Unit 2: Section 1 - Pearson Schools

Exercise XXFor Questions 1–8, write each number in standard form.1 0.1 2 0.01 3 0.001 4 0.000115 ​____1000 ​ 6 ___ ​ 1100 7 10 8 1For Questions 9–16, write each one as an ordinary number.9 10 23 10 10 25 11 1.2 3 10 23 12 8.7 3 10 2113 10 26 14 10 24 15 4.67 3 10 22 16 3.4 3 10 24For Questions 17–24, write each number in standard form.17 0.543 18 0.0708 19 0.007 20 0.000921 0.67 22 0.007 07 23 100 24 1000For Questions 25–34, write each one as an ordinary number.Check your answers with a calculator.25 10 22 3 10 4 26 10 3 3 10 2127 10 2 4 10 22 28 10 3 4 10 2329 (3.2 3 10 22 ) 3 (4 3 10 3 ) 30 (2.4 3 10 22 ) 4 (8 3 10 21 )31 (6 3 10 21 ) 4 (2 3 10 22 ) 32 (4 3 10 23 ) 3 (9 3 10 2 )33 (2 3 10 22 ) 3 (9 3 10 21 ) 34 (3.6 3 10 22 ) 4 (1.2 3 10 23 )Exercise XX*For Questions 1–8, write each answer as an ordinary number.1 10 3 3 10 22 2 10 21 3 10 22 3 10 22 1 10 23 4 10 21 2 10 235 10 24 3 10 2 6 10 23 3 10 21 7 10 23 1 10 24 8 10 23 2 10 21For Questions 9–16, write each answer in standard form.9 10 4 10 22 10 10 2 4 10 22 11 10 21 4 10 22 12 10 24 4 10 2313 10 3 4 10 21 14 10 21 4 10 3 15 10 22 4 10 24 16 10 25 4 10 22You will need the information given in the margin to answer Questions 17 and 18.17 How many viruses, to the nearest thousand, can be placed in a straight line across thewidth of a human hair?18 How many viruses, to the nearest thousand, can be placed in a straight line across thewidth of a pin?19 The radius of the nucleus of a hydrogen atom is 1 3 10 212 mm. How many would fit in astraight line across a human hair of diameter 0.06 mm?20 The average mass of a grain of sand is 10 24 g. How many grains of sand are there in 2 kg?21 Devise a sensible method to work out (3.4 3 10 23 ) 1 (3.4 3 10 22 ).22 A molecule of water is a very small thing, so small that its volume is 10 227 m 3 .a How many molecules are there in 1 m 3 of water?If you wrote your answer in full, how many zero digits would there be?b If you assume that a water molecule is in the form of a cube, show that its side lengthis 10 29 m.c If a number of water molecules were placed touching each other in a straight line, howmany would there be in a line 1 cm long?Cough virus9.144 1 6 mm diameterHuman hair5 10 2 mm diameterPin6 10 1 mm diameterUnit 2: Section 111

