Formulae

1
Formulae
S4 Credit
Using Formulae
Making Formulae
Change the Subject of Formula
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Harder Subject of Formula
Understanding Formulae
2
Starter Questions
S4 Credit
1. Does 3 2 x 4 11 or 20
3
Formulae
S4 Credit
Learning Intention
Success Criteria

1. 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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4
Formulae
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
5
Formula for Parallelogram
S4 Credit
Example 1 Find the area of parallelogram.
3cm
9cm
6
Formulae 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.
7
Formulae 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.

8
Formulae
S4 Credit
Now try MIA Ex 2.1 2.2 Ch4 (page 80)
9
Starter
S4 Credit
D 6 cm
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10
Making Formulae
S4 Credit
Learning Intention
Success Criteria

1. To explain how to construct a formula.

1. Understand the process of constructing a formula.

2. Apply knowledge to construct formulae.
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11
Making 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
12
Making 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
13
Making Formulae
S4 Credit
A internet café decides to change its table
design to.
14
Making 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
15
Making Formulae
S4 Credit
Find a number so formula works
Step 3
Step 4
S 2T 2
Correction factor add on 2
16
Making Formulae
S4 Credit
Now try MIA Ex 3.1 Ch4 (page 84)
17
Starter Questions
S4 Credit
D 6 cm h 10 cm
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18
Harder 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
19
Harder 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)
20
Harder 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)
21
Harder 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
22
Harder 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
23
Harder Formulae
S4 Credit
Now try MIA Ex 3.2 Ch4 (page 87)
24
Starter
S4 Credit
5 cm
3 cm
3 cm
2.5 cm
4 cm
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25
Formulae
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

1. Know The balancing Method for solving equations.

2. Apply knowledge to change subject of a formula.
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26
Changing 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.
27
Changing the Subject of a Formula
S4 Credit
We can make D the subject of the formula by
simple using The Balancing Method
28
What 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
29
Changing the Subject of a Formula
S4 Credit
Now try MIA Ex 4.1 Ch4 (page 88)
30
Starter Questions
S4 Credit
Make g the subject of each formula
Nothing new ! simply use the balancing method
31
Changing the Subject of a Formula
S4 Credit
Learning Intention
Success Criteria

1. To explain how to change the subject of a formula
   containing square and square root terms.

1. 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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32
Changing 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.
33
Changing 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.
34
Changing the Subject of a Formula
S4 Credit
Example The formula below is used to change
degrees Celsius to Fahrenheit. Change the
subject to C.
35
Changing the Subject of a Formula
S4 Credit
Now try MIA Ex 4.2 Ch4 (page 91)
36
Starter Questions
S4 Credit
Make w the subject of each formula
Nothing new ! simply use the balancing method
37
Understanding Formulae
S4 Credit
Learning Intention
Success Criteria

1. To explain the effect on the subject by changing
   one or more of the values in the formula.

1. 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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38
Understanding 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
39
Understanding 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
40
Understanding 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
41
Understanding 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
42
Understanding Formulae
S4 Credit
Now try MIA Ex 5.1 Ch4 (page 94)