Extended Mathematics For Igcse David Rayner Pdf Third Edition

N e w t h i r d e d i t i o n s

Endorsed by

University of Cambridge International Examinations

www.oxfordsecondary.co.uk/igcse

Visit us online to download some FREE worksheets from the Teacher's Resource Kits

Core and Extended

Mathematics

for Cambridge IGCSE

David Rayner

These internationally trusted Mathematics texts are now part of a

full course

complete with

teacher's resources

Why choose Oxford?

✓

Brand new Teacher's Resource Kits

loaded with worksheets, lesson plans and activities on CD-ROM that you

can fully customise

to suit the needs of your class

✓

New student CD-ROMs

with dedicated revision sections, a suite of mock exams, and even more practice questions, to ensure complete preparation

✓

Fully

differentiated resources

dedicated to fostering excellence amongst your most able, while supporting your lower-abilities in achieving the

best possible results

✓

Concise, straightforward language

which focuses on the Mathematics to support your EAL students

Concerned about covering the complete syllabus? Use the Teacher's CD-ROM to see exactly how the Student Book matches the syllabus, complete with page references.

Fully differentiated Student Books with brand new CD-ROMs

Endorsed by

University of Cambridge International Examinations

Help all of your students achieve their full potential in exams. Teachers all over the world trust David Rayner's

straightforward and practice-based approach

, which really helps students

focus on the Mathematics

and boost exam potential. Plus, new digital material means that students can now choose how they learn, with even more practice questions, revision support, and a whole suite of past exam questions. Accompanying teacher support and Revision Guide now available.

New Teacher's Resource Kits for a truly complete Cambridge IGCSE Mathematics course

Endorsed by

University of Cambridge International Examinations

Incorporating everything IGCSE Mathematics teachers say they need, these supportive kits will help you

align your teaching with the most recent Cambridge IGCSE syllabus

. Plus, they include customisable CD-ROMs so

you can tailor your teaching resources

to meet the needs of your students – whether that be ability, context or the freedom to easily add in your own questions!

Extended Mathematics for Cambridge IGCSE: Student CD-ROM

These new student CD-ROMs provide everything your students need to achieve the best possible result in exams

✓

Flexible approach

– students can practise and revise how they learn best, using the book or the CD-ROM

✓

Lessons are extended and solidiﬁed with even more practice questions and

conceptual support

✓

Dedicated 'Revision Section'

ensures students have the skills they need to succeed in exams

✓

A whole suite of past Cambridge IGCSE exam papers

ensures there are no surprises come exam time

Plus, the Teacher's Resource Kit comes with a free CD-ROM for structured and effective lessons with quick and painless planning!

✓

Differentiated, customisable worksheets

, levelled for all abilities

✓

Repeated

lesson plans

from the Teacher's book in digital form

✓

All the answers and

past exam questions

from the Student Book

✓

Clearly outlined links with the most recent Cambridge IGCSE syllabus, so you can be sure your teaching is

completely up-to-date

Extended Mathematics for Cambridge IGCSE

Student text

The scale of a map is 1:1000. What is the area, in cm

, on the map of a lake of area 5000m

The scale of a map is 1cm to 5km. A farm is represented by a rectangle measuring 1

󿿽

5cm by 4cm. What is the actual area of the farm?

On a map of scale 1cm to 250m the area of a car park is 3cm

. What is the actual area of the car park in hectares? (1hectare

10000m

)

The area of the playing surface at the Olympic Stadium in Beijing is

3 5

of a hectare. What area will it occupy on a plan drawn to a scale of 1:500?

On a map of scale 1:20000 the area of a forest is 50cm

. On another map the area of the forest is 8cm

. Find the scale of the second map.

1.6

Percentages

Percentages are simply a convenient way of expressing fractions or decimals. '50% of $60' means

50 100

of $60, or more simply

1 2

of $60. Percentages are used very frequently in everyday life and are misunderstood by a large number of people. What are the implications if 'inﬂation falls from 10% to 8%'? Does this mean prices will fall?

