Transcript A8 Changing the subject and deriving formulae

A8 Changing the subject and
deriving formulae
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Using inverse operations
Andy is 5 years older than his brother, Brian.
Their ages are linked by the formula:
A=B+5
where A is Andy’s age in years
and B is Brian’s age in years.
Using this formula it is easy to
find Andy’s age given Brian’s age.
Suppose we want to find
Brian’s age given Andy’s age.
Using inverse operations,
we can write this formula as:
B=A–5
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2014
The subject of a formula
Look at the formula,
V = IR
where V is voltage, I is current and R is resistance.
V is called the subject of the formula.
The subject of a formula always appears in front of the
equals sign without any other numbers or operations.
Sometimes it is useful to rearrange a formula so that
one of the other variables is the subject of the formula.
Suppose, for example, that we want to make I the subject
of the formula V = IR.
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Changing the subject of the formula
The formula:
V is the subject
of this formula
V = IR
can be written as:
I
×R
V
÷R
V
The inverse of this is:
I
or
V
I= R
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I is now the subject
of this formula
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2014
Matchstick pattern
Look at this pattern made from matchsticks:
Pattern
Number, n
1
2
3
4
Number of
Matches, m
3
5
7
9
The formula for the number of matches, m, in pattern
number n is given by the formula:
m = 2n + 1
Which pattern number will contain 47 matches?
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2014
Changing the subject of the formula
The formula:
m is the subject
of this formula
m = 2n + 1
can be written as:
n
×2
+1
m
The inverse of this is:
n
÷2
–1
or
m–1
n=
2
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m
n is the subject of
this formula
© Boardworks Ltd 2009
2014
Equivalent formulae
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© Boardworks Ltd 2009
2014