GCSE Maths Higher Lesson 11

Perimeter, area and volume – Homework ANSWERS

What is the value of x? 6

The area of this shape is 20cm2. What is the length, b ? 4cm b cm 5

What is the perimeter of this shape? 2.5cm 2.5cm 2 cm 7

What is the volume of this shape? 4

2 The perimeter of this shape is 7cm. What is the missing length x? x cm

What is the area of this shape? 12

What is the surface area of this shape? 18

The area of this shape is 46cm2. What is the value of y? 23

The area of this square is 100cm2. What is the length of each side? 10

1 The perimeter of this rectangle is 18cm What is the value of y? y cm

3

The area of this shape is 130cm2. What is the length, b ? 13 10cm b cm

11 The perimeter of this rectangle is 28cm What is the value of y? 3cm

8

6cm 4cm 6cm 9

What is the perimeter of this shape? 14

15

What is the area of this shape? 19 9.5cm

What is the perimeter of this shape? 16

What is the area of this shape? 17 8.5cm

3cm What is the area of this shape? 4cm 20 Clue

21 The perimeter of this shape is 71cm. What is the missing length x? x cm

What is the perimeter of this shape? 22 7cm 4cm

The area of this shape is 20cm2. What is the perimeter? 24

Also for homework SYWAGC – circles

Also for homework? Topic test circles

Mr Corbett 5-a-day for the day

Revision of ratio and proportion – exam practice Write the ratio 16:240 in its simplest form. Grade 2 question

In a class of 26 children, 12 are boys and 14 are girls. (a) What is the ratio of boys to girls? Give your answer in its simplest form. In another class, the ratio of boys to girls is 2:3. There are 25 children in the class. How many girls are there? Grade 3 question

Brian is making a fruit punch Brian is making a fruit punch. He mixes apple juice, pineapple juice and cherryade in the ratio 4 : 3 : 7. He makes 700ml of fruit punch. What volume of each drink does he use? Grade 4 question

4. Andy, Louise and Christine share a joint of beef in the ratio 3 : 6 : 7. Christine gets 300g more than Andy. What is the total weight of the joint of beef? Grade 5 question

Name 5 things you might use a scale drawing or model for Where could scale be used? eg 1:50

Architects make models of buildings Architects make models of buildings. Models are 3-D representations of objects.

People use maps to find their way People use maps to find their way. Maps are flat 2-D representations of a plan view of an area.

Every qualified tradesperson will come across, and have to use, scale drawings as a normal part of their job. Drawings are one of the most important methods of communicating technical information to the building team.

• the finished job being the wrong size • the job having to be done again • materials being under- or over-ordered • or even work stopping until the mistake has been sorted out. This will mean wasting time and money.

Estimations

The average man is between 1.6 m and 1.8 m tall 1 metre 11m

Estimate the heights of the buildings shown

Estimate the heights of the buildings shown 6.5 x 1.7 = 11.05 m 5 x 1.7 = 8.5 m 3.5 x 1.7 = 5.95 m 1.7 m

Estimate the length of the whale shown

Estimate the length of the whale shown The average whale is about 30m in length 30 m

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N Distance to Town 40 cm Real Distance : 80 km Scale 1 cm : 2 km Distance from Town to Shops 10 cm Airport Local Town Real Distance : 20 km Hospital Shops Distance from shops to Hospital 4.2 cm Real Distance : 8.4 km

N Distance to Town 40 cm Real Distance : 1000 m Scale 2 cm : 50 m Distance from Town to Shops 10 cm Airport Local Town Real Distance : 250 m Hospital Shops Distance from shops to Hospital 4.2 cm Real Distance : 105 m

N Distance to Town 40 cm Real Distance : 120 km Scale 1 cm :3 km Distance from Town to Shops 10 cm Airport Local Town Real Distance : 30 km Hospital Shops Distance from shops to Hospital 4.2 cm Real Distance : 12.6 km

Scale Drawings Here is a garden Scale 1 : 200 3 m 4.5 m 14 m 12 m 18 m greenhouse shed 3 m 4.5 m 14 m 12 m patio 18 m Calculate the scale diagram measurements

Scale Drawings ANSWERS Here is a plan of a garden Scale 1 : 200 greenhouse shed 1.5 cm 2.25 cm 7 cm 6 cm patio 9 cm Calculate the scale diagram measurements

Scale Drawing Quiz 1-5 1 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

A B C D What is the actual height of a wall that measures Question 1 What is the actual height of a wall that measures 6cm on the scale drawing with a scale of 1:50? A 600 cm B 120 cm C 14 cm D 300 cm 2 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 2 What does 5 cm on a map with scale 1:200 represent in actual distance? A 1000 cm B 2500 cm C 150 cm D 1500 cm 3 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 3 A house plan is drawn to a scale of 1:100. The lounge on the drawing is 9 cm long. What is the length of the lounge in metres? A 90 cm B 45 m C 9 m D 30 m 4 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 4 A house plan is drawn to a scale of 1:50. The lounge on the drawing is 15 cm long. What is the length of the lounge in metres? A 50 m B 7.5 m C 5 m D 65 m 5 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 5 A model is to be made of the new college which is 1125 m in length. The suggested scale is 1:750. How long will the model be? A 9 cm B 1.5 m C 2 m D 3.5 m 6 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Scale Drawing Quiz 7 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

