KEY SKILLSAPPLICATION OF NUMBER

Level 3[KSA31]

Question PaperMonday 12 January 2009

WHAT YOU NEED• This Question Paper • An eraser• An Answer Booklet • A ruler marked in mm and cm• A pen with black or blue ink • 2mm squared paper• Pencils • A scientific calculatorYou may use a bilingual dictionary

Do NOT open this Question Paper until you are told to by the invigilatorTHERE ARE TWO PARTS TO THIS TEST

Part A (total 35 marks) consists of 5 short-answer questionsPart B (total 15 marks) consists of 1 extended-answer question

Total marks available: 50

Try to answer ALL the questionsTIME ALLOWED: 15 MINUTES READING TIME PLUS 1 HOUR 30 MINUTES FOR THE TEST

INSTRUCTIONS• Ensure that your personal details are entered correctly on 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

invigilatorSPECIAL INSTRUCTIONSYou have 15 minutes to read through the paper prior to starting the test. Use this time toread through all the questions carefully, consider how you will attempt them and make roughnotes if you wish. Do not start writing in the Answer Book until you are told you can.

YOU WILL THEN HAVE 1 HOUR 30 MINUTES TO FINISH THE TESTFirst published in 2007.© Qualifications and Curriculum Authority 2007.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 1993.Qualifications and Curriculum Authority, 83 Piccadilly, London W1J 8QA. www.qca.org.ukRef: AON-L3-SQ-4-P3-V7.1-URN:655

2 Key skills application of number ⏐ Level 3 ⏐ January 2009 ⏐ URN:655

Part A – Short answer questions

1 Computer data can be stored using a variety of devices.

One of these devices, a floppy disk, can store 1.44 megabytes of data.

a How many bytes of data can a typical floppy disk store?1 mark

A 1.44Mb floppy disk costs 20p. A portable storage device that can store1 gigabyte of data costs £11.49.

b Which of these two storage devices offers better value for money forstoring computer data? Show calculations to support your answer.

3 marks

When computer files are compressed, the data requires less storage space.A computer file originally containing 174.54 megabytes only requires 74.65 megabytes of storage when compressed.

c Approximately, what is the ratio of the size of the original file to the sizeof the compressed file? Give your answer in a simple form.

1 markTotal 5 marks

1 kilobyte is equal to 1 024 bytes

1 megabyte (Mb) is equal to 1 024 kilobytes

1 gigabyte (Gb) is equal to 1 024 megabytes

2 A model maker has a model railway layout in his attic.

The model is built using a scale of 1 : 76. The model railway layout has a totalof 32.56 metres of track.

a How many kilometres of actual track does the model represent?1 mark

The longest continuous section of track measures 19.5 metres on the model.One of the model trains takes 1 minute 12 seconds to travel around this sectionof the track.

b What is the average speed, in metres per second, of this model train?1 mark

The model maker plans to extend his model railway layout by including a modelof an actual industrial estate to a scale of 1 : 76. The total area covered by theactual industrial estate is 2.8 hectares.

c How many square metres of floor area will be occupied by the modelindustrial estate in the model railway layout?

2 marksTotal 4 marks

Key skills application of number ⏐ Level 3 ⏐ January 2009 ⏐ URN:655 3

1 hectare is equal to 10 000 square metres

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3 The Royal Mint manufactures and distributes coins in the UK.

The table below gives numbers of coins of each type in circulation in the UK in 2005.

The Royal Mint has expressed concern over the large number of 1p coins incirculation, as many of these are inactive in jars and piggy banks in people’s homes.

a What percentage of the total number of coins in circulation in 2005 were 1p coins?

1 mark

The total value of all the coins in circulation in 2005 was £3 386.43 million.

b Approximately, what fraction of the total value of all the coins incirculation in 2005 was the value of the 1p coins? Give your answer in asimple form.

1 mark

On average, there were 2.5 people in each household in the UK in 2005.

c How many 1p coins were there, on average, in each household in the UK in 2005?

2 marks

d Show how to check your answer to part c by estimation without using acalculator.

1 mark

The population of the UK in 2005 was 6.02 x 107

A radio programme stated that if all the 10 586 million 1p coins in circulation inthe UK in 2005 were placed in a row as shown in the diagram below, the rowwould be long enough to go more than 5 times around the earth at the equator.

The diameter of a 1p coin is 2.03 centimetres.

e Was the statement made by the radio programme correct?Show calculations to support your answer.

3 marksTotal 8 marks

Key skills application of number ⏐ Level 3 ⏐ January 2009 ⏐ URN:655 5

The distance around the earth at the equator

is approximately 40 000 kilometres

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4 A gardener has a water feature in his garden.

The water feature consists of two ponds.

