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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

Complete the workings. Use factors to make these calculations easier.a 24 × 0.35 = 24 × 0.5 × 0.7 b 32 × 0.45 = 32 × 0.5 × 0.9 II = x0.7 x710 +10 = 0.9 x910 +10
Work out the answers to these calculations. Look for different ways to make the calculations easier.There are some tips in the cloud.a 2.5 × 32.7 × 4 b 02 × 2 3 / 0.1 c (420 + 360) × 0.7 d 8 × 1.32 × 2.5 e (720 − 120) × 0.07 bud. 4 x 2.5= 0.29 0.2 0.210 0.1 0.1x 10 780 0.7=78x7= 8x2.5=
A new medicine was given to 3200 patients.It made 99% of them feel better. For the other 1%the medicine made no difference.Work out how many of the patients the new medicine made better.
The diagram shows a rectangle.The width is 6 m and the length is 9.9 m.Work out the area of the rectangle. 9.9m 6m
Work in pairs or small groups to discuss this question.Look again at the working and method for Question 3a.a Describe a similar method you could use to work out 52 × 9.9 b Describe a similar method you could use to work out 52 × 0.99 c Use your methods to work out i 26 × 9.9 ii 26 × 0.99 Check
Use the same method as in Question 3 to work out a 28 × 0.9 b 17 × 0.9 c 4.9 × 0.9
Complete the workings to make these calculations easier. a 520.9 52x(1-0.1) =52x1-520.1 b 8.3x0.9 8.3x(1-0.1) 8.3x1-8.30.1
Use the same method as in Question 1 to work out a (0.7 + 0.1) × 0.6 b (0.3 + 0.9) × 0.5 c (0.6 − 0.4) × 1.2 d (1.8 − 1.5) × 1.1
Copy and complete the workings for these questions. a (0.3+0.4) 0.2= 0.2 b (1.1-0.8)0.4= 0.4
Work out mentally a (0.6 − 0.2) × 0.8 b 22 × 0.9 c 4 × 12.6 × 2.5 d 12 × 0.15
This is part B of Marcus’s homework.Use Marcus’s method to work out these calculations.Round each of your answers to the given degree of accuracy.a 3.79 ÷ 0.6 (1 d.p.)b 82.35 ÷1.1 (2 d.p.)c −5689 ÷ 2.3 (1 d.p.) Question Work out 1.7980.7 Give your answer to 1 d.p. Answer 1.798x10 17.98 I
Work with a partner to answer this question.a Balsem works out that 425 × 27 = 11 475 Use this information to work out i 11 475 ÷ 27 ii 11 475 ÷ 425 iii 11 475 ÷ 2.7 iv 11 475 ÷ 42.5 b Explain the method you used to work out the answers to part a.c Work out i 1147.5 ÷ 2.7 ii 114.75 ÷ 2.7 iii
The diagram shows a rectangle with an area of 50.15 m2.The width of the rectangle is 3.4 m.Work out the length of the rectangle. 3.4 m. Area = 50.15m == length
a Complete the table below showing the 25 times table.b Helen buys a piece of wood for $58.90 The piece of wood is 2.5 m long.Work out the cost per metre of the wood.c Show how to check your answer to part b is correct.Use estimation with a reverse calculation. 1 2 3 4 5 6 7 25 50 75 89
10 a Copy and complete the table below showing the 19 times table.b Use the table to help you work out 59.375 ÷1.9 c Show how to check your answer to part b is correct.Use estimation with a reverse calculation. 1 2 3 4 5 6789 19 38 57
Raffa works out 461.7 ÷1.8. This is what he writes.a What should Raffa have done, instead of stopping the division and writing ‘remainder 9’?b Work out the correct answer. 461.7x10 4617 = 1.8x10 18 This is my 18 times table: 1 2 3 4 5 6 7 8 9 18 36 54 I can use the table to work out the
Isla works out 50.46 ÷1.2. This is what she writes.a Explain the mistake that Isla has made.b Write the correct answer. 50.46x10 504.6 1.2x10 12 4 2 5 12 5 0 24 660 So, 50.46 1.242.5
This is part of Jamal’s homework.Use Jamal’s method to work out each of these divisions.i First, estimate the answer.ii Then calculate the accurate answer.a 27.6 ÷ 0.3 b −232 ÷ 0.4 c 306 ÷ 0.9 d −483 ÷ 0.7 e 43.76 ÷ 0.8 f −33972 ÷ 0.6 Question i Estimate an answer to 4980.6 Work
Discuss in pairs or small groups the answer to this question.What calculations can you do to check that the answer to a division is probably correct?For example, how can you check that 20.504 ÷ 0.8 = 25.63 is probably correct?
