Functional Skills: Formulas

Type 1: Formulas Using Words

You will need to interpret a question and produce a formula from it. They may have one, or more than one step in them.

Example: Radamel wants to hire a car for $textcolor{red}{12}$ days. The car hire company charges a $£75$ fixed fee for hiring the car, plus $£12.50$ per day of hiring. How much would it cost for Radamel to hire the car for $textcolor{red}{12}$ days?

This formula means $£12.50$ per day plus $£75$. This can be written as an formula with $2$ steps:

Step 1:    $£12.50 times text{number of days}$

Step 2:    $+ , £75$

So, put this into a single formula:

$text{Cost of car hire} = (£12.50 times text{number of days}) + £75$

Then, you need to put the missing numbers in. Here, ‘number of days’ $=textcolor{red}{12}$

$text{Cost of car hire} = (£12.50 times textcolor{red}{12}) + £75 = textcolor{limegreen}{£225}$

Type 2: Formulas Using Letters

You may also need to convert words into letters, or be able to use formulas given in terms of letters.

For formulas using letters, you need to replace each letter with a number. Some formulas don’t use $times$ and $div$, for example, instead, $a times b$ may be written as $ab$ and $a div b$ may be written as $dfrac{a}{b}$.

Example: A spherical football has a radius of $textcolor{blue}{11}$ cm. The surface area of a sphere is given by the formula

$A = 4pi r^2$

where $A$ is the surface area, $r$ is the radius and take $pi = 3.14$

What is the surface area of the football? Give your answer in cm$^2$ to the nearest $10$.

The radius of the football is $textcolor{blue}{11}$ cm, so $textcolor{blue}{textit{r} = 11}$

Substitute the value of each letter into the formula, to find the surface area of the football:

$begin{aligned} A &= 4pi r^2 \  &=4 times 3.14 times textcolor{blue}{11}^2 \  &= 4 times 3.14 times 121 \ &= 1519.76 = textcolor{limegreen}{1520 text{ cm}^2} text{    (to the nearest 10)} end{aligned}$

Type 3: Function Machines 

Function machines can help you break down a formula that has more than one step in it. They are useful, as they allow you to visualise the order of steps.

Example: This function machine helps you to work out how much Tony is going to be charged by the plumber he has hired.

The plumber worked for $textcolor{purple}{48}$ hours in total.

Work out how much Tony will be charged.

Step 1: Put in $textcolor{purple}{48}$ into the function machine – in place of ‘Hours worked’.

Step 2: Then follow the rest of the steps.

$textcolor{purple}{48times21+45=1008+45=£1053}$