# Functional Skills: Formulas

## 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.

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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 Â£75 fixed fee for hiring the car, plus Â£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 Â£12.50 per day plus Â£75. This can be written as an formula with 2 steps:

**Step 1:**Â Â Â£12.50 \times \text{number of days}

**Step 2:**Â Â + \, Â£75

So, put this into a single formula:

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

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

\text{Cost of car hire} = (Â£12.50 \times \textcolor{red}{12}) + Â£75 = \textcolor{limegreen}{Â£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 donâ€™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 \\Â &=4 \times 3.14 \times \textcolor{blue}{11}^2 \\Â &= 4 \times 3.14 \times 121 \\ &= 1519.76 = \textcolor{limegreen}{1520 \text{ cm}^2} \text{Â Â (to the nearest 10)} \end{aligned}

**Type 3: Function MachinesÂ **

**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:**Â 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.

## Functional Skills: Formulas Example Questions

**Question 1:** Mandy works in a shoe factory. She can make 15 pairs of shoes in a day. How many pairs of shoes can she make in 6 days?

**[1 mark]**

The formula is:

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

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

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

**Question 2:** Michelle pays for a gardener to cut her grass. The gardener charges a fixed fee of Â£15 plus Â£0.50 per \text{ m}^2 of grass. Michelle’s grass is 45\text{ m}^2 in area.

How much does Michelle pay for the gardener to cut her grass?

**[2 marks]**

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

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

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

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

**Question 3:** Calculate the value of \dfrac{3a^2}{5b} when a = 4 and b = 3

**[1 mark]**

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

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

**Question 4:Â **Manique needs to pay for a taxi. The cost of the taxi is calculated using the formula below:

\text{cost} = 0.5(3 + 5m)

Where m is the number of miles driven.

Manique travels 6.2 miles and pays with a Â£20 note. How much change would she receive from a Â£20 note?

**[2 marks]**

Put the value of m=6.2 into the formula:

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

So, from a Â£20 note she would receive

Â£20 - Â£17 = Â£3

**Question 5: **The following formula describes the volume of a gas under specific conditions:

V = \dfrac{nRT}{P}

where V is the volume of the gas in m^3

n is the number of moles (a fixed amount) of a gas

R = 8.31 is the ideal gas constant

T is the temperature of the gas in Kelvin (K)

P isÂ the pressure of the gas in Pascals (Pa)

Calculate the volume of 3 moles of gas at a temperature of 300 K, whenÂ the pressure is 100000 Pa.

Give your answer to 3 decimal places.

**[2 marks]**

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)

**Question 6: **Anne is going to cook a 2.5 kg chicken for a roast dinner. Use the function machine below to work out how long Anne will need to cook her chicken for (in minutes).

**[2 marks]**

Substituting in 2.5 kg into the function machine:

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

## Functional Skills: Formulas Worksheet and Example Questions

### Formulas L1

FS Level 1NewOfficial PFS### Formulas L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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