14-Jun-14Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Graphs Direct Proportion formula and calculations

11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Direct Direct ProportionProportion

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Direct Proportion Graphs

Direct Proportion formula and calculations

Inverse Direct Proportion

Direct Proportion

Other Direct Proportion formula


Starter QuestionsStarter Questionsw

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2. Calculate the area of the shape.

3 2+4 3

(a) 0.13 (b) 0.02 (c) 1.09

1. 3x + 5 = 17

3. How many significant numbers

4.

9

6

8

11 Apr 202311 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.


2. Solve simple Direct Proportional problems.

Direct Proportion


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“ .. 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 :

Direct Proportion

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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£ $

Direct Proportion

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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(a) Simply multiple by 2 :

Direct Proportion

Example : To make scrambled eggs for 2 people we need 2eggs, 4g butter and 40 ml of milk.How much of each for(a) 4 people (b) Just himself

4 eggs, 8g butter, 80 ml of milk.

(b) Simply half original amounts:

1 eggs, 2g butter, 20 ml of milk.


Now try Exercise 1Ch8 (page 101)

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Direct Proportion



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2.

4. Calculate 31 1 × 12 2

1. Simplfy the ratio 95 : 35

Calculate 2.5% of 500

3. Find the mean, median and mode for

5, 2, 5, 8


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1. To explain how Direct Direct Proportion Graph is always a straight line.

1. Understand that Direct Proportion Graph is a straight line.


2. Construct Direct Proportion Graphs.



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The table below shows the cost of packets of “Biscuits”.


No. of Pkts 1 2 3 4 5 6

Cost (p) 20 40 60 80 100 120

We can construct a graph to represent this data.

What type of graph do we expect ?


Direct Proportion

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

No. of Packets

Cos

t (p

)

Direct Proportion GraphsNotice that the points lie on a straight line

passing through the origin

This is true for any two quantities

which are in Direct Proportion.


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KeyPoint

Two quantities which are in Direct Proportion

always lie on a straight linepassing through the origin.


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Example : Plot the points in the table below. Are they in Direct Proportion?


We plot the points (1,3) , (2,6) , (3,9) , (4,12)

XX 11 22 33 44

yy 33 66 99 1212


1

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Plotting the points

(1,3) , (2,6) , (3,9) , (4,12)


0 1 2 3 4

101112

23456789

Since we have a straight linepassing through the origin

x and y are in Direct Proportion.

x

y


1

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Find the formula connectingy and x.


0 1 2 3 4

101112

23456789

Formula has the form :

x

y

Gradient = 3

Formula is :y = 3x

y = kx


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Key point of Ex 2Fill in table

Find gradient from graph

Write down formula using knowledge from straight line chapter


Now try Exercise 2Ch8 (page 104)

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Direct Proportion



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2. Calculate the area of the shape.

5 1+2 4

(a) 0.853 (b) 0.356 (c) 1.995

1. 6x + 5 = 59

3. Round to 2 decimal places.

4.

9

6

8


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1. To explain how to work out Direct Proportion formula.

1. Understand the process for calculating direct proportion formula.


2. Calculate gradient from information given.

Direct Proportion Formula


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Q. 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 the gradien

t20 = k(4)

k = 20 ÷ 4 = 5y = 5x


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Q. 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 the gradien

t3 = k(2)

k = 3 ÷ 2 = 1.5d = 1.5P


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Q. How much will I get for £20


d = 1.5P

d = 1.5 x 20 = 30 dollars


Exercise 3Ch8 (page 105)

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2. Calculate 20% of 220

(a) 123 (b) 202 (c) 0.09

1. 3x + 5 = 17

3. How many significant numbers

4. Car decreases by 20% in its first year. I f it was bought new for £10 000. How much is it worth now.


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1. To explain how to work out harder Direct Proportion formula.

1. Understand the process for calculating direct proportion formula.


2. Calculate k for harder direct proportion formula.

Harder Direct Proportion Formula


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Q. 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 = 10y = 10x2


y

x


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Q. Calculate y when x = 5

y = 10x2

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


y

x


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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 45p 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 P48 =k 36

C =8 P

y

x


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Q. How much will 100 pages cost.


C =8 100

C =8 100 =8×10 =80p

y

x


Exercise 4BCh8 (page 106)

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2.

3. Calculate 1 1 2 4

1. Simplfy the ratio 95 : 35

Calculate 0.5 + 1.45 x 2


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1. To explain the term Inverse Proportion.

1. Understand the idea of Inverse Proportion.

Inverse Inverse ProportionProportion

2. Solve simple inverse Proportion problems.

Inverse Proportion


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Inverse Proportion is when one quantity increasesand the other decreases. The two quantities are said

to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other.

Example : Fill in the following table given x and yare inversely proportional.

Inverse Proportion

XX 11 22 44 88

yy 8080 102040

y

x


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Men Hours

Inverse Proportion is the when one quantity increasesand the other decreases. The two quantities are said

to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other.

Example : If it takes 3 men 8 hours to build a wall.How long will it take 4 men. (Less time !!)

3 8 1 3 x 8 = 24 hours

4 24 ÷ 4 = 6 hours

Inverse Proportion

y

x


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Men Months

Example : It takes 10 men 12 months to build a house.How long should it take 15 men.

10 12 1 12 x 10 = 120

15 120 ÷ 15 = 8 months

Inverse Proportion

y

x


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Speed Time

Example : At 8 m/s a journey takes 32 minutes.How long should it take at 10 m/s.

8 32 mins 1 32 x 8 = 256 mins

10 256 ÷ 10 = 25.6 mins

Inverse Proportion

y

x


Exercise 5Ch8 (page 108)

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Inverse Proportion

Documents

14-Jun-14Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Graphs Direct Proportion formula and calculations