16-May-15Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Variation Harder Direct Variation (extension) Direct Proportion

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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Starter QuestionsStarter Questionsw

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1 12 2

1. 2x + 13 = 51

3.

2. Calculate the area of the shape.

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6

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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


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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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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


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£ $

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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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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Now try Ex 1Ch17 (page 187)

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ProportionProportionS4



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Calculate 0.5 + 1.45 x 21.

2. Calculate 1 11of 2 43

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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 !

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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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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


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Q. How much will I get for £20

d = 1.5Pd

P

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Now try Ex 2Ch17 (page 188)

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Calculate 0.75 + 1.2 x 31.

2. Calculate 1 11of 3 84

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1. To explain how to work out harder variation formulae.

1. Understand the process for calculating direct variation formulae.


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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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

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Q. Calculate y when x = 5

y = 10x2

y = 10(5)2 = 10 x 25 = 250

y

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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



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Q. How much will 100 pages cost.

C =8 100

C =8 100 =8 10 =80p

C

√P



Now try Worksheet

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Direct VariationDirect VariationHarder Direct Variation

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Documents

16-May-15Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Variation Harder Direct Variation (extension) Direct Proportion