Artur pays $1.08 for a piece of string 0.8 m long.Artur uses this formula to work out the cost of the string per metre.cost per metre = price of piece/length of piece What is the cost of the string per metre?
Work out a 0.92 ÷ 0.4 b 5.74 ÷ 0.7 c −774 ÷ 0.9 d −288 ÷ 0.3
Discuss this question with a partner or in a small group.Arun is working out 3 ÷ 0.6. This is what he says.What explanation could you give to Arun to show that he is wrong? do I understand that I must 3x10 30, 0.6 0.610 -5 because that makes the calculation a lot easier. But I don't understand why
Which of these calculation cards is the odd one out? Explain why. A 6.30.9 B 1.40.2 C 4.9 0.7 D 4.80.6 E 5.60.8
Copy and complete these divisions. a 2.4 +0.4 = 2.4 0.4 2.4 x 10 0.4 x 10 b 7.2 0.9= 7.2 7.2 x 10 0.9 0.9 10 -420.6=-42 -42 x 10 d -45+0.5=-45 -45 x 10 0.6 0.6 x 10 0.5 0.5 x 10
Work out a −32 ÷ 0.2 b 3.468 ÷ 0.8
A coin is made from silver and copper.The mass of the coin is 4.2 g.You can use this formula to work out the mass of silver in the coin:mass of silver = 0.775 × mass of coin a Work out an estimate of the mass of the silver in this coin.b Calculate the accurate mass of the silver in this coin.
A vet needs to work out how much medicine to give to a cat.The instructions for the medicine say:Give 7.3 mg (medicine) per kg (mass of cat)The cat has a mass of 5.8 kilograms.a Work out an estimate of the number of milligrams (mg) of medicine that the cat needs.b Calculate the accurate number of
This is part of Syra’s homework.Use estimation to check if Syra’s answers could be correct.If you don’t think they are correct, explain why. Question Work out a 0.45x2.8 Answer a 12.6 b 7.8x 0.0093 C c 0.065x0.043 b 0.07254 C 0.02795
Work out these multiplications.Show how to check your answers.a 6.7 × 9.4 b 0.56 × 8.3 c 0.23 × 8.15 d 0.69 × 0.254
Sam uses this method to work out and check her answer.a Write the advantages and disadvantages of Sam’s method.b Can you improve her method?c Which method do you prefer to use to multiply decimals?Write why you prefer this method. Question Work out 0.674.28 Answer First work out 67x428 400 20 8
a On a piece of paper, write a question of your own similar to Question 8.On a different piece of paper, write the answers to your question.b Exchange questions with a partner and work out the answers to their question.c Exchange back and mark each other’s work. Discuss any mistakes. 8 a Work out
a Work out 158 × 46 b Use your answer to part a to write the answers to these multiplications i 15.8 × 46 ii 158 × 4.6 iii 15.8 × 4.6 iv 1.58 × 4.6 v 15.8 × 0.46 vi 1.58 × 0.046
