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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
Copy and complete the side and angle properties of these three quadrilaterals.The missing words are all numbers. a C LD b A trapezium has: pair of parallel sides. An isosceles trapezium has: pair of sides the same length pair of parallel sides pairs of equal angles. A kite has: pairs of sides the
Look at isosceles trapezium ABCD.Write true or false for each statement.If the statement is false, write the correct statement.a AC is the same length as CD.b AB is parallel to CD.c Angle CAB is the same size as angle ACD.d Angle BDC is the same size as angle ACD. This is angle CAB A B C This is
Zara is describing a square to Marcus.Has Zara given Marcus enough information for him to work out that the quadrilateral is a square? Explain your answer. My quadrilateral has two pairs of parallel sides and all the angles are 90. What is the name of my quadrilateral?
Work with a partner or in a small group to discuss these questions.a Is a square a rectangle? Is a rectangle a square?b Is a square a rhombus? Is a rhombus a square?c Is a parallelogram a rectangle? Is a rectangle a parallelogram?d Is a parallelogram a rhombus? Is a rhombus a parallelogram?Discuss
Copy and complete the side and angle properties of these four quadrilaterals.Choose from the words in the box. opposite two all
Look at rectangle ABCD.Write true or false for each statement.If the statement is false, write the correct statement.a AC is the same length as BD.b AB is parallel to AC.c BD is parallel to AB.d All the angles are 90°. A B C D
This diagram shows some regular polygons. d b f
a Sketch a regular octagon. Describe the side length and symmetry properties of the octagon.b Sketch a parallelogram. Describe the side and angle properties of a parallelogram.
A scale drawing of a building uses a scale of 1 : 20 a The height of the building on the drawing is 25 cm.What is the height, in metres, of the building in real life?b The length of the building in real life is 12 m.What is the length, in centimetres, of the building on the drawing?
Match each 3D shape with its name. E d 6 b @ h 0 f cylinder tetrahedron cone cube sphere equilateral triangular prism square-based pyramid cuboid
Label the parts of the circle shown. All the words you need are in the cloud. centre chord diameter tangent radius circumference
Make h the subject of each formula. 200 a x=t+h-p b 4 y=3xh
a The diagram shows a cuboid.Write the number of i faces ii edges iii vertices of the cuboid.b Draw the top view, front view and side view of this cuboid.
a Write the number of lines of symmetry for each of these shapes.b Write the order of rotational symmetry for each of these shapes. iii iv
Work out a 6-2 b 49
Work out 315 +8 b 318 +6 a
Work out mentally 3225 + 254 a + 23 679 b d
Write the fractionsin order of size, starting with the smallest. 5 12,-27, -17 and 10 6 _ 38 15
Use a written method to convert these fractions into decimals.Write if the fraction is a terminating or recurring decimal.a. 3/8.b. 4/9.
Use a written method to convert these fractions into decimals. Write if the fraction is a terminating or recurring decimal. 3 a 8 b 2 Write the fractions -12, -77,-17 and -38 in order of size, starting with the smallest. 3 Work out 4 a 62-23 Work out a 9+3 5 Work out mentally a + 10 C 4+ b 49 b 8+
In this exercise, you have used mental methods to work out fraction calculations.Look back at the worked example and the types of question shown in partsa, b, c and d.a Which type of questions have you found i the easiest ii the hardest to work out mentally?b Which type of questions are you
Zara works out the answers to these calculation cards.Read what Zara says.Is Zara correct?Write the first term and the term-to-term rule of the sequences you can find. A B 3 (+) 2-(0-1) U 4(21-1) D 6+(-1])
12 Work out these calculations. If you cannot do them mentally, write down some workings to help you. a C e (+2)+ (10+ + (+) b d 4 *(1+1) (1+1)(-3) (1-2)9 ()
This is how Marcus mentally works out 1/3 × (5/6 − 1/2)a Explain the mistake Marcus has made.b Work out the correct answer. First, I work out- which equals which cancels down to 1. Then I work out 1, which equals
The diagram shows a path.The area of the path is 10 m2.The width of the path is 3/4 m.What is the length of the path? length 3+ m
a Work out mentallyb Use a calculator to check your answers to part a.c Did you get your answers to part a correct?If not, what mistakes did you make?!!!~!~!!! 451 i 9 315 ii 7+ 23 iii 11+ 57 iv 8
With a partner, work out how to use the fractions button on a calculator.The fractions button looks like this.Work out the answer to 18 ÷ 5/7. Write your answer as an improper fraction.Use the calculator to turn the improper fraction into a mixed number.You will need to use this button.
