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InteractiveInteractive Learner GuideCambridge IGCSE Mathematics 0580For examination from 2017

Learner GuideIn order to help us develop the highest quality resources, we are undertaking a continuous programme ofreview; not only to measure the success of our resources but also to highlight areas for improvement and toidentify new development needs.We invite you to complete our survey by visiting the website below. Your comments on the quality andrelevance of our resources are very important to us.www.surveymonkey.co.uk/r/GL6ZNJB IGCSE is a registered trademarkCopyright UCLES 2017Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment isthe brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of theUniversity of Cambridge.UCLES retains the copyright on all its publications. Registered Centres are permitted to copy material from this booklet fortheir own internal use. However, we cannot give permission to Centres to photocopy any material that is acknowledged to athird party, even for internal use within a Centre.2

Learner GuideContentsAbout this guide4Section 1: Syllabus content – what you need to know about5Section 2: How you will be assessed6Section 3: What skills will be assessed11Section 4: Example candidate response13Section 5: Revision243

Learner GuideAbout this guideThis guide introduces you to your Cambridge IGCSE Mathematics (0580) course and how you will be assessed. You shoulduse this guide alongside the support of your teacher.By the end of this guide, you should:99 have an overview of the course and what you will learn about99 understand the structure of the assessment that you will be taking99 be able to plan your revision99 know how to show your skills to the best of your ability.Section 1: Syllabus contentFind out what topics you will be learning about. Your teacher can give you more detail.Section 2: How you will be assessedFind out: how many examinations you will take how long each examination lasts what different question types the examination will contain how to tackle each examination.Section 3: What skills will be assessedFind out what areas of knowledge, understanding and skills you will need to demonstrate throughout the course and in yourexaminations.Section 4: Example candidate responseTake a look at a learner’s response taken from a real examination. Find out: how to interpret the question how to avoid common mistakes how to improve your exam technique.Section 5: RevisionDiscover: ways to help you plan your revision example revision planners some basic revision skills some ‘top revision tips’ revision checklist for each topic.4

Learner GuideSection 1: Syllabus content - what you needto know aboutThis section gives you an outline of the syllabus content for this course. Only the top-level topics of the syllabus have beenincluded here, which are the same for both the Core and Extended courses. In the ‘overview’ column you are given a verybasic idea of what each topic covers.Learners taking the Extended course need to know all of the Core content as well as some extra content. This extracontent requires learners to explore topics and sub-topics of the Core syllabus in more detail, to cover some morecomplex techniques, and to learn new sub-topics.Ask your teacher for more detail about each topic, including the differences between the Core and Extended courses.You can also find more detail in the Revision checklists of this guide.TopicOverviewNumberNumber, squares and cubes, directed numbers, fractions, decimals and percentages,ordering, indices, ‘four rules’, estimates, bounds, ratio, proportion, rate, percentage, time,money and financeSets, exponential growth and decay (Extended only)Algebra and graphsBasic algebra, algebraic manipulation, equations, sequences, proportion, graphs offunctionsLinear programming, functions (Extended only)GeometryLanguage, constructions, symmetry, angle properties, lociMensurationMeasures, mensurationCo-ordinate geometryStraight-line graphsTrigonometryBearings, trigonometryMatrices and transformationsVectors, transformationsMatrices (Extended only)ProbabilityProbabilityStatisticsStatistics5

Learner GuideSection 2: How you will be assessedYou will be assessed at the end of the course using two components: Paper 1 (Core) or Paper 2 (Extended) Paper 3 (Core) or Paper 4 (Extended).Your teacher will advise you which papers are best for you, depending on your progress and strengths.CoreExtendedYou will take two examinations at theend of the course:You will take two examinations at theend of the course: Paper 1 – Short-answer questions Paper 2 – Short-answer questions Paper 3 – Structured questions Paper 4 – Structured questionsComponents at a glanceThe table summarises the key information about each component for each syllabus. You can find details and advice on how toapproach each component on the following pages.ComponentCoreSkills assessedDetailsMathematical techniques,applying mathematicaltechniques to solve problemsYou are assessed on theCore syllabus content usingshort-answer questions35%Mathematical techniques,applying mathematicaltechniques to solve problemsYou are assessed on theCore syllabus content usingstructured questions65%Mathematical techniques,applying mathematicaltechniques to solve problemsYou are assessed on theExtended syllabus contentusing short-answerquestions35%Paper 42 hours 30 minutes Mathematical techniques,(Structuredapplying mathematical130 marksanswer)techniques to solve problemsYou are assessed on theExtended syllabus contentusing short-answerquestions65%Paper 1(Shortanswer)How long andhow many marks1 hour56 marksPaper 32 hours(Structured104 marksquestions)Extended Paper 2(Shortanswer)1 hour 30 minutes70 marks6Percentageof thequalification

