IGCSE Mathematics Revision Guide
BRADFIELD COLLEGEIGCSE MathematicsRevision GuideBradfield College Maths Department20101 Page
ContentsIntroduction to the Revision Guide. 3Aims . 3How to use the guide . 3Using the different resources . 4IGCSE Book 1 and Book 2 . 4MEP Books . 4MyMaths . 4Overview of topics . 5Revising Number . 6Revising Algebra . 10Revising Shape, Space and Measures . 17Revising Handling data . 26Target setting . 292 Page
Introduction to the Revision GuideAimsThe aim of the revision guide is to provide you with a resource that you can use to link to theory,examples and practice questions.The four main areas to revise are: NumberAlgebraShape, space and measureHandling dataHow to use the guideThe tables that follow include the following information: A summary of the area, including an indication of whether it is a Foundation (F) or Higher(H) tier topic An example of a question relating to the topic A link to a textbook or online resource An indication of the level of difficulty of a particular topic. (Please treat this with care, it is aguide only) A self assessment column for you to review your own strengths and weaknessesBefore you start your revision there are two questions that you need to consider: What grade am I aiming for?What topics do I need to improve to achieve my target grade?You should use the self assessment column to identify areas that you need to improve to achieveyour goal. There is little benefit to be gained from practising topics that you can already doconfidently. Equally, if you want to achieve a B it is not worth spending too much time revising A*topics. Think about where you need to improve and target these areas. If you get stuck then askyour teacher or come along to a Surgery 3 Page
Using the different resourcesThe Revision Guide provides links to three main resources.IGCSE Book 1 and Book 2You should have a copy of IGCSE Book 2. Copies of IGCSE Book 1 are available in the MathsDepartment. When working through exercises remember that you can check your work by lookingat the answers to the odd questions in the back of the bookMEP BooksThere are three books: Unit 1‐6, Unit 7‐12 and Unit 13‐19. Hard copies of the books are available inthe Maths Department. Alternatively, you can click on the links to access the books online.If you want to check your answers look in the back of the textbook or use the following links: Solutions to Unit 1‐6Solutions to Unit 7‐12Solutions to Unit 13‐19MyMathsThere are links to both online lessons (L1, L2 etc) and online homeworks (H1, H2 etc). To log on toMyMaths you need to know: School Password: BradfieldSchool Login: SevenIf you want to keep track of your scores, you will also need an individual login and password. If youhaven’t got this already you can obtain this from your teacher. Alternatively, you can do thehomework tasks for fun. In this case you do not need an individual password.4 Page
Overview of topicsNumberN1 IntegersN2 FractionsN3 DecimalsN4 Powers and RootsN5 Set Language and NotationN6 PercentagesN7 Ratio and ProportionN8 Degree of AccuracyN9 Standard FormN10 Applying NumberN11 Electronic CalculatorsAlgebraEquations, Formulae and IdentitiesA1 Use of symbolsA2 Algebraic ManipulationA3 Expressions and FormulaeA4 Linear EquationsA5 ProportionA6 Simultaneous Linear EquationsA7 Quadratic EquationsA8 InequalitiesSequences, functions and graphsA9 SequencesA10 Functional NotationA11 GraphsA12 CalculusShape, Space and MeasuresGeometryS1 Angles and trianglesS2 PolygonsS3 SymmetryS4 MeasuresS5 ConstructionS6 Circle propertiesS7 Geometrical reasoningS8 Trigonometry and Pythagoras’ TheoremS9 MensurationS10 SimilarityVectors and Transformation GeometryS11 VectorsS12 Transformation GeometryHandling dataHD1 Graphical Representation of DataHD2 Statistical MeasuresHD3 ProbabilityNote that the breakdown of exam questions is likely to follow the split below: Number and AlgebraShape, Space and MeasureHandling data5 Page55%25%20%
