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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

Razi and Jake are running laps of a running track.a How do you know from the graph that Jake is running faster than Razi?b For how long had Razi been running before Jake started?c Where were the runners 9 minutes after Razi started running? Laps ru 8 7 3. 2. 654321O 0 Razi Jake 0 1 2 3 4 5 6 7 8 9
Lucas is driving from Ackult to Bibas.Simone is driving from Bibas to Ackult.a How long did Lucas take to get to Middja?b For how long did Lucas stop in Middja?c How long did Simone take to get from Bibas to Ackult?d How far were the cars from Bibas when they passed one another? Bibas 300- Middja
Zalika and Tanesha are cycling on the same route.The graph shows their journeys.a Zalika started at 09 : 00.What time did Tanesha start?b How far did Zalika travel in the first hour?c How long was Tanesha cycling before he caught up with Zalika? Distance (km) 09:00- 35- 30- 25- 20- 15- 10- 5-
This graph shows the fares charged by two different taxis.Each taxi has a fixed charge and a charge per kilometre.a How much does each taxi charge for a journey of 7 km?b Find the fixed charge for each taxi.c Find the charge per kilometre for each taxi.d What distance will cost the same amount in
Here are three functions.y = x + 6 y = 2x + 6 y = 3x + 6 a Plot a graph of each function. Plot them all on the same axes.b Find the y-intercept for each line.c The x-intercept is the x-coordinate where the line crosses the x-axis.Find the x-intercept for each line.d Use your answers to part c to
Here is a function: y = 10x + 30 a Construct a table of values with x going from 0 to 6.b Use your table of values to draw a graph of y = 10x + 30 c Describe a situation that the function y = 10x + 30 could represent.i Explain what the variables x and y and the numbers 10 and 30 represent.ii
12 Water is flowing out of a tank.The amount of water is given by the function y = −3x + 40 where there are y litres of water in the tank after x minutes.a Copy and complete this table of values.b Plot a graph to show how the amount of water in the tank changes over time.c What does the
The cost of a holiday abroad is in two parts:• the cost of the airline flights• a charge for each night in the hotel The total cost is given by this function: y = 100x + 200, where• x is the number of nights• $y is the total cost.a Copy and complete this table of values.b Use your table to
The cost of a visit by an electrician is given by this function: y = 25x + 40• y is the total cost in dollars• x is the number of hours• there is a fixed charge and a charge per hour a Copy and complete this table for the function.b Use the table to plot a graph of y = 25x + 40 Use a scale of
a Copy and complete this table of values.b Use the table to plot graphs of y = x − 2, y = 3x − 2 and y = −2x − 2 Plot all three graphs on the same axes.c Write the gradient of each line.d Write the y-intercept of each line.e Write the equations of two more lines with the same y-intercept. x
a Copy and complete this table of values.b Use the table to plot graphs of y = x + 3, y = 2x + 3 and y = −x + 3 Plot all three graphs on the same axes.c On the same axes, draw the line y = 3 d Write the gradient of each line.e Write the y-intercept of each line.f Write the equations of two more
These three lines are parallel. One of the lines is y = 5x + 5a Write the equations of the other two lines.b Write the equation of a parallel line that passes through the origin. y 12 5 x
Here are six equations of lines.a Group together lines that are parallel.b Write the equation of one more line for each group. y=4x+6 y=6x+4 y=4x+2 y=2x+4 y=6x+2 y=2x+6
a Copy and complete this table of values for y = −2x + 9b Add another row to this table to show values for y = −2x + 6 c Draw graphs of y = −2x + 9 and y = −2x + 6 on the same axes.d Write the gradient of each line.e Write the equation of another line parallel to these lines. x -2-1 0 1 2 3
a Copy and complete this table of values for y = −x + 5b Add another row to this table to show values of y = −x + 2 c Draw graphs of y = −x + 5 and y = −x + 2 on the same axes.d Write the gradient of each line.e Write the equation of another line parallel to these lines. x -2 -1 0 1 2 3 4 5
Investigate the graphs of equations of the form y = 4x + c where c is an integer.What do you notice about all your graphs?