d The volume of a cup of tea is 200 cm 3 .How many molecules of water would the cup hold?If all these were placed end to end in a straight line, how long would the line be?Take the circumference of the Earth to be 40 000 km.How many times would the line of molecules go around the Earth?Four rules of fractionsThis section will give you practice in using fractions. The questions will help you to understandmuch of the algebra in this unit.Addition and subtractionA common denominator is required.Unit 2: Section 1Example 3 Example 4 Example 5Addition Subtraction With mixed fractions​ 3_ 4 ​1 ​1_ 63_4 ​2 ​2_ 5 ​ 3​1_ 3 ​2 1​3_ 4 ​5 __ ​ 912 ​1 __ ​ 212​5 ____ 1 2​912​5 __ ​1112 ​ 5 ​15 __20Multiplication and division​2 __ ​820​5 _____ 2 8​1520​5__​7Convert mixed fractions into improper fractions.20 ​ 5 ​10 __ 3 ​2 _​74 ​5 ______ 40 2 21​5 __ ​ 1912 ​12​5 1__​ 712 ​Example 6 Example 7Multiplication1​ 3_ 4 ​3 ​3_ 5 ​5_​ 7 4 ​3 ​3_ 5Cancelling1​5_ 9 ​3 2​1_ 7 ​____4 3 5 ​ 5 __ ​21 20​5 1​1__20 ​ 5 ​14 __ 9​3 __ ​157​5 ______ 3 15​149 3 7 ​Divide top and bottom by 7, and by 3.5 ​ ____ 2 3 5 ​5 __ ​103 ​5 3​1_ 3 ​​5 ​73 33 3 1Example 8 Example 9DivisionMultiplying with a whole number.​ 3_ 4​÷ ​5113_4 ​3 7Turn the divisor upside down and multiply. Change the whole number into a fraction.5 ​ 3_ 4​3 ​11​5 3 11​3 ​5 ​3320​5 1​1320 ​ 5 ​3_ 4 ​3 _​7 1​5 ____ 3 7​34 3 1​5 ​214 ​5 5​1_ 4 ​54 3 5Example 10Dividing into a whole number.8 ÷ 1​ 1_ 2 ​5 ​ 8_ 1 ​÷ ​3_ 2 ​5 ​8_ 1 ​3 ​2_ 3​5 ____ 3 2​8 ​5 __ ​163 ​5 5​1_ 3 ​1 3 312

Exercise XXWork these out.1 ​ 2_ 7 ​1 ​4_ 7 2 ​1_ 9 ​1 ​4_ 9 3 __ ​ 310​1 __ ​110 ​ 4 ​3_ 8 ​1 ​1_ 8 ​5_​ 7 9 ​1 ​4_ 9 6 ​3_ 8 ​1 _​7 8 7 ​5_ 6 ​– ​1_ 3 8 __ ​11 20​– ​310 ​9 ​ 3_ 8​1 __​712 ​ 10 ​5_ 6 ​– ​3_ 4 ​ 11 3​1_ 4 ​1 1​1_ 6 ​ 12 4​3_ 5 ​– 2​1_ 2 ​13 ​ 5_ 6 ​3 ​1_ 3 ​ 14 ​3_ 8 ​3 ​4_ 7 ​ 15 ​3_ 4 ​÷ _​7 8 ​ 16 __ ​ 310 ​÷ ​4_ 5 ​17 4 3 ​ 320 ​ 18 ​2_ 3​3 5 19 ​1225 ​÷ 4 20 6 ÷ ​3_ 4 ​21 2​ 1_ 7 ​3 1​2_ 5 ​ 22 1​1_ 4 ​3 1​1_ 5 ​ 23 1​1_ 8 ​÷ ​3_ 4 ​ 24 3​3_ 8 ​÷ 1​1_ 4 ​25 2​ 5_ 6 ​1 1​3_ 4 ​ 26 3​7 _8 ​1 4​1_ 4​ 27 5​310​– 2​1120 ​ 28 36​3_ 8​– __32​729 1​ 3_ 5 ​3 3 30 1​7 _8 ​3 4 31 1​4_ 5 ​÷ 6 32 8 ÷ 1​1_ 3 ​12 ​Exercise XX*Work these out.1 ​ 1_ 3​1 ​512 2 ​1_ 4​1 ​920 3 ​5_ 6​2 __​730 4 __ ​11 15​2 ​320 ​5 ​ 1_ 5​1 ​310​1 ​920 ​ 6 ​1_ 4​1 ​320​2 ​140 ​ 7 ​1_ 8 ​1 ​1_ 8 ​1 ​1_ 8 ​1 ​1_ 8 ​1 ​1_ 8 ​1 ​1_ 8 ​8 ​ 5_ 6 ​3 ​ 925 9 ​5_ 8 ​3 ​ 8 ​ 10 63 ​1_25 8 ​ 11 ​2_ 3​4 ​2021 ​12 ​ 815 ​4 ​5_ 6 ​ 13 ​2_ 3 ​4 3 14 ​2_ 3 ​4 2 15 ​1_ 2​3 ​15 ​3 ​4_1616 ​ 2_ 3​3 ​3_5 ​3 ​ 910 ​ 17 4​1_ 2 ​1 3​1_ 6 ​ 18 6​2_ 5 ​1 7​1_ 3 ​ 19 7​2_ 3 ​2 1​1_ 6 ​20 4​_ 7 9 ​2 3​1_ 3 ​ 21 7​2_ 3 ​2 ​8_ 9​ 22 6​112​2 __4​710 ​ 23 3​1_ 7 ​3 __ ​ 724 2​ 1_ 2 ​3 4​2_ 3​ 25 43 ​2_3 ​ 26 4​1_ 2 ​4 ​3_ 4 ​ 27 2​1_ 3 ​4 2​4_ 5 ​28 3​ 1_ 9 ​4 14 29 14 4 3​1_ 9 ​ 30 ​( 2​1_ 8 ​1 2​1_ 4 ​)​4 2​1_ 3 ​15 ​5 ​Unit 2: Section 1RatioExample 11A marinade in a recipe contains rice wine and soy sauce in the ratio 2 : 3.How much of each ingredient is needed for 100 ml of the mixture?(Add the ratios together: 2 1 3 5 5.)Then the parts are in the ratio ​ 2_ 5 ​: ​3_ 5 ​.Amount of rice wine 5 ​ 2_ 5 ​of 100 5 40 ml. Amount of soy sauce 5 ​3_ 5​of 100 5 60 ml.Exercise XX1 Divide $392 in the ratio of 3 : 4. 2 Divide 637 m in the ratio of 2 : 5.3 Divide 752 kg in the ratio of 1 : 7. 4 Divide 243 miles in the ratio of 4 : 5.5 Divide 984 in the ratio of 7 : 5. 6 Divide 405 in the ratio of 7 : 2.7 Divide 13.5 in the ratio of 3 : 2. 8 Divide 5.6 in the ratio of 4 : 3.13

