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Formulaew

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Change the Subject of Formula

Harder Subject of Formula

Understanding Formulae

Making Formulae

Using Formulae

S4 Credit

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Starter QuestionsStarter Questions

1. Does 3 + 2 x 4 = 11 or 20

212. Calculate of 6

2

3. True or f alse I f a = 9 and b = -3

b b - a = 4

a

S4 Credit

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www.mathsrevision.comwww.mathsrevision.comww

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1. To explain how to evaluate formulae

1.1. Understand the term Understand the term formulae.formulae.

Formulae

2.2. Be able to substitute Be able to substitute values into formulae and values into formulae and evaluate properly using evaluate properly using BODMAS.BODMAS.

S4 Credit

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Formulae

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.

BODMAS

Brackets

Other squares and square root etc....

Divide

Multiplication

Addition

Subtraction

S4 Credit

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Formula for Parallelogram

Example 1 : Find the area of parallelogram.

Parallelogram Area b h

Area = 9 32Area = 27cm

9cm

3cm

S4 Credit

1r = radius = D

2

3 34Volume = π(10) =4187cm ( to 4 sig. figs)

3

34Volume = πr

3

Formulae for the Volume of a Sphere

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S4 Credit

r

D

D = diameter

Q. If the above sphere has radius 10cm.

Calculate it’s volume.

Q. If the above cone has radius 15cm and height

of 10 cm. Calculate it’s volume.

Formulae for Volume of a Cone

h = Perpendicular height

2 31Volume = π(15) 10 = 2355cm

3

r = radius

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r

h21

Volume Cone = πr h3

S4 Credit

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Now try MIA

Ex 2.1 & 2.2

Ch4 (page 80)

FormulaeS4 Credit

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StarterStarter

Q1. Calculate the volume of the following sphere.

Q2. Car depreciates 10% each year. What is

it's value after 3 years if it's initial value was £3,000.

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D = 6 cm

r

D

4 3Volume = πr34 3 = π(3)3

3 = 36πcm

S4 Credit

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1. To explain how to construct a formula.

1.1. Understand the process of Understand the process of constructing a formula.constructing a formula.

Making Formulae

2.2. Apply knowledge to Apply knowledge to construct formulae.construct formulae.

S4 Credit

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Try and make a formula for

the money I have left, £M , after h hour.

S4 Credit

Making Formulae

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

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Try and make a formula for

the cost C of tiling a kitchen floor.

S4 Credit

Making Formulae

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

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A internet café decides to change it’s table design to.

1 Table 3 Tables2 Tables

Task :Find a formula connecting

the number of surfers and the number of tables.

S4 Credit

Making Formulae

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2 4 51 3Number of Tables

6 10 12

4 8Number of Surfers

Step 1 :

Fill empty boxes

2 2 2 2

Same difference

linear pattern

What is the formula

1 Table 3 Tables2 Tables

Step 2 : Find difference

S4 Credit

Making Formulae

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S4 Credit

2 4 51 3Number of Tables

6 10 12

4 8Number of Surfers

2 2 2 2

Can you write down formula connecting

the number of surfers and the number of tables.

S = 2T + 2

S = 2 x TPart of the Formula

Correction factor “add on 2”

Find a number

so formula works

Step 3 :

Step 4 :

Making Formulae

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Now try MIA

Ex 3.1

Ch4 (page 84)

Making FormulaeS4 Credit

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Q2. My wages increased by 10% this year. My new wage

is £1200. What was my wage before the increase.

Starter Questionsw

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D = 6 cm

h = 10 cmr

h

2

2

3

1Volume Cone = πr h

31

= π(3) ×10 3

= 30 cm

S4 Credit

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Find a formula for the :

(i)Perimeter

(ii)Area

for the shaded shape below.

