Version 1.0: Date 0511 klm General Certificate of Education Use of Mathematics 5351 2013 Material accompanying this Specification • Specimen and Past Papers and Mark Schemes • Reports on the Examination • A Teachers’ Guide SPECIFICATION This specification will be published annually on the AQA Website (www.aqa.org.uk) If there are any changes to the specification centres will be notified in print as well as on the Website The version on the Website is the definitive version of the specification Further copies of this specification booklet are available from: AQA Logistics Centre, Unit 2, Wheel Forge Way, Ashburton Park, Trafford Park, Manchester, M17 1EH Telephone: 0870 410 1036 Fax: 0161 953 1177 or can be downloaded from the AQA Website: www.aqa.org.uk Copyright © 2011 AQA and its licensors All rights reserved COPYRIGHT AQA retains the copyright on all its publications However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre Set and published by the Assessment and Qualifications Alliance The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales 3644723 and a registered charity number 1073334 Registered address AQA, Devas Street, Manchester, M15 6EX Advanced Subsidiary, 2013– Use of Mathematics Contents Background Information Advanced Subsidiary and Free-Standing Mathematics Qualifications Specification at a Glance Availability of Qualification and Entry Details Scheme of Assessment Introduction – Applying Mathematics Aims 10 Assessment Objectives 10 Scheme of Assessment – Advanced Subsidiary 11 Scheme of Assessment – Applying Mathematics 12 Subject Content Content and Assessment – Applying Mathematics 13 Key Skills and Other Issues 10 Key Skills 43 11 Spiritual, Moral, Ethical, Social, Cultural and Other Issues 46 Awarding and Reporting 12 Grading, Shelf-Life and Re-Sits 47 Use of Mathematics – Advanced Subsidiary, 2013 Appendices A FSMQ Using and Applying Statistics 6990 B FSMQ Working with Algebraic and Graphical Techniques 6991 49 87 C FSMQ Modelling with Calculus 6992 123 D FSMQ Using and Applying Decision Mathematics 6994 158 Advanced Subsidiary, 2013– Use of Mathematics Background Information 1.1 Advanced Subsidiary and Free-Standing Mathematics Qualifications Introduction to this Qualification It is the aim of each of the ten Free-Standing Mathematics Qualifications to encourage candidates to apply mathematical principles in their studies, work or interests The new Advanced Subsidiary qualification in Use of Mathematics has been developed to make a significant contribution towards the promotion of mathematical study beyond 16, especially among “non-mathematicians” However, the qualification is suitable for and may be used by both pre-16 and post-16 candidates It will prove particularly useful to those working in the areas of: • Technology, including engineering • Science • Economics • Business Studies The unit Applying Mathematics must be taken along with FSMQ Working with Algebraic and Graphical Techniques and either FSMQ Using and Applying Statistics or FSMQ Modelling with Calculus or FSMQ Using and Applying Decision Mathematics to complete the AS in Use of Mathematics Full specifications for these FSMQs can be found in the Appendices of this document Applying Mathematics does not exist as a separate Free-Standing Mathematics Qualification Candidates embarking on AS level study in mathematics subjects are expected to have achieved at least Grade C in GCSE Mathematics or equivalent, and to have covered all the material in the Intermediate Tier In addition, candidates will be expected to be able to use the material listed in section whenever it is required Advanced Subsidiary is designed to provide an appropriate assessment of knowledge, understanding and skills expected of candidates who have completed the first half of a full Advanced Level qualification The level of demand of the AS examination is that expected of candidates half-way through a full A Level course of study Use of Mathematics – Advanced Subsidiary, 2013 Specification at a Glance Use of Mathematics 5351 at Advanced Subsidiary Level This Advanced Subsidiary (AS) award comprises three assessment units of equal weighting AS Use of Mathematics 5351 FSMQ Working with Algebraic and Graphical Techniques 6991 coursework portfolio assessed by centre and moderated by AQA 50% of assessment for this unit written paper short and extended answer questions hour 30 minutes 50% of assessment for this unit + EITHER OR OR FSMQ Using and Applying Statistics FSMQ Modelling with Calculus 6990 6992 FSMQ Using and Applying Decision Mathematics 6994 coursework portfolio assessed by centre and moderated by AQA 50% of assessment for this unit coursework portfolio assessed by centre and moderated by AQA 50% of assessment for this unit coursework portfolio assessed by centre and moderated by AQA 50% of assessment for this unit written paper short and extended answer questions hour 30 minutes written paper short and extended answer questions hour 30 minutes written paper short and extended answer questions hour 30 minutes 50% of assessment for this unit 50% of assessment for this unit 50% of assessment for this unit + Applying Mathematics UOM4 Advanced Subsidiary Award written paper comprehension hour 30% of assessment for this unit 5351 written paper short and extended answer questions hour 30 minutes 70% of assessment for this unit Advanced Subsidiary, 2013– Use of Mathematics 3.1 Availability of Qualification and Entry Details Availability of Assessment