Example 12Divide £1170 in the ratio of 2 : 3 : 4. (Add the ratios together: 2 1 3 1 4 5 9.)Then the first part 5 ​ 2_ 9​of £1170 5 £260.The second part 5 ​ 3_ 9​of £1170 5 £390.The third part 5 ​ 4_ 9​of £1170 5 £520. (Check: £260 1 £390 1 £520 5 £1170.)Unit 2: Section 1Exercise XX*1 Divide $120 in the ratio 3 : 5.2 Divide $350 in the ratio 1 : 6.3 The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil isrequired to make 1 litre of fuel?4 A chicken stock contains chicken bones and chicken pieces in the ratio 20 : 7.What weight of chicken pieces is needed to make 2 kg of stock?5 Divide 702 in the ratio 1 : 2 : 3.6 Divide 576 tonnes in the ratio 4 : 3 : 2.7 Mr Chan has three daughters, An, Lien and Tao, aged 7, 8 and 10 years respectively.He shares $100 between them in the ratio of their ages. How much does Lien receive?8 A breakfast cereal contains the vitamins thiamin, riboflavin and niacin in the ratio2 : 3 : 25. A bowl of cereal contains 10 mg of these vitamins. Calculate the amount ofriboflavin in a bowl of cereal.Positive integer powers of numbersPowers are used to write certain numbers in a convenient way. To help you understand how therules of indices work, study the table carefully.Operation Example RuleMultiplying 3 4 3 3 2 5 (3 3 3 3 3 3 3) 3 (3 3 3)5 3 6 5 3 4 1 2 5 729Dividing3 4 4 3 2 5_____________​ 3 3 3 3 3 3 3 ​5 33 3 32 5 3 4 2 2 5 9Raising to a power (3 4 ) 2 5 (3 3 3 3 3 3 3) 3 (3 3 3 3 3 3 3)5 3 8 5 3 4 3 2 5 6561Add the indices(a m 3 a n 5 a m 1 n )Subtract the indices(a m 4 a n 5 a m 2 n )Multiply the indices(a m ) n 5 a mnExample 13Write 30 5 in standard form30 5 5 (3 3 10) 5 5 3 5 3 10 5 5 243 3 10 5 5 2.43 3 10 7Write 4 5 as a power of 24 5 5 (2 2 ) 5 5 2 1014