Example

(a) Change 80% to a fraction. (b) Change

3 8

to a percentage. (c) Change 8% to a decimal. (a) 80%

80 100

4 5 (b) 3 8

3 8

�

100 1

 

1 2

% (c) 8%

8 100

󿿽

Exercise 21

Change to fractions: (a) 60% (b) 24% (c) 35% (d) 2%

Change to percentages: (a)

1 4

(b)

1 10

(c)

7 8

(d)

1 3

(e) 0

󿿽

72 (f) 0

󿿽

Percentages

Change to decimals: (a) 36% (b) 28% (c) 7% (d) 13

􏿽

4% (e)

3 5

(f)

7 8

Arrange in order of size (smallest ﬁrst): (a)

1 2

; 45%; 0

􏿽

6 (b) 0

􏿽

38;

6 16

; 4% (c) 0

􏿽

111; 11%;

1 9

(d) 32%; 0

􏿽

1 3

The following are marks obtained in various tests. Convert them to percentages. (a) 17 out of 20 (b) 31 out of 40 (c) 19 out of 80 (d) 112 out of 200 (e) 2

1 2

out of 25 (f) 7

1 2

out of 20

Example 1

A car costing $400 is reduced in price by 10%. Find the new price. 10% of $2400

10 100

󿿽

2400 1

$240 New price of car

$(2400

�

240)

$2160

Example 2

After a price increase of 10% a television set costs $286. What was the price before the increase? The price before the increase is 100%.

;

110% of old price

$286

;

1% of old price

$ 286 110

;

100% of old price

$ 286 110

󿿽

100 1 Old price of TV

$260

Exercise 22

Calculate: (a) 30% of $50 (b) 45% of 2000kg (c) 4% of $70 (d) 2

􏿽

5% of 5000 people

Number

Fully updated and refreshed to match the most recent Cambridge IGCSE syllabus Questions are designed for the international classroom, with globally relevant context Focused approach helps students absorb important theories without distraction Lots and lots of graduated practice questions reinforce each concept, making sure that all variations are covered and understood Examples are used throughout to clearly demonstrate exactly how problems are solved, ensuring comprehension

Free Student CD-ROM

Extended Mathematics for Cambridge IGCSE Teacher's Resource Kit

Teacher's Kit – in print and digital

Mensuration

Exercise commentary

Questions1to4

and

questions 6and7

inexercise1arebasic exampleswhereas

questions5, 8and9

aremoreinvolved.More ablestudentswillnaturallyneedless routinepractice.

Questions10to 14

testthestudents'abilitytowork backwardswhile

questions15to 20

testproblem-solving.Thesecould beusedasextensionquestions. Exercise2 looksat trianglesand parallelograms.

Questions13 to 17

are routine practice (diagramsgiven) whilemanyof theother questions requirean accuratesketch and the use of trigonometry. Depending on theabilityof thestudentsand their trigonometricknowledge, these could beused sparingly. The exercise could be supplemented to provide further (simple) examplesfor less able students. From

question 24

onwards, studentsare problem-solving and working backwardsto ﬁnd missing dimensions. These questionscould beused asextension questions for more ablestudentsor simply avoided.

CHAPTER 3

MENSURATION

Lessons 1 and 2

– Area

Textbook pages92–7

Expectedpriorknowledge

Atthislevel,studentsshouldbefamiliarwith theformulaefortheareaofsimplegeometricalﬁgures.Theselessons provideanexcellentopportunitytorevisetheseformulaeandpracticeboth problem-solvingquestionsandoneswheretheyhavetoworkbackwards.

Objectives

31: Carry outcalculationsinvolving the area ofa rectangle and triangle, the area ofa parallelogram and trapezium (and kite).

Starter

Askstudentsto writedown thenamesof asmanyquadrilateralsas they can in60 seconds. Pool answersasagroup.

Lessoncommentary

●

Afast paced questionand answer session will test students' recall of theformulaefor theareaof arectangleand atriangle. Similarly, they should alsobeableto workout theareasof simple parallelogramsandtrapeziums. Although trapeziumsmayneed further revision sincetheformulaislessfamiliar. Encourage studentsto worktogether andcheck that studentsarehappy when theorientation of theshapeis'non-standard'.

