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Whiteboardmaths.com © 2009 All rights reserved 5 7 2 1

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Guidance Notes for Teachers Some indication of content and range at level 1 and 2 is shown on the next slide. Relevant slides show all the diagrams/questions/answers that are required. End slides have student question sheets and a teacher question/answer sheet. End slides have printable worksheets for students. Calculator symbols are suggestions only and could be removed depending on the group. The vast majority of questions in this presentation are designed to be non- calculator. Many people may find the result of the investigation on slide 19 surprising and it naturally leads to further investigation. The basic reason is that petrol is made up of hydrocarbons and since carbon has a relative atomic mass of 12 most of the petrol is carbon atoms. During combustion each of these join with two oxygen atoms (relative atomic mass 16) to become CO 2. Generic Advice: The preparation below is advisable in the majority of presentations. 1.Print off the teacher question and answer sheets/worksheets 2.Print off the student question sheets/worksheets 3.Run through the presentation yourself answering the questions 4.Decide how you are going to deliver the presentation. (a) Are you going to go through it from start to finish with the class, perhaps using it as an example/demonstration of functional maths and focusing on the development of the processing skills involved at each stage? (b) Are you going to use only part of the presentation? (c) Are you simply going to use the presentation to introduce the activity and let the class work on their own through the question sheets but refer to some of the elements/answers within the presentation when needed? 5.Remember the slides are editable so if you wish to introduce an open question/small investigation of your own then simply choose the relevant slide add/delete your own text (using a text box if needed).

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Content and Skills Coverage and range: Level 1 Understand and use whole numbers and recognise negative numbers in practical contexts Add, subtract, multiply and divide using a range of mental methods Multiply and divide whole numbers by 10 and 100 using mental arithmetic Understand and use equivalences between common fractions, decimals and percentages Add and subtract decimal up to two decimal places Solve simple problems involving ratio, where one number is a multiple of the other Use simple formulae expressed in words for one- or two-step operations Solve problems requiring calculation with common measures including money, time, length, weight, capacity and temperature Convert units of measure in the same system Work out areas, perimeters and volumes in practical situations Construct models and draw shapes, measuring and drawing angles and identifying line symmetry Extract and interpret information from tables, diagrams, charts and graphs Collect and record discrete data and organise and represent information in different ways Find mean and range Use probability to show that some events are more likely to occur than others Understand outcomes, check calculations and explain results Understand and use positive and negative numbers of any size in practical contexts Carry out calculations with numbers of any size in practical contexts Understand, use and calculate ratio and proportion, including problems involving scale Understand and use equivalences between fractions, decimals and percentages Add and subtract fractions; add, subtract, multiply and divide decimals to a given number of decimal places Understand and use simple equations and simple formulae involving one- or two-step operations Recognise and use 2D representations of 3D objects. Find area, perimeter and volume of common shapes Use, convert and calculate using metric and, where appropriate, imperial measures Collect and represent discrete and continuous data, using ICT where appropriate Use and interpret statistical measures, tables and diagrams, for discrete and continuous data using ICT where appropriate Use statistical methods to investigate situations Use a numerical scale from 0 to 1 to express and compare probabilities Title: Car Emissions Content and skills covered Coverage and range: Level 2 At least 1 from each area

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What mathematics might be involved with car emissions?

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Fuel Bands A B C D E F G CO 2 emissions figure (g/km) Fuel Economy ≤ 100 101-120 121-150 151-165 166-185 186-225 226 + This fuel economy chart shows the banding of cars from band A (green) to band G (red). The numbers represent CO 2 emissions in g/km. As an example, a car with a 200 g/km CO 2 emission would be placed in band F. F 200 g/km Q1. What is the maximum CO 2 emission for a car in Band E? 185 g/km Q2. What is the minimum CO 2 emission for a car in Band C? 121 g/km

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A B C D E F G CO 2 emissions figure (g/km) Fuel Economy ≤ 100 101-120 121-150 151-165 166-185 186-225 226 + This fuel economy chart shows the banding of cars from band A (green) to band G (red). The numbers represent CO 2 emissions in g/km. As an example, a car with a 200 g/km CO 2 emission would be placed in band F. F 200 g/km Q3. What is the mean value of the CO 2 emissions for a car in Band C? 135.5 g/km Q4. What is the range of CO 2 emissions for a band F car? 39 g/km *

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A B C D E F G CO 2 emissions figure (g/km) Fuel Economy ≤ 100 101-120 121-150 151-165 166-185 186-225 226 + This fuel economy chart shows the banding of cars from band A (green) to band G (red). The numbers represent CO 2 emissions in g/km. As an example, a car with a 200 g/km CO 2 emission would be placed in band F. F 200 g/km Q5. Which band has the lowest range for CO 2 emissions? Band D (14g/km) Q6. Which two bands have the same range for CO 2 emissions? Bands B & E *

