KEY SKILLS APPLICATION OF NUMBER Level 3 [KSA3N2] Question Paper. 18 November 2002

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1 KEY SKILLS APPLICATION OF NUMBER Level 3 [KSA3N2] Question Paper 18 November 2002 WHAT YOU NEED This Question Paper An Answer Booklet A pen with black or blue ink Pencils You may use a bilingual dictionary An eraser A ruler marked in mm and cm 2mm squared paper A scientific calculator Do NOT open this Question Paper until you are told to by the invigilator THERE ARE 2 PARTS TO THIS TEST Part A (total 3) consists of 5 short-answer questions Part B (total 18 marks) consists of 1 extended-answer question Total marks available: 50 Try to answer ALL the questions TIME ALLOWED: 1 HOUR 30 MINUTES INSTRUCTIONS Ensure that your personal details are entered correctly on the front of the Answer Booklet Read each question carefully Write in black or blue ink only Make sure that your writing is clear, and show all your working If you need extra paper, use a second Answer Booklet. Make sure you put your personal details on the front of the second Answer Booklet At the end of the test, hand the Question Paper, your Answer Booklets and all notes to the invigilator REMEMBER: YOU HAVE 1 HOUR 30 MINUTES TO FINISH THE TEST

2 Part A Short-answer questions 1 A shop advertises for an assistant manager. How much does the assistant manager earn in his or her first 52 weeks? 2

3 2 An electricity supplier guarantees that prices will not increase in the next year. A householder agrees to pay a fixed amount each month to cover her electricity bills. To estimate the fixed monthly amount she records the units used from the last four quarterly bills. Number of units used Price per unit First quarter Second quarter Third quarter Fourth quarter p p p p She looks carefully at the second quarter bill to see how the charges are calculated. VAT is calculated on both the costs of the units and the quarterly standing charge. Second Quarter Electricity Bill Number of units used Price per unit Cost p Quarterly standing charge Sub total Plus 5% Total charge for the quarter a b How much is the total charge for all the four quarters? 3 marks Calculate an estimate of the minimum amount the householder needs to pay each month over the next year to cover her electricity bills. 3 Turn Over

4 3 The label on a container of fresh semi-skimmed milk has this nutritional information. Typical values per 250ml serving Energy Protein 8.5g Carbohydrate: Total content 12.5g of which sugars 12.5g starch nil 516kJ (123kcal) Fat: Total content 4.3g of which saturated content 2.5g Fibre nil Sodium 0.1g Calcium 305mg** RDA = recommended daily allowance (**38% of RDA) a Calculate the percentage of the fat that is saturated in semi-skimmed milk litres are equivalent to 6 pints b c Calculate the number of pints in one serving (250ml) of semi-skimmed milk. How many pints of semi-skimmed milk are needed to provide the recommended daily allowance (RDA) of calcium? d A pudding recipe requires pint of semi-skimmed milk. How many kcal of energy does this contribute to the pudding? Show how you can check your answer by estimation

5 Please go on to the next page 5 Turn Over

6 4 A toilet cistern is 12 centimetres from front to back and has a cross-section that is a trapezium. At normal water level the vertical depth of the water is 30 centimetres. Diagram of a toilet cistern 12cm 40cm Diagram not to scale 30cm 12cm 25cm a Calculate the number of litres of water in the cistern when it is at the normal water level. A washing machine uses 65 litres per wash. The toilet cistern empties completely at each flush. On one day the washing machine is used once and the toilet is flushed 15 times. b Calculate the number of litres of water used during the day for the washing machine and the toilet. 6

7 An ecological builder installs a rainwater tank that collects rainwater falling on a house. A scale plan of the house shows that it is rectangular in shape. House Scale: 1cm = 4m The average daily rainfall is 2mm over any given area. c Calculate the average number of litres of water falling on the house per day. The builder installs a cylindrical rainwater tank, 2 metres high with a diameter of 1.5 metres. Volume of the tank (cubic metres) = 3.14 x r 2 h where r = radius of the tank in metres h = height of the tank in metres d e Calculate an estimate of how many days it will take to fill the tank with rainwater from the roof. The tank contains litres of rainwater. 3 marks The washing machine is used once per day and the toilet 15 times per day. Both use water from the rainwater tank. How many complete days will the rainwater tank supply the washing machine and the toilet, assuming there is no rainfall? 7 Turn Over

8 5 A group of students goes to a burger bar for lunch on three successive days. Their orders are as follows a Number of Number of burgers cheeseburgers Total cost ordered ordered Day Day Day Form two equations about the costs of orders on Day 1 and Day 2 from the information in the table. Use the equations to calculate the cost of a burger and a cheeseburger. What is the total cost of the order on Day 3? 3 marks On a typical weekday, the burger bar is open from 8am until 12 midnight and the burgers are cooked at the following rates per hour Number of burgers cooked per hour Between Between Between Between 8am and 11am 11am and 2pm 2pm and 5pm 5pm and 12 midnight b Calculate the total number of burgers cooked on a typical weekday. At 12 noon on a weekday there are burgers in the freezer. c Draw a line graph to show the estimated stock levels of burgers in the freezer at 2pm, 5pm and 12 midnight. 3 marks 8

9 d The manager orders more burgers when stock levels fall below burgers. Use your graph to estimate the time when this may happen. On a Saturday, 60% more burgers are cooked than on a weekday. There are 600 burgers in the freezer at 8am and burgers are delivered at 11:30am. e Calculate an estimate of the number of burgers in the freezer at the end of the Saturday. 9 Turn Over

10 Part B Extended-answer question 6 A surveyor calculates the height of a building. He has no access to the building so calculates the height using the angle between the ground and the top of the building. He stands 100 metres away from the building and measures an angle of 25 as shown below. Diagram not to scale a Calculate the height of the building to the nearest metre. The building has 16 floors. Each floor is approximately 3 metres high. b Use this information to comment on the accuracy of your answer to part a. 10

11 Each floor of the building is identical, rectangular in shape and measures 45 metres by 40 metres. On each floor 195 square metres of floor space are used for corridor, stair and lift access. c Recommend a suitable scale for a single floor plan of the building on an A4 sheet of paper (A4 is approximately 30cm by 21cm). Justify your answer. d Calculate the total working floor space area available within the whole building, excluding the corridor, stair and lift access areas. The first 2 floors of the building are let as retail shops. The next 6 floors are let as office space, and the top 8 floors are let as private accommodation. e What fraction of the total floor space let in the building is let as office space? The income generated from the different types of space is: RETAIL SHOPS: per square metre per year OFFICE SPACE: 160 per square metre per year PRIVATE ACCOMMODATION: 80 per square metre per year f When all the space is let, what is the ratio of income generated between shops, office space and private accommodation? The cost of renting office space is expected to increase by 6% per year for the next 3 years. g What will be the cost per square metre for renting office space after the yearly increases for all of the 3 years have been applied? 11 Turn Over

12 In the first 6 months that the building is open, the following income is generated. Month Income This data is used to estimate the expected income in month 8. h i Draw a suitable graph to investigate the trend in income over the first 8 months. Draw, by inspection, the line of best fit. j Use your graph to estimate the income in month 8. 4 marks k What assumption have you made in estimating the income for month 8? END OF TEST First published in Qualifications and Curriculum Authority Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Printed in Great Britain. The Qualifications and Curriculum Authority is an exempt charity under Schedule 2 of the Charities Act Qualifications and Curriculum Authority, 83 Piccadilly, London W1J 8QA. Ref: AoN/L3/1/P1 12