Units Assessments based on this specification are available in the Summer Summer Availability of Units Availability of AS Qualification 6990, 6991, 6992, 6994 and UOM4 Qualification Code 5351 3.2 Sequencing of units There is no pre-determined dependency of units, although in the case of the Applying Mathematics unit, candidates will build on the mathematical knowledge, skills and understanding they develop in working towards FSMQ Working with Algebraic and Graphical Techniques 3.3 Entry Codes The following unit entry codes should be used: FSMQ Working with Algebraic and Graphical Techniques 6991 FSMQ Using and Applying Statistics 6990 FSMQ Modelling with Calculus 6992 FSMQ Using and Applying Decision Mathematics 6994 Applying Mathematics UOM4 The Subject Code for entry to the Use of Mathematics AS award is 5351 3.4 Classification Codes Every specification is assigned to a national classification code indicating the subject area to which it belongs Centres should be aware that candidates who enter for more than one GCE qualification with the same classification code will have only one grade (the highest) counted for the purpose of the School and College Performance Tables The classification code for this specification is 2200 3.5 Private Candidates This specification is not available to private candidates Use of Mathematics – Advanced Subsidiary, 2013 3.6 Access Arrangements and Special Consideration We have taken note of equality and discrimination legislation and the interests of minority groups in developing and administering this specification We follow the guidelines in the Joint Council for Qualifications (JCQ) document: Access Arrangements, Reasonable Adjustments and Special Consideration: General and Vocational Qualifications This is published on the JCQ Website (http://www.jcq.org.uk) or you can follow the link from our website (http://www.aqa.org.uk) 3.7 Language of Examination Assessments in this subject are provided in English only Advanced Subsidiary, 2013– Use of Mathematics Scheme of Assessment Introduction – Applying Mathematics Before you start this unit Candidates must be able to: This includes: plot by hand accurate graphs of data pairs and linear and simple quadratic functions in all four quadrants quadratics of the type recognise and predict the general shapes of graphs of direct proportion, other linear and quadratic functions quadratics of the type y = kx + c find linear functions to model data pairs calculating gradients and intercepts of linear graphs rearrange basic algebraic expressions by • collecting like terms • expanding brackets • extracting common factors for example: y = ax + bx + c • • x + y + y + 3x = x + y • 2ab + 4a = 2a (b + 2a ) 4(2u + 3v ) = 8u + 12v solve basic equations by exact methods for example: use index notation indices which are positive and negative, integers and fractions solve quadratic equations • factorising • using the formula 2(5 + x ) − x = 18 x= understand basic ideas of probability − b ± b − 4ac 2a • understanding the difference between theoretical probabilities and those determined by survey or experimentation • understanding that if the probability of an event A occurring is p( A) then the probability of it not occurring is − p( A) Use of Mathematics – Advanced Subsidiary, 2013 Aims A course based on this specification aims to promote: • application of mathematical principles • the application of mathematics to candidates’ studies, work or interests • the development of a mathematics curriculum that is integrated with other areas of candidates’ studies, work or interests • development of skills that enable candidates to communicate, use and interpret their mathematics • the solution of substantial and realistic problems encountered by adults • the ability to solve open-ended problems • the development of mathematical modelling skills • the development of mathematical reasoning skills • appropriate use of ICT • enjoyment of mathematics and the development of confidence in using mathematics Assessment Objectives The Applying Mathematics unit will assess a candidate’s ability to apply mathematical principles to analyse and make sense of situations, to solve problems and to draw conclusions Candidates should be able to develop and use mathematics as a model of reality and have an awareness of any limitations this may introduce into their analysis of a situation In particular the assessment components will concentrate on: • the processes involved when mathematics is used to solve problems • developing clarity in the communication of mathematics • some new mathematical techniques associated with simulating random events and using recurrence relations • reading and making sense of the mathematics of other people In their studies of this unit candidates will build on the mathematical knowledge, skills and understanding they develop in working towards FSMQ Working with Algebraic and Graphical Techniques The two units can be studied alongside each other 10 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) Theme – Using appropriate mathematics and working accurately This theme requires candidates to be accurate in their mathematics At marks: work is likely to be littered with errors and the mathematical techniques selected and applied may be inappropriate At marks: candidates should produce work that at most contains minor errors It is important however that any errors not significantly affect the outcomes of the work At 10 marks candidates should