Learner GuideAbout the componentsIt is important that you understand the different types of question in each component and how you should approach them.Core: Paper 1 (Short-answer) and Paper 3 (Structured)Paper 1 and Paper 3 mainly assess your knowledge of mathematical techniques. Some questions will assess how you applymathematics to solve problems.You need to answer all questions on each paper.Paper 1Paper 3The number of marksfor each part is shown.Write your working andanswers in the spaces provided.You can use an electronic calculator inboth papers. You are not allowed algebraicor graphical calculators. Ask your teacherto recommend a calculator.Question types and advicePaper 1 contains onlyshort-answer questions.Paper 3 contains structured questions.This means that each question is splitinto parts. Often the answers to laterparts will depend on the answers toearlier parts.7

Learner Guide1. Read the questions carefully to make sure that youunderstand what is being asked.Use the value of π from your calculator, if it gives one.Or use 3.142, which is given on the front page of thequestion paper.2. Give your answers to the accuracy indicated in thequestion. If none is given, and the answer isn’t exact,then: give your answer to three significant figures12.3 Make sure that you give your answer in the formasked for in the question, e.g. some questions ask foranswers to be given in terms of π.12.298 xor if the answer is in degrees, then give it to onedecimal place23.1 23 x3. Include units with your answers if they are not givenon the paper.1 kg of apples costs 1.20 You can gain marks for the correct working even ifyou have an incorrect answer or cannot complete thewhole question.1.20 x4. Show your working. Show as much working as youcan for all your questions.Wrong workingIf you make a mistake, draw a line through theincorrect working and answer so that it is clear you donot want this to be marked.Wrong answerRight workingIf you need more space, ask for another sheet of paper.Right answerEquipment for the examMake sure you have: a blue or black pen (a spare pen is always a good idea) a pencil (for graphs and diagrams) an electronic calculator a protractor a pair of compasses a ruler.Timing If you are stuck on a question, don't waste too much time trying to answer it – go on to the next question and comeback to the one you are stuck on at the end. Use any time that you have left at the end of the exam to go back and check your answers and working.8

Learner GuideExtended: Paper 2 (Short–answer) and Paper 4 (Structured)Paper 2 and Paper 4 assess your knowledge of mathematical techniques and how you use mathematics to solve problems.You need to answer all questions on both papers.Paper 2Paper 4The number of marksfor each part is shown.Write your working andanswers in the spaces provided.You can use an electronic calculator inboth papers. You are not allowed algebraicor graphical calculators. Ask your teacherto recommend a calculator.Question types and advicePaper 2 questions are short-answerquestions. Towards the end of thepaper, questions may be longer.Paper 4 contains structured questions.This means that each question is splitinto parts. Often the answers to laterparts depend on the answers to earlierparts.9

Learner Guide1. Read the questions carefully to make sure that youunderstand what is being asked.Use the value of π from your calculator, if it gives one.Or use 3.142, which is given on the front page of thequestion paper.2. Give your answers to the accuracy indicated in thequestion. If none is given, and the answer isn’t exact,then: give your answer to three significant figures12.3 Make sure that you give your answer in the formasked for in the question, e.g. some questions ask foranswers to be given in terms of π.12.298 xor if the answer is in degrees, then give it to onedecimal place23.1 23 x3. Include units with your answers if they are not givenon the paper.1 kg of apples costs 1.20 You can gain marks for the correct working even ifyou have an incorrect answer or cannot complete thewhole question.1.20 x4. Show your working. Show as much working as youcan for all your questions.Wrong workingIf you make a mistake, draw a line through theincorrect working and answer so that it is clear you donot want this to be marked.Wrong answerRight workingIf you need more space, ask for another sheet of paper.Right answerEquipment for the examMake sure you have: a blue or black pen (a spare pen is always a good idea) a pencil (for graphs and diagrams) an electronic calculator a protractor a pair of compasses a ruler.Timing If you are stuck on a question, don't waste too much time trying to answer it – go on to the next question and comeback to the one you are stuck on at the end. Use any time that you have left at the end of the exam to go back and check your answers and working.10