The larger pond is circular with sloping sides; its diameter is 2.4 metres at the surface and 2.0 metres at the bottom. The depth of this pond is 80 centimetres.

The gardener uses a pond cleaner to stop the water turning green. The amount ofpond cleaner needed depends on the volume of water in the pond. He uses theformula below to calculate the pond’s capacity.

a Use the gardener’s formula to calculate the capacity of the pond to thenearest 10 litres.

3 marks

where V is the capacity of the pond in cubic centimetres

d is the depth of the pond in centimetres

R is the radius at the surface of the pond in centimetres

r is the radius at the bottom of the pond in centimetres

The gardener wants to know how long it will take to fill the smaller pond withwater using his hose pipe. This hose pipe delivers sufficient water to fill a 2-gallon watering can in 45 seconds.

b How many litres of water does this hose pipe deliver per minute?1 mark

c Write an equation about the time (T) in minutes that it will take to fill apond with V litres of water, using this hose pipe.

1 mark

When full, the smaller pond holds 2 500 litres of water.

d Use your equation to calculate how long it will take to completely fill thesmaller pond with water using the hose pipe.

1 mark

To prevent the water in the pond turning green, the manufacturer recommendstreating the water every week using 1 kilogram of pond cleaner for every 5 000gallons of water. A 750-gram pack of the pond cleaner costs £28.95.

e How much will it cost the gardener to buy sufficient pond cleaner to treatthe smaller pond for a year?

3 marksTotal 9 marks

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1 gallon is equivalent to 4.5 litres

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5 A farmer plans to build an extension on an existing shed.

The angle of the slope of the roof of the extension must be the same as theangle of slope of the roof of the shed. The shed and the planned extension areshown in the simplified diagram below.

a What is the angle (A) of the slope of the roof of the shed?2 marks

b Show how to check your answer to part a.1 mark

The wall of the extension needs to be 3 metres high so that the extension canbe used to store farm machinery.

c At what distance (D) from the wall of the shed should the farmer buildthe wall of the extension?

2 marks

The farmer plans to concrete the floor of the extension. The area of the flooris 82.5 square metres and the concrete needs to be 120 millimetres deep.To make the concrete the farmer needs to mix cement and aggregate in theratio of 1 : 5 by volume.

d How many tonnes of cement and how many tonnes of aggregate does thefarmer need to buy?

2 marks

The total cost of the materials for the extension is £8 542.25 including 17.5% VAT. This cost is a business expense so the farmer can reclaim the VAT she pays.

e How much VAT can the farmer reclaim?2 marks

Total 9 marks

Key skills application of number ⏐ Level 3 ⏐ January 2009 ⏐ URN:655 9

1 cubic metre of cement weighs 1.4 tonnes

1 cubic metre of aggregate weighs 1.7 tonnes

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Part B – Extended answer question

6 A travel agent researches trends in tourism to learn more about potential customers.

UK residents made a total of 64.195 million overseas visits in 2004. This was anincrease of 4.5% on the number of overseas visits made by UK residents in 2003.

a If the number of overseas visits made by UK residents continues toincrease at the same rate after 2004, in which year will the number ofoverseas visits made by UK residents exceed 90 million?

2 marks

Information about spending during overseas visits made by UK residents in2004 is given in the table below.

b What is the difference between the average spending per overseas visitby the over 65 years age group and the average spending per overseasvisit by the 16 to 24 years age group?

1 mark

The average spending per overseas visit by all UK residents between the years2000 and 2004 is shown in the table below.

c Use the data in this table to plot points for a scatter graph to show thepossible relationship between the year and the average spending peroverseas visit by UK residents. Use a horizontal scale which extends from2000 to 2008, and a vertical scale which extends from £400 to £550.

3 marks

d Draw, by inspection, a line of best fit through the points on your graphand use it to predict the spending per overseas visit in 2008.

2 marks

Overseas visits can be as short as a one-day trip or as long as a year.Information about the duration of the 64 195 thousand overseas visits made byUK residents in 2004 is given in the table below.

e Calculate an estimate of the mean duration of overseas visit in 2004.3 marks

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Part of a cumulative frequency graph showing the duration of the 64 195 thousand overseas visits made by UK residents in 2004 is shown below.

f Explain briefly why it is appropriate to leave out the part of the graphshowing the cumulative frequency between 28 and 366 nights.

1 mark

g Use the cumulative frequency graph to estimate the median duration ofoverseas visit in 2004.

1 mark

h Use the cumulative frequency graph to estimate the percentage ofoverseas visits in 2004 that were for 12 nights or less.

1 mark

i Which of the two averages, the mean or the median, is the betterrepresentation of the average duration of overseas visits in 2004? Give areason for your choice.

1 markTotal 15 marks

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End of test