interactive learner guide

Interactive Learner Guide

Cambridge IGCSETM Cambridge IGCSETM(9ndash1)Mathematics 0580 0980

For examination from 2020

Interactive

2

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wwwsurveymonkeycoukrGL6ZNJB

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3

About this guide 4

Section 1 Syllabus content ndash what you need to know about 5

Section 2 How you will be assessed 6

Section 3 What skills will be assessed 11

Section 4 Example candidate response 13

Section 5 Revision 24

Contents

4

This guide introduces you to your Cambridge IGCSE Mathematics course and how you will be assessed You should use this guide alongside the support of your teacher

It will help you to

9 understand what skills you should develop by taking this course

9 understand how you will be assessed

9 understand what we are looking for in the answers you write

9 plan your revision programme

9 revise by providing revision tips and an interactive revision checklist (Section 6)

About this guide

Key benefits

The course will help you to build your skills and knowledge across a range of mathematical techniques You will be able to develop your problem solving and reasoning skills in a variety of situations

The Extended course will provide you with a strong foundation to continue to study mathematics qualifications beyond IGCSE The Core course will equip you with skills needed to support your learning in other subjects and in your general working life

5

This section gives you an outline of the syllabus content for this course Only the top-level topics of the syllabus have been included here which are the same for both the Core and Extended courses In the lsquooverviewrsquo column you are given a very basic idea of what each topic covers Highlighted cells show Extended-only content

Learners taking the Extended course need to know all of the Core content as well as some extra content This extra content requires learners to explore topics and sub-topics of the Core syllabus in more detail to cover some more complex 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 in Section 6 of this guide

Topic Overview

Number Number sets and Venn diagrams squares and cubes directed numbers fractions decimals and percentages ordering indices lsquofour rulesrsquo estimates bounds ratio proportion rate percentage time money and finance Growth and decay (Extended only)

Algebra and graphs Basic algebra algebraic manipulation equations formulae sequences drawing sketching and interpreting graphs of functionsAlgebraic fractions harder simultaneous equations proportion linear programming functions gradients of curves derived functions and differentiation (Extended only)

Co-ordinate geometry Straight-line graphs

Vectors and transformations Vectors (column) transformations

Magnitude of a vector represent vectors by directed line segments position vectors (Extended only)

Geometry Language construction symmetry angle properties congruence similarity

Mensuration Measures mensuration

Trigonometry Bearings trigonometry in right-angled triangles

Sine rule cosine rule trig graphs solving simple trig equations (Extended only)

Probability Probability

Conditional probability (Extended only)

Statistics Statistics

Section 1 Syllabus content ndash what you need to know about

Make sure you always check the latest syllabus which is available at wwwcambridgeinternationalorg

6

You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses

bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions


Components at a glanceThe table summarises the key information about each component

Component How long and how many marks Skills assessed Percentage of the

qualificationCore Paper 1

(Short-answer questions)

1 hour

56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems

35

Paper 3 (Structured questions)

2 hours

104 marks 65

Extended Paper 2 (Short-answer questions)

1 hour 30 minutes

70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems

35


2 hours 30 minutes

130 marks 65

Section 2 How you will be assessed

Core Extended

Make sure you find out from your teacher which course you will be following

7

About the componentsIt is important that you understand the different types of question in each paper so you know what to expect

Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)

You need to answer all questions on each paper

Paper 3Paper 1

You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator

Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts

Write your working and answers in the spaces provided

The number of marks for each part is shown

Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages

Often the answers to later parts will depend on the answers to earlier parts

8

Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)

You need to answer all questions on both papers

Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts



Paper 4Paper 2




9

Equipment for the examMake sure you have

bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler

1 Read the questions carefully to make sure that you understand what is being asked

2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then

bull give your answer to three significant figures 123 9 12298 x

bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x

3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x

4 Show your working Show as much working as you can for all your questions

5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark

Use the value of π from your calculator or use 3142 which is given on the front page of the question paper

Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and

come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working

Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer

You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question

If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering

General advice for all Papers

10

The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course

AO1 Demonstrate knowledge and

understanding of mathematical techniques

AO2 Reason interpret and communicate

mathematically when solving problems

AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations

Section 3 What skills will be assessed

This means that you need to show that you can

bull organise process and present information accurately in written tabular graphical and diagrammatic forms

bull use and interpret mathematical notation correctly

bull perform calculations and procedures by suitable methods including using a calculator

bull understand systems of measurement in everyday use and make use of these

bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms

bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy

bull recognise and use spatial relationships in two and three dimensions

AO1 is assessed in all papers

Use tables graphs and diagrams

An example of degress of accuracy include significant figures or decimal places

An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form

eg a pair of compasses a protractor and a ruler

11

AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution


bull make logical deductions make inferences and draw conclusions from given mathematical data

bull recognise patterns and structures in a variety of situations and form generalisations

bull present arguments and chains of reasoning in a logical and structured way

bull interprete and communicate information accurately and change from one form of presentation to another

bull assesses the validity of an argument and critically evaluate a given way of presenting information

bull solve unstructured problems by putting them into a structured form involving a series of processes

bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving

bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained


Recognise and extent patterns

Take information and organise it to answer a problem

12

Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context

Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment

37wwwcambridgeinternationalorgigcseBack to contents page

Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context

Command word What it means

Calculate work out from given facts figures or information generally using a calculator

Construct make an accurate drawing

Describe state the points of a topicgive characteristics and main features

Determine establish with certainty

Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence

Give produce an answer from a given source or recallmemory

Plot mark point(s) on a graph

Show (that) provide structured evidence that leads to a given result

Sketch make a simple freehand drawing showing the key features

Work out calculate from given facts figures or information with or without the use of a calculator

Write give an answer in a specific form

Write down give an answer without significant working

The question below is taken from Paper 4 and illustrates the use of two command words

The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this

The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result

The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space

13

This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response

This section is structured as follows

QuestionThe command words and instructions in the question have

been highlighted and explained This should help you to understand clearly what is required by the question

Mark schemeThis tells you as clearly as possible what an examiner expects

from an answer to award marks

Example candidate responseThis an exemplar answer written in the style of

a high level candidate

How the answer could have been improvedThis summarises what could be done to gain more marks

All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do

Common mistakesThis will help you to avoid common mistakes made by

candidates So often candidates lose marks in their exams because they misread or misinterpret the questions

Section 5 Example candidate response

14

QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see 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

This means that you cannot find the answer by

measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks

The allocation of 1 mark indicates that the answer can be obtained with minimum working

Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer

Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks

15

Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached

Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer

Learner Guide

16

Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question

(a)(ii) 74 1 This is the only acceptable answer for this part of the question

(b) 43deg and correct mathematical reasons

3 Two marks are awarded for the final answer of 43deg

The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used

If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working

180 ndash 128 or 128 ndash 85

(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question

The answer has to be rounded correct to three significant figures or can be given with more figures in the answer

Those that did not get this answer can score one method mark for showing the following in their working

sin = 8 divide 15

(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not

show this can have one method mark for showing the following in their working

300deg + 225deg

(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks

If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers

Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade

Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers

Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method

example of a final answer

example of a method mark

17

Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13

180 ndash 74 + 71 = 177

177

74

0 out of 1

The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question

1 out of 1

The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg

180 ndash 128 = 52 180 ndash 85 ndash 52 = 43

43 angles on a straight line add up to 180deg

2 out of 3

The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg

sin p = 8 divide 15 = 053

p = sinndash1 (053)

p = 32005 320

1 out of 2

The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make

18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2

The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line

T = = = 08333333hellip

08333333 hours = 08333333 times 60 minutes = 50 minutes

arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4

The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer

19

How the answer could have been improvedThis answer could have been improved by

bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question

bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable

bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures

bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious

bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well

Common mistakesThere were a number of common mistakes made by other candidates on this question

bull Accuracy of answers

In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures

bull Using incorrect terminology when giving reasons

In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks

bull Lack of knowledge

In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important

bull Not checking answers

In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working

20

bull Inefficient method shown

In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem

General adviceIn order to do your best when answering a mathematics question make sure you

bull revise all of the topics for the syllabus you are studying before the exam

bull understand what all the key terms and command words in the question mean

bull read the questions carefully and consider what you need to do before you do it

bull only round the final answer not intermediate values

bull show all steps in your working and show them clearly

bull round to the correct degree of accuracy

bull use the correct mathematical terminology

bull check your answers seem reasonable given the context or details of the question