Here are three equations.y = 3x y = 3x + 3 y = 3x − 1 a Draw a graph of each line. Use a table of values to help you.b Find the gradient and the y-intercept of each line.All the equations are of the form y = 3x + c where c is an integer.c Draw the graph of another line of the same type.
a Complete this table of values.b Use the table to draw, on the same axes, graphs of i y = 2x ii y = 2x + 4 iii y = 2x − 3 c Find the gradient and the y-intercept of each line.The equations in part b are of the form y = 2x + c where c is an integer.d i Write another equation of this type.ii
A function is y = 2x + 5 a Copy and complete this table of values.b Draw a graph of y = 2x + 5 c Where does the graph cross i the y-axis ii the x-axis?d Is there a way to use the function to predict where the line will cross the axes, before you make a table of values? Explain how you can do this.e
A plant is initially 10 cm high. It grows 2 cm a week.After x weeks the height is y cm.a Write a function to show y in terms of x.b Copy and complete this table of values.There are three lines on this graph, A, B and C.c Which line shows the growth of the plant?d The other two lines show the growth
The cost of hiring a van is $60 plus $20 per hour.a Work out a function to show the cost in dollars (c) of hiring the van for n hours.b Copy and complete this table of values.c Use your table to plot a graph to show the cost.d Read what Zara says:Is Zara correct? Give a reason for your answer. C 0
The cost of hiring a car is a fixed charge of $35 plus $15 per day.a Write a function to show the cost in dollars (y) of hiring a car for d days.b Copy and complete this table of values.c Use the table to plot a graph of the function.d Use the graph to find the cost of hiring a car for 7 days.Use
A motor runs on diesel. Initially there are 40 litres of diesel in the fuel tank.The motor uses 5 litres per hour.After h hours there are f litres of diesel remaining.a Explain why f = 40 − 5h b Copy and complete this table of values.c Use the table to draw a graph of f = 40 − 5h d How does the
The cost of hiring a drill is in two parts. There is a delivery charge of $5 plus $2 per day.a The cost of hire for n days is $c. Explain why c = 2n + 5 b Copy and complete this table of values.c Use the table to plot a graph of c = 2n + 5. You only need positive axes.d Why do you only need
Here is a function: y = 2x + 40 a Complete this table of values.b Use the table of values to plot a graph of y = 2x + 40 c Where does the graph cross the y-axis?d Which of these points are on the line?P (15, 70) Q (50, 140) R (37, 114)S (−20, 0) T (100, 240)e Compare your answer to part d with a
a Copy and complete this table of values for the function y = 10x + 30b Use the table to plot a graph of y = 10x + 30.Use a scale of 1 cm = 1 unit on the x-axis and 1 cm = 10 units on the y-axis.c Where does the graph cross the y-axis?d i Use the function to find the value of y when x = 2.5 ii Does
a Copy and complete this table of values for the function y = 4 − xb Use the table to plot a graph of y = 4 − x c Where does the graph cross the x-axis?d Where does the graph cross the y-axis?e i Use the function to show that if x = 10 then y = −6 ii Is the point (10, −6) on your line? 0 1
a Copy and complete this table of values for the function y = −2xb Use the table to plot a graph of y = −2x x -2-10 12 3 y 4 -6
a Copy and complete this table of values for the function y = 2x + 6b Use the table to plot a graph of y = 2x + 6 c Extend the line on the graph to show that it goes through the point (3, 12).d Show that the coordinates (3, 12) are correct for the function y = 2x + 6 .x -3-2-101 y 2 8 2
a Copy and complete this table of values for the function y = 3x + 2b Use the table to plot a graph of y = 3x + 2 x -2-1 0 1 2 J-4 3 11
a Copy and complete this table of values for the function y = 2x + 3b Use the table to plot a graph of y = 2x + 3 x y -2-1 0 1 1 2 3 7
Here is a function: y = 8x + 4 a Copy and complete this table of values.b Use the table to draw the graph of y = 8x + 4 x -2-1 -1 0 1 2 3 y=8.x +4 4
Here is a function: y = 20x +15 a Describe a situation that this function could represent.You must explain what x and y stand for.You must explain what the numbers 20 and 15 tell you.b Look at a partner’s answer to parta. Is the answer clear?Can you improve it?
