18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Direct Direct ProportionProportion
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Direct Variation
Harder Direct Variation (extension)
Direct Proportion
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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1 12 2
1. 2x + 13 = 51
3.
2. Calculate the area of the shape.
9
6
8
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To explain the term Direct Proportion.
1. Understand the idea of Direct Proportion.
Direct Direct ProportionProportion
2. Solve simple Direct Proportional problems.
Direct ProportionS4
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
“ .. When you double the number of cakes you double the cost.”
Cakes Cost
Two quantities, (for example, number of cakes and totalcost) are said to be in DIRECT Proportion, if :
Example : The cost of 6 cakes is £4.20. find the cost of 5 cakes.
6 4.20 1 4.20 ÷ 6 = 0.70 5 0.70 x 5 = £3.50
Write down two quantities that
are in direct proportion.
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
Example : Which of these pairs are in proportion.
(a) 3 driving lessons for £60 : 5 for £90
(b) 5 cakes for £3 : 1 cake for 60p
(c) 7 golf balls for £4.20 : 10 for £6
Same ratio means in
proportionS4
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
£ $
Example : On holiday I exchanged £30 for $45.How many $ will I get for £50.
30 45 1 45 ÷ 30 = 1.5 50 1.5 x 50 = $75
What name do we give to
this valueExchang
e rate
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
Pencils Cost
Example : 300 pencils cost £6. How much will 200 cost.
300 £6.00
100 £6.00 ÷ 3 = £2.00200 £2.00 x 2 = £4.00
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Ex 1Ch17 (page 187)
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ProportionProportionS4
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Calculate 0.5 + 1.45 x 21.
2. Calculate 1 11of 2 43
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To explain what direct variation is and how to work out simple direct variation formulae.
1. Understand the process for calculating direct variation formulae.
Direct VariationDirect Variation
2. Calculate the constant k from information given and write down formula.
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VariationVariation
If you double the number of cakes you double the cost
Variation is the ALGEBRA form of Proportion.S4
If you treble the number of cakes you treble the cost
If you half the number of cakes you half the cost
We say the cost (C) VARIES as the number (n) of cakes
Mathematically we say, C n
It should be obvious that if you increase the number of cakes you buy from a shop then you increase the cost.
= C knNot a
formula !
Formula !
18 Apr 202318 Apr 2023ww
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Direct VariationDirect Variation
Given that y is directly proportional to x,and when y = 20, x = 4.
Find a formula connecting y and x.
Since y is directly proportional to x the formula is of the form
y = kx k is a constan
t20 = k(4)
k = 20 ÷ 4 = 5
y = 5x
y = 20x =4
y
x
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Direct VariationDirect Variation
The number of dollars (d) varies directly as the
number of £’s (P). You get 3 dollars for £2. Find a formula connecting d and P.
Since d is directly proportional to P the formula is of the form
d = kP k is a constan
t3 = k(2)
k = 3 ÷ 2 = 1.5
d = 1.5P
d = 3P = 2
d
P
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d = 1.5 x 20 = 30 dollars
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct VariationDirect Variation
Q. How much will I get for £20
d = 1.5Pd
P
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Ex 2Ch17 (page 188)
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Direct VariationDirect Variation
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Calculate 0.75 + 1.2 x 31.
2. Calculate 1 11of 3 84
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To explain how to work out harder variation formulae.
1. Understand the process for calculating direct variation formulae.
Direct VariationDirect Variation
2. Calculate the constant k from information given and write down formula and use it to solve problems.
S4Harder Direct Variation
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Direct VariationDirect Variation
Given that y is directly proportional to the square of x, and when y = 40, x = 2.
Find a formula connecting y and x when .
Since y is directly proportional to x squaredthe formula is of the form
y = kx2
40 = k(2)2
k = 40 ÷ 4 = 10
y = 10x2
y
x2
y = 40x = 2
Harder Direct VariationS4
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct VariationDirect Variation
Q. Calculate y when x = 5
y = 10x2
y = 10(5)2 = 10 x 25 = 250
y
x2
Harder Direct VariationS4
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Direct VariationDirect Variation
Q. The cost (C) of producing a football magazine varies as the square root of the number of pages (P). Given 36 pages cost 48p to produce. Find a formula connecting C and P.
Since C is directly proportional to “square root of” P the formula is of the form
k = 48 ÷ 6 = 8
C =k P
48 =k 36
C =8 P
C
√P C = 48P = 36
Harder Direct VariationS4
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct VariationDirect Variation
Q. How much will 100 pages cost.
C =8 100
C =8 100 =8 10 =80p
C
√P
Harder Direct VariationS4
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Worksheet
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Direct VariationDirect VariationHarder Direct Variation
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