additionally: show that they have used a range of suitable methods to check their work Any of a range of checking techniques may be available At 15 marks candidates should additionally: use efficient and concise methods It should be expected that efficient and concise methods be used throughout most of the Coursework Portfolio rather than on only a few occasions Theme - Interpreting mathematics This theme is central to the aim of Free-Standing Mathematics Qualifications, at all levels, to encourage candidates to apply mathematical principles to make sense of real situations At marks: candidates will have carried out mathematical analysis but will have little evidence of making sense of their solutions, or made significant errors in their interpretation of situations At marks: candidates should show that they can use mathematics to write about the main features of situations they investigate This should include coming to some conclusion at the end of key parts of a piece of work and when solutions are reached They should demonstrate that they know what their mathematics is telling them about the real situations At 10 marks candidates should additionally: be able to use their mathematics to summarise their work This should involve them in drawing conclusions at the end of an overall piece of work Their comments should be reasoned and refer to their main findings 177 Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 At 15 marks candidates should additionally: consider how their findings are restricted by their initial choice of data, the assumptions they made etc They should comment on how their mathematical findings may be at odds with reality (if this is the case), and how the accuracy of the initial data may have affected their findings It is likely that candidates working at this level may identify further and possibly new lines of approach, although they not need to pursue them 7.6 Evidence to Support the Award of Marks Coursework Portfolios must be presented in a clear and helpful way for the moderator An indication must also be given at the appropriate point in the work, or in accompanying information, of any further guidance given by the teacher (or other person) which has significant assessment implications When the assessment of the Coursework Portfolio is complete, the mark awarded for each grading theme and the total mark awarded must be entered on the Candidate Record Form, with supporting information given in the spaces provided The Candidate Record Form must be attached to the candidate’s work Candidate Record Forms are available on the AQA website in the Administration area They can be accessed via the following link http://www.aqa.org.uk/admin/p_course.php 178 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) Key Skills and Other Issues Key Skills The work that candidates produce for a Free-Standing Mathematics Qualification will allow them to gather evidence toward the Key Skill in Application of Number, although the two qualifications are substantially different Free-Standing Mathematics Qualifications allow candidates to develop a branch of mathematics to some depth while Application of Number is concerned with developing a wide range of underpinning number skills Study of this qualification will provide candidates with a suitable programme of study to develop the Key Skill of Application of Number at level and above A detailed commentary of how this qualification relates to this Key Skill and others is given in Appendix B 179 Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 9.1 Spiritual, Moral, Ethical, Social, Cultural and Other Issues Spiritual, Moral, Ethical, Social and Cultural Issues The study of mathematics can contribute to a candidate’s understanding of moral and cultural issues Contexts used during the study of this qualification may contribute to the candidate’s understanding of spiritual, moral and cultural issues 9.2 European Developments AQA has taken account of the 1988 Resolution of the Council of the European Community in preparing this specification and associated specimen papers 9.3 Environmental Issues AQA has taken account of the 1988 Resolution of the Council of the European Community and the Report “Environmental Responsibility: An Agenda for Further and Higher Education, 1993” in preparing this specification and associated specimen papers 9.4 Avoidance of Bias AQA has taken great care in the preparation of this specification and associated specimen papers to avoid bias of any kind 9.5 Issues for centres in Wales and Northern Ireland Terms, legislation or aspects of government that are different from those in England should not disadvantage candidates in Wales or Northern Ireland Where such situations might occur, including in the external tests, the terms used have been selected as neutral 180 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) Centre-Assessed Component 10 Supervision and Authentication 10.1 Supervision of Candidates’ Work Candidates’ work for assessment must be undertaken under conditions which allow the teacher to supervise the work and enable the work to be authenticated If it is necessary for some assessed work to be done outside the centre, sufficient work must take place under direct supervision to allow the teacher to authenticate each candidate’s whole work with confidence 10.2 Guidance by the Teacher The work assessed must be solely that of the candidate concerned Any assistance given to an individual candidate which is beyond