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1
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PLT Skills
LESSON OBJECTIVES

• We are learning to
• Enhance Mathematical basic skills knowledge.
  (Which PLT skills?)
• Accurately solve direct proportion/variation
  problems. (Grade A).

Always aim high!
AUTHOR
2
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STARTER
PLT Skills
TASK
2)
3)
Write in standard form
1)
Make x the subject of y mx c
8m
0.0067
-3
6.7
x 10

y - c
mx

20m
Work out the volume
Solve 7x 5y 22 3x - 2y 26
5)
Volume pi x radius x radius x length
x

x
x
x
Volume
3.14
4
20
4
Volume
4)
Write down all the integer values of x satisfying
this inequality 8 2x lt 8
14x 10y 44
6)
2
(a) Factorise fully 8x 12xy (b) Simplify (5a
b)
15x - 10y 130

174
29x

( )
2
-
y
4
x
x
3

8 2x lt 8
x
6
3

5

4
x
4
lt
18 - 2y 26
This means that x is greater than or equal to -4
but less than 3
125

-2y 8
-4, -3, -2, -1, 0, 1, 2, 3
-4
y

EXTENSION
Calculate the compound interest for amount of
4000 invested for 4 years at 3.2 interest.
4

x
(
1
)

4000
0.032
4537.10

3
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PLT Skills
DIRECT PROPORTION
EXAMPLE 1
W a F
Means W is directly proportional to F
W kF
k is the constant of proportionality
Substitute in the values of W and F
24

k
6
24 6k
k

4
Substitute k back into the original equation W kF

W
F
4
Substitute in F 10 to work out W

10
W
4
x

W
40
4
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T a M
T 6M
T kM
10 6M
30

k
5
30 5k
1.67 M
M 1.67 (2d.p.)
Effective Participator
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6 k
PLT Skills
DIRECT PROPORTION
TASK 1 (GRADE A)
1)
T is directly proportional to M. If T 30 and M
5, find (a) T when M 3 (b) M when T 10
W a F
W 12F
W kF
90 12F
36

k
3
36 3k
7.5 F
F 7.5
12 k
2)
W is directly proportional to F. If W 36 and F
3, find (a) W when F 5 (b) F when W 90
W a F
W kF
W 12 x 5

3
36
k
W 60
36 3k
12 k
5
Which ones are you using?
T a M
T 6M
T kM
10 6M
30

k
5
30 5k
1.67 M
M 1.67 (2d.p.)
Effective Participator
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6 k
PLT Skills
DIRECT PROPORTION
TASK 2 (GRADE A)
1)
Q varies directly with P. If Q 100 when P 2,
find (a) Q when P 4 (b) P when Q 400
X a Y
X 2.5Y
X kY
X 2.5 x 11
17.5

k
7
Q 27.5
17.5 7k
2.5 k
2)
X varies directly with Y. If X 17.5 when Y 7,
find (a) X when Y 11 (b) Y when X 40
X a Y
X 2.5Y
X kY
40 2.5Y
17.5

k
7
17.5 7k
16 Y
Y 16
2.5 k
W a F
W kF
W 12 x 5

3
36
k
W 60
36 3k
12 k
6
Which ones are you using?
T a M
T 6M
T kM
10 6M
30

k
5
30 5k
1.67 M
M 1.67 (2d.p.)
Effective Participator
Self Manager
Independent Enquirer
Creative Thinker
Team Worker
Reflective Learner
6 k
PLT Skills
DIRECT PROPORTION
TASK 3 (GRADE A)
1)
The distance covered by a train is directly
proportional to the time taken for the journey.
The train travels 105 miles in 3 hours.
C a W
(b) How much time will it take for the train to
cover 315 miles?
(a) What distance will the train cover in 4 hours?
C 0.19W
C kW
34.20 0.19W
47.50

k
250
47.50 250k
180 W
W 180kg
0.19 k
2)
The cost of fuel delivered to your door is
directly proportional to the weight received.
When 250kg is delivered, it costs 47.50.
X a Y
X 2.5Y
X kY
(a) How much will it cost to get 450kg delivered?
(b) How much would be delivered if the cost were
34.20
40 2.5Y
17.5

k
7
17.5 7k
16 Y
Y 16
2.5 k
W a F
W kF
W 12 x 5

3
36
k
W 60
36 3k
12 k
7
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PLT Skills
DIRECT PROPORTION
EXAMPLE 2
153p
Substitute in the values of C and r
Substitute in the values of C and r