21

It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers

Use the tick boxes to keep a record of what you have done what you plan to do or what you understand

For more advice on revision see the Cambridge Learner Revision Guide on our website

Section 6 Revision

Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic

Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course

Write a summary of all the key information for a topic ndash use the checklists at the end of this section

Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean

Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths

Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly

Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions

Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things

Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded

Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator

Practice the areas you can do well not just those that you find more difficult

Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising

Before the examination

22

During the examination

Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time

Read each question very carefully

Identify the command words ndash you could underline or highlight them

Identify the other key words and information and perhaps underline them too particularly where

questions require reasoning or problem solving

Read the questions careully and make you have answered the question that is being asked

Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo

Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space

Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures

Check your working and answers to avoid errors

Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper

Avoid rounding intermediate values part way through your calculation only round the final answer

Check that the answer that you have given is sensible and realistic for what is being asked

Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake

Take care when reading scales

If you are asked for reasons for your answer then use the correct mathematical terms

Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part

23

Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam

i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice

questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of

the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you

collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge

v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic

On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve

Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute

2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas

i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo

ndash The first branches are from the central topic to sub-topics draw these as thick lines

ndash Add new branches from the sub-topics to include more detail draw these as thinner lines

ndash Add even more detail to a point by adding more branches

This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)

iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens

24

3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision

i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-

whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation

4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic

i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers

ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course

iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the

correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space

in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs

5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is

i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme

ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this

iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check

iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later

You can find plenty of past exam papers and mark schemes on the Cambridge International public website

httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers

25

Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it

bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks

bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on

bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand

bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination

Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher

You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows

bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help

bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic

As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise

You can use the lsquoCommentsrsquo column to

bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about

There is a set of checklist for the Core syllabus and a different set for the Extended syllabus

Learner Guide

26

Core syllabus contentCore Number

Category You should be able to R A G CommentsNumber Identify and use

bull natural numbers

bull integers (positive negative and zero)

bull prime numbers

bull write a number as a product of its prime factors

bull square numbers and cube numbers

bull common factors and highest common factor of two numbers

bull common multiples and lowest common multiple of two numbers

bull rational numbers

bull irrational numbers (eg π radic2 )

bull real numbers

bull reciprocals

Learner Guide

27

Core Number

Question type You should be able to R A G CommentsSets and Venn diagrams

Understand notation of Venn diagrams

Definition of sets

eg A = xx is a natural number

B = abchellip

Notation

Number of elements in set A n(A)

Universal set

Union of A and B A cup B

Intersection of A and B A cap B

Squares square roots cubes and cube roots

Calculate

bull squares and cubes of numbers

bull square roots and cube roots of numbers

Learner Guide

28

Core Number

Question type You should be able to R A G CommentsDirected numbers

Use directed numbers in practical situations for example temperature changes

Fractions decimals and percentages

Use the language and notation of simple vulgar and decimal fractions and percentages

Recognise equivalent fractions decimals and percentages

Convert between fractions decimals and percentages

Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽

Indices and standard form (links to Algebraic manipulation)

Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23

Use the rules of indices for

bull multiplication of indices eg 4ndash3 times 45

bull division of indices eg 57 divide 53

bull index numbers raised to an index eg (23)2 (43)2

Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10

bull convert numbers into and out of standard form

bull calculate with numbers in standard form

Learner Guide

29

Core Number

Question type You should be able to R A G CommentsFour rules

( + ndash times divide )

Use the four rules for calculations with

bull whole numbers

bull decimals

bull vulgar and mixed fractions

bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths

Give approximations to a specified number of

bull significant figures

bull decimal places

Round off answers to reasonable accuracy in the context of a given problem

Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths

Ratio proportion rate

Understand ratio

Divide a quantity in a given ratio

Understand direct and inverse proportion

Use scales in practical situations

Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)