Work out these calculations. Use the same method as in part c of the worked example.Some working has been shown to help you with the first two. a 443+2= C 9 b 8+ d 62 e 9+3 5 4 =8x5+4= 56 f 10+ 10+ 0
In a box of fruit, 2/5 are apples, 1/6 are guavas and the rest are coconuts.What fraction of the fruit in the box are coconuts?
In a hockey squad, 1/3 of the players are short, 1/4 of the players are medium height and the rest are tall.What fraction of the squad are tall?
a Work with a partner. Discuss the best method to use to work out the answer to this question.In a box of chocolates, 1/5 of the chocolates are white chocolate, 1/2 are milk chocolate, and the rest are dark chocolate.What fraction of the chocolates are dark chocolate?b Compare your methods with
Work out these additions and subtractions.Use the same method as in part b of the worked example. e 15 15 2 + + 1358 15/7 b - + 1756 27 + I 3 9 23 14 34 + 4589 34 P h 15 13 + - 3100 291272 k
Work out these additions and subtractions.Use the same method as in part a of the worked example. a + 810 45 + + 3 72 23: b f j 165295 + 123415 e i C 16 + P 61 101910 35 13 45. 9 k T + 3888 25 121118 -
Work out these additions and subtractions.Some working has been shown to help you. 91 + 26 9 b -19 88 16 + 13 || -19 45 a C 00 9 + 18 56 -+ 13 +
Work out mentally a + 38 3/00 34 b 34 45 C -- 6+2 34 d 25 X 23 12 +
11 a Here is a sequence of calculationsi Work out the sequence of answers.ii Write the next two terms of the sequence.iii Describe the sequence of answers in words. 1- 2+ 9 4+ 6'
Sofia is looking for patterns in the division questions.She has come up with two ideas.Are Sofia’s ideas correct?Explain your answers.Look back at the questions you have done in this exercise to help you explain.
Read what Marcus says.a Whose method do you prefer, Anil’s or Marcus’s? Explain why.b Work out these calculations.Give each answer as a mixed number in its lowest terms. i 6+ iii 1210 ii 4- 4+ iv 9 1=22 13
This is part of Anil’s homework.You can see that he simplified the improper fraction to its lowest terms before he changed it into a mixed number. Question Work out 10 Answer 5 10 1 =10x-4 = 50 4 25 2 12
Work out the answers to these calculations. Use the reciprocal method.The first two have been started for you. a Ei#xu-t+u C 7 45 d 12+ 70 10 b 6= 9+1-9-8-08 e 10+ 1
Work with a partner or in a small group to answer this question.Read what Zara says. Use the diagram to show that Zara is correct. b Use the diagram to work out 4+ d e The answer to 3+ is 4 Complete the reciprocal method to check your answer to part c is correct. 4+=4x-6=0 If your answers to parts
Work out the answers to these calculations. Use the diagrams to help you. a 4 + b 6 C d 4% ++ 8 + 23 34 25 47
Work with a partner or in a small group to answer this question. a How can you use this diagram to work out 2+ b How can you use this diagram to work out 3+ C Discuss your methods with other learners in the class. Write the method that you like better.
4 Kai uses this formula to work out the average speed of a car in kilometres per hour (km/h), when he knows the distance it has travelled and the time it has taken.speed = distance ÷ time Work out the average speed of these cars. The first one has been done for you. B distance = 30 km, time = hour
The area of a rectangle is 16 m2.The width of the rectangle is 1/5m.What is the length of the rectangle?
Read what Sofia says about dividing an integer by a unit fraction.a Can you explain why Sofia’s method works?b Check your answers to Question 1 using Sofia’s method.c Use Sofia’s method to work out i 12 25+ 4 iii 8-
Work out the answers to these calculations. Use the diagrams to help you. a + 2 + 1/1/143 31 b d + 12
Work out a 4 ÷ 1/3.b 10 ÷ 3/4.
Look back at this section on multiplying an integer by a mixed number.a What did you find easy?b What did you find hard?c Are there any parts that you think you need to practise more?