that given to the group as a whole must be recorded on the Candidate Record Form 10.3 Unfair Practice At the start of the course, the supervising teacher is responsible for informing candidates of the AQA Regulations concerning malpractice Candidates must not take part in any unfair practice in the preparation of coursework to be submitted for assessment, and must understand that to present material copied directly from books or other sources without acknowledgement will be regarded as deliberate deception Centres must report suspected malpractice to AQA The penalties for malpractice are set out in the AQA Regulations 10.4 Authentication of Candidates’ Work Both the candidate and the teacher are required to sign declarations on the Candidate Record Form confirming that the work submitted for assessment is the candidate’s own The teacher declares that the work was conducted under the specified conditions, and records details of any additional assistance 181 Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 11 11.1 Standardisation Standardising Meetings Annual standardising meetings will usually be held in the autumn term Centres entering candidates for the first time must send a representative to the meetings Attendance is also mandatory in the following cases: • where there has been a serious misinterpretation of the specification requirements • where the nature of coursework portfolio tasks set by a centre has been inappropriate • where a significant adjustment has been made to a centre’s marks in the previous year’s examination Otherwise attendance is at the discretion of centres At these meetings support will be provided for centres in the development of appropriate tasks and assessment procedures 11.2 Internal Standardisation of Marking Teachers will be required to authenticate and mark the Coursework Portfolios of their candidates Where more than one teacher is involved in assessing Coursework Portfolios, Internal Standardisation will be required to ensure that there is a consistent standard of marking within the centre 182 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) 12 Administrative Procedures 12.1 Recording Assessments The candidate’s work must be marked according to the assessment criteria The marks and supporting information, must be recorded in accordance with the instructions in Section 7.5 The completed Candidate Record Form for each candidate must be attached to the work and made available to AQA on request At the beginning of the course, centres must inform AQA on Form A (Early Information) of the approximate number of candidates to be entered for the qualification so that the appropriate number of Candidate Record Forms may be sent 12.2 Submitting Marks and Sample Work for Moderation The total component mark for each candidate’s coursework portfolio must be submitted to AQA, by the date specified, either on Mark Sheets supplied by AQA or via Electronic Data Interchange (EDI) Centres will be informed which candidate’s work is required to be submitted in the samples to the moderator 12.3 Factors Affecting Individual Candidates Special consideration should be requested for candidates whose work has been affected by illness or other exceptional circumstances Information about the procedure is issued separately If work is lost, AQA should be notified immediately of the date of the loss, how it occurred, and who was responsible for the loss AQA will advise on the procedures to be followed in such cases Where special help, which goes beyond normal learning support, is given, AQA must be informed so that such help can be taken into account when assessment and moderation take place Candidates who move from one centre to another during the course sometimes present a problem for a scheme of internal assessment Possible courses of action depend on the stage at which the move takes place If the move occurs early in the course the new centre should take responsibility for assessment If it occurs late in the course it may be possible to accept the assessments made at the previous centre Centres should contact AQA at the earliest possible stage for advice about appropriate arrangements in individual cases 12.4 Retaining Evidence and Re-Using Marks The centre must retain the work of candidates, with Candidate Record Forms attached, under secure conditions, from the time it is assessed, to allow for the possibility of an enquiry upon result The work may be returned to candidates after the issue of results provided that no enquiry upon result is to be made which will include re-moderation of the coursework component If an enquiry upon result is to be made, the work must remain under secure conditions until requested by AQA Candidates re-taking a unit containing coursework may carry forward their moderated coursework marks These marks have a shelf-life which is limited only by the shelf-life of the specification, and they may be carried forward an unlimited number of times within this shelf-life 183 Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 13 13.1 Moderation Moderation Procedures Moderation of the coursework is by inspection of a sample of candidates’ work, sent by post from the centre to a moderator appointed by AQA The centre marks must be submitted to AQA and the sample of work must reach the moderator by the specified date Following the re-marking of the sample work, the moderator’s marks are compared with the centre marks to determine whether any adjustment is needed in order