formulaeformulae. objectives grade d objectives grade c

FormulaeFormulae

Objectives grade DObjectives grade D

9

1)D(A:assuch formulae dcomplicate

more more into numbers Substitute

C

Objectives grade CObjectives grade C

53qp:assuch formulaelinear Rearrange

it. solving andequation an formingby problem asolution a Find

Objectives Grade BObjectives Grade B

Rearrange formulae that include brackets, fractions, squares and square roots. Such as:

subject them make

2mcE

Objectives Grade BObjectives Grade B

Rearrange formulae that include brackets, fractions, squares and square roots. Such as:

subject x themake)( bxaz

Objectives Grade BObjectives Grade B

Rearrange formulae that include brackets, fractions, squares and square roots. Such as:

subject theC make

325

9

CF

Objectives Grade BObjectives Grade B

Rearrange formulae that include brackets, fractions, squares and square roots. Such as:

subject thel make

2g

lT

Objectives Grade AObjectives Grade A

Rearrange formulae where the variable appears twice

subject x themake

bx

axy

What is:What is:

If a=3 b=2 c=-1

a + b + c

ab

2a + 3b – 4c

When two letters are beside each other it means they multiply each other

When a number and a letter are beside each other it means they multiply each other

What is:What is:

If a=3 b=2 c=-1

3 + 2 + -1 =

3 x 2 =

2 x 3 + 3 x 2 – 4 x -1 =

Add a negative number

Negative Numbers Negative Numbers

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Adding a positive number

Subtracting a negative number

Adding a negative number

Subtracting a positive number

What is:What is:

If a=3 b=2 c=-1

3 + 2 + -1 =

3 x 2 =

2 x 3 + 3 x 2 – 4 x -1 =

B O D M A S

4

6

16

Add a negative number

Negative times a negative

Substitute A=-7, D=30 to work out what the

value of C

Substitute A=-7, D=30 to work out what the

value of C

9

1)D(A C

Substitute A=-7, D=30 to work out what the

value of C

Substitute A=-7, D=30 to work out what the

value of C

9

306

9

1)30(-7

C

Substitute A=-7, D=30 to work out what the

value of C

Substitute A=-7, D=30 to work out what the

value of C

209

180

9

306

9

1)30(-7

C

Create an equation to work out the value of x

Create an equation to work out the value of x

x+10

x x+50

Create an equation to work out the value of x

Create an equation to work out the value of x

x+10

x x+50

How many x’s ? 3x

How many degrees are their around a point?

360

Create an equation to work out the value of x

Create an equation to work out the value of x

x+10

x x+50

3x + 60 = 360

Now solve

3x = 300

- 60

÷ 3

x = 100

P=3q + 5Make q the subject

P=3q + 5Make q the subject

Just like solving equations we do the same to both sidesJust like solving equations

we do the same to both sides

P=3q + 5Make q the subject

P=3q + 5Make q the subject

P = 3q + 5 -5

P - 5 = 3q÷ 3

qp

3

5

Rearranging formulae

when expression

includes brackets – make x the

subject

Rearranging formulae

when expression

includes brackets – make x the

subject

)( bxaz

bxa

z

÷ a

xba

z

+ b

Make c the subject

Make c the subject

325

9

CF

- 32

5

932

CF

x 5

CF 9325

C

F

9

325 ÷ 9

Pythagoras Theorema2 + b2 = c2

Pythagoras Theorema2 + b2 = c2

3.00 cm

4.00 cm

5.00 cm

90.0 °

5.00 cm

3.00 cm

4.00 cm

5.00 cm

4.00 cm

4.00 cm

3.00 cm

3.00 cm

Pythagoras Theorema2 + b2 = c2

Pythagoras Theorema2 + b2 = c2

3.00 cm

4.00 cm

5.00 cm

90.0 °

5.00 cm

3.00 cm

4.00 cm

5.00 cm

4.00 cm

4.00 cm

3.00 cm

3.00 cm

222 cba Make a the subject

222 bca

22 bca

- b2

Pythagoras Theorema2 + b2 = c2

Pythagoras Theorema2 + b2 = c2

3.00 cm

4.00 cm

5.00 cm

90.0 °

5.00 cm

3.00 cm

4.00 cm

5.00 cm

4.00 cm

4.00 cm

3.00 cm

3.00 cm

222 cba Make b the subject

222 acb

22 acb

- a2

Pythagoras Theorema2 + b2 = c2

Pythagoras Theorema2 + b2 = c2

3.00 cm

4.00 cm

5.00 cm

90.0 °

5.00 cm

3.00 cm

4.00 cm

5.00 cm

4.00 cm

4.00 cm

3.00 cm

3.00 cm222 cba Make c the subject

cba 22

Pendulum swing

Pendulum swing

g

lT 2

Activity – substitute

g stands for gravity and in GCSE maths we round gravity to 10 m/sec/sec

Pendulum swing

Pendulum swing

102

lT

Activity – substitute

g stands for gravity and in GCSE maths we round gravity to 10 m/sec/sec

Pendulum swing

Pendulum swing

10

402T

Activity – substitute

l is the length of the pendulum.

Lets call it 40m

T is the time it takes in seconds to make one swing

Pendulum swing

Pendulum swing

10

402T

Activity – substitute

42T

4T

Pendulum swing

make l, the length, the

subject

Pendulum swing

make l, the length, the

subject

g

lT 2

How long should it take for one swing of

the pendulum?

Then we need to make l the subject as

we know T

Pendulum swing

make l, the length, the

subject

Pendulum swing

make l, the length, the

subjectg

lT 2 2π is a number

Π is a number a little over 3, it is not a

variable

Divide by 2π

g

lT

2 Square

g

lT

2

2

g

lT 2

Divide by 2π

g

lT

2Square

g

lT

2

2

lT

g

2

2

Times by g

Variable appears in more than one

place

Variable appears in more than one

place

bx

axy

axbxy )(axbyxy

Variable appears in more than one

place

Variable appears in more than one

place

bx

axy

axbxy )( axbyxy

abyxxy abyxxy abyyx )1(

Variable appears in more than one

place

Variable appears in more than one

place

bx

axy

axbxy )( axbyxy abyxxy

abyxxy abyyx )1(

1

y

abyx