The cost of booking a room for a meeting is a fixed charge plus an amount for each person.The cost is $c for n people and c = 8n + 40 Explain what the numbers 40 and 8 show.
When x = 4, y = 6 a Show that a possible function connecting y and x is y = 2x − 2 b Show that a possible function connecting y and x is y = 0.5x + 4 c Find three more possible functions if y = 6 when x = 4 Write them in the form y = ...................
If x = 5 then y = 30 Which of these functions could be correct?A y = 6x B y = 4x +10 C y = x + 30 D y = 40 − 2x E y = 8x −10
There are 108 litres of water in a tank. 9 litres flow out of the tank every hour.a How much water is in the tank after i 1 hour ii 3 hours iii 7 hours?b How long will it be until the tank is empty?c There are l litres of water in the tank after h hours.Complete this function: l =
Here is a shape. All the lengths are in cm.The perimeter is p cm and the area is a cm2.a Show that p = 2L + 22 b Find a function for a in terms of L. L 2 3 8 6 L 3
Here is a function: r = 18 − 3t a Work out the value of r when i t = 2 ii t = 5 iii t = 0 iv t = 6 b What happens when the value of t is more than 6?c A car is on a journey. The amount of fuel in the tank of the car after t hours is r litres, where r = 18 − 3t What can you say about the
Read what Zara says:a How old is Zara if her father is i 40 ii 52?b Zara is z years old and her father is f years old.Write a function for z in terms of f.c How old is Zara’s father if Zara is 30 years old? I am 2 years less than half my father's age.
A bamboo plant is 1.5 m tall. It grows 0.2 m every week.a Work out the height after i 2 weeks ii 4 weeks.b How long will it take until the bamboo is 3.5 m tall?Justify your answer.c Write a function to show the height in metres (h) after t weeks.
The cost of hiring a car is a fixed fee of $25 plus $45 per day.a Show that the cost of hiring a car for 7 days is $340.b Read what Sofia says:Explain why Sofia is not correct.c Write a function to show the cost in dollars (a) of hiring a car for n days. If the cost of hiring a car for 7 days is
The cost of printing photos is $2 per photo plus a fixed charge of $3.a Work out the cost of printing 40 photos.b The cost of n photos is $c. Write a function for c.c Marcus pays $49.How many photos were printed for Marcus?
The cost of scaffolding is $80 delivery plus $50 per week.a Work out the cost of hiring scaffolding for i 2 weeks ii 4 weeks iii 7 weeks.b The cost is $y for w weeks. Find an expression for y.
Theatre tickets cost $12 each plus a booking fee of $3.a Work out the total cost, including the booking fee, of i 4 tickets ii 6 tickets iii 10 tickets.b If t tickets cost $d, write a function for d in terms of t.
A plumber comes to a house to do a repair.He charges a fixed fee of $45 plus $30 per hour.a Work out the total cost for a job that lasts i one hour ii 3 hours iii 1.5 hours.b Write a function to show the cost in dollars (c) of a job that takes h hours.
Arun buys some books online. The cost is $6 for each book plus postage of $4.a Work out the total cost, including postage, of i 3 books ii 6 books iii 12 books.b Write a function to show the cost in dollars (c) of b books.
The cost of hiring a digger is a fixed charge of $35 plus $10 per day.a Find the cost of hiring the digger for 7 days.b The cost of hiring the digger for n days is $y Write a function to find the cost for any number of days.
This graph shows the temperature of some water.a How does the graph show that the water is cooling?b How long does it take for the water to cool by 10 Temperature (C) 40- 30 y= -2x+30 20 20 10 0 1 2 3 4 5 6 7 8 Time (minutes)
Here is a function: y = x + 2 a Copy and complete this table of values.b Use the table in part a to draw a graph of y = x + 2 x y -3-2 -1 0 1 0 2 3 4
One Singapore Dollar can be exchanged for 80 Japanese Yen.If d Singapore Dollars can be exchanged for y Japanese Yen, which of these equations is correct? y=d+80 y=d-80 y=80d y= 80
A pair of shoes costs $25 less than a coat.a If the coat costs $110, find the cost of the shoes.b The coat costs $x and the shoes cost $y Write a function to show y in terms of x.