Learner GuideSection 3: What skills will be assessedThe areas of knowledge, understanding and skills that you will be assessed on are called assessment objectives (AOs).AO2Applying mathematical techniques tosolve problemsAO1Mathematical techniquesThe tables explain what each assessment objective means and what percentage of the whole qualification is assessed usingthat objective. Your teacher will be able to give you more information about how each of the assessment objectives are testedin each component.AO1AO1 is all about demonstrating that you have knowledge of mathematical techniques.Candidates should be able to:organise, interpret and presentinformation accurately in written,tabular, graphical and diagrammaticformsWhat this meansWhereCore assessmentuse tables, graphs and diagramsperform calculations by suitablemethodsPercentage of IGCSE: 75–85%Extended assessmentuse an electronic calculator andalso perform some straightforwardcalculations without a calculatorAll two components:Paper 2 (28–35 marks)Paper 4 (52–65 marks)understand systems ofmeasurement in everyday use andmake use of them in the solution ofproblemsestimate, approximate and work todegrees of accuracy appropriate tothe context and convert betweenequivalent numerical formsAll two components:Paper 1 (42–48 marks)Paper 3 (78–88 marks)Percentage of IGCSE: 40–50%degrees of accuracy, e.g. decimal places orsignificant figuresequivalent numerical forms, e.g. betweenfractions, decimals and percentages, or betweennormal numbers and standard formuse mathematical and otherinstruments to measure and to drawto an acceptable degree of accuracymathematical instruments, e.g. a pair ofcompasses, a protractor and a rulerinterpret, transform and makeappropriate use of mathematicalstatements expressed in words orsymbolsuse mathematical statements written in words orsymbolsrecognise and use spatialrelationships in two and threedimensions, particularly in solvingproblemsrecall, apply and interpretmathematical knowledge in thecontext of everyday situations11

Learner GuideAO2AO2 is all about applying mathematical techniques to solve problemsIn questions which are set incontext and/or which requirea sequence of steps to solve,candidates should be able to:What this meansWheremake logical deductions from givenmathematical dataCore assessmentrecognise patterns and structuresin a variety of situations, and formgeneralisationsrecognise and extend patternsrespond to a problem relating to arelatively unstructured situation bytranslating it into an appropriatelystructured formtake information and organise it to answer aproblemanalyse a problem, select a suitablestrategy and apply an appropriatetechnique to obtain its solutionidentify and use suitable approaches to problemsAll two components:Paper 1 (8–14 marks)Paper 3 (16–26 marks)Percentage of IGCSE: 15–25%Extended assessmentAll two components:Paper 2 (35–42 marks)Paper 4 (65–78 marks)Percentage of IGCSE: 50–60%apply combinations of mathematicalskills and techniques in problemsolvingset out mathematical work,including the solution of problems,in a logical and clear formusing appropriate symbols andterminologyset out work in a clear and logical way usingmathematical symbols and languageYour teacher will be able to give you more information about how each of the assessment objectives is tested.12

Learner GuideSection 4: Example candidate responseThis section takes you through an example question and learner response from a Cambridge IGCSE Mathematics (0580) pastpaper. It will help you to see how to identify words within questions and to understand what is required in your response.Understanding the questions will help you to know what you need to do with your knowledge, for example, you might need todescribe something, explain something, argue a point of view, apply the knowledge in a different way, or list what you know.All information and advice in this section is specific to the example question and responsebeing demonstrated. It should give you an idea of how your responses might be viewed by anexaminer but it is not a list of what to do in all questions. In your own examination, you willneed to pay careful attention to what each question is asking you to do.This section is structured as follows:A. QuestionWords in the question have been highlighted and theirmeaning explained. This should help you to understandclearly what is required by the question.B. Mark schemeThis tells you as clearly as possible what an examiner expectsfrom an answer to award marks.C. Example candidate responseThis is an answer by a real candidate in exam conditions.Good points and problems have been highlighted.D. How the answer could have been improvedThis summarises what could be done to gain more marks.E. Common mistakesThis will help you to avoid common mistakes made bycandidates. So often candidates lose marks in their examsbecause they misread or misinterpret the questions.13

