 km/h. A cheetah runs at 27 m/s.
Which is faster, and by how many m/s? You must show your working.
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Level 4
3 marks
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Water flows through a pipe at a constant rate of 0.3 litres per second, into an empty tank with a capacity of 0.72 m³.
Given that 1 m³ = 1000 litres, work out how many minutes it takes to fill the tank.
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Level 4
4 marks
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A car uses petrol at a rate of
6.2
6.2
6.2
litres per
100
100
100
km.
Petrol costs £
1.45
1.45
1.45
per litre.
(a)
Work out how many litres of petrol the car uses on a journey of
350
350
350
km.
(b)
Work out the cost of the petrol for the journey.
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Level 4
4 marks
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A closed cylindrical water tank has radius
1.2
1.2
1.2
m and height
2.5
2.5
2.5
m.
The whole outside surface of the tank, including the top and bottom, is to be painted.
One litre of paint covers
12
12
12
m
2
^2
2
. Paint is sold in
1
1
1
-litre tins costing £
8.50
8.50
8.50
each.
Work out the cost of the paint. You must show your working. [5]
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Level 4
5 marks
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A bottling machine fills
750
750
750
ml bottles at a rate of
40
40
40
bottles per minute.
(a)
Work out the rate of the machine in litres per hour.
The machine must fill a vat order of
13
500
13\,500
13
500
litres.
(b)
Work out how long this takes. Give your answer in hours and minutes.
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Level 5
5 marks
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