In 1960 the population of Indonesia was 88 million.In 2010 the population of Indonesia was 242 million.a Calculate the percentage increase from 1960 to 2010.b Estimate the population in 2060 if the rate of increase does not change.
Increase $240 by 35%a by first finding the increase in dollars b by using a multiplier.
a Write 32 as a percentage of 80.b Write 80 as a percentage of 32.
Read what Marcus says:a Describe two different ways to check that Marcus is correct.b Which way do you think is better?Give a reason. When 650 is increased by 184% the answer is 1846.
In this exercise, always use a multiplier to calculate a percentage increase or decrease.Here are two sentences.• The population of India is 407% of the population of the USA.• The population of India is 307% more than the population of the USA.a Explain why both these sentences can be
In this exercise, always use a multiplier to calculate a percentage increase or decrease.The depth of water in a well is decreasing.Day Depth Monday 5.75 m Tuesday 5.10 m Wednesday 4.31 m Thursday 3.58 m Friday 2.46 m Calculate the percentage reduction from a Monday to Tuesday b Tuesday to Thursday
In this exercise, always use a multiplier to calculate a percentage increase or decrease.The height of a tree is 3.65 m. Find the new height if the height increases by a 15%b 132%c 260%
In this exercise, always use a multiplier to calculate a percentage increase or decrease.Prices in a shop are reduced. Copy and complete this table. Original price Percentage reduction Reduced price $280 20% $420 45% $620 $217 $750 $705
In this exercise, always use a multiplier to calculate a percentage increase or decrease.Work with a partner on this question.This table shows the changing population of China.Year Population in millions 1950 554 1960 660 1970 828 1980 1000 1990 1177 2000 1291 2010 1369 a Calculate the percentage
In this exercise, always use a multiplier to calculate a percentage increase or decrease.a The population of a town increases from 63 200 by 17%.Calculate the new population.b The population of a city increases from 7.35 million to 12.82 million.Calculate the percentage change.c The population of
a Increase 96 by 25%b Decrease 200 by 40%c Increase 60 by 100%d Decrease 240 by 50%In this exercise, always use a multiplier to calculate a percentage increase or decrease.
An athlete has a resting pulse rate of 60 beats per minute.In this exercise, always use a multiplier to calculate a percentage increase or decrease.During a race, this increases to 160 beats per minute.a Calculate the percentage increase.b Calculate the percentage decrease after the race, when his
Change each length by the percentage shown.In this exercise, always use a multiplier to calculate a percentage increase or decrease. 90 b 240 a 10 Length (mm) Change 180% increase 12% increase U 660 70% decrease P 320 7% decrease New length (mm)
a Increase 964 by 65%b Increase 357 by 195%c Decrease 560 by 84%In this exercise, always use a multiplier to calculate a percentage increase or decrease.
a The mass of a girl is 26.5 kg.In this exercise, always use a multiplier to calculate a percentage increase or decrease.Several years later her mass has increased by 62%.Calculate her new mass. Round your answer to 1 d.p.b A man has a mass of 172.4 kg. He reduces his mass by 38%.Calculate his new
Find the value of 45 kg after the following changes.In this exercise, always use a multiplier to calculate a percentage increase or decrease.a an increase of 20%b an increase of 170%c a decrease of 60%
Increase each of these numbers by 85%In this exercise, always use a multiplier to calculate a percentage increase or decrease.a 40 b 180 c 12
Here are some multipliers.In this exercise, always use a multiplier to calculate a percentage increase or decrease.Write the percentage change in each case.a × 0.75 b × 1.22 c × 3.33 d × 0.33 e × 0.03
Write the multiplier for a an increase of 45%b an increase of 245%c a decrease of 45%In this exercise, always use a multiplier to calculate a percentage increase or decrease.
