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computer science
cambridge international as & a level computer science

Cambridge Lower Secondary Mathematics Learners Book 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions

For each diagram, write the bearing of B from A.Use a protractor to measure the angle from north in a clockwise direction. a N B b N N d N B B-
The diagram shows three towns, A, B and C.a Write the bearing of B from A.b Write the bearing from A to C.c Write the bearing of B from C. A C. .B
Copy this shape onto squared paper.Enlarge the shape using scale factor 2.
Copy the diagram.Rotate the shape about the centre C a 90° anticlockwise b 180° C
Make a copy of this diagram.a Reflect shape A in the x-axis. Label the shape B.b Reflect shape A in the y-axis. Label the shape C. y 4 32 4-3-2 1 -2- -3- 4- -~ 4 x
A point P has coordinates (6, 1). P is translated 3 squares right and 4 squares up to point P′.Work out the coordinates of P′.
Work out the distance between these coordinates.a (9, 2) and (9, 11)b (3, 8) and (5, 8)
Use a protractor toa measure the size of this angle b draw an angle of 125°.
Here are the results of a computer simulation of throwing a dice 40 times. 3 5 4 3 1 22 6 16 4 53 1 6 1 4 2 6 3 26 222 22665133631631 6 10 a Find the experimental probability of getting 3. b Compare the experimental and theoretical probabilities of getting a 3.
An unbiased tetrahedral dice has four faces showing the numbers 1, 2, 3 and 4.a Two unbiased tetrahedral dice are thrown.Copy and complete this table to show the possible totals.b Work out the probability of i a total of 6 ii a total of less than 6 iii the same number on each dice. First dice 3 2 5
Zara writes the digits 3, 6 and 9 in a random order to make a 3-digit number.a List all the possible 3-digit numbers she could make.b Find the probability that Zara’s number is i less than 500 ii an odd number iii a multiple of 3.
1 A spinner has a yellow section. The probability of landing on yellow is 0.27.Work out the probability of getting a different colour.
You need a spreadsheet to answer this question. You also need to know how to use it to generate random numbers.a Carry out a simulation to model throwing a coin 50 times.Find the experimental probability of throwing a head and compare it with the theoretical probability.b Repeat part a another 5
Work with one or more other learners on this question.You learnt about the number π (pi) in Unit 8. It is the ratio of the circumference of a circle to its diameter.The value of π is a decimal that does not terminate and has no pattern to its digits.Here are the first 200 decimal places of
Work with another learner on this question. Each pair will need a dice.Design and carry out an experiment to answer this question:Is your dice unbiased?Before you start, you need to decide:• how many times to throw a dice• how to record your data• how to compare experimental probabilities and
This question is about throwing six dice together and seeing if there is at least one 6.Four learners each threw six dice together a number of times. Here are their results.a Work out the experimental probability of at least one 6 for each learner.b Combine the four sets of results to get another
This spinner has 3 sectors.The probability of red, P(red) = 0.6 The probability of white, P(white) = 0.3 The probability of blue, P(blue) = 0.1 Here are the results of 50 spins. RWRRR W W R W R RRB BBB W R W R W R R R W R R RR R R R W RRRRR BRRBM R RR R B W R BRRR RR W RMRRR
A learner throws a coin 50 times. This table shows the results.a Use the first row of the table to calculate the experimental probability of a head based on the first 10 throws.b Use the first two rows of the table to calculate the experimental probability of a head based on 20 throws.c In the same
Read what Marcus says.a Calculate the experimental probability of each outcome.b Calculate the theoretical probability of each outcome.c Marcus’s teacher thinks Marcus has made up his results.What do you think? Give a reason for your answer. Event 2 heads 2 tails 1 head and 1 tail Frequency 17 14
Zara has three cards with numbers on them.Now Zara takes three cards at random and places them side by side to make a 3-digit number.e List all the possible numbers she can make.f Find the probability that the 3-digit number is i an odd number ii an even number iii less than 500. 2 4 5 She puts the
Investigate the possible outcomes when 4 fair coins are thrown.You should find all the possible outcomes and find probabilities of different events.Use your experience from Question 10 to help you.
