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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
Not started
Mark as done
12 identical bricks weigh 30 kg. Work out the weight of 20 of these bricks.
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Level 3
3 marks
Start
→
Mark as done
y
y
y
is directly proportional to
x
x
x
. When
x
=
8
x = 8
x
=
8
,
y
=
36
y = 36
y
=
36
.
(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
=
14
x = 14
x
=
14
.
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Level 3
3 marks
Start
→
Mark as done
y
y
y
is directly proportional to
x
x
x
. When
x
=
6
x = 6
x
=
6
,
y
=
21
y = 21
y
=
21
.
(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
=
10
x = 10
x
=
10
.
(c)
Work out the value of
x
x
x
when
y
=
56
y = 56
y
=
56
.
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●●
Level 3
4 marks
Start
→
Mark as done
The exchange rate is £
1
=
€
1.15
1 = €1.15
1
=
€1.15
.
(a)
Convert £
240
240
240
into euros.
(b)
Convert €
69
69
69
into pounds.
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Level 3
2 marks
Start
→
Mark as done
A recipe for
12
12
12
biscuits needs
150
150
150
g of flour and
100
100
100
g of butter.
Priya has
400
400
400
g of flour and
250
250
250
g of butter.
Work out the greatest number of biscuits Priya can make. You must show your working. [3]
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●●
Level 3
3 marks
Start
→
Mark as done
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
Start
→
Inverse proportion
16 questions
Lesson
Not started
Mark as done
It takes 8 workers 9 days to build a wall. Working at the same rate, how many days would it take 6 workers to build the same wall?
●●●
●●
Level 3
3 marks
Start
→
Mark as done
y
y
y
is inversely proportional to
x
x
x
. When
x
=
10
x = 10
x
=
10
,
y
=
12
y = 12
y
=
12
.
(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
=
48
x = 48
x
=
48
.
(c)
Work out the value of
x
x
x
when
y
=
300
y = 300
y
=
300
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
6
6
6
identical taps fill a pool in
10
10
10
hours.
Working at the same rate, how long would
4
4
4
taps take to fill the pool?
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Level 3
2 marks
Start
→
Mark as done
y
y
y
is inversely proportional to
x
x
x
. When
x
=
4
x = 4
x
=
4
,
y
=
9
y = 9
y
=
9
.
(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
=
12
x = 12
x
=
12
.
(c)
Work out the value of
x
x
x
when
y
=
24
y = 24
y
=
24
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
p
p
p
is inversely proportional to the square of
q
q
q
.
When
q
=
4
q = 4
q
=
4
,
p
=
5
p = 5
p
=
5
(a)
Find a formula for
p
p
p
in terms of
q
q
q
. (2 marks)
(b)
Work out the value of
p
p
p
when
q
=
2
q = 2
q
=
2
(1 mark)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
y
y
y
is inversely proportional to the square of
x
x
x
.
When
x
=
4
x = 4
x
=
4
,
y
=
3
y = 3
y
=
3
(a)
Find a formula for
y
y
y
in terms of
x
x
x
. (3 marks)
(b)
Find the value of
y
y
y
when
x
=
10
x = 10
x
=
10
(1 mark)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The time,
t
t
t
days, taken to build a wall is inversely proportional to the number of workers,
n
n
n
.
8
8
8
workers take
9
9
9
days.
(a)
How long would
6
6
6
workers take? [2]
(b)
How many workers are needed to build the wall in
4
4
4
days? [2]
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●●
Level 3
4 marks
Start
→
Proportion with squares, cubes and roots
14 questions
Lesson
Not started
Mark as done
y
y
y
is directly proportional to the square of
x
x
x
. When
x
=
5
x = 5
x
=
5
,
y
=
75
y = 75
y
=
75
.
(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
=
8
x = 8
x
=
8
.
(c)
Work out the positive value of
x
x
x
when
y
=
300
y = 300
y
=
300
.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
y
y
y
is directly proportional to the
square
of
x
x
x
. When
x
=
4
x = 4
x
=
4
,
y
=
48
y = 48
y
=
48
.
(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
=
6
x = 6
x
=
6
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
y
y
y
is inversely proportional to the square of
x
x
x
.
When
x
=
4
x = 4
x
=
4
,
y
=
3
y = 3
y
=
3
(a)
Find a formula for
y
y
y
in terms of
x
x
x
. (3 marks)
(b)
Find the value of
y
y
y
when
x
=
10
x = 10
x
=
10
(1 mark)
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●●
Level 3
4 marks
Start
→