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Car Table MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Q 7. The table below gives some data on a variety of cars. Use the fuel economy chart to complete the missing entries in the banding column. C G D B E F Q 8. Which car has the lowest annual fuel cost? Mazda 3 Q 9. What is the range in engine sizes in (a) litres (b) cm 3 3.2 l 3200 cm 3 *

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MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Q 10. How many miles would you expect to get from 5 gallons of diesel when urban driving a Mazda 3? (2 sig fig) C G D B E F Q 11. How many litres would this be? 210 Q 12. One car should get 422 miles from 10 gallons of petrol when the mpg is combined. Which one? 22½ Fiat Bravo *

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MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Q 13. What is the median mpg for extra urban driving for this group of cars? C G D B E F Q 14. How many miles would you expect to get from 45 litres of petrol when driving the BMW (extra urban). 50.4 Q 15. What is the annual saving when driving a Mazda 3 rather than an Avensis? 332 £439 *

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MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Q 16. What is the ratio of diesel to petrol cars in this table? C G D B E F Q 17. What fraction of the cars in the table have an extra urban mpg greater than 50? 2 : 5 Q 18. What is the mean and range of the CO 2 emissions for the cars shown in the table? (you may use a calculator) 4/7 Mean = 170 g/km, range = 147 g/km

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MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Q 19. If a Ford Focus went on a journey of 850 km, calculate how much CO 2 would be emitted in kg. (3 sig fig) C G D B E F 127 kg Q 20. Emma drives 25 000 km/year in her BMW. By how much would she reduce her CO 2 emissions if she changed her car to an Avensis? Give your answer in (a) kg (b) tonnes 1975 kg 1.975 T *

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Car Tax BandsCO 2 Emissions g/km12 Months6 months A Up to 100 N/A B 101 - 110 £35N/A C 111 - 120 £35N/A D 121 - 130 £120£66.00 E131 - 140 £120£66.00 F141 - 150 £125£68.75 G151 - 165 £150£82.50 H166 - 175 £175£96.25 I176 - 185 £175£96.25 J186 - 200 £215£118.25 K201 - 225 £215£118.25 L226 - 255 £405£222.75 MOver 255 £405£222.75 For cars registered on or after 1 March 2001: Prices correct as at May 2009 The table below is an expanded version of the earlier fuel economy table and is used to work out how much vehicle tax a driver has to pay each year. Q 21 Why do you think that bands L and M are so much higher than the other bands? Government encouraging people to buy more fuel efficient cars.

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BandsCO 2 Emissions g/km12 Months6 months A Up to 100 N/A B 101 - 110 £35N/A C 111 - 120 £35N/A D 121 - 130 £120£66.00 E131 - 140 £120£66.00 F141 - 150 £125£68.75 G151 - 165 £150£82.50 H166 - 175 £175£96.25 I176 - 185 £175£96.25 J186 - 200 £215£118.25 K201 - 225 £215£118.25 L226 - 255 £405£222.75 MOver 255 £405£222.75 For cars registered on or after 1 March 2001: Prices correct as at May 2009 The table below is an expanded version of the earlier fuel economy table and is used to work out how much vehicle tax a driver has to pay each year. Q 22 Is it more economical to purchase 1 years tax or 6 months tax. 1 year *

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BandsCO 2 Emissions g/km12 Months6 months A Up to 100 N/A B 101 - 110 £35N/A C 111 - 120 £35N/A D 121 - 130 £120£66.00 E131 - 140 £120£66.00 F141 - 150 £125£68.75 G151 - 165 £150£82.50 H166 - 175 £175£96.25 I176 - 185 £175£96.25 J186 - 200 £215£118.25 K201 - 225 £215£118.25 L226 - 255 £405£222.75 MOver 255 £405£222.75 For cars registered on or after 1 March 2001: Prices correct as at May 2009 The table below is an expanded version of the earlier fuel economy table and is used to work out how much vehicle tax a driver has to pay each year. Q 23 How much money do you save if you drive a band J car and purchase 12 months tax rather than two lots of 6 months? £21.50 *

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BandsCO 2 Emissions g/km12 Months6 months A Up to 100 N/A B 101 - 110 £35N/A C 111 - 120 £35N/A D 121 - 130 £120£66.00 E131 - 140 £120£66.00 F141 - 150 £125£68.75 G151 - 165 £150£82.50 H166 - 175 £175£96.25 I176 - 185 £175£96.25 J186 - 200 £215£118.25 K201 - 225 £215£118.25 L226 - 255 £405£222.75 MOver 255 £405£222.75 For cars registered on or after 1 March 2001: Prices correct as at May 2009 The table below is an expanded version of the earlier fuel economy table and is used to work out how much vehicle tax a driver has to pay each year. Q 24 Excluding Band A cars, what is the median cost of 12 months tax. £162.50 *