a Two fair coins are flipped.Copy and complete this table to show the outcomes. H First coin T Second coin HT HT
Here are two spinners.a The two spinners are spun. Draw a diagram to show all the outcomes.b Work out the probability that i both spinners show a 1 ii neither spinner shows a 1 iii both spinners show the same number iv the spinners do not show the same number.c The two scores are added
A fair coin and a fair dice are thrown. This table shows the possible outcomes.a Copy and complete the table.b How many outcomes are there? Are they all equally likely?c Find the probability of i 6 and a tail ii 4 and a head iii a head and an even number iv a tail and a number less than 3.d Find
Two dice are thrown. The numbers are added together.a Find the probability that the total is i 5 or less ii more than 5 iii 10 or more iv less than 10 v a prime number.b Find an event with a probability of 7/36 c Give your answer to part b to a partner to check it is correct.
Two dice are thrown. The numbers are added together.a Draw a table to show all the possible outcomes.b Find the probability that the total is i 3 ii 7 iii 12 iv 9 c Copy and complete this table of probabilities. Total Probability 2 3 4 5 6 7 00 8 9 10 11 12
Two dice are thrown. Find the probability that a both dice show 5 b one dice shows a 5 and the other does not c neither dice shows a 5.
There are lots of coloured toys in a box. Here are the percentages of some of the colours.a Why do the percentages add up to less than 100%?A child takes a toy at random.b Find the probability that the toy is i not orange ii not green iii not red iv not yellow. Colour yellow orange red green
A spinner has five colours on it.The probability it shows green is 0.32.The probability it shows purple is 0.17.Find the probability that the colour is a not green b not purple.
Tomorrow must be hotter, colder or the same temperature as today.The probability it will be hotter is 55%.The probability it will be colder is 25%.Work out the probability that it will a not be hotter b not be colder c not be the same temperature.
The probability that a football team will win a match is 0.3.The probability that the team will draw is 0.1.Work out the probability that the team will a not win b not draw c lose d not lose.
Two unbiased 6-sided dice are thrown.Find the probability of getting a the same number on both dice b a total of 6 c a total of 9 or more.
The probability that it will be sunny tomorrow is 40%.The probability it will not rain tomorrow is 95%.Find the probability that tomorrow a will not be sunny b it will rain.
A large number of drawing pins are dropped on the floor.87 land point up and 135 land point down.Work out the experimental probability of landing point up.
Tomorrow at 11:00 it will be sunny, cloudy or wet.The probability it will be sunny is 25% and the probability it will be cloudy is 40%.Find the probability it will be wet.
An unbiased 6-sided dice is thrown.Work out the probability of getting a 3 b 6 c an even number d less than 5.
This is a spinner.Each colour is equally likely.a Find the probability of green.b Find the probability of blue or yellow. Red White Yellow Green Blue
Ellen mixes two shades of grey paint in the following ratios of black: white.a. Simplify these expressions by collecting like term is white?b. Which shade of grey paint is lighter? Show all your working. Justify your choice. Silver grey 2:5 Stone grey 3:8
A school quiz club has 45 members. The ratio of boys to girls is 4:5.a What fraction of the club members are boys?b How many boys are in the club?
A running club is made up of men, women and children in the ratio 8:5:7.Altogether, there are 260 members of the running club.How many members of the running club are a men b women C children?
Five bags of peanuts have a mass of 1.375 kg and two bags of walnuts have a mass of 540 g.Which has a greater mass, one bag of peanuts or one bag of walnuts?
1 Simplify these ratios.a 6cm:5mm b 12 seconds: 1 minute C 400ml: 1.61
Two jewellery shops sell watches and rings.Bright Jewellery has 12 watches and 180 rings for sale.Mega-Jewellery has 30 watches and 438 rings for sale.Which shop has the greater proportion of watches? Justify your choice.
Liam and Hannah collect coins and stamps.Liam has 20 coins and 320 stamps.Hannah has 15 coins and 270 stamps.Use your favourite method from Question 12 to decide who has the greater proportion of stamps. Justify your choice.
a Work with a partner or in a small group to discuss the different methods you could use to answer this question.Lin has black and white counters in the ratio 40 : 840 Ian has black and white counters in the ratio 25 : 535 Who has the greater proportion of black counters, Lin or Ian?b Compare and
In the Seals swimming club there are 13 girls and 17 boys.a What fraction of the children are boys?In the Sharks swimming club there are 17 girls and 23 boys.b What fraction of the children are boys?c Which swimming club has the higher proportion of boys?Show all your working. Justify your choice.