Jamal works in a garden centre.It takes him 5 ¼ minutes to plant one tray of seedlings.How long will it take him to plant 50 trays of seedlings?Give your answer in hours and minutes.Tip Seedlings are seeds that are just starting to grow into plants.Think like a mathematician Work with a partner or
This is how Zara works out 2 1/6 × 15. 215=215+15 = 30 + 15 = 30+2- = 30 +2 = 32 Sofia says, 'You changed to a mixed number and then simplified to. I would have simplified 15 to 3 before changing it to a mixed number.' a Do you prefer Zara's method or Sofia's method? Explain why. b Use your
Work with a partner or in a small group to discuss this question.Look at the different methods that Anders and Xavier use to work out 3 2/3 * 8. Anders 2 338=3x8+ 38 = 24 + = 16 3 = 24 +5 Xavier Change 3 into 8-88 = = 29- = 29/ = 29- 1/3 a What are the advantages and disadvantages of i Ander's
Martha is going to lay paving slabs on part of her garden.This part of her garden is a rectangle with length 3 3/5m and width 2 m.a Martha estimates that the area of the rectangle is 6 m2. Is Martha correct? Explain your answer.b Work out the area of the rectangle.Martha buys paving slabs that cost
The diagram shows a square joined to a rectangle.Work out a an estimate for the area of the shape b the accurate area of the shape. 5 cm 5cm 4 12cm
Copy and complete these multiplications. Use estimation to check your answers. b 311=311+211 + 6x+6x=6x+ +[ || 80+0= +4 d 26=26+26 C 52x7=5x+2x7 8 80+0- 80- -08 80+0- 8
Lin has 20 containers.The mean amount of water the containers hold is 2 2/5litres.Lin uses this formula to work out the total amount of water that the containers hold.Lin thinks the total amount of water the containers can hold is 46 litres.Is Lin correct? Explain your answer. total amount of water
This rectangle has length 15 m and width 2 1/3 m.Work out a an estimate for the area of the rectangle b the accurate area of the rectangle. 15m 2m
Copy and complete these multiplications. a 318=38+18 + 2112=212+112 + C 49-4x9+x9 + d 8310=810+210 +
Work out i an estimate and ii the accurate answer to a 216 b 420
The perimeter of this quadrilateral is 35 13/36m.Work out the length of the missing side. 5 m 8m 9m
In this pyramid, you find the mixed number in each block by adding the mixed numbers in the two blocks below it.Complete the pyramid. 12 2/3 0 199 2 413 2/3 12-8
This is part of Rio’s homework. He has made a mistake in his solution.a Explain the mistake Rio has made.b Work out the correct answer. Question Work out 4 - Answer 10 40-2=40 10
Fina has two bags of lemons.One bag has a mass of 4 7/10 kg.The other bag has a mass of 2 4/15 kg.What is the difference in mass between the two bags of lemons? jkg 2 kg
Sami drives 16 5/8 km from his home to work.Sami drives 1 12/5 km from his home to the supermarket.What is the difference between the distance he drives from his home to work and from his home to the supermarket?
Work with a partner or in a small group to discuss this question.What is the quickest method to use to work out the answer to 6 5/8 − 3 1/2?
The diagram shows the lengths of the three sides of a triangle. a estimate, then b calculate, the difference in length between the longest and shortest sides of the triangle.Write your answer to part b as a mixed number in its simplest form. 3m 5m 7-m
Zalika has a length of wood that is 5 1/4m long.First, Zalika cuts a piece of wood 1 3/5m long from the length of wood.Then she cuts a piece of wood 2 9/10m long from the piece of wood she has left.How long is the piece of wood that Zalika has left over? 5m 1 m 9 2 10 B ? m
Shen has two pieces of fabric.One of the pieces is 1 3/4m long. The other is 2 3/8m long.a estimate, then b calculate, the difference in length between the two pieces of material. 1m 2m B
Work with a partner or in a small group to answer this question.Marcus is looking at the question 9 2/7 − 3 8/9.a Is Marcus correct? Explain your answer.b Choose two mixed numbers of your own but don’t subtract them yet.Write between which two whole numbers your total will be.Check that your
Work out these subtractions. Show all the steps in your working.Use your preferred method.
Work with a partner or in a small group to discuss this question.Look at the different methods that Anders and Xavier use to work out 9 4/3 - 6/7.a What are the advantages and disadvantages of:i Ander’s method ii Xavier’s method?b Which method do you prefer: Anders’ method, Xavier’s method
Work out these subtractions. Show all the steps in your working. a 300 2 55100 b 3/5 3 C 4-111 d 23 51-3/4
Copy and complete these subtractions. 10 a 51/3-2/3 Step 1: 16- 3 Step 2: 16 3 8 8 Step 3: 4-24 C 52-33 Step 1: 23 Step 2: Step 3: 4 6 b 91-31 Step 1: Step 2: 6 9 2 12 12 12 12 Step 3: _____ 12 4 d 4-1 Step 1: 4 5 Step 2: 4 6 12 12 12 4 5 20 20 20 Step 3: 2 20 20 23 = 12 12
Work outa. 3 1/5 −1 4/5b. 6 1/3 − 2 4/9.
17 Li has 5 improper fraction cards. He puts them in order, starting with the smallest.There are marks on two of his cards.What fractions could be under the marks?Give two examples for each card. 20 7 9 13 25
16 In a science experiment, two groups of seeds are planted.In group A, 175 seeds are planted and 156 start to grow.In group B, 220 seeds are planted and 189 start to grow.Use a calculator to work out which group is better at growing.
