Title: Formulae
1Formulae
S4 Credit
Using Formulae
Making Formulae
Change the Subject of Formula
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Harder Subject of Formula
Understanding Formulae
2Starter Questions
S4 Credit
1. Does 3 2 x 4 11 or 20
3Formulae
S4 Credit
Learning Intention
Success Criteria
- To explain how to evaluate formulae
- Understand the term
- formulae.
2. Be able to substitute values into formulae and
evaluate properly using BODMAS.
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4Formulae
S4 Credit
A formula is the process calculating a quantity
based on a known relationship e.g. Length, Area,
Volume etc........
It is VERY important that we remember a keypoint
when working with formulae.
B
Brackets
O
Other ? squares and square root etc....
D
Divide
M
Multiplication
A
Addition
S
Subtraction
5Formula for Parallelogram
S4 Credit
Example 1 Find the area of parallelogram.
3cm
9cm
6Formulae for the Volume of a Sphere
S4 Credit
D diameter
r
D
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Q. If the above sphere has radius 10cm.
Calculate its volume.
7Formulae for Volume of a Cone
S4 Credit
h
r
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- If the above cone has radius 15cm and height
- of 10 cm. Calculate its volume.
8Formulae
S4 Credit
Now try MIA Ex 2.1 2.2 Ch4 (page 80)
9Starter
S4 Credit
D 6 cm
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10Making Formulae
S4 Credit
Learning Intention
Success Criteria
- To explain how to construct a formula.
- Understand the process of constructing a formula.
2. Apply knowledge to construct formulae.
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11Making Formulae
S4 Credit
Try and make a formula for the money I have
left, M , after h hour.
I started my shopping trip with 250. On
average, each hour I spent 40.
M
250
-
40h
Calculate M for h 3
M 250 40 x 3
250 -120
130
12Making Formulae
S4 Credit
Try and make a formula for the cost C of tiling
a kitchen floor.
A tile fitter charges 20 per hour h. The tiles
cost 15 per m2 A.
C
20h
15A
Calculate C for h 5 and A 10
C 20 x 5
15 x 10
250
13Making Formulae
S4 Credit
A internet café decides to change its table
design to.
14Making Formulae
S4 Credit
Fill empty boxes
Number of Tables
Step 1
10
12
Number of Surfers
Step 2 Find difference
What is the formula
Same difference linear pattern
15Making Formulae
S4 Credit
Find a number so formula works
Step 3
Step 4
S 2T 2
Correction factor add on 2
16Making Formulae
S4 Credit
Now try MIA Ex 3.1 Ch4 (page 84)
17Starter Questions
S4 Credit
D 6 cm h 10 cm
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18Harder Formulae
S4 Credit
1 cm
- Find a formula for the
- Perimeter
- Area
- for the shaded shape below.
2x 2cm
C pDbig - pDsmall
2x cm
C p(Db Ds)
C p(2x 2 2x)
C 2p
19Harder Formulae
S4 Credit
1 cm
- Find a formula for the
- Perimeter
- Area
- for the shaded shape below.
2x 2cm
A pr2big - p r2small
2x cm
A p(r2b r2s)
A p((x 1)2 x2)
A p(x2 2x 1 x2)
p(2x 1)
20Harder Formulae
S4 Credit
1 cm
- Find a formula for the
- Perimeter
- Area
- for the shaded shape below.
2x 2cm
A pr2big - p r2small
2x cm
A p(r2b r2s)
A p((x 1)2 x2)
A p(x2 2x 1 x2)
p(2x 1)
21Harder Formulae
S4 Credit
- Show that for the square with and equilateral
triangle cut out has - Perimeter 10x
- Area (4 - v3)x2
- for the shaded shape below.
2x
v3x
P 2x
2x
2x
2x
2x
10x
P
22Harder Formulae
S4 Credit
- Show that for the square with an equilateral
triangle cut out has - Area (4 - v3)x2
- for the shaded shape below.