Angelica mixes a fruit drink using mango juice and orange juice in the ratio 3 : 5.Sanjay mixes a fruit drink using mango juice and orange juice in the ratio 5 : 11.a What fraction of each fruit drink is orange juice?b Whose fruit drink, Angelica’s or Sanjay’s, has the higher proportion of
Shani mixes two shades of blue paint in the following ratios of blue : white.a What fraction of each shade of blue paint is white?b Which shade of blue paint is lighter?Show all your working. Justify your choice. Sky blue 3:2 Sea blue 7:3
This is part of Jan’s classwork.Use Jan’s method to work out the following.a A bag contains green and red counters. 2/3 of the counters are green.What is the ratio of green to red counters?b A box of books contains history and science books. 3/7 of the books are science books.What is the ratio
The ratio of men to women in a book club is 3 : 5.The number of adults in the book club is greater than 20 but fewer than 30.How many adults are in the book club?
The ratio of boys to girls in class 8C is 5 : 7.Which of these cards shows the number of learners that could be in class 8C?Justify your choice. A 25 B 28 C 32 D 36 E 38
Work with a partner or in a small group to discuss this question.The ratio of red to blue counters in a bag is 5 : 4.Read what Sofia and Zara say.Is either of them correct? Explain how you know.Discuss your answers with other groups in the class. It is possible that there are 62 counters in the
A school tennis club has 35 members. The ratio of boys to girls is 4 : 3.a What fraction of the club members are girls?b How many girls are in the club?
A tin of biscuits contains coconut and ginger biscuits in the ratio 3 : 7.The tin contains 50 biscuits.a What fraction of the biscuits in the tin are coconut biscuits?b How many coconut biscuits are in the tin?
Tio and Kai work out the answer to this question.A school choir is made up of girls and boys in the ratio 2 : 1.There are 36 students in the choir altogether.How many of the students are girls?Tio uses the ‘sharing in a ratio’ method. Kai uses the ‘fraction of an amount’ method.Work with a
Copy and complete the workings to change each ratio into a fraction.a A bag of nuts contains cashew nuts and peanuts in the ratio 2 : 7.What fraction of the nuts are i cashew nuts ii peanuts? Total number of parts = 2+7= i fraction that are cashew nuts = fraction that are peanuts = 7 2 b A box of
Pablo mixes two shades of pink paint in the ratios of red : white paint shown below.a What fraction of each shade of pink paint is red?b Which shade is darker? Justify your choice. Perfect pink 3:4 Rose pink 2:3
Akello, Bishara and Cora are going to share $960, either in the ratio of their ages or in the ratio of their heights.Akello is 22 years old and has a height of 168 cm.Bishara is 25 years old and has a height of 152 cm.Cora is 33 years old and has a height of 160 cm.a Without working out the answer,
Zhi, Zhen and Lin buy a house for $180 000.Zhi pays $60 000, Zhen pays $90 000 and Lin pays the rest.Five years later, they sell the house for $228 000.They share the money in the same ratio that they bought the house.Lin thinks he will make $9000 profit on the sale of the house.Is Lin correct?
Every year, on his birthday, David shares $300 among his children in the ratio of their ages.This year the children are aged 4, 9 and 11.Show that, in two years time, the oldest child will receive$7.50 less than he receives this year.
In pairs or groups, look at the following question and answer.This is part of Zara’s homework.Question A grandmother leaves $2520 in her will, to be shared among her grandchildren in the ratio of their ages.The grandchildren are 6, 9 and 15 years old.How much does each child receive?Answer Ratio
The angles in a triangle are in the ratio 2 : 3 : 5.Work out the size of the angles.