A B C D What is the actual height of a wall that measures Question 1 What is the actual height of a wall that measures 6cm on the scale drawing with a scale of 1:50? A 600 cm B 120 cm C 14 cm D 300 cm 8 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 2 What does 5 cm on a map with scale 1:200 represent in actual distance? A 1000 cm B 2500 cm C 150 cm D 1500 cm 9 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 3 A house plan is drawn to a scale of 1:100. The lounge on the drawing is 9 cm long. What is the length of the lounge in metres? A 90 cm B 45 m C 9 m D 30 m 10 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 4 A house plan is drawn to a scale of 1:50. The lounge on the drawing is 15cm long. What is the length of the lounge in metres? A 50 m B 7.5 m C 5 m D 65 m 11 of 12 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Question 5 A model is to be made of the new college which is 1125 m in length. The suggested scale is 1:750. How long will the model be? A 9 cm B 1.5 m C 2 m D 3.5 m 12 of 12 Copyright © 2015 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Direct proportion

Inverse proportion

Direct Proportion Given that 5 miles is equivalent to 8 km, convert each of these quantities to the other unit of measurement… 40 miles 12 miles 140 miles 24 km 50 km 3 km Now use your answers to draw a graph of miles (horizontal axis) versus kilometres (vertical axis)… What is the gradient of your graph…?? Now write a formula that connects the number of miles (M) to the number of kilometres (K)…

Direct proportion Directly proportional: as one amount increases, another amount increases at the same rate. For example, how much you earn is directly proportional to how many hours you work. Work more hours, get more pay; in direct proportion.

Does your graph look like this? Miles and kilometres are ___________ proportional x of x Version 3.0 Copyright © AQA and its licensors. All rights reserved.

Inverse Proportion If it takes 10 builders 18 days to complete the building of a house, then how long would it take… 20 builders 5 builders 9 builders 12 builders 45 builders…?? Use your results to draw a graph of builders versus days…. Write a formula that connects the number of builders (B) to the number of days (D)…

Inversely Proportional: when one value decreases at the same rate that the other increases. Example: speed and travel time Speed and travel time are Inversely Proportional because the faster we go the shorter the time. •As speed goes up, travel time goes down •And as speed goes down, travel time goes up

are _______ proportional. Does your graph look like this? y and x are _______ proportional.

Homework

Homework

Answer 1 monkey can eat 4.5 bananas in 1 minute. 13 monkeys can eat 58.5 bananas in 1 minute. How long would it take 3 monkeys to eat 81 bananas? 1 monkey can eat 4.5 bananas in 1 minute 3 monkeys can eat 13.5 bananas in 1 minute - 81 ÷ 13.5 = 6 times as many bananas – so it will take 6 minutes Monkeys to bananas is direct proportion – the more monkeys there are, the more bananas they eat Bananas to time is direct proportion – the more bananas a monkey eats, the more time it takes Monkeys to time is inverse proportion – the more monkeys there are, the less time it will take to eat 4.5 bananas

Two-way tables and frequency trees.

How could we display the information below in an easier format How could we display the information below in an easier format? A school chess club has 70 members of which 40 are boys. Students play in competitions on a regular basis. Last month, 13 girls and 11 boys played in competitions. 2 of 4 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

A two way table might be helpful…. Played in competition last month Did not play in competition last month Boys 11 29 40 Girls 13 17 30 24 46 70 What other methods might we use to display the information? 3 of 4 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

11 40 Boys 29 70 13 Girls 30 17 Use a frequency tree Played in competition 11 40 Boys Didn’t play in competition 29 70 Played in competition 13 Girls 30 17 Didn’t play in competition 4 of 4 Copyright © 2015 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

x of x Version 3.0 Copyright © AQA and its licensors. All rights reserved.

x of x Version 3.0 Copyright © AQA and its licensors. All rights reserved.

x of x Version 3.0 Copyright © AQA and its licensors. All rights reserved.

x of x Version 3.0 Copyright © AQA and its licensors. All rights reserved.

x of x Version 3.0 Copyright © AQA and its licensors. All rights reserved.

