Page 30 - Mathematics Coursebook

2.5 Deriving and using formulae

4 Landon uses this formula to work
out the pay of his employees. How P = hr + b
P = hr + b
much does he pay each where: P is the pay
where:
P is the pay
of these employees?
h is the number of hours worked
a Cole: works 20 hours at $22 per h is the number of hours worked
r is the rate of pay per hour
r is the rate of pay per hour
hour and gets a $30 bonus.
b Avery: works 32 hours at $20 per b is the bonus
hour and gets a $50 bonus.
hr means h × r
5 What value of k can you substitute into each of these expressions to give you the same answer?

k + 10 3k 4k − 5
6 A cookery book shows how long it takes, in minutes, to cook a joint of meat.

Electric oven time = (66 × weight in kg) + 35
Microwave oven time = (26 × weight in kg) + 15

a Compare the two formulae for cooking times. If a joint of meat takes about 2 hours to cook in
an electric oven, roughly how long do you think it would take in a microwave oven?
b i Work out how much quicker is it to cook a 2 kg joint of meat in a microwave oven than in an
electric oven.
ii Does your answer to part a seem sensible?

Summary

You should now know that: You should be able to:

+ Each number in a sequence is called a term and + Generate terms of an integer sequence and find a
terms next to each other are called consecutive term, given its position in the sequence.
terms. + Find the term-to-term rule of a sequence.
+ A sequence that continues for ever is called an + Generate sequences from patterns and describe

infinite sequence. the general term in simple cases.
+ A sequence that doesn’t continue for ever is called + Use function machines and mapping diagrams to

a finite sequence. represent functions.
+ Number sequences can be formed from patterns + Work out input and output numbers of function
of shapes. machines.
+ The numbers that go into a function machine are + Construct simple algebraic expressions.
called the input. The numbers that come out of a Derive and use simple formulae.
function machine are called the output. +
+ In algebra you can use a letter to represent an + Substitute positive integers into simple linear
unknown number. expressions and formulae.
+ Identify and represent information or unknown
+ Equations and expressions contain numbers and numbers in problems.
letters. Only an equation contains an equals sign.
+ Recognise mathematical properties, patterns and
relationships, generalising in simple cases.

2 Sequences, expressions and formulae 29