Here is a set of ratio cards.Sort the cards into their correct groups.Each group must have one pink, one yellow and three blue cards. $50 $84 Share $150 ... ... in the ratio 2:3:1 Share $120 ... $75 ... in the ratio 2:6:1 $25 $45 ... in the ratio 3:1:4 Share $132 ... $60 $55 $11 $15 $28 ... in the
Aden, Eli, Lily and Ziva run their own business.They share the money they earn from a project in the ratio of the number of hours they put into the project.On the right is the time-sheet for one of their projects.How much does each of them earn from this project? Project earnings: $450 Time spent
A box of fruits contains oranges, apples and peaches in the ratio 4 : 2 : 3.The box contains 72 fruits altogether.a How many fruits in the box are i oranges ii apples iii peaches?b The ratio of the number of oranges, apples and peaches is changed to 3 : 1 : 4.There are still 72 fruits in the
A choir is made up of men, women and children in the ratio 5 : 7 : 3 Altogether, there are 285 members of the choir.a How many members of the choir are i men ii women iii children?b How many more women than men are there in the choir?c How many more men than children are there in the choir?
Dave, Ella and Jia share their electricity bills in the ratio 3 : 4 : 5.a How much does each of them pay when their electricity bill is i $168 ii $192 iii $234?b Show how to check your answers to part a.
Look again at your answers to questions 1 and 2.a Think about a method you can use to check you have shared each amount correctly.b Discuss your method with a partner. Do they have the same method?If they have a different method, which method do you think is better?Explain your answer.
Share these amounts between Mia, Beth and Fen in the given ratios.a $90 in the ratio 1 : 2 : 3 b $225 in the ratio 2 : 3 : 4 c $432 in the ratio 3 : 5 : 1 d $396 in the ratio 4 : 2 : 5
Copy and complete the workings to share $80 between So, Luana and Kyra in the ratio 3 : 2 : 5. Total number of parts: 3+2+5= Value of one part: $80 = So gets: 3 = Luana gets: 2 =]] Kyra gets: 5 =
Share $840 between Alan, Bob and Chris in the ratio 2 : 3 : 1
Oditi goes for a run three times a week.Her notebook shows the time she took for each run one week.a Oditi thinks the ratio of her times for Monday to Wednesday to Friday is 1 : 2 : 3.Without doing any calculations, explain how you know Oditi is wrong.b Oditi’s mum uses this method to work out
Use Jed’s method to simplify these ratios.a 0.5 : 2 b 1.5 : 3 c 1.2 : 2.4 d 3.6 : 0.6 e 7.5 : 1.5 f 2.4 : 4 g 1.8 : 6.3 h 2.1 : 0.7 : 1.4 TTTTTTTT Monday 1 hour 40 mins Wednesday 50 mins Friday 2 hours
Work with a partner or in a small group to answer this question.This is part of Jed’s homework.a Explain why Jed’s first step is to multiply both of the numbers in the ratio by 10.b What are the advantages of Jed’s method? Can you think of any disadvantages?c How could you adapt Jed’s
Preety answers this question.Five cups hold 1.2 litres and three mugs hold 900 ml.Which holds more liquid, one cup or one mug?This is what she writes.Use Preety’s method to answer these questions.a Four bags of sugar have a mass of 1.3 kg and three bags of flour have a mass of 960 g.Which has a
Marcus and Sofia are mixing paint. They mix 250 ml of white paint with 750 ml of red paint and 1.2 litres of yellow paint.Is either of them correct? Explain your answer. The ratio of white to red to yellow paint is 1:3:5. The ratio of white to red to yellow paint is 25:75:12.
Simplify these ratios.a 600 m : 1 km : 20 m b 75 cm : 1 m : 1.5 m c 300 ml : 2.1 l : 900 ml d 3.2 kg : 1600 g : 0.8 kg e $1.08 : 90 cents : $9 f 4 cm : 8 mm : 0.2 m
Zara uses this recipe for orange preserve.Is Zara correct? Explain your answer. Orange preserve 750 g oranges 1.5 kg sugar juice of one lemon The ratio of oranges to sugar is 2:1.
Simplify these ratios.a 500 m : 1 km b 36 seconds : 1 minute c 800 ml : 2.4 l d 1.6 kg : 800 g e 3 cm : 6 mm f 2 days : 18 hours g 2 hours : 48 minutes h 8 months : 1 year
Arun and Sofia compare methods to simplify the ratio 4 mm : 6 cm.a Who do you think has the better first step? Explain why.b Discuss your answer with other learners in the class. My first step is to change 4 mm into 0.4 cm. My first step is to change 6 cm into 60 mm.