to bring the centre’s assessments into line with standards generally In some cases it may be necessary for the moderator to call for the work of other candidates In order to meet this possible request, centres must have available the coursework portfolio, and Candidate Record Form of every candidate entered for the qualification and be prepared to submit it on demand Mark adjustments will normally preserve the centre’s order of merit, but where major discrepancies are found, AQA reserves the right to alter the order of merit 13.2 Post-Moderation Procedures On publication of the results, the centre is supplied with details of the final marks for the coursework portfolio component The candidates’ work is returned to the centre after the examination with a report form from the moderator giving feedback to the centre on the appropriateness of the task set, the accuracy of the assessments made, and the reasons for any adjustments to the marks Some candidate’s work may be retained by AQA for archive purposes 184 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) Awarding and Reporting 14 14.1 Grading, Shelf-Life and Re-Sits Grading System Individual Qualification results will be certificated Candidates who not achieve grades A - E will be reported as U (unclassified) and will not receive a qualification certificate 14.2 Minimum requirements Candidates will be graded on the basis of the work submitted for the coursework portfolio and examination components Where a candidate is absent for one of the two components, the candidate will be graded with a contribution of zero marks for that component 14.3 Re-Sits and Carrying Forward of Component Grades Candidates re-taking a unit containing coursework may carry forward their moderated coursework marks These marks have a shelf life which is limited only by the shelf-life of the specification, and they may be carried forward an unlimited number of times within this shelf-life There is no facility to decline an award once it has been issued Candidates may re-sit the whole qualification more than once There is no facility to decline an award once it has been issued 14.4 Quality Assurance The process for both internal and external assessment (including the mechanism for the award of grades) for this qualification will conform to agreed procedures of the GCSE, GCE, Principal Learning and Project Code of Practice April 2011, as laid down by QCA AQA is committed to the maintenance of national standards and will provide advice about, and moderate, the assessment of candidates’ work 185 Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 A Candidate Record Form Candidate Record Forms and Centre Declaration Sheets are available on the AQA website in the Administration area They can be accessed via the following link http://www.aqa.org.uk/admin/p_course.php (NB to type the link: http://www.aqa.org.uk/admin/p_course.php) 186 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) B Summary of Key Skills Opportunities As might be expected, the work that candidates produce for a FreeStanding Mathematics Qualification will allow them to gather evidence for the Application of Number Key Skill, although the two qualifications are substantially different Free-Standing Mathematics Qualifications allow candidates to develop applications of a branch of mathematics to some depth while Application of Number is concerned with candidates developing a wide range of underpinning number skills In general, work produced for a particular Free-Standing Mathematics Qualification will provide the majority of evidence required for the Application of Number Key Skill at the same level and at the level above There will, however, be additional evidence that the candidate will need to provide to satisfy the Key Skills requirements (Each FreeStanding Mathematics Qualification also, of course, develops aspects of mathematical skills and knowledge beyond the requirements of Application of Number.) Application of Number The following tables show in detail how Using and Applying Decision Mathematics can provide evidence for the Application of Number key skill at Level Note that ! indicates that a skill will certainly be covered by a candidate successfully completing the qualification, whereas (!) indicates partial coverage and * indicates that the skill may or may not be developed depending on the work completed by individuals Subsequent tables give for each qualification: • • • details of the extra work that needs to be done for skills marked as (!) the approach needed where skills are marked as * suggestions for ways in which the remaining unmarked skills may be developed Application of Number Level Part A: What you need to know Interpreting information: you need to know how to plan a substantial and complex activity by breaking it down into a series of tasks obtain relevant information from different sources, including a large data set, and use this to meet the purpose of the activity use estimation to help you plan, multiplying and dividing numbers of any size rounded to one significant figure make accurate and reliable observations over time and use suitable equipment to measure in a variety of appropriate units read and understand scale drawings, graphs, complex tables and charts read and understand ways of writing very large and very small numbers understand and use compound measures choose appropriate methods for obtaining results needed and justify choice Carrying out calculations: you need to know how to show methods clearly and work to appropriate level of accuracy carry out multi-stage calculations with numbers of any size 187 ! *1 *2 *1 ! ! ! ! Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 use powers and roots work out missing angles and sides in right angled triangles from known sides and angles work out proportional change work out actual measurements from scale drawing and scale quantities up and down work with large data sets using measures of average and range to compare distributions, and estimate mean, median and range of grouped data rearrange and use formulae, equations and expressions use checking procedures to identify errors in methods and results Interpreting results and presenting findings: you need to know how to select and use appropriate methods to illustrate findings, show trends and make comparisons examine critically and justify choice of methods construct and label charts, graphs, diagrams and scale drawings using accepted conventions draw appropriate conclusions based on findings, including how possible sources of error may have affected results explain how the results relate to the purpose of the activity *3 *4 ! ! ! ! ! ! Application of Number Level Part B: What you must You must carry through at least one substantial activity that includes tasks for N3.1, N3.2 and N3.3 N£.1: You must Plan and interpret information from two different sources This should include a large data set N3.2: You must Carry out multi-stage calculations to with: a amounts and sizes b scales and proportion c handling statistics d rearranging and using formulae including working with a large data set N3.3: You must Interpret the results of your calculations and present your findings and justify your one graph methods You must use at least: one chart one diagram Application of Number Level Part A Reference Skill obtain relevant information from *1 different sources, including a large data set, and use this to meet the purpose of the activity *2 make accurate and reliable observations over time and use suitable equipment to measure in a variety of appropriate units use estimation to help plan, multiplying and dividing numbers of any size rounded to one significant figure work out proportional change (!)5 *1 ! *1,4 ! *6 *6 Suggestions Where possible encourage candidates to collect their own data by observation or measurement Pooling resources would enable them to work with and extract information from large data sets For example, candidates can estimate the number of steps an algorithm would take in order to plan how detailed their model of a real world situation should be Work involving changes in the number of vertices can provide an opportunity for developing this skill *3 188 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) *4 rearrange and use formulae, equations and expressions Unmarked Extension work on the order of algorithms provides opportunities for this sort of activity It is not likely that these requirements will be satisfied by work produced for the Coursework Portfolio Where possible use topics from the candidates’ other studies or interests Application of Number Level Part B Reference Skill Plan and carry through at least one substantial activity that (!)5 includes tasks for N3.1, N3.2 and N3.3 *1 *6 Unmarked Suggestions Most of the requirements for N3.1, N3.2 and N3.3 will be satisfied if the candidate completes a Coursework Portfolio for Using and Applying Decision Mathematics However, the extra items identified below will also be required Plan and interpret information Pooling results could enable candidates to work with from two different sources and model information from large data sets including a large data set Carry out multi-stage calculations including working with a large data set You must use one chart one diagram It is likely that a candidate’s coursework will naturally satisfy this requirement It may prove difficult to relate these skills to the rest of the work covered in this unit Where possible use topics from the candidates’ other studies or interests 189 Using and Applying Decision Mathematics (Advanced Level) – Free-Standing Mathematics Qualification, 2013 Information Technology The following table indicates how study of this qualification may provide evidence for the Key Skill of Information Technology at Level This qualification allows candidates to make proficient use of network drawing software on a computer If candidates wish to illustrate work that they produce using word-processing or desktop publishing software, they will need to consider how they can import images of networks into such packages Planning and selecting information In this qualification candidates are required to model data using networks It may be possible to find relevant data from IT sources (such as the Internet or CD-ROMs) as well as non-IT sources (such as from experiments, newspapers, magazines or books) Candidates should be encouraged to provide their own data and this will require them to plan, search for and select information If they use a variety of different sources they will be able to compare their advantages and limitations Developing information Candidates will be able to demonstrate their competence in this area of the Key Skill when completing tasks for their Coursework Portfolios using network-plotting software on a computer Candidates may use IT to carry out calculations and analysis of networks as well as displaying networks in order to explore their key features