Exercise XXWrite these as a single power and then calculate the answer.1 2 2 3 2 2 2 3 2 3 3 3 3 2 3 2 3 2 3 2 3 2 4 5 3 5 3 5 3 55 2 4 4 2 2 6 4 4 4 4 2 7 5 5 4 5 2 8 8 6 4 8 39 ​___ 383 2 ​ 10 ​___ 656 2 ​ 11 (2 2 ) 5 12 (2 4 ) 213 0.1 3 (0.1) 2 14 0.2 3 (0.2) 2 15 2.1 10 4 2.1 8 16 1.3 5 4 1.3 317 ​_______ 42 3 4 54 3 ​ 18_______​ 74 3 7 27 3 ​ 19 20 2 3 20 2 20 30 2 3 30 2Exercise XX*For Questions 1–16, write as a single power and then calculate the answer.1 8 4 3 8 5 4 8 6 2 9 4 3 9 5 4 9 6 3 (7 2 ) 3 4 7 3 4 (4 2 ) 4 4 4 45 5 5 4 25 6 4 6 4 64 7 216 4 6 2 8 2 10 4 5129 125 2 4 5 3 10 100 3 4 10 5 11 (10 3 ) 3 4 1000 12 (2 5 ) 3 4 4 313 8 4 4 4 6 14 27 3 4 9 4 15 ​_____ 125325 3 ​ 16________ 64​22 3 (2 5 ) 2 ​17 Given that 2 20 5 1 048 576, calculate 2 21 and 2 19 .18 Which is larger, 8 10 or 4 14 ?19 Which is larger, 3 27 or 9 13 ?20 A large sheet of paper is 0.1 mm thick. It is cut in half, and one piece is placed on top of theother. These two pieces are then cut in half a second time to make the pile four sheets thick.Unit 2: Section 1Copy and complete this table.No. of times done No. of sheets in pile Height of pile mm2 4 0.4351050How many times would you have to do this for the pile to reach the Moon, approximately3.84 3 10 5 km away?15

Direct proportionIn mathematics, there are many ways to relate two quantities together. Here are a few examples.Change of units: 1 mile 1.609 kmGradients: 1 in 5Velocities: 30 miles travelled in 1 hour (30 miles/hour)Scales: 1 : 50Bureau de Change 1 mile 1.6 kmUnit 2: Section 1Remember‘Per’ means divide. Forexample, ‘miles per hour’means miles divided byhours, or miles/hour.Exchange rates: £1 $1.60Ratio: 4 : 5Densities: 13 g is the mass of 1 cm 3 (13 g/cm 3 )Problem solving: 3.4 m of timber costs $6.80 ($2/m)Equations: 3x 5 16yGraphs(two axes)xTwo different ways of doing the same calculation are shown in Example 14.Example 14The committee that organised the Athens Olympics in 2004 recycled 108 tonnes ofpaper, saving 1836 trees and cutting energy consumption by 442 800 kW.Calculate the amount of energy saved by recycling one tonne of paper.Method 1 ‘unitary method’108 tonnes save 442 800 kWSo 1 tonne saves________ 442 800​ ​kW 5 4100 kW108Method 2 ‘per method’Total energy savedEnergy saved per tonne 5 ​________________​5________ 442 800​ ​5 4100 kW per tonneTotal tonnage 108Exercise XXFor Questions 1–6, find the exchange rate in the form £1 5 … .1 £6 5 ¥1080 2 US$15 5 £9 3 Aus$62 5 £264 £7 5 US$13 5 NZ$22 5 £8 6 Can$54 5 £247 4 m of timber costs $33.60.a What is the cost of 1 m?b What is the cost of 9 m?8 Three CDs cost $33.75.a What is the cost of one CD?b What is the cost of seven CDs?16