This is part of Ben’s classwork.a Explain the mistake that Ben has made.b Work out the correct answer. Question Simplify the ratio 6:12:3 Answer 6 6 1 and 126 = 2 So the ratio is 1:2:3
Simplify these ratios.a 5 : 10 : 15 b 8 : 10 : 12 c 20 : 15 : 25 d 18 : 15 : 3 e 27 : 9 : 45 f 72 : 16 : 32
Simplify these ratios.a 2 : 10 b 3 : 18 c 5 : 25 d 30 : 5 e 36 : 12 f 180 : 20 g 4 : 6 h 9 : 15 i 10 : 35 j 75 : 10 k 72 : 20 l 140 : 112
Simplify these ratios.a 12 : 20 b 12 : 30 : 24 c 2 m : 50 cm
Write the missing numbers in these conversions. a d 4m= = cm 0.8 kg = g b 6.5 cm = mm C 5t= kg e 2.31=ml f 0.75 km = m
Share these amounts between Tim and Chan in the ratios given.a $18 in the ratio 1 : 2 b $25 in the ratio 2 : 3
Write each of these ratios in its simplest form.a 2 : 4 b 18 : 6 c 6 : 9 d 32 : 24
For each of these shapes, write the ratio of green squares to blue squares.Write each ratio in its simplest form. a b
The depth of water in two flasks is changing. This graph shows the changes.a Describe how the depth in flask 1 is changing.b When do the two flasks have the same depth of water?c The depth of water in flask 2 is d cm after t minutes.Choose the correct equation of the line for flask 2.d = 5t + 30 d
Here is the equation of a line: y = 12 − 2x a Where does the line cross the y-axis?b What is the gradient of the line?
Here is a function: y = 3x + 6 a Copy and complete this table of values.b Use the table to draw a graph of y = 3x + 6 c Find the gradient and the y-intercept of the line y = 3x + 6 d Write the equation of a line parallel to y = 3x + 6 that passes through the origin. x -3-2-1 0 0 1 2 3 y=3x+6
The perimeter of this shape is p cm.a Write a function for p in terms of w.b Copy and complete this table of values.c Use the table to draw a graph to show the perimeter for different values of w. 4cm wcm 3 cm wcm 3cm
The cost of a holiday is $200 for travel plus $150 per night for a hotel.a Work out the cost of a 7-night holiday.b A holiday that lasts n nights costs $c. Write a function for c in terms of n.
This graph shows the changing temperatures of two liquids.a Describe how the temperature of each liquid changes. Give as much detail as you can.b When are the two liquids at the same temperature? Temperature (C) 50 05 Liquid B 0 1 2 3 4 5 6 7 8 x Time (minutes) Liquid A
Arun and Marcus are walking along the same path but in different directions.The graph shows how far they are from home.a How far from home is each person when they start walking?b How far does Arun walk in 5 hours?c Arun is y km from home after x hours.Write an equation for the line that shows
A car and a van travel 70 km.This graph shows the fuel in the tank of each vehicle.a Work out how much fuel each vehicle had at the start of the journey.b Work out how much fuel each vehicle used to travel 70 km.c The two lines cross at one point.What does this indicate? Litres y 20 15 10- 5 0+ 0
This graph shows the growth of two plants over a period of 6 weeks.a Which plant grew more quickly?Explain how the graph shows this.b Work out the initial height of plant X.c When were the plants the same height?d Work out how many centimetres plant Y grew each week. y 40- Plant Y Height (cm) 20 20
There are two different tariffs for a long-distance phone call.Each tariff has a connection charge plus a charge for each minute.The tariffs are shown on this graph.a Which tariff is cheaper for a 5-minute call?b A call costs 200 rupees on tariff B.How long does it last?c What length of call costs
Two plumbers charge different rates.Each plumber has a fixed charge and a charge per hour.a Find the cheaper plumber for a job that takes 2 hours.b Plumber B charges $250 for a job.Find the time for the job.c Copy and complete this table to show the total cost for plumber A.d Find the fixed charge
This graph shows the journeys of a van and a car.The van is travelling at a constant speed.a i What is the speed of the van?ii For how long does the van travel at that speed?The speed of the car increases steadily from 0 m/s for 20 seconds.b What is the speed of the car after 20 seconds?After the

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