Calculate average speed

Learner Guide

30

Core Number

Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity

Express one quantity as a percentage of another quantity

Calculate percentage increase or decrease

Use of an electronic calculator

Use a calculator efficiently

Check accuracy of calculations

Time Calculate times in terms of the 24-hour and 12-hour clock

Read

bull clocks

bull dials

bull timetables

Money Calculate using money

Convert from one currency to another

Learner Guide

31

Core Number

Question type You should be able to R A G CommentsPersonal and small business finance

Use given data to solve problems on

bull earnings

bull simple interest

bull compound interest (you will need to know the compound interest formula)

bull discount

bull profit and loss

Extract data from tables and charts

Learner Guide

32

Core Algebra and graphs

Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers

Express basic arithmetic processes algebraically

Substitute numbers in formulae

Construct simple expressions and set up simple equations

Rearrange simple formulae

Algebraic manipulation

Manipulate directed numbers

Use brackets

bull expand a single bracket eg 3x(2x ndash4y)

bull expand a pair of brackets eg (x + 3) (x ndash 7)

Extract common factors eg factorise 9x2 + 15xy

Rules of indices Use and interpret positive negative and zero indices

Use the rules of indices eg to simplify algebra such as

bull 3x4 times 5x

bull 10x3 divide 2x2

bull (x6)2

Learner Guide

33


Question type You should be able to R A G CommentsEquations and inequalities

Derive and solve simple linear equations in one unknown

Derive and solve simultaneous linear equations in two unknowns

Number sequences

(links to Squares square roots cubes and cube roots)

Continue a number sequence

Recognise patterns in sequences

Recognise relationships between difference sequences

Find the nth term of sequences for

bull liner sequences

bull simple quadratic sequences

bull cubic sequences

Practical graphs

(links to Mensuration)

Interpret and use graphs in practical situations including

bull travel graphs

bull conversion graphs

Draw graphs from given data

Learner Guide

34


Question type You should be able to R A G CommentsGraphs of functions

(links to Co-ordinate geometry)

Construct tables of values for functions of the form

bull ax + b (linear)

bull plusmn x2 + ax + b (quadratic)

bull (x ne 0) (reciprocal)

where a and b are integer constants

Draw and interpret such graphs

Solve linear and quadratic equations approximately by graphical methods

Recognise and sketch the graphs of linear and quadratic functions

ax

Learner Guide

35

Core Co-ordinate geometry

Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions

Gradients Find the gradient of a straight line graph

Equation of straight line

Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given

Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)

Learner Guide

36

Core Geometry

Question type You should be able to R A G CommentsGeometrical language

Use and interpret the geometrical terms

bull point

bull line

bull parallel

bull perpendicular

bull bearing

bull right angle acute obtuse and reflex angles

bull similar

bull congruent

Use and interpret the vocabulary of

bull triangles right-angled scalene isosceles equilateral

bull quadrilaterals

bull circles

bull polygons

bull simple solid figures including nets

Learner Guide

37

Core Geometry

Question type You should be able to R A G CommentsGeometrical constructions

Measure and draw lines and angles

Construct a triangle given the three sides using a ruler and a pair of compasses only

Scale drawings Read and make scale drawings

Similar figures Calculate lengths of similar figures

Congruent Recognise congruent shapes

Symmetry Recognise symmetry properties for triangles quadrilaterals and circles

Recognise line symmetry in two dimensions

Recognise and find the order of rotational symmetry in two dimensions

Learner Guide

38

Core Geometry

Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you

are using in geometrical language for angles

bull angles at a point

bull angles on a straight line and intersecting straight lines

bull angles within parallel lines

bull angles in triangles

bull angles in quadrilaterals

bull angles in regular polygons

bull angle in a semi-circle

bull angle between tangent and radius of a circle

Learner Guide

39

Core Mensuration

Question type You should be able to R A G CommentsMeasures bull Use current units of

bull mass

bull length

bull area

bull volume

bull capacity

Express quantities in terms of smaller or larger units including units of area and volume

Convert between units including units of area and volume

Perimiter Carry out calculations involving

bull perimeter and area of a rectangle

bull perimeter and area of a triangle

bull perimeter and area of parallelogram

bull perimeter and area of a trapezium

bull perimeter and area of shapes made by combining

bull rectangles triangles parallelograms andor trapeziums

Learner Guide

40

Core Mensuration

Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a

circle

Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg

Surface area and volume

Carry out calculations involving

bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)

bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)

