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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

Here are five fraction cards.a Without doing any calculations, do you think these fractions are terminating or recurring decimals? Explain why.b Use a written method to convert the fractions to decimals.c Write the fractions in order of size, starting with the smallest. A 56 B 23 C 72 D 59 E
Here are five fraction cards.a Without doing any calculations, do you think these fractions are terminating or recurring decimals? Explain why.b Use a written method to convert the fractions to decimals.c Write the fractions in order of size, starting with the smallest. A 518 B 3+ C D E 3/5
Use a written method to convert these unit fractions into decimals.Write if the fraction is a terminating or recurring decimal.The first two have been done for you. 2 a 12 21 0 2=0.5 127 6711 . b 5 10 Terminating decimal d 1317 (1) 1617 13 31 0.3 3 3 10 10 10 |1=0.3 Recurring decimal + k 1712
Use division to convert each fraction to an equivalent decimal.a 3/8 b 5/11 c 11/12
Work these out using a method to make the calculation easier. Show all your working. a 600 009: b 320 C 22 x 4000
Work these out. Give each answer in its simplest form. 7100 X 2/3 17|0 ++ 23 b
Work these out. Give each answer as a mixed number in its simplest form. a 2+3 b + 213 5 34
Write the correct symbol, , between each pair of fractions. a 5/3 23 b 04 C 37 25
Write the correct symbol, = or ≠, between each pair of fractions. a b 210 C
You want to answer these questions:• Are girls or boys better at throwing a ball through a basketball hoop?• Does height make a difference?1 What data could you collect to answer these questions?What type of data is it?2 How would you collect the data you need?3 Explain how you could select a
An examiner has marked 250 examination papers.To check the accuracy of her marking, a sample of 10 papers will be re-marked.a Describe three different ways of choosing the sample.b Which of the three ways do you think is the best?Explain why you think so.
Here is a conjecture about the cars using a particular road:The modal number of people in a car is 1.Marcus, Zara and Sofia each do a survey of cars on the road.They count the number of people in each car, including the driver.Each person does the survey for 15 minutes.They do their surveys at
A large factory has a restaurant where employees go for lunch. Arun is investigating ways to improve the restaurant.a Give one disadvantage of Arun’s method.b Describe a better way of doing the survey. I will give a questionnaire to the first 50 workers visiting the restaurant this lunchtime.
Arun and Sofia carry out a survey of parents about school homework. One conjecture is that parents want more homework.To test this, each asks this question of a sample of 50 parents:Is the amount of homework your child gets too little / about right /too much ? (choose one)This chart shows the
You have been asked to carry out an investigation. You want to find out if learners would like to change the school homework policy.You will choose a sample of about 50 learners.Explain how you will choose your sample. Explain why you have chosen this method.
Zalika is investigating the number of people in each car on a busy road. She predicts that most cars will contain only one person, the driver.Zalika says, ‘I will start at 08:00 and observe 200 cars.’a Write one advantage and one disadvantage of Zalika’s method.b Describe a better way to take
Work with a partner to answer this question.You are going to find the lengths of the words in a novel. Choose a book to use.You want a sample of 50 words.a Describe three different ways of choosing a sample of 50 words.b Use one of your methods from part a to sample 50 words from your chosen
A manager wants to find customers’ opinions about his shop.The manager wants to choose a sample of 50 customers.a The sample could be the first 50 customers in the shop after it opens.i Write one advantage of this method.ii Write one disadvantage of this method.b The sample could be 10 customers
A palace has visitors every day. You are doing a survey to find out what visitors think of the visit. You want to talk to a sample of 100 people. The survey must be done on one day.a What factors might affect a person’s opinion of the visit?b Describe how you can choose a sample. Take account of
Anders is comparing two books, X and Y.He thinks book X is harder to read than book Y.a What things make a book hard or easy to read?b What statistical questions can you ask to compare how easy it is to read each book?c What data can you collect to answer your questions?d How would you collect data
Sofia surveys cars using a busy road.She wants to answer these questions:• What percentage of drivers are male?• What percentage of cars carry only one person?• What is the average number of people in a car?a What data does Sofia need to collect?b What type of data is this?c Design a data