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BandsCO 2 Emissions g/km12 Months6 months A Up to 100 N/A B 101 - 110 £35N/A C 111 - 120 £35N/A D 121 - 130 £120£66.00 E131 - 140 £120£66.00 F141 - 150 £125£68.75 G151 - 165 £150£82.50 H166 - 175 £175£96.25 I176 - 185 £175£96.25 J186 - 200 £215£118.25 K201 - 225 £215£118.25 L226 - 255 £405£222.75 MOver 255 £405£222.75 For cars registered on or after 1 March 2001: Prices correct as at May 2009 Q 25 The cost of 12 months tax for a Band B car is what percentage of the cost of a Band H car. 20 % Q 26 Write the Q25 answer as (a) A fraction (b) A decimal 1/50.2 *

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Investigation MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Investigation: This investigation is based on urban driving a Honda Jazz. Assume that a Jazz has a petrol tank with a capacity of 40 litres and a fuel consumption of 15 km/litre. Petrol has a density of 0.7g/cm 3. Use these facts together with its CO 2 emissions to compare the weight of petrol in a full tank with the weight of CO 2 produced when the car is driven from full tank empty tank. C G D B E F

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MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles Investigation: 0.7 g/cm 3 = 700 g/litre 2800 g = 28 kg So weight of petrol in a full tank = 28 kg. C G D B E F Distance driven on full tank = 15 x 40 = 600 km Weight of emitted CO 2 = 600 x 129g = 77400g = 77.4 kg A RATHER STARTLING FACT!!

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Teacher Q + A Q 1. What is the maximum CO 2 emission for a car in Band E? 185 g/km Q 2. What is the minimum CO 2 emission for a car in Band C? 121 g/km Q 3. What is the mean value of the CO 2 emissions for a car in Band C? 135.5 g/km Q 4. What is the range of CO 2 emissions for a band F car? 39 g/km Q 5. Which band has the lowest range for CO 2 emissions? Band D (14g/km) Q 6. Which two bands have the same range for CO 2 emissions? Bands B & E Q 7. The table below gives some data on a variety of cars. Use the fuel economy chart to complete the missing entries in the banding column. C, G, D, B,E,F Q 8. Which car has the lowest annual fuel cost? Mazda 3 Q 9. What is the range in engine sizes in (a) litres (b) cm 3 3.2 l 3200 cm 3 Q 10. How many miles would you expect to get from 5 gallons of diesel when urban driving a Mazda 3? (2 sig fig) Q 11. How many litres would this be? 210 Q 12. One car should get 422 miles from 10 gallons of petrol when the mpg is combined. Which one? 22½ Fiat Bravo Q 13. What is the median mpg for extra urban driving for this group of cars? Q 14. How many miles would you expect to get from 45 litres of petrol when driving the BMW (extra urban). 50.4 Q 15. What is the annual saving when driving a Mazda 3 rather than an Avensis? 332 £439 Teacher Q + A (1)

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Q 16. What is the ratio of diesel to petrol cars in this table? Q 17. What fraction of the cars in the table have an extra urban mpg greater than 50? 2 : 5 Q 18. What is the mean and range of the CO 2 emissions for the cars shown in the table? (you may use a calculator) 4/7 Mean = 170 g/km, range = 147 g/km Q 19. If a Ford Focus went on a journey of 850 km, calculate how much CO 2 would be emitted in kg. (3 sig fig) 127 kg Q 20. Emma drives 25 000 km/year in her BMW. By how much would she reduce her CO 2 emissions if she changed her car to an Avensis? Give your answer in (a) kg (b) tonnes 1975 kg1.975 T Q 21 Why do you think that bands L and M are so much higher than the other bands? Government encouraging people to buy more fuel efficient cars. Q 22 Is it more economical to purchase 1 years tax or 6 months tax. 1 year Q 24 Excluding Band A cars, what is the median cost of 12 months tax. £162.50 Q 23 How much money do you save if you drive a band J car and purchase 12 months tax rather than two lots of 6 months. £21.50 Q 25 The cost of 12 months tax for a Band B car is what percentage of the cost of a Band H car. 20 % Q 26 Write the Q25 answer as (a) A fraction (b) A decimal 1/5 0.2 Investigation: This investigation is based on urban driving a Honda Jazz. Assume that a Jazz has a petrol tank with a capacity of 40 litres and a fuel consumption of 15 km/litre. Petrol has a density of 7g/cm 3. Use these facts together with its CO 2 emissions to compare the weight of petrol in a full tank with the weight of CO 2 produced when the car is driven from full tank empty tank. (See slide 18) Teacher Q + A (2)