●

Introduce'reverse'exampleswheremissingdimensionsneedtobe foundandinvitestudentstodiscussthemethodstheymightuse.Rather thanmodellingastandardapproach,encouragestudentstodevelop theirownmethods,thekeyobjectivebeingtogetthecorrectanswer.

●

Thesecondlessonwillprovidestudentswithanopportunityto furtherconsolidatethisworkandmoreablestudentswillbeneﬁtfrom workingonchallengingquestions.

Plenary

Ask studentsto createacompound shapeand marksufﬁcient lengths to enableanother student to workout the areaof it. Studentscould then swap shapesand solveeach other'sproblemsbefore discussing the answersat the end. Check studentshavecorrectlysolved their problems and discussanyissues(not enough information, etc.) The supplementaryworksheet for Chapter 3 maybeusefulto support lessons1, 4 and 5. The extension worksheet for Chapter 3 maybe usefulto support lesson 3.

Mensuration

Lessons 3 and 4

– The circle

Textbook pages97–101

Expected priorknowledge

Studentsshould havemet theformulae for theareaand circumferenceof acirclebeforeand thereforethese lessonsprovidean ideal opportunity to revisetheseand work on more difﬁcult questions.

Objectives

31: Carryoutcalculationsinvolving the circumference and area ofa circle.

Starter

Ask studentsto writedown asmany partsof thecircle(radius, circumference, sector, diameter, arc, etc.) that they can in oneminute. Theycanthen compareanswersand you can haveashort discussion asto what theyhavewritten down (making surestudentscan deﬁne them).

Plenary

Afast paced quizwhich not onlytestsgoing forwardswith the formulae but also includesexampleswhich need to be worked backwards. Include asemicircle or quadrant. Studentscould be given 30 secondsto work out theanswerson their calculatorsfor each one.

Exercise commentary

Questions1and2

inexercise3are routinepracticewhichmayneedto besupplemented,dependingonthe abilityofthegroup.From

question3

onwards,studentsareworkingwith semicircles,quadrantsandcompound shapes.Ensurethattheyaresetting outtheirworkingclearlyinorderto communicatetheirsolutionsproperly.

Questions1to4

inexercise4are examplesofworkingbackwards while

questions5and6

require studentstogofromareato circumferenceorviceversa.From

question7

onwards,thequestions testthestudents'abilitytosolve problemsinvolvingthecircumference andareaofcirclesandcouldbeused moreextensivelyforablegroupsand forextensionwork.

Lessoncommentary

●

Students'familiaritywiththeformulaefortheareaandcircumferenceofacirclecouldbegiventhediameter orradiusofacircleandthenbeaskedtoquicklyworkoutthecircumferenceorareausingthestandard formulaeandwritedowntheanswers.Avoidusingradiusforcircumferenceanddiameterforareaatthisstage.

●

Developtheuseof theformulaefor caseswherediameter isgiven for areaand radiusfor circumferenceto ensurethat studentsarehappy to work with either. Thisisoften acommon areafor mistakessincestudents just without thinking'plug in' thenumber given. Work also with aseriesof exampleswhich go backwards. Youcoulddo thisasathought experiment. Ask questionslike'what would happen if you weregiven the circumferenceand asked to ﬁnd thediameter?' Try to avoid any moreformulaehere(



for example) and get studentsto understand the

process

●

At thispoint, further practicecould begiven to thestudentsduring aconsolidation phaseof thelesson.

●

Introducemore'what if ...' situations. Thesecould begiven out on prepared worksheetsand could include areaof semicircle, perimeter of quadrant, etc. and studentscould begiven two or threeof these(in pairsor groupsif appropriate) and asked to justify their methods.

●

Thesecond lessonprovidesagood opportunity for further consolidation of thiswork.

Prior knowledge

introductions ﬂag up the knowledge required for each lesson, helping you prepare your students

Lesson commentaries

provide useful guidance and structure for lessons that you can easily infuse with your own ideas Plenary exercises accompany all lessons and add interactivity that will hold students' interest Lesson plans clearly indicate when to integrate each resource into your lessons

Exercise commentaries

help you quickly separate the basics from the challenges, helping you stretch and support all of your ability levels