Work with a partner or in a small group to discuss this question.Jan works out that 42 × 87 = 3654 a Use this information to write the answers to these multiplications.i 42 × 8.7 ii 42 × 0.87 iii 4.2 × 87 iv 4.2 × 8.7 b Explain why your answers to ai and aiii are the same, and why your answers
Fill in the missing spaces in this spider diagram.All the calculations give the answer in the middle.All the answers are in the yellow rectangle on the right. 6x x 0.12 0.6x0.6 x9 0.36 0.9 1.2 3 0.4 0.3 X0.01 36 0.04 0.06 0.09
a Copy and complete these patterns.b Work out.i 0.1 × 0.09 ii 0.6 × 0.8 iii 0.07 × 0.4 iv 0.03 × 0.05 v 0.12 × 0.3 vi 0.06 × 0.11 i 24=8 0.24=[ 0.2x0.4= 0.20.04= 0.2x0.004= ii 35=15 0.3 5= 0.3 0.5= 0.3 0.05= 0.3x0.005
Work with a partner or in a small group to discuss this question.Look at what Arun says. I don't understand why 0.2 0.3 is 0.06 and not 0.6 Zara shows Arun this pattern. 2x3=6 0.2x3=0.6 0.2x0.3 = 0.06 0.2x0.03 0.006 0.2x0.003 0.0006 How can you use the place value of the digits in 0.2 and 0.3 to
Here are five calculation cards.a Work out the answers to the calculations on the cards.b Write the answers in order of size, starting with the smallest. A 0.6x-12 B 0.039-180 C 0.85 x-9 D 0.44x-16 E 0.04x-182
Use a mental method to work outa −6 × 0.03 b −9 × 0.2 c −18 × 0.001 d −20 × 0.9 All the answers are in the cloud. -18 -0.18 -1.8 -0.018
Use a mental method to work out a 0.1 × −8 b 0.2 × 3 c 0.3 × −7 d 0.7 × 8 e 0.9 × −4
a Work out mentally i 0.02 × −12 ii 3.2 × 0.04 b Use a written method to work out 5.96 × 0.35 Check your answer using estimation.
y is a number with three decimal places, and –0.274 < y ⩽ –0.27 Write all the possible numbers that y could be.
In this exercise you have written positive decimal numbers, negative decimal numbers and decimal measurements in order of size.a Which have you found the easiest? Explain why.b Which have you found the hardest? Explain why.
Zara is looking at this inequality: 3.27 ⩽ x Is Zara correct? Explain your answer. If x is a number with two decimal places, there are 8 possible numbers that x could be.
Each of the cards describes a sequence of decimal numbers.a Work out the fifth term of each sequence.b Write the numbers from part a in order of size, starting with the smallest. A First term: 0.5 B First term: 0.15 C First term: -1.7 D First term: 33.6 E First term: 1.25 F First term: 10.45
Shen and Mia swim every day. They record the distances they swim each day for 10 days.These are the distances that Shen swims each day. 250m 1.25km 0.5km 2500m 2km 1.75km 750m 1500m 25km 0.75km a Shen has written down one distance incorrectly. Which one do you think it is? Explain your answer.