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Student Question Sheet Q 1. What is the maximum CO 2 emission for a car in Band E? Q 2. What is the minimum CO 2 emission for a car in Band C? Q 3. What is the mean value of the CO 2 emissions for a car in Band C? Q 4. What is the range of CO 2 emissions for a band F car? Q 5. Which band has the lowest range for CO 2 emissions? Q 6. Which two bands have the same range for CO 2 emissions? Q 7. The table below gives some data on a variety of cars. Use the fuel economy chart to complete the missing entries in the banding column. Q 8. Which car has the lowest annual fuel cost? Q 9. What is the range in engine sizes in (a) litres (b) cm 3 Q 10. How many miles would you expect to get from 5 gallons of diesel when urban driving a Mazda 3? (2 sig fig) Q 11. How many litres would this be? Q 12. One car should get 422 miles from 10 gallons of petrol when the mpg is combined. Which one? Q 13. What is the median mpg for extra urban driving for this group of cars? Q 14. How many miles would you expect to get from 45 litres of petrol when driving the BMW (extra urban). Q 15. What is the annual saving when driving a Mazda 3 rather than an Avensis? Student Questions (1)

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Q 16. What is the ratio of diesel to petrol cars in this table? Q 17. What fraction of the cars in the table have an extra urban mpg greater than 50? Q 18. What is the mean and range of the CO 2 emissions for the cars shown in the table? (you may use a calculator) Q 19. If a Ford Focus went on a journey of 850 km, calculate how much CO 2 would be emitted in kg. (3 sig fig) Q 20. Emma drives 25 000 km/year in her BMW. By how much would she reduce her CO 2 emissions if she changed her car to an Avensis? Give your answer in (a) kg (b) tonnes Q 21 Why do you think that bands L and M are so much higher than the other bands? Q 22 Is it more economical to purchase 1 years tax or 6 months tax. Q 24 Excluding Band A cars, what is the median cost of 12 months tax. Q 23 How much money do you save if you drive a band J car and purchase 12 months tax rather than two lots of 6 months. Q 25 The cost of 12 months tax for a Band B car is what percentage of the cost of a Band H car. Q 26 Write the Q25 answer as (a) a fraction (b) a decimal Investigation: This investigation is based on urban driving a Honda Jazz. Assume that a Jazz has a petrol tank with a capacity of 40 litres and a fuel consumption of 15 km/litre. Petrol has a density of 7g/cm 3. Use these facts together with its CO 2 emissions to compare the weight of petrol in a full tank with the weight of CO 2 produced when the car is driven from full tank empty tank. (See slide 18) Student Questions (2)

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Worksheet 1 A B C D E F G CO 2 emissions figure (g/km) Fuel Economy ≤ 100 101-120 121-150 151-165 166-185 186-225 226 + This fuel economy chart shows the banding of cars from band A (green) to band G (red). The numbers represent CO 2 emissions in g/km. As an example, a car with a 200 g/km CO 2 emission would be placed in band F. F 200 g/km Worksheet 1

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Worksheet 2 MakeModel Engine Size (litres) Fuel Type MPG Urban MPG Extra Urban MPG Combined CO 2 Emissions g/km Band *Fuel Cost/ year HondaJazz1.2Petrol41.560.151.4129 £934 BMW7 series4.4Petrol17.233.224.8266 £1936 FordFocus2.0Diesel38.760.149.6149C £1100 FiatBravo1.4Petrol32.550.442.2158 £1138 MazdaMazda 31.6Diesel42.774.362.8119 £869 RenaultLaguna2.0Petrol26.545.035.9185£1337 ToyotaAvensis1.8Petrol26.444.836.7187£1308 *Estimated based on 12 000 miles * Worksheet 2

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Worksheet 3 BandsCO 2 Emissions g/km12 Months6 months A Up to 100 N/A B 101 - 110 £35N/A C 111 - 120 £35N/A D 121 - 130 £120£66.00 E131 - 140 £120£66.00 F141 - 150 £125£68.75 G151 - 165 £150£82.50 H166 - 175 £175£96.25 I176 - 185 £175£96.25 J186 - 200 £215£118.25 K201 - 225 £215£118.25 L226 - 255 £405£222.75 MOver 255 £405£222.75 For cars registered on or after 1 March 2001: Prices correct as at May 2009 The table below is an expanded version of the earlier fuel economy table and is used to work out how much vehicle tax a driver has to pay each year. * Worksheet 3

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