Match each percentage change to the correct multiplier.In this exercise, always use a multiplier to calculate a percentage increase or decrease.The first one is done for you: A and ii A 50% increase i × 0.2 B 80% increase ii × 1.5 C 80% decrease iii × 1.8 D 120% increase iv × 1.2 E 20% decrease
What multiplier would you use to In this exercise, always use a multiplier to calculate a percentage increase or decrease.a increase a value by 63%b decrease a value by 63%c increase a value by 103%d decrease a value by 88%
The cost of a flight is $2300 Calculate the percentage change if a the cost is increased to $2850 b the cost is reduced to $1690
a Sofia has savings of $500. She spends some money and says:What can you say about this statement? My savings have decreased by 150%. Is it possible for her savings to decrease by more than 100%? b Arun has 500 g of rice. He says: I cooked some rice and the amount I have has decreased by 150%.
The same shop is selling a television for $400.a The shop increases the price by 20%. Find the new price.b The shop increases the price by a further 20%.Here are three statements:• The new price is $560• The new price is more than $560• The new price is less than $560 Which statement is
A shop is selling a phone for $80. The shop increases the price by 10%.a Find the new price.After two weeks, the shop decreases the new price by 10%.Read what Arun and Sofia say.b Explain why Arun is wrong and Sofia is correct.c Find the price of the phone after the decrease. The price will go back
There are 2000 people in a room.The number increases by P%. Then the number decreases by P%.a How many people are in the room if P = 50?Show how you calculated your answer.b What happens if P = 25?c Investigate other values of P.d Compare your answers with a partner’s.
Mia sees this sign in a shop window:She says: ‘The original price of a coat was $120 so the price is now $84’a Explain the calculation that Mia has done and why her statement is incorrect.b What is the price of the coat now? Prices reduced by 70%
A garage is reducing the prices of cars. Calculate the new prices. Model Old price ($) Decrease (%) Absolute change ($) New price ($) 15800 Ace 2.0 Beta 21 300 12.0 Carro 24200 0.5
Electricity costs are rising by 8%.The table shows the costs for one year for four customers.Copy the table and fill in the last column to show the costs for one year after the price rise. Customer Cost before the rise Absolute change ($) A B C $415 $629 $1390 Cost after the rise
A shop lists its prices in a table.a In a sale, all the prices are reduced by 30%. Calculate the sale prices.b How much would you save if you bought all three items in the sale? Item Price table $280 armchair $520 bed $1040
12 The mass of a child is 22 kg. In the next 10 years, this mass increases by 150%.a Find 150% of 22 kg. b Find the mass after 10 years.
Copy and complete this table. Amount $20 40% 140% 280% 420% $8 $84 50kg 90m 126m
Work out a 20% of 60 km b 90% of 60 km c 170% of 60 km d 260% of 60 km
A metal bar is 1.80 metres long.It is heated and the length increases by 0.5%.a What is the absolute increase in length?b How long is the bar now?
a What percentage of 40 years is 8 years?b What percentage of 8 years is 40 years?
a What percentage of 950 is 380?b What percentage of 380 is 950?
Show that a 81 is 135% of 60 b 60.8 is 190% of 32 c 308 is 220% of 140
The population of a town is 45 000.The population is expected to rise by 85% in the next ten years.Estimate the population in ten years’ time.
How much will she have if she increases her savings by a 10%b 50%c 70%d 100%e 120%?
a Find 2% of 19.00 kg b Increase 19.00 kg by 2%c Decrease 19.00 kg by 2%
a Find 80% of 3200 people b Increase 3200 by 80%c Decrease 3200 by 80%
a Find 15% of $70 b Increase $70 by 15%c Decrease $70 by 15%
A library has 2800 books. Find the number of books if it a increases by 84%b decreases by 37%
Copy and complete this table. 100% 10% 60% 120% 350% $850 $85 4.50 m 5.40 m
Xavier earns $20 per hour. Sasha earns $25 per hour.They are both given a pay increase of $2 per hour.a Write the increase as a percentage of Xavier’s pay.b Write the increase as a percentage of Sasha’s pay.
Explain the difference between 25% and 0.25%
Estimate, then work out a 40% of 600 b 140% of 600 c 0.5% of 600
There are 279 girls in a group of 450 children.What percentage of the group are a girls b boys?

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