Cambridge International Mathematics

152 Formulae and simultaneous equations (Chapter 7)

3 Makeythe subject of:

a mx¡y=c b c¡ 2 y=p c a¡ 3 y=t

d n¡ky=5 e a¡by=n f p=a¡ny

4 Makezthe subject of:

a az=

b

c

b

a

z

=d c

3

d

=

2

z

d

z

2

=

a

z

e

b

z

=

z

n

f

m

z

=

z

a¡b

5 Make:

a a the subject of F=ma b r the subject of C=2¼r

c d the subject of V=ldh d K the subject of A=

b

K

e h the subject of A=

bh

2

f T the subject of I=

PRT

100

g M the subject of E=MC^2 h a the subject of M=

a+b

2

REARRANGEMENT AND SUBSTITUTION

In the previous section on formula substitution, the variables were replaced by numbers and then the equation

was solved. However, often we need to substitute several values for the unknowns and solve the equation

for each case. In this situation it is quicker torearrangethe formulabefore substituting.

Example 5 Self Tutor

The circumference of a circle is given by C=2¼r, whereris the circle’s radius.

Rearrange this formula to makerthe subject, and hence find the radius when the

circumference is: a 10 cm b 20 cm c 50 cm.

2 ¼r=C,sor=

C

2 ¼

a WhenC=10, r=

10

2 ¼

¼ 1 : 59 ) the radius is about 1 : 59 cm.

b WhenC=20, r=

20

2 ¼

¼ 3 : 18 ) the radius is about 3 : 18 cm.

c WhenC=50, r=

50

2 ¼

¼ 7 : 96 ) the radius is about 7 : 96 cm.

EXERCISE 7B.2

1 The equation of a straight line is 5 x+3y=18.

Rearrange this formula into the form y=mx+c.

Hence, state the value of: a the gradientm b they-interceptc.

2aMakeathe subject of the formula K=

d^2

2 ab

.

b Find the value ofawhen:

i K= 112, d=24, b=2 ii K= 400, d=72, b=0: 4 :

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Y:\HAESE\IGCSE01\IG01_07\152IGCSE01_07.CDR Monday, 15 September 2008 4:08:53 PM PETER