# Ratio and Formula Revision

Today's Objectives
Recap Ratio and Formula concepts

Practice Examples

Typical Exam questions for both Ratio and Formula

Exam Prep

1 / 33
Slide 1: Tekstslide
MathematicsUpper Secondary (Key Stage 4)Further Education (Key Stage 5)

In deze les zitten 33 slides, met interactieve quizzen en tekstslides.

Lesduur is: 60 min

## Onderdelen in deze les

Today's Objectives
Recap Ratio and Formula concepts

Practice Examples

Typical Exam questions for both Ratio and Formula

Exam Prep

#### Slide 1 -Tekstslide

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;

#### Slide 2 -Tekstslide

Ratio

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

#### Slide 3 -Tekstslide

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

Example

Sharing Ratio

Sharing Ratio

#### Slide 10 -Tekstslide

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.

A
34
B
36
C
24
D
32

#### Slide 11 -Quizvraag

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)

A
£20.50
B
£24.00
C
£23.00
D
£24.50

#### Slide 13 -Quizvraag

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?

#### Slide 14 -Tekstslide

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

#### Slide 15 -Tekstslide

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.
Show your working out. see quiz next slide

A
£253.75
B
£242.25
C
£300
D
£252.50

#### Slide 17 -Quizvraag

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

#### Slide 19 -Tekstslide

What do you do with the A and R?

0.85A + 0.15R
A
Multiply
B
Divide
C
Take away
D

#### Slide 20 -Quizvraag

What does this mean?

3(p+2)
A
I don't know!
B
Multiply then do Brackets
C
Brackets first then multiply by 3
D

#### Slide 21 -Quizvraag

What does this mean?
A
Divide 9 by 5
B
Multiply 9 by 5
C
D
Minus 5 from 9

Try these!

#### Slide 23 -Tekstslide

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.

#### Slide 25 -Tekstslide

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
A
134
B
143
C
124
D
148

#### Slide 26 -Quizvraag

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.

A
£50.09
B
£54.90
C
£45.99
D
£44.90

#### Slide 28 -Quizvraag

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.

#### Slide 29 -Tekstslide

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

#### Slide 30 -Tekstslide

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

#### Slide 31 -Tekstslide

V = 3.14 x 10x10 x 5
V = 3.14x100x5
V= 314 x 5
V=1570 ml

= 1.57 litres

Any Questions?

Practice Paper