Learner GuideA. QuestionThe question used in this example, question 9, is from Paper 3 (Core). It represents the type of structured question you willsee in both Paper 3 (Core) and Paper 4 (Extended). A structured question means that it is broken into several parts. Often,later parts will depend on your answers to earlier parts.14

Learner GuideNow let's look more closely at the question.NOT TOSCALEIn the diagram above.means that you need touse the diagram to helpyou answer the question.NOT TO SCALEThis means that youcannot find the answer bymeasuring the diagram.In the diagram above,CalculateCalculate. means that you need to give a numerical answer.Make sure you show steps in your working, especially whenthere is more than one step in your calculation.Complete the statement. means thatyou need to use the correct mathematicalword(s) to fill in the gap(s). Here, the gap isat the end of the sentence.Calculate the statement.FindFind. in this question, find is another word for'calculate', meaning you need to calculate thesize of the angle. Find can also mean 'measure',it depends on the question being asked.15

Learner GuideOn the grid. tells youthat you need to draw youranswer on the grid provided.On the grid,Complete the tableComplete the table. means that you need to putyour answers in the table. Look carefully at the table toidentify what data you need to enter. Here, you need toenter the number of lines for diagrams 3,4 and 5. Youcan use the diagrams for 3 and 4, but have to spot apattern in the data to find the answer for diagram 5.How manyHow many. requires anumerical or algebraic answer.B. Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded. Your marks will thenbe converted to a grade.16

Learner GuideThe mark scheme provides the final answers for each sub-part of a question and, when appropriate, the required lines of working to reach that answer.Answer(a)(i)3.82Final answerMarkNotes2Full marks (2) are awarded for any answer that rounds to 3.82.(1)If the candidate's answer is incorrect, 1 method mark can be awarded for sight ofone of the following in their working (maximum 1 mark):2.72 2.72ORsin 45 27BDORcos 45 (a)(ii)Isosceles1This is the only acceptable answer for this part of the question.(a)(iii)451This is the only acceptable answer for this part of the question.1This is the only acceptable answer for this part of the question.(b)(i)27BDSometimes the answer has to be exactlyas given in the mark scheme. Othertimes there will be a range of acceptableanswers.Sometimes marks can be awarded forcorrect lines or steps of the working ina calculation even if the final answer isincorrect. This is why it's so important toalways show your working.If you use a correct method that is notincluded in the mark scheme, then methodmarks can still be awarded.(b)(ii)Diagram345Number of lines1013162Full marks (2) are awarded is all gaps are correctly filled.(1)If the candidate's answer is not fully correct, 1 mark can be awarded for one of thefollowing (maximum 1 mark):Two correct values in the table, e.g. 10 and 13 correct, but a number other than 16as the third value.ORIncorrect values for diagram 4 and diagram 5 but the correct difference betweenthem. The correct difference is 3, so the values 14 and 17, or 15 and 18, for example,would be awarded 1 mark.17

Learner GuideAnswerMarkNotes(c)(i)281This is the only acceptable answer for this part of the question.(c)(ii)3n 12Full marks (2) are awarded for 3n 1.(1)ORAny expression that would simplify to 3n 1, e.g. 6n 2.If the candidate's answer is not correct, then 1 mark can be awarded for one of thefollowing (maximum 1 mark):Having '3n' in the expression but adding/subtracting incorrectly, e.g. 3n a, where ais not 1, such as 3n 4 or 3n – 2.ORHaving ' 1' in the expression but multiplying n incorrectly, e.g. dn 1, where d is anumber other than 3, such as 5n 1 or 2n 1.(d)252Full marks (2) are awarded for the answer '25'(1)OR3n 1 763n 76n 25If the candidate's final answer is incorrect, then 1 method mark can be awarded for:Incorrectly solving 3n 1 76ORPutting their incorrect expression from (c)(ii) equal to 76 and solving, e.g.3n 4 763n 72n 24(e)3

Cambridge IGCSE Mathematics 0580 . included here, which are the same for both the Core and Extended courses. In the ‘overview’ column you are given a very basic idea of what each topic covers. Learners taking the Extended course need to know all of the Core content as well as some extra content. This extra

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