You are going to plan and trial the collection of data from learners in your school.a Think of three questions you can ask about aspects of school life.b What data do you need to answer these questions?c Decide how you will collect the data you need.You could use a questionnaire or a data
Xavier has a simple puzzle for children.He asks these questions:• How long does it take to solve the puzzle?• Can girls solve it more quickly than boys?• Can older children solve it more quickly than younger ones?a What data must Xavier collect? What type of data is it?b Xavier gives the
A cinema manager asks these questions.• How often do people visit the cinema?• Do younger people visit more often than older people?• What type of film do people like?a What data is required?b Describe two ways to collect the data.c The manager decides to give a questionnaire to a sample of
Ahmad uses a gym. He asks these questions.• Do people visit this gym every week?• Do people come at a particular time of day?• Is there a difference between the habits of men and women?He interviews a sample of people at the gym.a What data does he need to collect?b What type of data is it?c
How would you collect data to answer these questions? State the type of data each time.a When a drawing pin is dropped, is it more likely to land point up or point down?b How many people visit a particular shop before 09:00?c How many brothers and sisters do the members of your class have?d How
The head teacher wants answers to the following questions:• Are learners happy with the length of lessons? Should they be longer or shorter?• Are learners happy with the length of their lunch break?Your task is to investigate these questions using a sample of the learners in the school.a What
You want to find the number of brothers and sisters of a group of children.Describe two different ways you could collect this data.In the United States of America, elections are held every two years to choose members for the House of Representatives. This is one of the groups of people who run the
a Write one advantage of a large sample size.b Write one disadvantage of a large sample size.
You want to choose a sample of 3 boys and 3 girls from your class.Describe three different ways to do this.
Give an example of a discrete data b continuous data c categorical data.
a Draw triangle ABC accurately.b Construct the perpendicular bisector of AC.The perpendicular bisector meets BC at P.c Measure PC. 6cm B 75 A 8cm C
The sides of a triangle are 5.1 cm, 6.8 cm and 8.5 cm.a Draw the triangle.b Construct the bisector of the smallest angle.c The angle bisector divides one of the other sides into two parts.How long is each part?
Show that triangle ABC is isosceles. B A D 40 70 C E
Work out x and y. The 50 118 60
ABCD is a trapezium.Work out the angles of the trapezium.Give a reason for each answer. C 64 B A D 105
a Write the correct words to complete these sentences.i c and h are ................... angles.ii f and l are ................... angles.iii g and k are ................... angles.b Explain why e = j + k c Explain why c = i + j e hm d g. h
Read what Marcus and Sofia say.a Draw a triangle. Construct the perpendicular bisector of each side to test Marcus’s theory.b Look at the triangles that other learners have drawn.Do you think Marcus is correct?c Draw another triangle. Construct the bisector of each angle to test Sofia’s
a Draw this triangle accurately.b Construct the bisector of angle A.c The bisector of angle A intersects BC at X.Mark X on your triangle and measure BX. A 7 cm 10cm B 8cm C
RST is a triangle. RS = 5 cm, RT = 6 cm.a If ST = 9 cm, use a diagram to show that angle R is obtuse.Write the size of angle R.b If angle R is obtuse what can you say about the length of ST?Give reasons for your answer. S 5 cm, R 6cm T
a Draw this diagram accurately.b Construct the perpendicular bisector of AB.c The perpendicular bisector of AB intersects AC at D.Label D on your diagram and measure AD. A 39 7.5cm C 10cm. B
Two sides of a right-angled triangle are 10.5 cm and 8.3 cm.Zara and Arun give different answers.Use accurate drawings to show that both of them could be correct. The third side is 6.4 cm The third side is 13.4 cm
The sides of a triangle are 5.8 cm, 7.8 cm and 7.1 cm.a Make an accurate drawing of the triangle.b Give your triangle to a partner to check the accuracy of your drawing.If necessary, correct your drawing.
The sides of a triangle are 7 cm, 8.5 cm and 9.7 cm.a Make an accurate drawing of the triangle.b Measure the largest angle of the triangle.
The hypotenuse of a right-angled triangle is 12.5 cm.One of the other sides is 10 cm.a Make an accurate drawing of the triangle.b Measure the third side.c Measure the other two angles.
