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GCSE Maths(Higher)
Indirect Proportion
Types of proportion
Time (min)
mph
90
60
?
70More Less
MoreLess
?5
MoreLess
MoreLess
508
Direct Proportion• percentage • Conversions• Ratio• Fractions• Similar shapes• Arc & sectors• How many more can you
think of?
km
miles
Inverse Proportion
Any question where increasing one number has the effect of reducing the other
What is number?Can you think of any more?
Number
RatioPe
rcen
tage
s
Money
Numbe
r
Fractions
Time
Length
s
Weights
Standard Index Form
Below is a good rule of thumb for questions on proportion.
Number Number
Area (square number)
Area (square number)
Volume(cube number)
Volume (cube number)
Relationships that don’t fit
Number Number
Area (square number)
Area (square number)
Volume(cube number)
Volume (cube number)
No
No
No
But what do you do when you are given a questions that don’t seem to fit?
Number Number
Area (square number)
Area (square number)
Volume(cube number)
Volume (cube number)
Number
Volume (cube number)
A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.
No
What price are the large candles, if the cost of the candle is proportional to its volume?
Strategy – extract information onto 3 lines
A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.
Cost
Height cm
Height cm3
8
512
3.20 ?
14
274415.17?
2744512
2.3?
512
2.3
2744
?
Large candles cost £17.15 in the gift shop
What price are the large candles, if the cost of the candle is proportional to its volume (not its height)?
Number
Area (square number)
No
A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.
It takes 144cm2 of plastic film to wrap the small candle. How much does the large candle need?
Strategy extract information onto 3 lines
A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.
It takes 144cm2 of plastic film to wrap the small candle. How much does the large candle need?
area
Height cm
Height cm2
8
64
144 ?
14
196
441?
19664
144?
64
144
196
?
Large candles need 441cm2 of wrap
Strategy for Indirect proportion
Answer – make sure it is in context with the question
a) T in terms of L is:
T= 4
Calculation – to get method marks.
a)
Extract information from question onto lines.
QuestionA simple pendulum of length L cm,
takes T seconds to swing from A to B. T is proportional to square root of L. When T = 34 sec, L = 72.25cm
a) Express T in terms of Lb) Find T when L = 400c) Find L when T = 60
Lcm
√L
T = sec
72.25 L
√72.25 √L
34 T
LLT
L
T
425.72
3425.72
34
L
Strategy for Indirect proportion
Answer – make sure it is in context with the question
a) T in terms of L is:
T= 4
b) T=80
Calculation – to get method marks.
b) From a)
Extract information from question onto lines.
QuestionA simple pendulum of length L cm,
takes T seconds to swing from A to B. t is proportional to square root of L. When T = 34 sec, L = 72.25cm
a) Express T in terms of Lb) Find T when L = 400c) Find L when T = 60
Lcm
√l
T = sec
72.25 L
√72.25 √L
34 T
LT 4
L80204
4004
T
T
Strategy for Indirect proportion
Answer – make sure it is in context with the question
a) T in terms of L is:
T= 4
b) T=80 when L = 400
c) L = 225 when T=60
Calculation – to get method marks.
c)
Extract information from question onto lines.
QuestionA simple pendulum of length L cm,
takes T seconds to swing from A to B. T is proportional to square root of L. When T = 34 sec, L = 72.25cm
a) Express T in terms of Lb) Find T when L = 400c) Find L when T = 60
Lcm
√l
T = sec
72.25 L
√72.25 √L
34 T
L
LT
LT
LT
2
444
L
225154
60 22
Strategy for Indirect proportion
Answer – make sure it is in context with the question
Calculation – to get method marks.
Extract information from question onto lines.
Question
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