Write these decimal numbers in order of size, starting with the smallest.a −4.67, −4.05, −4.76, −4.5 b −11.525, −11.91, −11.08, −11.6
Write the correct sign, , between each pair of numbers. a -4.27 -4.38 b -6.75 -6.25 C -0.2 -0.03 d -8.05 -8.9
Look at Arun’s solution to this question.Write these decimal numbers in order of size, starting with the smallest.−4.52 −4.31 −4.05 −4.38Discuss the answers to these questions with a partner.a Is Arun correct? Explain your answer.b What do you think is the best method to use to order
Write these measurements in order of size, starting with the smallest.a 2.3 kg, 780 g, 2.18 kg, 1950 g b 5.4 cm, 12 mm, 0.8 cm, 9 mm c 12 m, 650 cm, 0.5 m, 53 cm d 0.55 l, 95 ml, 0.9 l, 450 ml e 6.55 km, 780 m, 6.4 km, 1450 m f 0.08 t, 920 kg, 0.15 t, 50 kg
Write the correct sign, , between each pair of measurements. a 4.51 2700 ml b 0.45t 0.45t 547 kg 3.5 cm 345mm d 0.06 kg 550g e 7800m 0.8 km f 0.065m 6.7 cm
Write the correct sign, = or ≠, between each pair of measurements. a 6.71 670ml b 4.05t 4500 kg c 0.85 km[ 850m d 0.985m 985 cm e 14.5cm 145mm f 2300 g 0.23 kg
Use your preferred method to write these decimal numbers in order of size, starting with the smallest.a 23.66, 23.592, 23.6, 23.605 b 0.107, 0.08, 0.1, 0.009 c 6.725, 6.78, 6.007, 6.71 d 11.02, 11.032, 11.002, 11.1
Maya uses this method to order decimals.Discuss the answers to these questions with a partner.a Do you understand how Maya’s method works?b Do you like Maya’s method?c Do you prefer Maya’s method to the method shown in Worked example 4.1?Explain your answer. Question Write these numbers in
Write the correct sign, , between each pair of numbers. a 4.23 4.54 C 0.27 0.03 b 6.71 6.03 d 27.9 27.85 e 8.55 8.508 f 5.055 5.505
Write these decimal numbers in order of size, starting with the smallest.They have all been started for you. a 5.49, 2.06, 7.99, 5.91 2.06, b 3.09, 2.87, 3.11, 2.55 2.55, C 12.1, 11.88, 12.01, 11.82 11.82, d 9.09, 8.9, 9.53, 9.4 8.9,
a Write these decimal numbers in order of size. 5.6, 4.95, 5.68, 5.609 b Write the correct symbol, = or ≠, between these measures. 7.5 m ___ 75 cm c Write the correct symbol, > or
Work out.a 12.3 ÷ 3 b 44.1 ÷ 7 c 152.88 ÷ 6 d 28.86 ÷ 12
Match each blue question card with the correct yellow answer card. 12x1.8 191.2 92.5 25 0.87 3200.07 21.75 22.4 21.6 22.5 22.8
Write true (T) or false (F) for each of these.a 6 × 0.1 = 0.6 b 12 × 0.7 = 0.84 c 0.03 × 2500 = 750 d 0.04 × 25 = 1
Here are four decimal number cards.Write the numbers in order of size, starting with the smallest. 0.763 0.756 0.761 0.759
Write the correct symbol, , between each pair of decimal numbers. a 4.5 4.54.1 b 6.57 6.68 C 10.52 10.59 d 2.784 2.781
Use a calculator to work out the answer to √89/482 Give your answer correct to two significant figures.
Round each of these numbers to the given degree of accuracy.a 78.023 (2 s.f.)b 0.067 91 (3 s.f.)c 1.549 62 (4 s.f.)d 12 452 673 (5 s.f.)
Which calculation, A, B, C or D, gives a different answer from the others?Show your working.A 5.2 × 0.1 B 5.2 ÷ 0.01 C 0.052 ÷ 0.1 D 52 × 0.01
Work out a 90 × 0.1 b 552 × 0.1 c 135 × 0.01 d 8 × 0.01 e 6 ÷ 0.1 f 23.5 ÷ 0.1 g 5.2 ÷ 0.01 h 0.68 ÷ 0.01
This is part of Jake’s homework.He works out an estimate by rounding each number to one significant figure.Follow these steps for each of the calculations below.i Use Jake’s method to work out an estimate of the answer.ii Use a calculator to work out the accurate answer.Give this answer correct
This formula is often used in science.F = ma Work out the value of a when F = 32 and m = 15.Round your answer to an appropriate degree of accuracy.
A rugby club sells, on average, 12 600 tickets to a match each week.The average cost of a ticket is $26.80 How much money does the club get from ticket sales, on average, each week?Round your answer to an appropriate degree of accuracy.