153
17
x

68
k
68 4k
9

k

17
3
r


r
3cm

C
17
Substitute in r 2.4 to work out W

C
17
x

5.76
C
17
x


C
98p
C
97.92
8
Which ones are you using?
T a M
T 6M
T kM
10 6M
30

k
5
30 5k
1.67 M
M 1.67 (2d.p.)
Effective Participator
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6 k
PLT Skills
DIRECT PROPORTION
X a vF
EXTENSION 1 (GRADE A)
X kvF
X 32vF
2
1)
W is directly proportional to M . If W 12 when
M 2, find (a) W when M 4 (b) M when W 75
X 32 x v49
X 32 x 7
128 4k
X 224
32 k
X 32vF
48 32vF
1.5 vF
2)
X is directly proportional to vF. If X 128 and
F 16, find (a) X when F 49 (b) F when X
48
2.25 F
5 M
F 2.25
M 5
12 4k
W 48
3 k
5 M
M 5
9
Which ones are you using?
T a M
T 6M
T kM
10 6M
30

k
5
30 5k
1.67 M
M 1.67 (2d.p.)
Effective Participator
Self Manager
Independent Enquirer
Creative Thinker
Team Worker
Reflective Learner
6 k
PLT Skills
DIRECT PROPORTION
3
y a vb
EXTENSION 2 (GRADE A)
3
3
y kvb
y 20vb
3
1)
P is directly proportional to f . If P 400 when
f 10, find (a) P when f 6 (b) f when P
50
3
3
100 kv125
40 20 x vb
100 5k
3
2 vb
20 k
8 b
b 8
3
2)
y is directly proportional to vb. If y 100 when
b 125, find (a) y when b 8 (b) b when y
40
F 2.25
2.25 F
5 M
M 5
X kvF
X 32vF
X 32 x v49
X 32vF
X 32 x 7
P 86.4
0.4 k
5 f
f 5
10
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T a M
37.50 2.5vp
15 vp
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PLT Skills
DIRECT PROPORTION
225 p
p 225 people
EXTENSION 3 (GRADE A)
1)
The cost of serving tea and biscuits varies
directly with the square root of the number of
people at the buffet. It costs 25 to serve tea
and biscuits to 100 people.
(b) For a cost of 37.50, how many could be
served tea and biscuits?
(a) How much will it cost to serve tea and
biscuits to 900 people?
3 r
1.8 k
r 3mm
2)
The mass, in grams, of ball bearings varies
directly with the cube of the radius, measured in
millimetres. A ball bearing of radius 4mm has a
mass of 115.2g.
(a) What will be the mass of a ball bearing of
radius 8mm?
(b) A ball bearing has a mass of 48.6g. What is
the radius?
f 5
W a F
X 32vF
W kF
48 32vF
W 12 x 5

3
36
k
W 60
1.5 vF
36 3k
2.25 F
12 k
5 M
F 2.25
M 5
11
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PLT Skills
DIRECT PROPORTION
MINI-PLENARY FUNCTIONAL MATHS QUESTION
C a A
(b) A playgroup has 24 children. What is the
smallest playground area in which they could
safely play?
C 0.2857A
C kA
24 0.2857A

210
60
k
60 210k
84 A
0.2857 k
2
A 84m
12
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DISCOVERY
PLT Skills
13
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PLT Skills
DIRECT PROPORTION
PLENARY 1 PROBLEM SOLVING QUESTION
The sketched graphs show each of these proportion
statements.
(a) y a x
(b) y a x
2
(c) y a vx
C a A
C 0.2857A
C kA
24 0.2857A