9 In one of the strongest hurricanes to sweep across South America, 63 cm of rainfell in 6 hours.a Find the amount of rain that fell in millimetres per hour.b Find the amount of rain that fell per minute.10 At blast off, the US Saturn rocket uses 104.5 tonnes of fuel in 9.5 s.a Find the amount of fuel used per second.b Find the amount of fuel used per minute.11 A military jet uses 3000 litres of fuel on a 45-minute flight.a For how long would it travel using 1 litre?b How many litres does it use in 1 minute?12 A spacecraft travelled 22 billion miles between 1977 and 1999.a Find, correct to 3 significant figures, its speed in miles per day.b Find, correct to 3 significant figures, its speed in miles per hour.Exercise XX*1 6 Hong Kong dollars can be exchanged for 80 Japanese yen.a How many dollars can be exchanged for 200 yen?b How many yen can be exchanged for 200 dollars?2 When 18 g of peanuts are burned, 390 kJ (kilojoules) of energy are produced.a How much energy is produced if 24 g of peanuts are burned?b How many grams of peanuts must be burned to produce 130 kJ?3 Red blood cells are replaced by the bone marrow at the rate of 8.28 3 10 9 per hour.How many are replaced per second?4 There are 25 3 10 11 red blood cells in the human body. Suppose that the total mass of redblood cells is 2.5 kg and the total volume is 2.75 litres.a Find the number of cells in 1 g.b Find the density of red blood cells in grams per cubic centimetre.(Give your answer as a fraction.)5 In its 12 years of life, it is estimated that a bird called the chimney swift flies 1.25 millionmiles and can sleep while flying.Approximately how far would you expect it to fly in 1 hour?6 It is estimated that by the age of 18, the average American child has seen 350 000commercials on television. How many is this per day, approximately?7 At full speed, the cruise ship QE 2 uses 40 000 litres of fuel in 55 minutes.a Find the time, in seconds, taken to use 1 m 3 of fuel.b Find the fuel consumption in litres per second.8 A supersonic aircraft uses 12 000 litres of fuel every 25 minutes.a Find the time, in seconds, taken to use 1 m 3 .b Find the fuel consumption in litres per second.9 Air bags in a car ‘explode’ at 340 km/h.a Convert this to metres per second.b How long would the air bag take to move 10 cm?Give your answer to the nearest thousandth of a second.10 In Portuguese (standard of Lisbon) wine measures, 1 quartilo 5 397 ml and1 almude 5 48 quartilos. Convert 1000 litres into almudes.Unit 2: Section 117

Converting measurementsConverting lengthsRemember10 mm 1 cm1000 mm 1 m100 cm 1 m1000 m 1 kmExample XXChange 3 km to cm.3 km 3 1000 m (as 1 km 1000 m) 3 1000 100 cm (as 1 m 100 cm) 3 10 5 cmExample XXChange 5 10 6 mm to km.5 10 6 mm _______​ 5 3 106 ​m (as 1000 mm 1 m)10005 3 10 ​_____________6​km (as 1000 m 1 km)1000 3 1000 5 kmUnit 2: Section 1Exercise XXFill in the gaps in the following table.km m cm mm1 52 83 20004 70005 50006 60007 10 68 10 7Exercise XX*Fill in the gaps in the following table.km m cm mm1 2.5 10 42 4.3 10 33 5 10 64 7 10 55 506 607 9 10 98 8 10 1118