Arun takes two English tests.In the first test he scores 65/72. In the second test he scores 35/38 Read what Arun and Sofia say.a Use Arun’s method to compare the scores.b Use Sofia’s method to compare the scores.c Which method do you prefer and why?d In which test did Arun get the better
One day, a farmer sells 92% of her eggs.The following day, she sells 56 out of 62 eggs.Use a calculator to work out on which day she sold the greater percentage of eggs.
Write these fractions in order of size, starting with the smallest. 107 20 37 -53 82 7 8 15
a. Match each fraction with the correct decimal. 9 21/10 25 209 47 50 11 -4.18 -4.27... -4.16... -4.11... -37,-25,- b Write the fractions - 37, 25, -209 and -47 in order of size, starting with the smallest.
a Complete the workings to write each fraction as a decimal.Work out the first four decimal places.b Write the fractions −11/7, −14/9 and −19/12 in order of size, starting with the smallest. == 19 12 -=-12 -14=-196 0 5 7 1 4 0 5 5 5 5 0 5 8 3 3 74 7 440 50 10 30 95 50 50 50 50 12 7 70 100 40
Two driving instructors compare the pass rates for their students in January.Steffan had 34 out of 40 students pass.Irena had 87% of students pass.Who had the higher pass rate for their students in January?Show how you worked out your answer.
Three sisters sat a maths test on the same day.Adele scored 16/25, Belle scored 13/20 and Catrina scored 63%.Who had the highest percentage score?
Put these fraction cards in order of size, starting with the smallest. = 11 19 5 2/5
Work with a partner. Discuss different methods you could use to answer this question.Put these fraction cards in order of size, starting with the smallest.What do you think is the best method to use? Explain why. 17 8 -31/11 13 6 13
Write the correct symbol, , between each pair of fractions. 2 3=81 P b 8 e 19 5696 C 2757 27 61 f
Work with a partner or in a small group to answer this question. a With each pair of fractions, decide which is larger. i / or / b Discuss your answers to part a. 7 or 1/ iii 13 or 14 Copy and complete this sentence. Use either 'larger' or 'smaller'.| When the denominators are the same, the larger
Work out which is larger. 13 Or b 83 37 or C 16 20 6
Zara and Sofia compare the methods they use to work out which is larger −8/3 or −2 4/7 They both use this method to start with.Read what Zara and Sofia do next.a Write the advantages and disadvantages of each method.b Can you improve either method?c What is your preferred method for comparing
Write the correct symbol, , between each pair of fractions.Parts a and e have been done for you. a 13 63 Answer: 13 -4 f --23 9 -14 h--1
This is part of Seren’s homework.She uses the symbol = to show that one fraction is equal to another.She uses the symbol ≠ to show that one fraction is not equal to another. Question Write the correct sign, = or, between each pair of fractions. a 14 = 14 Answer a-and 2-2 11 b-1=-3=-300 b -
a Write these fractions in order of size, starting with the smallest: 7/3, 8/9 and 12/5 b Use decimals to decide which is smaller: −3 4/7 or − 43/12.
Rajim has 8 weeks holiday a year.There are 52 weeks in a year.What fraction of the year does he have on holiday?Write your answer as a decimal.
This is part of Ada’s homework.Use Ada’s method to write these lengths of time as recurring decimals.a 4 hours 20 minutes b 1 hour 40 minutes c 6 hours 10 minutes d 3 hours 50 minutes Question Write 2 hours and 10 minutes as a recurring decimal. Answer 10 1 10 minutes is the same as 606 of an
Without using a calculator, write these fractions as decimals. 2 b d
This is part of Kim’s homework.a Use a calculator to check Kim’s homework.b Explain any mistakes she has made and write the correct answers. Question Write these fractions as decimals. i 52 12 Answer i=0.416 6 10 11 i = 0.857142 w 37 iii 7 10 = = 0.90 11 1 w 37 = 0.027
Use a calculator to convert these fractions to recurring decimals.a 2/7 b 9/13 c 11/14
Marcus and Sofia are discussing the fraction 5/13.What do you think? Explain your answer. My calculator tells me that 5+13= 0.38461538, so I think that 5 is a recurring decimal which I can write 13 as 0.384615 I don't think the calculator shows you enough decimal places to decide it is a recurring
Use a calculator to convert these fractions to decimals. a 7925 C b d 2899
Work with a partner or in a small group to discuss these questions.Maddie converts four fractions to recurring decimals on her calculator.These are the answers she gets. These are the answers she gets. 0.111111111 0.733333333 0.888888889 0.388888889 a Why has the calculator put a 9 at the end of
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