14-Jun-14Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Graphs Direct...
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Transcript of 14-Jun-14Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Graphs Direct...
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
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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.
Direct Direct ProportionProportion
2. Solve simple Direct Proportional problems.
Direct Proportion
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct 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 :
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.
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
£ $
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
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
(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.
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 1Ch8 (page 101)
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Direct Direct ProportionProportion
Direct Proportion
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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
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 how Direct Direct Proportion Graph is always a straight line.
1. Understand that Direct Proportion Graph is a straight line.
Direct Direct ProportionProportion
2. Construct Direct Proportion Graphs.
Direct Proportion Graphs
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
The table below shows the cost of packets of “Biscuits”.
Direct Proportion Graphs
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 ?
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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.
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
Direct Proportion Graphs
KeyPoint
Two quantities which are in Direct Proportion
always lie on a straight linepassing through the origin.
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Direct Direct ProportionProportion
Example : Plot the points in the table below. Are they in Direct Proportion?
Direct Proportion Graphs
We plot the points (1,3) , (2,6) , (3,9) , (4,12)
XX 11 22 33 44
yy 33 66 99 1212
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Direct Direct ProportionProportion
Plotting the points
(1,3) , (2,6) , (3,9) , (4,12)
Direct Proportion Graphs
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
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
1
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Direct Direct ProportionProportion
Find the formula connectingy and x.
Direct Proportion Graphs
0 1 2 3 4
101112
23456789
Formula has the form :
x
y
Gradient = 3
Formula is :y = 3x
y = kx
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
Direct Proportion Graphs
Key point of Ex 2Fill in table
Find gradient from graph
Write down formula using knowledge from straight line chapter
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 2Ch8 (page 104)
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Direct Direct ProportionProportion
Direct Proportion
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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
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 how to work out Direct Proportion formula.
1. Understand the process for calculating direct proportion formula.
Direct Direct ProportionProportion
2. Calculate gradient from information given.
Direct Proportion Formula
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
Q. Given that y is directly proportional to x, and when y = 20, x = 4.
Find a formula connecting y and x
Direct Proportion Formula
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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Direct Direct ProportionProportion
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.
Direct Proportion Formula
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
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
Q. How much will I get for £20
Direct Proportion Formula
d = 1.5P
d = 1.5 x 20 = 30 dollars
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Exercise 3Ch8 (page 105)
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Direct Direct ProportionProportion
Direct Proportion Formula
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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.
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 how to work out harder Direct Proportion formula.
1. Understand the process for calculating direct proportion formula.
Direct Direct ProportionProportion
2. Calculate k for harder direct proportion formula.
Harder Direct Proportion Formula
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
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
Harder Direct Proportion Formula
y
x
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Direct Direct ProportionProportion
Q. Calculate y when x = 5
y = 10x2
y = 10(5)2 = 10 x 25 = 250
Harder Direct Proportion Formula
y
x
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Direct Direct ProportionProportion
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
Harder Direct Proportion Formula
C =k P48 =k 36
C =8 P
y
x
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
Q. How much will 100 pages cost.
Harder Direct Proportion Formula
C =8 100
C =8 100 =8×10 =80p
y
x
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Exercise 4BCh8 (page 106)
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Direct Direct ProportionProportion
Harder Direct Proportion Formula
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2.
3. Calculate 1 1 2 4
1. Simplfy the ratio 95 : 35
Calculate 0.5 + 1.45 x 2
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 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 Inverse ProportionProportion
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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Inverse Inverse ProportionProportion
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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Inverse Inverse ProportionProportion
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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Inverse Inverse ProportionProportion
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
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Exercise 5Ch8 (page 108)
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Inverse Inverse ProportionProportion
Inverse Proportion