Cambridge International Mathematics

158 Formulae and simultaneous equations (Chapter 7)

8 According to Einstein’s theory of relativity, the mass of a particle is given by the formula

m=

m 0

r

1 ¡

³v

c

́ 2 where m^0 is the mass of the particle at rest,

v is the speed of the particle, and

c is the speed of light.

a Makevthe subject of the formula.

b Find the speed necessary to increase the mass of a particle to three times its rest mass,

i.e., so that m=3m 0. Give the value forvas a fraction ofc.

c A cyclotron increased the mass of an electron to 30 m 0 :At what speed was the electron travelling,

given that c¼ 3 £ 108 m/s?

If we have two equations and we wish to make both equations true at the same time, we require values

for the variables which satisfy both equations. These values are thesimultaneous solutionto the pair of

equations.

Discovery The coin problem

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In my pocket I have 8 coins. They are$1and$2coins, and their total value is$11.

How many of each type of coin do I have?

What to do:

1 Copy and complete the following table:

Number of$1coins 0 1 2 3 4 5 6 7 8

Value of$1coins

Number of$2coins 8 7

Value of$2coins

Total value of coins

2 Use the table to find the solution to the problem.

3 Suppose I havex$1coins andy$2coins in my pocket.

a By considering the total number of coins, explain why x+y=8.

b By considering the total value of the coins, explain why x+2y=11.

4 You should have found that there were five$1coins and three$2coins.

a Substitute x=5and y=3into x+y=8. What do you notice?

b Substitute x=5and y=3into x+2y=11. What do you notice?

5 My friend has 12 coins in her pocket. They are all either$ 1 or$ 2. If the total value of her coins

is$ 17 , how many of each type does she have? Can you find the solution by algebraic means?

E SIMULTANEOUS EQUATIONS [2.6]

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Y:\HAESE\IGCSE01\IG01_07\158IGCSE01_07.CDR Monday, 15 September 2008 4:31:52 PM PETER