Areas and volumes of compound shapes

Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume

Learner Guide

41

Core Trigonometry

Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise

from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by

applying

bull Pythagorasrsquo theorem

bull sine cosine and tangent ratios for acute angles in right-angled triangles

Learner Guide

42

Core Vectors and transformations

Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)

Describe a translation by using a vector represented by

AB or a

Add and subtract vectors

Multiply a vector by a scalar

Transformations Reflect simple shapes in horizontal or vertical lines

Rotate simple shapes through multiples of 90deg about

bull the origin

bull their vertices

bull the midpoints of their sides

Construct translations of simple shapes

Construct enlargements of simple shapes (positive and fractional scale factors)

Recognise and describe using the correct language

bull reflections

bull rotations

bull translations

bull enlargements (positive and fractional scale factors)

( )x

y

Learner Guide

43

Core Probability

Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal

or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1

Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring

Relative frequency

Understand relative frequency as an estimate of probability

Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using

bull tree diagrams

bull possibility diagrams (points on a grid)

bull Venn diagrams (2 sets only)

Learner Guide

44

Core Statistics

Question type What I need to do R A G CommentsClassify Collect classify and tabulate data

Interpret and compare

Read interpret and draw simple inferences from tables and statistical diagrams

Compare sets of data using

bull tables

bull graphs

bull statistical measures

Be aware of restrictions when making conclusions from data

Charts Construct and use

bull bar charts

bull pie charts

bull pictograms

bull stem-and-leaf diagrams

bull frequency distributions

bull histograms with equal intervals

bull scatter diagrams

Learner Guide

45

Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data

bull mean

bull median

bull mode

bull range

and distinguish between their useCorrelation Understand what is meant by positive negative and zero

correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye

Learner Guide

46

Extended syllabus content (includes required Core content)Extended Number

Question type You should be able to R A G CommentsNumber Identify and use



bull prime numbers


bull square and cube numbers

bull common factors and highest common factor of two or more numbers

bull common multiples and lowest common multiple of two or more numbers



bull real numbers

bull reciprocals

Learner Guide

47

Extended Number

Question type You should be able to R A G CommentsSet notation and language

Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows

Definition of sets egA = x x is a natural number

B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip

Notation egnumber of elements in set A n(A)

lsquois an element ofrsquo isin

lsquois not an element ofrsquo notin

complement of set A

the empty set empty

the universal set

A is a subset of B A sube B

A is a proper subset of B A sub B

A is not a subset of B A ⊈ B

A is not a proper subset of B A nsub B

union of A and B A cup B

intersection of A and B A cap B

Learner Guide

48

Extended Number

Question type You should be able to R A G CommentsSquares square roots cubes and cube roots

Calculatebull squares of numbers

bull square roots of numbers

bull cubes of numbers

bull cube roots of numbers

bull other powers and roots of numbers

Directed numbers



Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts



Convert recurring decimals to fractions


Learner Guide

49

Extended Number

Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)

Evaluate indices including fractional negative and zero

eg 25 5ndash2 1000 10012 8ndash23

Use the rules of indices forbull multiplication of indices eg 43 times 45


bull index numbers raised to an index eg (43)2

Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form


Four rules


Use the four rules for calculations withbull whole numbers

bull decimals


bull correct ordering of operations (BIDMAS) and use of brackets

Learner Guide

50

Extended Number

Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths



bull decimal places



Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle


(links to Direct and inverse proportion)

Understand ratio

Divide quantities in a given ratio

Increase and decrease a quantity by a given ratio

Understand numerical problems involving direct and inverse proportion

Use ratio and scales in practical situations



Learner Guide

51

Extended Number

Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity



Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit





Read clocks dials and timetables



Learner Guide

52

Extended Number



bull earnings


bull compound interest

ndash you must know the compound interest formula

bull discount



Exponential growth and decay

Use exponential growth and decay in population and finance eg depreciation bacteria growth

Learner Guide

53

Extended Algebra and graphs



Substitute numbers in complicated formulae

Construct and rearrange complicated formulae eg where the subject appears twice



Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)

bull expand a pair of brackets eg (x ndash 4)(x + 7)

bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)