9 A nanometre is 10 9 metres.a How many nanometres are there in 200 km?b How many km are there in 10 18 nanometres?10 A micrometre is 10 6 metres.a How many micrometres are there in 5000 km?b How many km are there in 10 15 micrometres?Converting areasA diagram is useful, as shown in the following examples.Example XXA rectangle measures 1 m by 2 m. Find the area in mm 2 .1 m is 1000 mm.2 m is 2000 mm.So the diagram is as shown on the right.So the area is 1000 2000 mm 2Example XXChange 30 000 cm 2 to m 2 . 2 000 000 mm 2 2 10 6 mm 21 m 2 1 m 1 m 100 cm 100 cm 10 000 cm 2So 30 000 cm 2 _______ 30 000​10 000 ​m2 3 m 22 m1000 mm 1 m1 m100 cm2000 mm100 cm 1 mUnit 2: Section 1Exercise XXFill in the gaps in the following table.km 2 m 2 cm 2 mm 21 22 43 504 805 6 10 66 3 10 77 10 138 10 1419

Exercise XX*Fill in the gaps in the following table.km 2 m 2 cm 2 mm 21 60002 40003 6 10 104 3 10 125 2 10 216 5 10 197 7 10 28 9 10 4Remember1 litre 1000 cm 3Converting volumesAgain diagrams are very helpful.Unit 2: Section 1Example XXA cuboid measures 1 m by 2 m by 3 m.Find the volume in mm 3 .1 m is 1000 mm.2 m is 2000 mm.3 m is 3000 mm.1000 mm2000 mm3000 mmSo the volume is 1000 2000 3000 mm 3 6 10 9 mm 3Example XXChange 10 7 cm 3 to m 3 .1 m 3 1 m 1 m 1 m 100 cm 100 cm 100 cm 10 6 cm 3100 cm100 cm100 cmSo 10 7 cm 3 ​____ 10710 6 ​m 3 10 m 320

Exercise XXFill in the gaps in the following table.km 3 m 3 cm 3 mm 31 12 23 84 65 4 10 36 5 10 57 10 158 10 149 How many litres are there in 1 m 3 ? 10 How many litres are there in 1 km 3 ?11 How many m 3 are there in 10 000 litres? 12 How many mm 3 are there in 10 litres?Exercise XX*Fill in the gaps in the following table.km 3 m 3 cm 3 mm 31 6002 5003 3 10 84 6 10 105 5 10 256 2 10 237 4 10 68 8 10 8Unit 2: Section 19 How many litres are there in 512 m 3 ? 10 How many litres are there in 12 km 3 ?11 How many m 3 are there in 10 6 litres? 12 How many mm 3 are there in 100 litres?13 A picometre is 10 12 m. How many cubic picometres are there in 1 km 3 ?14 Light travels at about 300 000 km/s. A light year is the distance light travels in one year.How many mm 3 are there in 1 cubic light year?Exercise XX (Revision)Calculate the following showing all of your working.1 ​ 3_ 7 ​1 ​2_ 5 ​ 2 ​3_ 7 ​2 ​2_ 5 ​ 3 ​3_ 7 ​3 ​2_ 5 ​4 ​ 3_ 7 ​4 ​2_ 5 ​ 5 2​3_ 5 ​1 1​1_ 7 ​ 6 2​3_ 5 ​2 1​1_ 7 ​7 2​ 3_ 5 ​3 1​1_ 7 ​ 8 2​3_ 5 ​4 1​1_ 7 ​9 Divide 36 m in the ratio of 1 : 2. 10 Divide 105 kg in the ratio of 3 : 4.21