Zara and Sofia are looking at this question.Read Zara’s and Sofia’s comments.What do you think? Explain your answers. Work out the area of this rectangle. 0.87 m 9.6m Give your answer to an appropriate degree of accuracy.
The speed of light is approximately 670 616 629 miles per hour.This formula changes a speed in miles per hour into a speed in metres per second.Work out the speed of light in metres per second.Give your answer correct to three significant figures. metres per second = miles per hour 2.25
Ahmad has a bag of peanuts that weighs 150 g.There are 335 peanuts in the bag.Work out the average (mean) mass of one peanut.Give your answer correct to one significant figure.
At a football match there were 63 475 Barcelona supporters and 32 486 Arsenal supporters.How many supporters were there altogether?Give your answer correct to two significant figures.
a Use a calculator to work out the answer to 262 + 58.Write all the numbers on your calculator display.b Round your answer to part a to the stated number of significant figures (s.f.).i 1 s.f. ii 2 s.f. iii 3 s.f.iv 4 s.f. v 5 s.f. vi 6 s.f.
Round the number 209.095 046 to the stated number of significant figures (s.f.).a 1 s.f. b 2 s.f. c 3 s.f.d 4 s.f. e 5 s.f. f 6 s.f.
Which answer is correct: A, B, C or D?a 2569 rounded to 1 s.f. A 2 B 3 C 2000 D 3000 b 47.6821 rounded to 3 s.f. A 47.6 B 47.682 C 47.7 D 48.0 c 0.0882 rounded to 2 s.f. A 0.08 B 0.088 C 0.09 D 0.1 d 3.089 62 rounded to 4 s.f. A 3.089 B 3.0896 C 3.09 D 3.090 e 19.963 rounded to 3 s.f. A 2 B 20 C
Round each number to the stated number of significant figures (s.f.).a 135 (1 s.f.) b 45 678 (2 s.f.) c 18.654 (3 s.f.)d 0.0931 (1 s.f.) e 0.7872 (2 s.f.) f 1.409 48 (4 s.f.)g 985 (1 s.f.) h 0.697 (2 s.f.) i 8.595 (3 s.f.)
Work with a partner to discuss the answers to this question.This is part of Harry’s homework.Harry has rounded one large number and one small number to two significant figures.Both of his answers are wrong.a Explain the mistakes he has made.Write the correct answers.b What must you remember to do
Round each of these numbers to one significant figure (1 s.f.).Choose the correct answer: A, B or C.a 352 A 4 B 40 C 400 b 7.291 A 7 B 7.3 C 7.29 c 11 540 A 12 000 B 10 000 C 11 000 d 0.0087 A 9 B 0.09 C 0.009
Round each of these numbers to two significant figures (2 s.f.).All the answers are in the cloud.a 243 b 0.235 c 24.15 d 0.002 380 1 e 2396 f 2.3699 0.0024 0.24 2.4 24 240 2400
a Round 4286 to one significant figure.b Round 0.080 69 to three significant figures.c Round 0.7963 to two significant figures.
Look at these two questions.a 56 × 0.1 b 3.2 ÷ 0.01 Explain to a partner the methods you would use to work out the answers to these questions.Explain why you would use these methods.Does your partner use the same methods?If they use different methods, do you understand their methods?
This is part of Harsha’s homework.Write down one example to show that each of these statements is not true.a When you multiply a number other than zero by 0.1 you will always get an answer that is greater than zero.b When you divide a number with one decimal place by 0.01 you will always get an
Razi thinks of a number. He multiplies his number by 0.1, and then divides the answer by 0.01.Razi then divides this answer by 0.1 and gets a final answer of 12 500.What number does Razi think of first?Explain how you worked out your answer.