Factorise expressions of the formbull ax + bx + kay + kby

bull asup2xsup2 ndash bsup2ysup2

bull asup2 + 2ab + bsup2

bull axsup2 + bx + c

Learner Guide

54


Question type You should be able to R A G CommentsAlgebraic fractions

Manipulate algebraic fractions eg

bull

bull

bull

bull

bull

Factorise and simplify algebraic fractions such as


Use and interpret fractional indices eg solve 32x = 2

Use the rules of indices to simplify algebra eg

x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3

x2 ndash 2xx2 ndash 5x + 6

3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55



bull Derive and solve simple linear equations in one unknown

bull Derive and solve simultaneous linear equations in two unknowns

bull Derive and solve simultaneous equations involving one linear and one quadratic

Solve quadratic equations by

bull factorisation

bull completing the square

bull using the formula

Derive and solve simple linear inequalities including representing solutions on a number line

Linear programming

Represent inequalities graphically including using the conventions of

bull broken lines for strict inequalities

bull shading unwanted regions

Solve simple linear programming problems using graphical representations of inequalities

Learner Guide

56


Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)



Recognise relationships between different sequences

Find the nth term of sequences of

bull linear sequences

bull quadratic sequences


bull exponential sequences

and simple combinations of these

Direct and inverse proportion (links to Ratio proportion rate)

Express direct proportion algebraically

Express inverse proportion algebraically

Use algebraic expressions of direct and inverse proportion to find unknown quantities

Practical graphs

(links to Coordinate geometry)


bull travel graphs



Learner Guide

57


Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued

Apply the idea of rate of change to simple kinematics involving

bull distancendashtime graphs

bull speedndashtime graphs

bull acceleration and deceleration

This may involve estimation and interpretation of the gradient of a tangent at a point

Calculate distance travelled as an area under a linear speedndash time graph

Learner Guide

58


Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)

Construct tables of values and draw graphs for functions of the form

bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these

bull abx + c where a and c are rational constants and b is a positive integer

Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square

Draw and interpret graphs representing exponential growth and decay problems

Recognise sketch and interpret graphs of

bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential

(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents

Learner Guide

59


Question type You should be able to R A G CommentsFunctions Use function notation eg

f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions

Find inverse functions f ndash1 (x)

Form composite functions as defined by gf(x) = g(f(x))

Derivatives Understand the idea of a derived function

Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)

Apply differentiation to gradients and turning points (stationary points)

Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point

Learner Guide

60

Extended Co-ordinate geometry

Question type You should be able to R A G CommentsStraight line graphs

Work with co-ordinates in two dimensions

Gradient Find the gradient of a straight line graph

Calculate the gradient of a straight line from the co-ordinates of two points on it

Length and midpoint

Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points

Equation of line Interpret and obtain the equation of a straight line graph


Perpendicular lines

Find the gradient of parallel and perpendicular lines eg

bull find the gradient of a line perpendicular to y = 3x + 1

bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)

Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry

Question type What I need to do R A G CommentsGeometrical constructions





Use relationships between areas of similar triangles and in similar figures

Use relationships between volumes and surface areas of similar solids

Congruent triangles

Use the congruence criteria for triangles (SSS ASA SAS RHS)




Learner Guide

63

Extended Geometry

Question type You should be able to R A G CommentsSymmetry (continued)

Use the following symmetry properties of circles

bull equal chords are equidistant from the centre

bull perpendicular bisector of a chord passes through the centre

bull tangents from an external point are equal in length

Recognise and use symmetry properties of

bull prism cylinder cone and pyramid

Learner Guide

64

Extended Geometry

Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that

you are using in geometrical language for the following geometrical properties


bull angles at a point on a straight line and intersecting straight lines

bull angles formed within parallel lines

bull angle properties of triangles and quadrilaterals

bull angle properties of regular polygons



bull angles properties of irregular polygons

bull angle at the centre of a circle is twice the angle at the circumference

bull angles in the same segment are equal

bull angles in opposite segments are supplementary cyclic quadrilaterals

bull alternate segment theorem

Learner Guide

65

Extended Mensuration

Question type What I need to do R A G CommentsMeasures Use current units of

bull mass

bull length

bull area

bull volume

bull capacity


Perimeter Carry out calculations involving





bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums

Learner Guide

66



circle

Solve problems involving arc length and sector area of a circle





Compound shapes


bull area of a shape made by combining cuboids prisms andor cylinders

bull volume of a shape made by combining cuboids prisms andor cylinders

Learner Guide

67

Extended Trigonometry



applying



Solve problems in two dimensions involving angles of elevation and depression

Know that the perpendicular distance from a point to a line is the shortest distance to the line

