Page 36 - 新思维数学学生用书8 样章

2.2 Using expressions and formulae

2.2 Using expressions and formulae

In this section you will … Key words

• use the correct order of operations in algebraic changing the
expressions subject
• represent a situation either in words or as a formula derive

• change the subject of a formula.
formula
formulae
A formula is a mathematical rule that shows the relationship between
two or more quantities (variables). It is a rule that can be written in inverse operation
letters or words. The plural of formula is formulae. solve

You can write, or derive, your own formulae to solve problems. subject of a
An example of a formula is F = ma. formula
In this formula, F is the subject of the formula. The variable F is written substitute

on its own on the left hand side of the formula.
You may need to rearrange a formula to make a different F =
variable the subject. This is called changing the subject of ma
F = m
the formula. a
For example, if you know the values of F and a, and m = F
a
you want to find the value of m, you will rearrange the
equation like this: Tip
When you substitute numbers into formulae and expressions, remember Examples of

the order of operations. Brackets and indices must be worked out before indices are 2 , 5 ,
2
2
divisions and multiplications. Additions and subtractions are always 4 and 7 .
3
3
worked out last.
Worked example 2.2

a Work out the value of the expression 2x + 4y when x = 5 and y = −2.

b Work out the value of the expression 3x + 4 when x = 10.
2
c Write a formula for the number of hours (h) in any number of days (d), using
i words ii letters.

d Use the formula in part c to work out the number of hours in 7 days.
e Rearrange the formula in part c ii to make d the subject.

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