Page 31 - Cambridge Checkpoint Mathematics Coursebook 7_Slide 02

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:
where: P is the payP 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 fi nd 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
infi nite 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 fi nite 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