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Direct & inverse proportion
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42 questions at your level
Difficulty
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Level 1
Level 2
Level 3
Level 4
Level 5
Direct proportion
15 questions
Lesson
Not started
Mark as done
5
5
5
pens cost £
1.20
1.20
1.20
. How much do
8
8
8
pens cost?
●
●●●●
Level 1
2 marks
Start
→
Mark as done
5
5
5
identical pens cost £
3.20
3.20
3.20
.
Work out the cost of
8
8
8
of these pens.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
y
y
y
is directly proportional to
x
x
x
.
When
x
=
4
x = 4
x
=
4
,
y
=
18
y = 18
y
=
18
Work out the value of
y
y
y
when
x
=
10
x = 10
x
=
10
(3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
y
y
y
is directly proportional to the square root of
x
x
x
.
When
x
=
9
x = 9
x
=
9
,
y
=
12
y = 12
y
=
12
Work out the value of
y
y
y
when
x
=
25
x = 25
x
=
25
(3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
12 identical bricks weigh 30 kg. Work out the weight of 20 of these bricks.
●●●
●●
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
.
●●●
●●
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
.
●●●
●●
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.
●●●
●●
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]
●●●
●●
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)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
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.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
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.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
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.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
y
y
y
is directly proportional to
x
x
x
. When
x
=
20
x = 20
x
=
20
,
y
=
15
y = 15
y
=
15
.
When
x
=
c
x = c
x
=
c
,
y
=
c
−
2
y = c - 2
y
=
c
−
2
. Work out the value of
c
c
c
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
y
y
y
is directly proportional to
x
x
x
. When
x
=
12
x = 12
x
=
12
,
y
=
9
y = 9
y
=
9
.
When
x
=
c
x = c
x
=
c
,
y
=
c
−
4
y = c - 4
y
=
c
−
4
.
Work out the value of
c
c
c
.
●●●●●
Level 5
3 marks
Start
→
Inverse proportion
16 questions
Lesson
Not started
Mark as done
It takes
2
2
2
people
6
6
6
hours to paint a fence. How long would it take
3
3
3
people, working at the same rate?
●
●●●●
Level 1
2 marks
Start
→
Mark as done
4
4
4
taps fill a tank in
30
30
30
minutes. How long would
6
6
6
taps take?
●
●●●●
Level 1
2 marks
Start
→
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?
●●●
●●
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]
●●●
●●
Level 3
4 marks
Start
→
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
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
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?
●●●●
●
Level 4
3 marks
Start
→
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
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
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?
●●●●
●
Level 4
3 marks
Start
→
Mark as done
4 identical pumps can empty a tank in 18 hours.
All 4 pumps run for the first 6 hours, and then one pump breaks down. How many more hours do the remaining 3 pumps take to finish emptying the tank?
●●●●●
Level 5
4 marks
Start
→
Mark as done
A job takes
10
10
10
workers exactly
12
12
12
days.
All
10
10
10
workers work for the first
4
4
4
days. Then
2
2
2
workers leave, and the remaining
8
8
8
finish the job.
Work out the
total
number of days the job takes.
●●●●●
Level 5
4 marks
Start
→
Mark as done
P
P
P
is inversely proportional to
q
q
q
.
q
q
q
is directly proportional to the cube root of
r
r
r
.
When
q
=
4
q = 4
q
=
4
,
P
=
15
P = 15
P
=
15
When
q
=
10
q = 10
q
=
10
,
r
=
125
r = 125
r
=
125
Find the value of
r
r
r
when
P
=
40
P = 40
P
=
40
(5 marks)
●●●●●
Level 5
5 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 root of
x
x
x
.
When
x
=
9
x = 9
x
=
9
,
y
=
12
y = 12
y
=
12
Work out the value of
y
y
y
when
x
=
25
x = 25
x
=
25
(3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
y
y
y
is directly proportional to
x
2
x^2
x
2
.
When
x
=
2
x = 2
x
=
2
,
y
=
12
y = 12
y
=
12
Work out the value of
y
y
y
when
x
=
5
x = 5
x
=
5
[3]
●●
●●●
Level 2
3 marks
Start
→
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)
●●●
●●
Level 3
4 marks
Start
→
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
.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
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
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
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.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
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
.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
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
.
●●●●
●
Level 4
3 marks
Start
→
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.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
a
a
a
is directly proportional to the square of
b
b
b
, and
b
b
b
is directly proportional to the square root of
c
c
c
.
When
c
=
16
c = 16
c
=
16
,
b
=
12
b = 12
b
=
12
. When
b
=
12
b = 12
b
=
12
,
a
=
36
a = 36
a
=
36
.
(a)
Find a formula for
a
a
a
in terms of
c
c
c
.
(b)
Work out the value of
a
a
a
when
c
=
64
c = 64
c
=
64
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
a
a
a
is directly proportional to the
square
of
b
b
b
: when
b
=
2
b = 2
b
=
2
,
a
=
16
a = 16
a
=
16
.
b
b
b
is directly proportional to the
cube root
of
c
c
c
: when
c
=
8
c = 8
c
=
8
,
b
=
4
b = 4
b
=
4
.
Work out the value of
a
a
a
when
c
=
27
c = 27
c
=
27
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
P
P
P
is inversely proportional to
q
q
q
.
q
q
q
is directly proportional to the cube root of
r
r
r
.
When
q
=
4
q = 4
q
=
4
,
P
=
15
P = 15
P
=
15
When
q
=
10
q = 10
q
=
10
,
r
=
125
r = 125
r
=
125
Find the value of
r
r
r
when
P
=
40
P = 40
P
=
40
(5 marks)
●●●●●
Level 5
5 marks
Start
→