S4 Credit

Harder Formulae

2x cm

1 cm

C = π(Db – Ds) C = π(2x + 2 – 2x) C = 2π

2x + 2cm

C = πDbig - πDsmall

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Find a formula for the :

(i)Perimeter

(ii)Area


S4 Credit

Harder Formulae

2x cm

1 cm

A = π(r2b – r2

s) A = π((x + 1)2 – x2)

2x + 2cm

A = πr2big - π r2

small

A = π(x2 +2x + 1 – x2) = π(2x + 1)

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Show that for the square with and equilateral triangle cut out has :

(i)Perimeter = 10x

(ii)Area = (4 - √3)x2


S4 Credit

Harder Formulae

√3x

P = 2x

2x

+ 2x + 2x + 2x + 2x = 10x P =

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AT = 0.5 x 2x x √3x

Show that for the square with an equilateral triangle cut out has :

(i)Area = (4 - √3)x2


S4 Credit

Harder Formulae

√3x

As = 2x x 2x =

2x

Area = Square - Triangle

4x2

√3x2

h

AT = 4x2 - √3x2 = (4 - √3)x2

=

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Now try MIA

Ex 3.2

Ch4 (page 87)

Harder FormulaeS4 Credit

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StarterStarter

1. Calculate the area of the following shapes.

2. Write to 3 sig. figures.

(a) 47856 (b) 0.065797 (c) 2.05700

Q3. Explain why 15% of £ 360 = £ 54

5 cm

2.5 cm 3 cm

4 cm

3 cm

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S4 Credit

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1. To explain how to change the subject of a formula using

“The balancing Method”

1.1. Know “The balancing Know “The balancing Method” for solving Method” for solving equations.equations.

Formulae

2.2. Apply knowledge to change Apply knowledge to change subject of a formula.subject of a formula.

The Subject of a FormulaS4 Credit

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Changing the Subject of a Formula

The formula below is used to work out

the circumference of a circle

C D

Since the formula works out C , then C is called

the subject of the formula.

S4 Credit

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We can make D the subject of the formula

by simple using

“ The Balancing Method “

C D

C

D C

D

S4 Credit

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What Goes In The Box ?

1y = x - 1

4

Make y the subject of the formulae using

“the balancing method” x + y = 8

y2 = x

-x + 2y = 2

x = 4( y + 1 )

y = 8 - x

y = √x

1y = x + 1

2

Rearrange into y =

1y = x + k

3

2x =√y x = 3( y - k )

y = 4x2

S4 Credit

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Now try MIA

Ex 4.1

Ch4 (page 88)

S4 Credit


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Make g the subject of each formula :

F mg

E mgh

212

w mg

S4 Credit

Nothing new ! simply use the

“balancing method”

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

1.1. Know “ The balancing Know “ The balancing Method” for solving Method” for solving equations.equations.

2.2. Apply knowledge to Apply knowledge to change subject of harder change subject of harder formulae including square formulae including square and square root terms.and square root terms.


S4 Credit

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Example : The force of the air against a train is given by the formula below.

Make the speed (S) the subject of the formula.

2 F

Sk

F

Sk

S4 Credit

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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.

49

W

T

94

T

W

294

T

W

294

T

W

S4 Credit

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Example : The formula below is used to change degrees Celsius to Fahrenheit.

Change the subject to C.

932

5F C

532

9C F

S4 Credit

932

5C F

932

5C F

9 5( 32)C F

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Now try MIA

Ex 4.2

Ch4 (page 91)

S4 Credit


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Make w the subject of each formula :

2 2 2 z w q

hPw

12 3

wk

S4 Credit

Nothing new ! simply use the

“balancing method”

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

1.1. Understand the meaning of Understand the meaning of doubling and halving.doubling and halving.

2.2. Apply knowledge so far to Apply knowledge so far to work out the effect on the work out the effect on the subject by varying one or subject by varying one or more values in the formula.more values in the formula.


S4 Credit

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S4 Credit


The Circumference of circle is given by the formula :

C = πDWhat happens to the Circumference

if we double the diameter

C = π(2D)New D = 2D

The Circumferenc

e doubles

In real-life we often want to see what effect changing the value of one of the variables has on

the subject.

= 2πD

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In real-life we often want to see what effect changing the value of one of the variables has on

the subject.

S4 Credit


The Area of circle is given by the formula :

A = πr2

What happens to the Area

if we double the radius r

C = π(2r)2New r = 2r

The Area increasing by a factor of 4.

= 4πr2

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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.

45W

T

S4 Credit


New W = 100W

4 1005W

T 4

105W

T

The thickness of the rope T increasing by a factor of 10.

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Now try MIA

Ex 5.1

Ch4 (page 94)

S4 Credit


www.mathsrevision.com formulae change the subject of formula harder subject of formula...

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