In Year 6 at a local primary school there are 120 students In Year 6 at a local primary school there are 120 students. The ratio of boys to girls is 9:6. The girls were twice as likely to own a mobile phone as they were to not own a mobile phone. The ratio of boys who own a mobile phone to those who don’t own a mobile phone is 5:3 2 of 3 AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

45 72 Boys 27 120 32 Girls 48 16 Use a frequency tree Owns a mobile phone 45 72 Boys Doesn’t own a mobile phone 27 120 Owns a mobile phone 32 Girls 48 Doesn’t own a mobile phone 16 3 of 3 Copyright © 2015 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

More probability 1.

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Last bit of probability for now - tree diagrams

TREE DIAGRAMS First coin Second coin H H T H T T

H T

H T

Imagine choosing a ball from this bag and then replacing it Imagine choosing a ball from this bag and then replacing it. If you did this three times, what's the probability that you would pick at least one green ball? What’s the best method to use to answer this question? What if you didn't replace the ball each time?

Replacing it - if you did this three times, what's the probability that you would pick at least one green ball?

Not replacing it - if you did this three times, what's the probability that you would pick at least one green ball?

Two cards are drawn from a pack with replacement 13 52 39 A spade Not a spade 1st card 2nd card

Two cards are drawn from a pack without replacement 13 52 39 A spade Not a spade 1st card 2nd card

Exam question 11

Looking back at targets Do you understand that the sum of the probabilities of all possible mutually exclusive outcomes is 1? Do you understand the difference between theoretical and experimental probability? Can you calculate probability using a tree diagram?

Probability revision quiz HIGHER In teams of 3 work together to answer all the questions

Finding probabilities 1 (words) 5 points 10 points 15 points P(roll an odd number on a dice) is P(it will rain tomorrow) is P(baby born is a girl) is P(being younger tomorrow) is P(win lottery) is P(sun rising tomorrow) is

Finding probabilities 2 (fractions) 5 points (dice) 10 points (cards) 15 points P(red prime)= P(black)= P(4)= P(even)= P(red picture card)= P(less than 5) =

Finding probabilities 3 (OR rule) 5 points (dice) 10 points (cards) 15 points P(prime or square)= P(6 or 7)= P(4 or 5)= P(2, 3 or 4)= P(red 3 or black queen)= P(2 or 3) =

Finding probabilities 4 (2 events) 5 points (2 dice) 10 points 15 points P(2 numbers the same)= P(5 or 6)= P( 7 )= P(13)= P(less than 4) = P(even) = You have 1 minute to list all the outcomes of 2 dice before the questions come up.

Finding probabilities 5 (biased dice) 1 2 3 4 5 6 0.2 0.1 0.05 x 0.15 5 points 10 points 15 point P(not 4)= P(6)= P(2)= P(1 or 3)= P(not 2)= P(odd) =

Finding probabilities 6 (tree diagrams) Copy down this information: The probability it rains on a Monday is 0.3 The probability it rains on Tuesday is 0.25 5 points 20 points 30 points P( it rains on both days) Draw a tree diagrams to show all outcomes P( it does not rain on Monday)= P(It does not rain on Tuesday)=

Bonus question (40 points) Based on the following tree diagram what is the probability I pick 2 different colours?

Relative frequency in a graph

PLENARY Who wants to be a millionaire? millionaire_probability.ppt

Enlargement by a scale factor Could do enlargement by a scale factor here but you may choose to do this when we do all the other transformations.

Enlargements Objective: Transform a shape given a centre of enlargement and a scale factor (including fractional)

Enlarge this triangle by a scale factor of 3.

Enlarge this triangle by a scale factor of 3. X 3 6 2 1 3 X 3

Enlarge this triangle by a scale factor of 3 using (2, 1) as the centre of enlargement.

Enlarge this triangle by a scale factor of 3 using (2, 1) as the centre of enlargement.

Enlarge this triangle by a scale factor of 3 using (2, 1) as the centre of enlargement. 1. Draw lines from the centre of enlargement through the vertices (corners) of the shape. 1 2

Enlarge this triangle by a scale factor of 3 using (2, 1) as the centre of enlargement. 2. Use the lines to find the corners of the enlarged shape Draw lines from the centre of enlargement through the vertices (corners) of the shape. 1 2

Enlarge this triangle by a scale factor of 3 using (2, 1) as the centre of enlargement. Use the lines to find the corners of the enlarged shape Draw lines from the centre of enlargement through the vertices (corners) of the shape. 1 2

What about if I need to find the centre of enlargement? 0 1 2 3 4 5 6 7 8 9 x 1 9 8 7 6 5 4 3 2 y We have found the centre of enlargement! (2, 1)

Enlargement Now enlarge shape Q about the point y x 2 4 6 -2 -4 -6 Now enlarge shape Q about the point (-4, -5) with scale factor ⅓. Q Try it before clicking to see the answer! 6→ and 12↑ x ⅓ gives 2→ and 4↑ Q’ 12→ and 3↑ x ⅓ gives 4→ and 1↑ Back to main menu Next

Need to do recurring decimals

Still to do Use pi in an answer