All the angles and sides of this triangle are shown.a Choose either 2 sides and the angle between them(SAS) or 2 angles and the side between them (ASA).Use your chosen measurements to draw an accurate copy of the triangle.b Measure the three values you did not choose.Was your drawing accurate? If
a Draw an accurate copy of this triangle.b Measure angle F. D. 10cm E 117 6cm F
a Draw an accurate copy of this triangle.b Measure angle Q 7cm P 50 10cm R
a. Draw an accurate copy of this triangle.b. Measure the length of XY and XZ. Y 5cm 36 Z 100 X
a Draw an accurate copy of this triangle.b Measure the length of AC and BC. C 165 A 6cm 42 B
There are two other constructions that you need to be able to do using a ruler and compasses:1 Construct the bisector of a line segment.This is a line through the mid-point of the line segment and perpendicular to it.2 Construct the bisector of an angle.This is a line that divides an angle into two
When one angle is a right angle, and you know the length of the hypotenuse and one other side, this is known as RHS. Step 1: Draw the side. Draw a right angle at one end. Step 2: At the other end, draw an arc equal to the hypotenuse. Draw the third side. 9cm A 7cm B A 7cm B 9cm A 7cm B
When you know the three sides but no angles, this is known as SSS. 4.5 cm 5cm Step 1: Draw one side. Open your compasses to the length of a second side. Put the point of the compasses on one end of the side and draw an arc. Step 2: Open your compasses to the length of a second side. Put the point
When you know two sides and the angle between them, this is known as SAS. 10cm, 42 Step 1: Draw the angle first. 12cm Step 2: Open your compasses to 12 cm. Put the point of the compasses on A and draw an arc to mark B. Mark C in a similar way. Draw the side BC. 42 10cm 42 A 12cm
When you know two angles and the side between them, this is known as ASA. Step 1: Draw the side. Draw an angle at one end. Step 2: Draw the angle at the other end. Where the two lines cross is the third vertex of the triangle. 60 50 B 8cm 60 8cm B 60 50 B 8 cm
a Explain why x = b + d b Explain why y = c + e c Show that the sum of the angles in the points of the star, a + b + c + d + e = 180°. y b
Work out anglesa, b and c. b 40 80 95
a. Show that w + y = a + b + c + db. Show that w + x + y + z = 360°
ABCD is a parallelogram.Show that p + q = r A B D C
PQRS is a parallelogram.a Explain why x must be 22°.b Work out angle y. x S 39 22 R
This pentagon is divided into a triangle and a quadrilateral.a Show that the angle sum of the pentagon is 540°.b Compare your explanation with a partner’s.Do you both have a similar explanation?
ABC is an isosceles triangle.AB = AC.AB is parallel to DE.Angle ABC = 68°Work out the size of angle EDC.Give a reason for your answer. E B C 68 D A
Look at the diagram.a Explain why d = a + c b Write similar expressions for e and f.c Show that the sum of the exterior angles of a triangle is 360°. 9.
AB and CD are straight lines.Explain why the angles cannot all be correct. A 150 30 20 C- 160 -B -D
DX is parallel to BC.ZD is parallel to AB.BDY is a straight line.a Explain why angles BAD and ADZ are equal.b Explain why angles ABD and ZDY are equal.c Use the diagram to prove that the angle sum of quadrilateral ABCD is 360°.Do not use the fact that the angle sum of a triangle is 180°. A B Z D
PBC is a straight line. AQ is parallel to PC.a Explain why y = c b Explain why x = a + y c Use your answers to a and b to prove that the exterior angle at B of triangle ABC is the sum of the two interior opposite angles. P A xb B
An exterior angle of a triangle is 108°.One of the interior angles of the triangle is 40°.a Work out the other two interior angles of the triangle.b Work out the other two exterior angles of the triangle. 108 40
a. Work out each of the exterior angles shown in this triangle.b. Work out the size of the exterior angle x in this quadrilateral. 70% (67 b
Calculate the sizes of anglesa, b and c.
Work out x and y. A B 40 45 105 Do C D
ABCD is a parallelogram.a Show that opposite angles of the parallelogram are equal.b Compare your answer to part a with a partner’s answer. Can you improve his or her answer? Can you improve your own answer? A B D C
ABCD is a trapezium.Two sides are extended to make the triangle AXB.a Show that the angles of triangles ABX and DCX are the same size.b Show that angles A and D of the trapezium add up to 180°.c What can you say about angles B and C of the trapezium?Give a reason for your answer. D D X A B A B
Show that the sum of the angles of triangle XYZ must be 180°.
AB and CD are parallel.a Give a reason why a and d are equal.b Give a reason why b and e are equal.c Use your answers to a and b to show that the sum of the angles of triangle ABC must be 180°. d C D A a b B
Arun gives this explanation of why angles h and d are equal.a Arun’s explanation is not correct. Write a correct version.b Write a different explanation of why h = d that does not use corresponding angles. b h g h=b because they are corresponding angles. b=d because they are alternate angles.
