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Direct & inverse proportion
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42 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Direct proportion
15 questions
Lesson
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Box A contains 300 g of cereal and costs £1.86. Box B contains 500 g of the same cereal and costs £3.20.
Which box is better value for money? You must show your working.
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Level 4
3 marks
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A recipe for 12 cookies uses 150 g of flour. Aisha has 400 g of flour and plenty of every other ingredient. Work out the greatest number of cookies Aisha can make.
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Level 4
3 marks
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Kitchen roll is sold in two pack sizes.
Pack A:
4
4
4
rolls for £
2.28
2.28
2.28
Pack B:
9
9
9
rolls for £
5.22
5.22
5.22
Which pack is better value for money? You must show your working.
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Level 4
3 marks
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Inverse proportion
16 questions
Lesson
Not started
Mark as done
The table shows pairs of values of
x
x
x
and
y
y
y
.
x
x
x
2
5
8
y
y
y
30
12
7.5
(a)
Show that
y
y
y
is inversely proportional to
x
x
x
, and find a formula for
y
y
y
in terms of
x
x
x
.
(b)
Use your formula to find the value of
y
y
y
when
x
=
24
x = 24
x
=
24
.
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Level 4
3 marks
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A train journey takes 45 minutes at an average speed of 64 km/h. How many minutes would the same journey take at an average speed of 48 km/h?
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Level 4
3 marks
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→
Mark as done
The table shows pairs of values of
x
x
x
and
y
y
y
.
x
x
x
2
2
2
3
3
3
6
6
6
y
y
y
18
18
18
12
12
12
6
6
6
(a)
Show that
y
y
y
is inversely proportional to
x
x
x
.
(b)
Work out the value of
y
y
y
when
x
=
9
x = 9
x
=
9
.
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Level 4
3 marks
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A bus journey takes
40
40
40
minutes at an average speed of
72
72
72
km/h.
How many minutes would the same journey take at an average speed of
96
96
96
km/h?
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Level 4
3 marks
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Proportion with squares, cubes and roots
14 questions
Lesson
Not started
Mark as done
From a viewpoint
h
h
h
metres above sea level, the distance
d
d
d
km to the horizon is directly proportional to the square root of
h
h
h
. When
h
=
16
h = 16
h
=
16
,
d
=
4.8
d = 4.8
d
=
4.8
.
(a)
Find a formula for
d
d
d
in terms of
h
h
h
.
(b)
Work out the value of
d
d
d
when
h
=
100
h = 100
h
=
100
.
(c)
Work out the value of
h
h
h
when
d
=
9
d = 9
d
=
9
.
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Level 4
5 marks
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F
F
F
is inversely proportional to the square of
d
d
d
. When
d
=
3
d = 3
d
=
3
,
F
=
20
F = 20
F
=
20
.
Work out the value of
F
F
F
when
d
=
6
d = 6
d
=
6
.
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Level 4
3 marks
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→
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The mass of a solid sphere is directly proportional to the cube of its radius. A sphere of radius 2 cm has mass 33.6 g.
(a)
Work out the mass of a sphere of radius 5 cm made of the same material.
(b)
Write down the number the mass of any of these spheres is multiplied by when its radius is doubled.
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Level 4
4 marks
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y
y
y
is directly proportional to the
square root
of
x
x
x
. When
x
=
25
x = 25
x
=
25
,
y
=
10
y = 10
y
=
10
.
(a)
Find a formula for
y
y
y
in terms of
x
x
x
.
(b)
Work out the value of
y
y
y
when
x
=
64
x = 64
x
=
64
.
(c)
Work out the value of
x
x
x
when
y
=
18
y = 18
y
=
18
.
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Level 4
4 marks
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y
y
y
is inversely proportional to the
square
of
x
x
x
. When
x
=
5
x = 5
x
=
5
,
y
=
8
y = 8
y
=
8
.
Work out the value of
y
y
y
when
x
=
10
x = 10
x
=
10
.
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Level 4
3 marks
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→
Mark as done
The mass of a solid sphere is directly proportional to the
cube
of its radius.
A sphere of radius
3
3
3
cm has mass
81
81
81
g.
(a)
Work out the mass of a sphere of radius
5
5
5
cm.
(b)
Work out the radius of a sphere of mass
648
648
648
g.
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Level 4
4 marks
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