Unit 2: Section 111 Divide $400 in the ratio of 2 : 3. 12 Divide 360 minutes in the ratio of 4 : 5.13 Divide £133 in the ratio of 1 : 2 : 4. 14 Divide 352 km in the ratio of 2 : 3 : 6.Write the following in standard form correct to 3 significant figures.15 0.012 345 16 0.012 35517 0.000 159 5 18 0.008 88819 (1.25 3 10 22 ) 3 (3.45 3 10 5 ) 20 (7.58 3 10 25 ) 3 (1.35 3 10 12 )21 (7.25 3 10 23 ) 3 (3.45 3 10 210 ) 22 (8.5 3 10 22 ) 3 (3.45 3 10 27 )23 (1.25 3 10 22 ) 4 (3.45 3 10 5 ) 24 (7.58 3 10 25 ) 4 (1.35 3 10 12 )25 (7.25 3 10 23 ) 4 (3.45 3 10 210 ) 26 (8.5 3 10 22 ) 4 (3.45 3 10 27 )27 Four tonnes of limestone blocks cost $600. Find the cost ofa 1 tonne b 11 tonnes c 500 kg.28 Seven identical pens cost €8.40. Find the cost ofa one pen b five pens. c a dozen pens.29 Stella Pajunas typed 216 words in 1 minute in Chicago, U.S.A. to set a new world record. Ifshe maintained this rate, how many words would you expect her to type ina 45 seconds b 50 seconds c an hour?30 Avind Pandya of India ran backwards from Los Angeles to New York, U.S.A. in 107 dayscovering 5000 km.a If he maintained this rate, how far would you expect him to travel ini 1 dayii a year?b How long would it have taken him to traveli 10 km ii 3500 m?c Calculate his speed in mm/sec writing your answer in standard form to 3 significantfigures.Exercise XX* (Revision)Calculate the following, showing all of your working.1 ​__ 2 ​ 3___​ 55 11 ​ 3 __ ​ 3 ​ 2 ​__ 1 ​1__​ 4 ​2___​ 28 3 7 15 ​ 3 ​4 __​4__​ 2 ​3___​ 35 7 14 ​4 ​ 1 __7​ 4 ​( 3 __5​)​ 2 5 1 3 1​ 1_ 2 ​3 1​1_ 3 ​3 1​1_ 4 ​3 1​1_ 5 ​3 1​1_ 6 ​3 1​1_ 7 ​6 ​( 2​ 3_ 7 ​)​2 4 ​( 1​ 3_ 7 ​)​27 The ratio of 5 : x is equal to the ratio of x : 20. Calculate the value of x.8 A bed of roses consists of m roses. The ratio of pink roses to white roses is 2 : 3.Find the number of pink roses expressed in terms of m.9 Xavier, Yi and Zazoo decide to share their lottery winnings of £11 000 such that Yi hasthree times as much as Zazoo and Xavier has a half of Yi’s winnings.How much should each receive?10 The plan for an office block is produced to a scale of 1 : 50.a Find the length, in mm, which represents the height of the building on the plan if theactual height is 25 m.b Find the area of the actual front door, in m 2 , if the door on the plan has an area of80 cm 2 .22

Write the following in standard form correct to 3 significant figures:11 (1.36 3 10 23 ) 2 12 (3.75 3 10 25 ) 2 3 (4.35 3 10 27 ) 213 √ ​ _____________5.785 3 10 212 ​ 14 √ ____________3.85 3 1029​ ​____________1.47 3 10 23 ​15 If p 5 9.47 3 10 25 and q 5 4.31 3 10 23 , find the following in standard form correct to3 significant figures.a pq b pq 2 c p 2 q d__​( ​ p 2q ​)​​16 The smallest mammal is the Kitti’s hog-nosed bat in Thailand which has a body length of29 mm. Find this length in km in standard form correct to 3 significant figures.17 The biggest known star is the M-class supergiant Betelgeuse which has a diameter of980 million km.a Assuming it to be a sphere, calculate its surface area in mm 2 , giving your answer instandard form correct to 3 significant figures.b Given that the Earth has a radius of 6370 km, express its surface area as a percentage ofBetelgeuse’s. Give your answer in standard form correct to 3 significant fgures.(The surface area of a sphere 5 4pr 2 , where r is the radius of the sphere.)18 Kaylan Ramji Sain of India grew a moustache to a length of 339 mm from 1976 until 1993.Calculate the speed of his moustache growth in km/s . Give your answer in standard formcorrect to 3 significant figures.Unit 2: Section 123