Cambridge International Mathematics

148 Formulae and simultaneous equations (Chapter 7)

Aformulais an equation which connects two or more variables.

The plural of formula isformulaeorformulas.

For example, the formula s=

d

t

relates the three variable quantities speed (s), distance travelled (d), and

time taken (t).

We usually write formulae with one variable on its own on the left hand side. The other variable(s) and

constants are written on the right hand side.

The variable on its own is called thesubjectof the formula.

If a formula contains two or more variables and we know the value of all but one of them, we cansubstitute

the known values into the formula and hence find the value of the unknown variable.

Step 1: Write down the formula.

Step 2: State the values of the known variables.

Step 3: Substitute into the formula to form a one variable equation.

Step 4: Solve the equation for the unknown variable.

Example 1 Self Tutor

When a stone is dropped from a cliff into the sea, the total distance fallen,Dmetres, is

given by the formula D=^12 gt^2 wheretis the time of fall in seconds andgis the

gravitational constant of 9 : 8 m/s^2. Find:

a the distance fallen after 4 seconds

b the time (to the nearest 1001 th second) taken for the stone to fall 200 metres.

a D=^12 gt^2 where g=9: 8 and t=4

) D=^12 £ 9 : 8 £ 42

=78: 4

Calculator:

0 : 5 £ 9 : 8 £ 4 x^2 ENTER

) the stone has fallen 78 : 4 metres.

b D=^12 gt^2 where D= 200 and g=9: 8

)^12 £ 9 : 8 £t^2 = 200

) 4 : 9 t^2 = 200

) t^2 =

200

4 : 9

) t=§

r

200

4 : 9

) t¼ 6 : 39 fas t> 0 g

Calculator:

p

200 ¥ 4 : 9 ) ENTER

) the time taken is about 6 : 39 seconds.

A FORMULA SUBSTITUTION [2.5]

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