a Sort these expressions into groups of the same value.There should be one expression left over.A 24 × 0.1 B 240 × 0.1 C 2.4 ÷ 0.01 D 24 ÷ 0.01 E 2.4÷0.1 F 240 × 0.01 G 24 ÷ 0.1 H 0.24 ÷ 0.01 I 2400 × 0.1 J 0.24÷0.1 b Write two new expressions that have the same value as the
A jeweller uses this formula to work out the mass of copper in green gold.a Work out the mass of copper in 125 g of green gold.The jeweller uses this formula to work out the mass of zinc in yellow gold.b Work out the mass of zinc in 80 g of yellow gold.The jeweller says, ‘I think that 10% of
Which of 0.1 or 0.01 goes in each box? PP d 26x=0.26 7=70 b 3.4=34 C e 8.99 = 0.899 f 52 x 0.06 = 0.0006 =520
Which symbol, × or ÷, goes in each box? a 6.7 0.1=67 b 4.5 0.01=0.045 d 550 0.01 5.5 e 0.23 0.1 2.3 C 0.9 0.1=0.09 f 12 0.011200
Jake works out 23 × 0.1 and 8.3 ÷ 0.01 He checks his answers by using an inverse operation.Work out the answers to these questions.Check your answers by using inverse operations.a 18 × 0.1 b 23.6 × 0.01 c 0.6 ÷ 0.1 d 4.5 ÷ 0.01 i 23x 0.1=2310 = 2.3 Check: 2.3x 10 = 23 8.3 0.01 = 8.3x 100 =
8 Work out a 7 ÷ 0.1 b 4.5 ÷ 0.1 c 522 ÷ 0.1 d 0.67 ÷ 0.1 e 2 ÷ 0.01 f 8.5 ÷ 0.01 g 0.32 ÷ 0.01 h 7.225 ÷ 0.01
Work with a partner or in a small group to discuss this question.Win uses equivalent calculations to work out 3.2 ÷ 0.1 and 12.8 ÷ 0.01 This is what she writes.a Can you explain how Win’s method works? Do you like her method?Explain your answer.b Work out 0.45 ÷ 0.1 and 78 ÷ 0.01 using
Copy and complete these calculations.All the answers are in the cloud. a 4 0.01 4100=| 40 40000 400 4000 b 40 0.01 40100=| C 400 0.01 400 x 100 = P 0.4 0.01 0.4 100=|
Copy and complete these calculations.All the answers are in the cloud. a 2+0.1=210=| b 20 0.1 20x10 = 200 2000 2 20 200 0.1 200 10= d 0.2 0.1 0.2 10=
Work out a 62 × 0.1 b 55 × 0.1 c 125 × 0.1 d 3.2 × 0.1 e 37 × 0.01 f 655 × 0.01 g 750 × 0.01 h 4 × 0.01
Work with a partner or in a small group to discuss this question.Sofia and Arun are discussing the best way to work out 56 × 0.1a Can you explain how both of these methods work?Whose method do you prefer?b Describe how you would work out 56 × 0.01 using Sofia’s method and using Arun’s method.
Copy and complete these calculations.All the answers are in the cloud. a b C 4000.01 400100=| 40 0000.01 = 40 000 100=| 400.01 40 100= d 4000 0.01 4000100=| 0.4 40 400 4
Copy and complete these calculations.All the answers are in the cloud. a 200.1 20 10=|||| b 2000.1 20010=| C 20000.1 200010=| d 20.1=210=
Work out a 32 × 0.1 b 4.2 × 0.01 c 6 ÷ 0.1 d 4.156 ÷ 0.01
4 Round each number to the given degree of accuracy.a 4.587 (2 d.p.) b 0.672 315 (4 d.p.)c 54.788 99 (3 d.p.) d 12.050 299 7 (5 d.p.)
3 Write the correct answer, A or B, for each part.Round each number to one decimal place.a 7.23 A 7.2 B 7.3 b 12.45 A 12.4 B 12.5 c 0.793 A 0.7 B 0.8
Work out a 70 ÷ 10 b 342 ÷ 10 c 140 ÷ 100 d 3120 ÷ 100

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