Such processing will allow candidates to effectively demonstrate many of the demands of the Key Skill If candidates are allowed to some of the work in groups they will gain experience of sharing and exchanging information Presenting information The work demanded by the qualification can be effectively produced using networkplotting software on a computer Candidates will need output of such work Output obtained in this way will allow candidates to satisfy some of the demands of the Key Skill To satisfy further demands, candidates may consider preparing their reports with software that allows them to combine text, graphics and numerical information For example, they could be encouraged to import numerical work and graphics into their word-processed text It is possible that candidates will use word-processing packages that allow them to produce correctly formatted mathematical expressions quickly and effectively The production of such text will allow them to demonstrate a high level of proficiency of use of IT As work proceeds they could discuss the structure with their teacher and other members of the group They may be asked to prepare some of the work for use in a presentation as well as in written reports Candidates should be encouraged to save information so that it can be retrieved easily and always required to work safely and take care of equipment They should know when it is necessary to observe copyright or confidentiality and how to identify errors and their causes and minimise risks from viruses Reflecting on the implications of using IT and comparing it with other systems would not normally be expected of candidates within their work for a Free-Standing Mathematics Qualification However in the production of Coursework Portfolios candidates will have the opportunity of demonstrating competence with IT and they may therefore wish to evaluate their use of IT within this setting 190 Free-Standing Mathematics Qualification, 2013 – Using and Applying Decision Mathematics (Advanced Level) Communication The following table indicates how study of this qualification may provide evidence for the Communication key skill at Level Discussions There is potential to develop activities in the teaching of this qualification in such a way that they allow candidates to show their competence in this area of the Key Skill For example, candidates could discuss possible approaches to a piece of work in groups before tackling it individually Group discussion would be particularly valuable in work such as the use of networks to model real data where there may be a variety of networks which could be used Candidates could also report back to groups after completing a piece of work to share findings and discuss differences in the approaches used Making a presentation Candidates could be asked to present a summary of some of their Coursework Portfolio to a small group, the whole class or other groups who are not familiar with the work done Such presentations may suffice as a “report” required for the Coursework Portfolio if accompanied by sufficient documentary evidence However, because of the level of this qualification and the complexity of the work required it is advisable to support the presentation with a written report The mathematical nature of presentations will require a structured logical approach if it is to be followed easily by the audience The qualification requires candidates to produce and present appropriate networks These can be used effectively in presentations to help communicate ideas to the audience The networks, graphs, tables and diagrams used will provide candidates with evidence of working within complex subject areas Reading and synthesising information The starting points or introductory activities leading to the production of portfolio evidence will provide candidates with opportunities of selecting and extracting information that they need from a variety of sources Ideally some of these sources should contain more information than is required to complete their investigations It is likely that the content of such sources will satisfy the demands of the Key Skill in working with complex subjects Writing documents The written work that candidates produce for their Coursework Portfolio is likely to satisfy the evidence required by the Key Skill at Level The focus of candidates’ work is mathematics and they will need to use appropriate forms of layout and specialist vocabulary when appropriate It is expected that the work will be presented clearly, structured logically, and follow correct spelling, punctuation and grammar conventions (although candidates would not be penalised heavily in the marking of their Coursework Portfolio if they were to make mistakes with the latter) In addition to formal mathematical techniques the written work should include explanations of how these relate to real situations and interpretation of findings and the conclusions drawn The qualification requires candidates to produce and present appropriate networks and candidates should be aware of, and use, graphical techniques to ensure that their findings are illustrated as clearly as possible The networks, graphs, tables and diagrams that illustrate reports within their Coursework Portfolios will provide candidates with evidence of working within complex subject areas Candidates could also be encouraged to illustrate their reports with other images such as photographs and drawings of the situations they are investigating 191