Functional Skills: Formulas

FS Level 1FS Level 2AQACity & GuildsEdexcelHighfield QualificationsNCFEOpen Awards

Functional Skills: Formulas Revision

Formulas

A formula is a rule used to calculate a value. They can be written 2 different ways, either using words or letters. You may also see formulas expressed as function machines.

Make sure you are happy with the following topics before continuing.

Improve your chances of passing your functional skills maths exam.

Take a subject knowledge assessment and understand what topic areas you need to work on to ensure you pass for level 2 maths exam first time.

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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}

FS Level 1FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

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 = 4\pi 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 &= 4\pi 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}

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See what level 2 maths topics you need support with.

The subject knowledge assessment tests your skills on a number of topics that will come up in the actual exam. You then get feedback on what you need to revise.

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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}{48\times21+45=1008+45=£1053}

 

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Functional Skills: Formulas Example Questions

The formula is:

Number of pairs of knickers = 15 \times number of days

 

We want to find the number of pairs of knickers can she make in 6 days, so we put 6 into the formula:

 

Number of pairs of knickers = 15 \times 6 = 90

This formula means £15 plus £0.50 per m^2. This can be written as a formula with 2 steps:

 

\text{Cost of gardener} = (£0.50 \times \text{area of grass in m}^2) + £15

 

Then, put in the missing numbers. Here, the area of grass is 45 m^2:

 

\text{Cost of gardener} = (£0.50 \times 45) + £15 = £37.50

Substitute a = 4 and b = 3 into the equation:

\dfrac{3 \times 4^2}{5 \times 3} = \dfrac{48}{15} = 3.2

Put the value of m=6.2 into the formula:

\text{cost} = 0.5(3 + 5 \times 6.2) = £17

So, from a £20 note she would recieve

£20 - £17 = £3

We first need to work out what the value of each number is:

n = 3

R = 8.31

T = 300

P = 100000

 

Then, substitute them into the formula, to find the volume of the gas:

 

V = \dfrac{3 \times 8.31 \times 300}{100000} = \dfrac{7479}{100000} = 0.07479 = 0.075 (3 dp)

Substituting in 2.5 kg into the function machine:

 

2.5\times45 +20=112.5+20=132.5 minutes

Additional Resources

PFS

Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Formulas Worksheet and Example Questions

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Formulas L1

FS Level 1NewOfficial PFS
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Formulas L2

FS Level 2NewOfficial PFS

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