210
60
k
60 210k
84 A
0.2857 k
2
A 84m
(a)
(b)
(c)
Match each statement to the correct sketch.
14
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PLT Skills
DIRECT PROPORTION
3
V a h
PLENARY 2 EXAM QUESTION
The volume, V cubic metres, of a hot-air balloon
is proportional to the cube of its height, h
metres. A balloon with a height of 10m has a
volume of 500 cubic metres.
(a) Find an equation connecting V and h. (3
marks)
(b) Find the volume of a hot-air balloon which
has a height of 30 metres. (1 mark)
C 0.2857A
24 0.2857A
500 1000k
V 0.5 x 27000
84 A
0.5 k
0.5 k
2
A 84m
(c) Another hot-air balloon has a volume of 5000
cubic metres. Find its height. (3 marks)
h 21.5m
21.5 h
15
What have you learnt?
Draw your brain
In your brain, write or draw everything you can
remember about solving direct proportion
problems. It can be a skill or a reflection, or
something else that might be prominent in your
brain.
16
Creative Entrepreneur
Responsible Citizen
Independent Learner
Positive Thinker
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Reflective Learner
SELF ASSESSMENT
Enterprise Skills
Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I dont understand
I nearly understand
I fully understand
17
Creative Entrepreneur
Responsible Citizen
Independent Learner
Positive Thinker
Team Worker
Reflective Learner
SELF ASSESSMENT
Enterprise Skills
Which ones are you using?
Plenary Activity
WWW (What Went Well) EBI (Even Better If)
On your post it notes Think about how you can
improve your work.
18
Which ones are you using?
Effective Participator
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PLT Skills
DIRECT PROPORTION
TASK 1 (GRADE A)
1)
T is directly proportional to M. If T 30 and M
5, find (a) T when M 3 (b) M when T 10
2)
W is directly proportional to F. If W 36 and F
3, find (a) W when F 5 (b) F when W 90
19
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PLT Skills
DIRECT PROPORTION
TASK 2 (GRADE A)
1)
Q varies directly with P. If Q 100 when P 2,
find (a) Q when P 4 (b) P when Q 400
2)
X varies directly with Y. If X 17.5 when Y 7,
find (a) X when Y 11 (b) Y when X 40
20
Which ones are you using?
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PLT Skills
DIRECT PROPORTION
TASK 3 (GRADE A)
1)
The distance covered by a train is directly
proportional to the time taken for the journey.
The train travels 105 miles in 3 hours.
(b) How much time will it take for the train to
cover 315 miles?
(a) What distance will the train cover in 4 hours?
2)
The cost of fuel delivered to your door is
directly proportional to the weight received.
When 250kg is delivered, it costs 47.50.
(a) How much will it cost to get 450kg delivered?
(b) How much would be delivered if the cost were
34.20
21
Which ones are you using?
Effective Participator
Self Manager
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PLT Skills
DIRECT PROPORTION
EXTENSION 1 (GRADE A)
2
1)
W is directly proportional to M . If W 12 when
M 2, find (a) W when M 4 (b) M when W 75
2)
X is directly proportional to vF. If X 128 and
F 16, find (a) X when F 49 (b) F when X
48
5 M
M 5
22
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PLT Skills
DIRECT PROPORTION
EXTENSION 2 (GRADE A)
3
1)
P is directly proportional to f . If P 400 when
f 10, find (a) P when f 6 (b) f when P
50
3
2)
y is directly proportional to vb. If y 100 when
b 125, find (a) y when b 8 (b) b when y
40
23
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Effective Participator
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Independent Enquirer
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Reflective Learner
PLT Skills
DIRECT PROPORTION
EXTENSION 3 (GRADE A)
1)
The cost of serving tea and biscuits varies
directly with the square root of the number of
people at the buffet. It costs 25 to serve tea
and biscuits to 100 people.
(b) For a cost of 37.50, how many could be
served tea and biscuits?
(a) How much will it cost to serve tea and
biscuits to 900 people?
2)
The mass, in grams, of ball bearings varies
directly with the cube of the radius, measured in
millimetres. A ball bearing of radius 4mm has a
mass of 115.2g.
(a) What will be the mass of a ball bearing of
radius 8mm?
(b) A ball bearing has a mass of 48.6g. What is
the radius?
M 5
24
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PLT Skills
DIRECT PROPORTION
MINI-PLENARY FUNCTIONAL MATHS QUESTION
(b) A playgroup has 24 children. What is the
smallest playground area in which they could
safely play?
25
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PLT Skills
DIRECT PROPORTION
PLENARY 1 PROBLEM SOLVING QUESTION
The sketched graphs show each of these proportion
statements.
(a) y a x
(b) y a x
2
(c) y a vx
Match each statement to the correct sketch.
26
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PLT Skills
DIRECT PROPORTION
PLENARY 2 EXAM QUESTION
The volume, V cubic metres, of a hot-air balloon
is proportional to the cube of its height, h
metres. A balloon with a height of 10m has a
volume of 500 cubic metres.
(a) Find an equation connecting V and h. (3
marks)
(b) Find the volume of a hot-air balloon which
has a height of 30 metres. (1 mark)
(c) Another hot-air balloon has a volume of 5000
cubic metres. Find its height. (3 marks)