6
Changing the subject of a formula
SKILL
EXAM FACTS
Change the subject of a formula
H
M
KEY FACTS
• To change the subject of a formula, rearrange the terms in the formula
using inverse operations.
• To change the subject of a formula where the required subject occurs
twice, first collect the terms in the required subject, then factorise by
taking out the required subject and rearrange the terms in the formula.
Getting it right
Factorise the terms in r. This
gets 1 mark.
Make R the subject of the formula A = π(R + r)(R − r)
Divide both sides by
(2π + 3) to get r = …
(4400 May 2006)
Expand (R + r)(R − r) by
multiplying out or by
recognising the difference of
two squares to get R 2 − r 2
Expand the bracket and
isolate the term in R.
This gets 1 mark.
Divide both sides by π
The inverse of squaring is
taking the square root.
So take the square root of
both sides to get R = ...
Changing the subject of a formula
AIMH_2_C06.indd 27
!
Subtract 6a from both sides.
This gets 1 mark.
(2π + 3)
R=
Marks
available
A common error is to
rearrange the formula so that
the required subject is on the
left hand side, but leaving a
term including the required
subject on the right hand
side. This gets no marks.
D = 2πr + 3r + 6a
D − 6a = 2πr + 3r
D − 6a = r (2π + 3)
D − 6a
r = –––––––
π
A
− –––
πr 2
––––
π
Marks
lost (%)
WARNING
Make r the subject of the formula D = 2πr + 3r + 6a
A = π(R + r)(R −r)
A = π(R 2 −Rr + Rr − r 2)
A = π(R 2 − r 2)
A = πR 2 − πr 2
A + πr 2 = πR 2
− –––
πr 2
––––
R2 = A
L
27
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Now try these
1 Make v the subject of the formula m(v − u) = I
(4400 November 2004)
2 Make u the subject of the formula v2 = u2 + 2as
(1384 June 1996)
3 Make W the subject of the formula h =
W
–
I
(4400 May 2005)
4 Make p the subject of the formula M = 2(a − p2)
1
5 V = 3– π(a2 + b2)
Rearrange the formula to make b the subject.
6 Make g the subject of the formula T = 2π
–l
g
uv
7 f = –––––
u+v
Rearrange the formula to make v the subject.
n2 + a
8 P = ––––––
n+a
Rearrange the formula to make a the subject.
(1387 June 2006)
k
9 Rearrange the formula y = ––––––
to express x in terms of k, y and a.
(x + a)2
(1384 June 1998)
x = –p
10 –––––
x+c q
Make x the subject of the formula.
(1387 November 2006)
28
AIMH_2_C06.indd 28
Changing the subject of a formula
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