Trig graphs and equations

Recognise sketch and interpret graphs of simple trigonometric functions

Graph and know the properties of trigonometric functions

Solve simple trigonometric equations for values between 0deg

and 360deg eg Solve sin x = radic32

for values of x between 0deg and

360degGeneral trig Solve problems using sine and cosine rules for any triangle

Find the area of any triangle using frac12absinC

Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane

Learner Guide

68

Extended Vectors and transformations



AB or a




Rotate simple shapes through multiples of 90deg about any point


Construct enlargements of simple shapes (positive fractional and negative scale factors)

Recognise and describe

bull reflections

bull rotations

bull translations

bull enlargements (positive fractional and negative scalefactors)

( )x

y

Learner Guide

69


Question type You should be able to R A G CommentsHarder vectors

Calculate the magnitude of a vector as and

understand that magnitude is denoted by modulus signs |A B| or |a|

Represent vectors by directed line segments

Use the sum and difference of two vectors

Use position vectors

( )x

yradicx2 + y2

Learner Guide

70

Extended Probability

Question type You should be able to R A G CommentsProbability (links to Four rules)

Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)

Probability scale Understand and use the probability scale from 0 to 1


Relative frequency


Work out expected frequencies using relative frequency

Combined events Calculate the probability of combined events using

bull tree diagrams

bull possibility diagrams

bull tables

Learner Guide

71

Extended Statistics

Question type You should be able to R A G CommentsClassify Collect classify and tabulate data




bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms

bull stem ndash and ndash leaf diagrams


bull histograms with equal and unequal intervals


Learner Guide

72

Extended Statistics

Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data

bull mean

bull median

bull mode

bull range

and distinguish between their use

Estimated mean Calculate an estimate of the mean for grouped and continuous data

Identify the modal class from a grouped frequency distributionCumulative frequency

Construct and use cumulative frequency diagrams to estimate and interpret

bull the median

bull percentiles

bull quartiles

bull inter-quartile range

Construct and interpret box-and-whisker plots

Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram

Lines of best fit Draw interpret and use a ruled line of best fit by eye

Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg

Copyright copy UCLES October 2017

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2

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3

About this guide 4






Contents

4


It will help you to






About this guide

Key benefits



5




Topic Overview















6








1 hour


35


2 hours

104 marks 65


1 hour 30 minutes


35


2 hours 30 minutes

130 marks 65


Core Extended


7




Paper 3Paper 1







8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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3

About this guide 4






Contents

4


It will help you to






About this guide

Key benefits



5




Topic Overview















6








1 hour


35


2 hours

104 marks 65


1 hour 30 minutes


35


2 hours 30 minutes

130 marks 65


Core Extended


7




Paper 3Paper 1







8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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Text Field 3063




Text Field 309

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Text Field 3012

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Text Field 3013




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Text Field 3015

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Text Field 3016

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Text Field 3017







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Text Field 3019

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Text Field 3020

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4


It will help you to






About this guide

Key benefits



5




Topic Overview















6








1 hour


35


2 hours

104 marks 65


1 hour 30 minutes


35


2 hours 30 minutes

130 marks 65


Core Extended


7




Paper 3Paper 1







8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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Text Field 315

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5




Topic Overview















6








1 hour


35


2 hours

104 marks 65


1 hour 30 minutes


35


2 hours 30 minutes

130 marks 65


Core Extended


7




Paper 3Paper 1







8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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Text Field 351













Text Field 318

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6








1 hour


35


2 hours

104 marks 65


1 hour 30 minutes


35


2 hours 30 minutes

130 marks 65


Core Extended


7




Paper 3Paper 1







8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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Text Field 3025

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Text Field 3060


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Text Field 3063




Text Field 309

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Text Field 3017







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Text Field 315

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Text Field 351













Text Field 318

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Text Field 338


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7




Paper 3Paper 1







8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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Text Field 3063