Look at this diagram.Write whether these are corresponding angles, alternate angles or neither.a a and d b b and f c c and g d d and e e a and h 4 D P9 C eg
This diagram has three parallel lines and a transversal.a Write a set of three corresponding angles that includes angle f.b Write a pair of alternate angles that includes angle c.c Write another pair of alternate angles that includes angle c. d b h
Look at this diagram.Explain why AB and CD cannot be parallel lines. X-50% S 130 40 T 140 Y D B
PQ and RS are parallel lines.Find the sizes of anglesa, b, c and d.Give a reason in each case. P. 136% R b S
Angle APY is marked on the diagram.Complete these sentences.a APY and CQY are .................. angles.b APY and XQD are .................. angles.c APX and ......... are corresponding angles.d CQX and ......... are alternate angles.e CQP and ......... are vertically opposite angles. A- P X B C Y D
The sizes of two angles are marked in the diagram.a Which other angles are 105°?b Which other angles are 75°? 105 75 P 9 rs t/u
a One angle of 62° is marked in the diagram.Copy and complete these sentences.i Because corresponding angles are equal, angle = 62°ii Because alternate angles are equal, angle = 62°b Write the letters of a pair of vertically opposite angles. b 9. D P 62
Look at the diagram.a Write four pairs of corresponding angles.b Write two pairs of alternate angles. P S W
a Use the measurements shown to make an accurate drawing of this shape.b Measure the length of RS. 5cm S P 100% 4cm 140 2.5cm R
There are two parallel lines in this diagram.One of the angles is 76°.Copy the diagram and write in the values of the other angles.You do not have to draw the angles accurately. 76
a Work out the size of angle D.b Work out the value of x. 42 A C D 127 50 B
Two angles of a triangle are 55° and 70°.a Work out the third angle.b What is the name of this type of triangle? Choose the correct word.equilateral isosceles right-angled perpendicular
The Decimal Diamond on the right was generated from the diamond on the left.Work out how the values in the squares were calculated.Look at this Decimal Diamond. Choose a value for the top circle w, and choose a decimal g, between 0 and 1, which will fill the gaps between the values, so that:w + g =
Work out the answers to these calculations.Use the methods you have learned to make the calculations easier.a (0.7 − 0.4) × 0.12 b 0.9 × 27 c 14 × 0.35
a Complete the table below showing the 15 times table.b Use the table to help you work out 38.205 ÷1.5 c Show how to check your answer to part b is correct.Use a reverse calculation. 1 2 3 4 5 6 7 8 9 15 30 45
Work out 5.4 ÷ 0.9
Sam works out that 365 × 24 = 8760 Use this information to write the answers to these calculations.a 365 × 2.4 b 36.5 × 2.4 c 3.65 × 0.24 d 8760 ÷ 24 e 8760 ÷ 2.4 f 876 ÷ 2.4
Work out 0.57 × 4.62
Use a mental method to work out a 0.2 × 0.4 b 0.7 × 0.3
Write these decimals in order of size, starting with the smallest.−3.482 −3.449 −3.6 −3.44 −3.06
Write the correct sign, , between these. a 6.75 6.7 b -4.87 -4.81 0.65 kg 67g
Zara and Sofia are trying to solve this puzzle. What is the missing number in this calculation? 32x(0.8- ) 0.02 I think the missing number is 0.4 = 800 I think the missing number is 0.3 Who is correct? Explain how you worked out your answer.
A grandmother gives $12 600 to be shared between her grandchildren.Abdul gets 0.35 of the money.Zhi gets 0.25 of the money.Paula gets 0.22 of the money.Yola gets 0.18 of the money.a Work out how much they each get.b Show how you can check that your answers are correct.
This is part of Pedro’s classwork.Use Pedro’s method to work out a 180 × 0.14 (use 0.14 = 0.2 × 0.7)b 120 × 0.16 c 250 × 0.18 d 450 × 0.24 Question Work out 280x 0.12 Answer 0.2x0.6 Use 0.12 280x 0.12 2800.2x0.6 = 280x210x610 = 560 10x610 = 56x610 = 33610 = 33.6
Use the same method as in Question 9 to work out a 80 × 0.15 b 116 × 0.25

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