Ratio and Formula Revision

• Mathematics
• Upper Secondary (Key Stage 4)
• Further Education (Key Stage 5)

Today's Objectives

Recap Ratio and Formula concepts

Practice Examples

Typical Exam questions for both Ratio and Formula

Exam Prep

Ratio

The relationship between two amounts, represented by two numbers or a percentage, expressing how much bigger one is than the other

Formula

What is substitution? Substitution means replacing the variables (letters) in an algebraic expression with their numerical values. We can then work out the total value of the expression.

°C = (°F - 32) × 5/9;

Ratio

The relationship between two amounts, represented by two numbers or a percentage, expressing how much bigger one is than the other

Examples

Simplifying Ratio

Like a fraction divide both sides by the same number until you can divide no more!

Example

corbettmaths.com

Sharing Ratio

Sharing Ratio

corbettmaths.com

Last week 1600 hot drinks were sold in Ella’s Café.



The ratio of cups of coffee to cups of tea sold is 7:3.



A cup of coffee on average costs £2.30.



A cup of tea on average costs £1.80.

1. 34
2. 36
3. 24
4. 32

Exam Question

Mike and Anne buy a takeaway.

The bill comes to £38.50

They agree to split the bill in the ratio 7:4

Calculate how much Mike pays for his share of the bill?

(3 marks) 

Answer

1. £20.50
2. £24.00
3. £23.00
4. £24.50

Exam Question

Last week 1600 hot drinks were sold in Ella’s Café.

The ratio of cups of coffee to cups of tea sold is 7:3.

A cup of coffee on average costs £2.30.

A cup of tea on average costs £1.80.

How much can Ella expect to have made through sales of cups of coffee and tea last week? 

Worked Answer

7+3 +10 parts

1600 / 10 = 160 = one part

160 x 7 =1120 coffee

160 x 3 = 480 tea

1120 x 2.30 = £2576

480 x 1.80 =£864

£2576 + £864 = £3440

Exam Question

£290 of all money raised will be split between the cost of the activities and the cost of transport using a ratio of 7:1.

Calculate how much of the £290 will go towards the cost of the

activities.

Answer below.

Show your working out. see quiz next slide 

What's the answer?

1. £253.75
2. £242.25
3. £300
4. £252.50

Substitution

What is substitution? 

Substitution means replacing the variables (letters) in an algebraic expression with their numerical values. 

We can then work out the total value of the expression.

Formula - BIDMAS

What do you do with the A and R?

0.85A + 0.15R

1. Multiply
2. Divide
3. Take away
4. Add

What does this mean?

3(p+2)

1. I don't know!
2. Multiply then do Brackets
3. Brackets first then multiply by 3
4. Brackets first then add 3

What does this mean?

1. Divide 9 by 5
2. Multiply 9 by 5
3. Add 9 and 5
4. Minus 5 from 9

Try these!

corbettmaths.com

Exam Question

Dr. Khan uses the following formula to calculate a patient’s recommended maximum heart rate after intensive exercise.

M = 187 – 0.85A + 0.15R

Where M = maximum heart rate in beats per minute (bpm)

A = age (years)

R = heart rate when resting (bpm)

Glenn is 60 years old.

His heart rate when resting is 80 beats per minute. Find the recommended heart rate.

M = 187 – 0.85A + 0.15R
A = age (years)
R = heart rate when resting (bpm)
Glenn is 60 years old.
Heart rate when resting is 80 beats

1. 134
2. 143
3. 124
4. 148

Exam Question

Tim has bought new furniture for one of his rental properties.

He considers 2 options for transferring the furniture to the property.

Option A: Use the furniture shop’s delivery service.

The cost to the customer of this service can be calculated using the formula below:

C = 25 + 0.65d

C = cost in pounds

d = distance in miles from shop to delivery point

The shop is 46 miles from the property where it is to be delivered to. 

What is the answer?

1. £50.09
2. £54.90
3. £45.99
4. £44.90

Exam Question

Mrs Wallis has heard that the average monthly temperature in the Loire in August last year was 70°F.

She knows of 2 methods for changing temperatures in degrees Fahrenheit to degrees Celsius.

Method A: As an estimate, subtract 30 from the given temperature and divide by 2.

Method B: For an accurate result use the formula:

                                                                        

    where C = temperature in °C and F = temperature in °F

Convert 70°F to °C using both methods and compare the results.

Comment on the accuracy of method A.   

Worked Answer

Method A

70 - 30 = 40 / 2 = 20 degrees C

Method B

C= 5/9 (F-32)

C = 5/9 (70-32)

C= 5/9 (38)

C= 0.5555 x 38

C= 21.1 degrees F

Exam Question

The tins have a diameter of 20cm and a height of 9cm

Tins are filled to 4cm below the top to allow room for the cake mixture to rise.

Delia has made 2 litres of cake mix.

Will this be enough for one tin? (6 marks)

Use the following formula:

                                                            V = 11 r2 h

where r is the radius of the circular cake tin base and h is the height of the cake tin.

Let p = 3.14 or use the π button on your calculator.

Note that 1cm3 = 1ml

Worked Answer

V = 3.14 x 10x10 x 5

V = 3.14x100x5

V= 314 x 5

V=1570 ml

= 1.57 litres

Any Questions?

Practice Paper