Text Field 309

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Text Field 338


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8






Paper 4Paper 2




9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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9

















10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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10





















11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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11














12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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12






















13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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13














14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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14







15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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15



Learner Guide

16











sin = 8 divide 15



300deg + 225deg








17


180 ndash 74 + 71 = 177

177

74

0 out of 1


1 out of 1




2 out of 3



p = sinndash1 (053)

p = 32005 320

1 out of 2


18

AB2 = 3002 + 2252

= 140625

AB = 375

1 out of 2


T = = = 08333333hellip


arrives at 14 45 + 50 mins = 3 35

DS

375450

3 35

3 out of 4


19
















20












21




Section 6 Revision














22



















23
















24

















25














Learner Guide

26





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

27

Core Number



Definition of sets


B = abchellip

Notation


Universal set




Calculate



Learner Guide

28

Core Number

















Learner Guide

29

Core Number




bull whole numbers

bull decimals





bull decimal places




Understand ratio






Learner Guide

30

Core Number








Read

bull clocks

bull dials

bull timetables



Learner Guide

31

Core Number



bull earnings



bull discount



Learner Guide

32









Use brackets






bull 3x4 times 5x


bull (x6)2

Learner Guide

33





Number sequences









Practical graphs



bull travel graphs



Learner Guide

34












ax

Learner Guide

35







Learner Guide

36

Core Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

37

Core Geometry










Learner Guide

38

Core Geometry











Learner Guide

39

Core Mensuration


bull mass

bull length

bull area

bull volume

bull capacity










Learner Guide

40

Core Mensuration


circle








Learner Guide

41

Core Trigonometry



applying



Learner Guide

42




AB or a





bull the origin

bull their vertices





bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

43

Core Probability




Relative frequency



bull tree diagrams



Learner Guide

44

Core Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

45


bull mean

bull median

bull mode

bull range



Learner Guide

46





bull prime numbers







bull real numbers

bull reciprocals

Learner Guide

47

Extended Number




B = (xy) y = mx + c

C = x a ⩽ x ⩽ b

D = a b c hellip




complement of set A

the empty set empty

the universal set







Learner Guide

48

Extended Number







Directed numbers








Learner Guide

49

Extended Number



eg 25 5ndash2 1000 10012 8ndash23






Four rules



bull decimals



Learner Guide

50

Extended Number




bull decimal places






Understand ratio







Learner Guide

51

Extended Number












Learner Guide

52

Extended Number



bull earnings




bull discount





Learner Guide

53
















Learner Guide

54




bull

bull

bull

bull

bull





x3 + x ndash 4

22x3 +

3(x ndash 5)2

3a4 +

5ab3

3a4 divide

9a10

1x ndash 2 +

2x ndash 3


3xndash4 times23

x12

32x5( )

3

2xndash2divide25

x12

Learner Guide

55







bull factorisation




Linear programming





Learner Guide

56
















Practical graphs



bull travel graphs



Learner Guide

57









Learner Guide

58









bull linear

bull quadratic

bull cubic

bull reciprocal

bull exponential


Learner Guide

59










Learner Guide

60






Length and midpoint




Perpendicular lines




Learner Guide

61

Extended Geometry



bull point

bull line

bull parallel

bull perpendicular

bull bearing


bull similar

bull congruent



bull quadrilaterals

bull circles

bull polygons


Learner Guide

62

Extended Geometry








Congruent triangles





Learner Guide

63

Extended Geometry








Learner Guide

64

Extended Geometry















Learner Guide

65



bull mass

bull length

bull area

bull volume

bull capacity








Learner Guide

66



circle






Compound shapes




Learner Guide

67




applying














Learner Guide

68




AB or a








bull reflections

bull rotations

bull translations


( )x

y

Learner Guide

69








( )x

yradicx2 + y2

Learner Guide

70






Relative frequency




bull tree diagrams


bull tables

Learner Guide

71

Extended Statistics





bull tables

bull graphs




bull bar charts

bull pie charts

bull pictograms





Learner Guide

72

Extended Statistics


bull mean

bull median

bull mode

bull range





bull the median

bull percentiles

bull quartiles







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