2x
h
v3x
Area Square - Triangle
As 2x x 2x
4x2
AT 0.5 x 2x x
v3x
v3x2
AT 4x2 - v3x2
(4 - v3)x2
23Harder Formulae
S4 Credit
Now try MIA Ex 3.2 Ch4 (page 87)
24Starter
S4 Credit
5 cm
3 cm
3 cm
2.5 cm
4 cm
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25Formulae
The Subject of a Formula
S4 Credit
Learning Intention
Success Criteria
- To explain how to change the subject of a formula
using - The balancing Method
- Know The balancing Method for solving equations.
2. Apply knowledge to change subject of a formula.
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26Changing the Subject of a Formula
S4 Credit
The formula below is used to work out the
circumference of a circle
Since the formula works out C , then C is called
the subject of the formula.
27Changing the Subject of a Formula
S4 Credit
We can make D the subject of the formula by
simple using The Balancing Method
28What Goes In The Box ?
Rearrange into y
S4 Credit
Make y the subject of the formulae using the
balancing method
x y 8
-x 2y 2
y 8 - x
y2 x
x 4( y 1 )
y vx
2x vy
x 3( y - k )
y 4x2
29Changing the Subject of a Formula
S4 Credit
Now try MIA Ex 4.1 Ch4 (page 88)
30Starter Questions
S4 Credit
Make g the subject of each formula
Nothing new ! simply use the balancing method
31Changing the Subject of a Formula
S4 Credit
Learning Intention
Success Criteria
- To explain how to change the subject of a formula
containing square and square root terms.
- Know The balancing Method for solving
equations.
2. Apply knowledge to change subject of harder
formulae including square and square root terms.
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32Changing the Subject of a Formula
S4 Credit
Example The force of the air against a train
is given by the formula below. Make the speed
(S) the subject of the formula.
33Changing the Subject of a Formula
S4 Credit
Example The thickness of a rope T cm to lift a
weight W tonnes can be worked out by the
formula below. Make W the subject of the formula.
34Changing the Subject of a Formula
S4 Credit
Example The formula below is used to change
degrees Celsius to Fahrenheit. Change the
subject to C.
35Changing the Subject of a Formula
S4 Credit
Now try MIA Ex 4.2 Ch4 (page 91)
36Starter Questions
S4 Credit
Make w the subject of each formula
Nothing new ! simply use the balancing method
37Understanding Formulae
S4 Credit
Learning Intention
Success Criteria
- To explain the effect on the subject by changing
one or more of the values in the formula.
- Understand the meaning of doubling and halving.
2. Apply knowledge so far to work out the effect
on the subject by varying one or more values in
the formula.
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38Understanding Formulae
S4 Credit
In real-life we often want to see what effect
changing the value of one of the variables has on
the subject.
The Circumference of circle is given by the
formula
C pD
The Circumference doubles
What happens to the Circumference if we double
the diameter
C p(2D)
2pD
New D 2D
39Understanding Formulae
S4 Credit
In real-life we often want to see what effect
changing the value of one of the variables has on
the subject.
The Area of circle is given by the formula
A pr2
The Area increasing by a factor of 4.
What happens to the Area if we double the
radius r
C p(2r)2
4pr2
New r 2r
40Understanding Formulae
S4 Credit
In real-life we often want to see what effect
changing the value of one of the variables has on
the subject.
The Area of circle is given by the formula
A pr2
The Area increasing by a factor of 4.
What happens to the Area if we double the
radius r
C p(2r)2
4pr2
New r 2r
41Understanding Formulae
S4 Credit
The thickness of a rope T cm to lift a weight W
tonnes can be worked out by the formula below.
If we increase W by a factor of 100. What effect
does this have on the thickness of the rope T.
The thickness of the rope T increasing by a
factor of 10.
New W 100W
42Understanding Formulae
S4 Credit
Now try MIA Ex 5.1 Ch4 (page 94)