IGCSE Mathematics NumberRevising NumberTopicSub topicNotes / example questionReferenceGradeN1 IntegersNegative numbers (F)Calculate 7CN1 IntegersBidmas (F)Calculate 2N1 IntegersPrime factors, lowestcommon multiple, highestcommon factor (F/H)Express 12 and 42 as the product of prime factors.Find the HCF and LCM of 12 and 42N2 FractionsEquivalent fractions, mixedSimplifynumbers and vulgar fractions(F)ConvertIGCSE 1: p2‐3MEP: Unit 1‐6: p30‐32, Unit7‐12: p184‐186MyMaths: L1, H1, L2, H2IGCSE 1: p2‐3MEP:MyMaths: L1, H1IGCSE 1: p124‐127MEP: Unit 1‐6: p11‐12MyMaths L1, H1, L2, H2, L3,H3IGCSE 1: p1‐2MEP:MyMaths: L1, H1, L2 , H2426to a mixed numberN2 FractionsConvert between fractions,decimals and percentages (F)Write 0.75 as a fraction and a percentageN2 FractionsAdd and subtract fractions(F)Work out 21N2 FractionsMultiply and divide fractions(F)Work out 146 PageIGCSE 1: p1‐2MEP: Unit 7‐12: p213‐217,p234‐236MyMaths: L1, H1, L2, H2IGCSE 1: p63‐64MEP: Unit 7‐12: p249‐252MyMaths: L1, H1IGCSE 1: p63‐64MEP: Unit 7‐12: p252‐256MyMaths: L1, H1, L2, H2, L3,H3Selfassessment1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/a
IGCSE Mathematics NumberTopicSub topicNotes / example questionReferenceGradeN3 DecimalsConvert recurring decimalsinto fractions (H)Change 0. 79 to a fractionBN4 Powersand rootsCalculate squares, squareroots, cubes and cube roots(F)Use index notation and indexlaws with positive integerpowers(F)Use index notation and lawswith fractional and negativepowers (H)Evaluate 8 , 16IGCSE 2: p5‐8MEP:MyMaths: L1, H1, L2, H2IGCSE 1:MEP: Unit 1‐6: p 3‐5MyMaths: L1, H1IGCSE 1: p79‐80MEP: Unit 1‐6: p 5‐9MyMaths: L1, H1IGCSE 2: p72‐76MEP: Unit 1‐6: p 13‐15MyMaths: L1, H1N4 Powersand rootsN4 Powersand rootsN4 Powersand rootsUnderstand and manipulatesurds (H)N5 SetLanguage andNotationUnderstand basic set theoryand notation(eg , , (F)N5 SetLanguage andNotationUnderstand more advancednotation (eg complement,subset and n(A) ) (H)N5 SetLanguage andNotationUse Venn Diagrams torepresent sets and use setsin practical situations (H)Find 22 ,7Evaluate 8 ,Simplify 3Rationalise76255 2 12 ,A 2, 4, 6, 8, 10 , B 4, 5, 5, 7, 8ListA 2, 4, 6, 8, 10 , B 4, 5, 5, 7, 8and find12 ,A 2, 4, 6, 8, 10 , B 4, 5, 5, 7, 8Show the information in a Venn Diagram7 PageC1 2 3 4 5n/aC1 2 3 4 5n/aA1 2 3 4 5n/aIGCSE 2: p260‐268MEP: Unit 1‐6: p246‐250MyMaths: L1, H1, L2, H2IGCSE 1: p43‐53MEP:MyMaths:A*1 2 3 4 5n/aB/C1 2 3 4 5n/aIGCSE 1: p43‐53IGCSE 2: p57‐65MEP:MyMaths:IGCSE 1: p43‐53IGCSE 2: p57‐65MEP:MyMaths:A/B1 2 3 4 5n/aA1 2 3 4 5n/aand12 ,ListSelfassessment1 2 3 4 5n/a
IGCSE Mathematics NumberTopicSub topicNotes / example questionReferenceGradeN6PercentagesExpress a number as apercentage of anothernumber (F)Solve simple percentageproblems including increaseand decrease (F)Solve inverse percentageproblems (H)Jack scores 72 out of 80 on a test. What is this as apercentage?CDivide a quantity in a givenratio and solve wordproblems about ratio (F)Round to a given number ofsignificant figures or decimalplaces (F)Use estimates to evaluateapproximations tocalculations (F)Identify upper and lowerbounds (F)Share 416 in the ratio 5:3IGCSE 1: p3‐5MEP: Unit 7‐12: p240‐242MyMaths:IGCSE 1: p3‐5, 119‐124MEP: Unit 7‐12: p242‐248MyMaths: L1, H1, L2, H2IGCSE 1: p183‐185MEP: Unit 7‐12: p259‐261MyMaths: L1, H1IGCSE 1: p65‐69MEP: Unit 13‐19: p162‐176MyMaths: L1, H1, L2, H2IGCSE 1: p7‐9MEP: Unit 1‐6: p221‐224MyMaths: L1, H1, L2, H2IGCSE 1: p190‐191MEP: Unit 1‐6: p228‐230MyMaths: L1, H1IGCSE 1: p186‐189MEP: Unit 1‐6: p237‐241MyMaths: L1, H1IGCSE 1: p186‐189MEP: Unit 1‐6: p237‐241MyMaths: L1, H1N6PercentagesN6PercentagesN7 Ratio andproportionN8 Degree ofaccuracyN8 Degree ofaccuracyN8 Degree ofaccuracyN8 Degree ofaccuracySolve problems involvingupper and lower bounds (H)Find the interest earned after one year on 3000invested at 5% per annumA jumper is reduced in a sale by 30% and now costs 17.50. What was the original price of the jumperWrite 672900 correct to 3 significant figures.Write 23.428 correct to 1 decimal placeBy rounding each number to 1 significant figure.estimate the value of.The quantities of x and y are given to 1 significant figureas x 20 and y 40.Find the upper and lower bound of x and yThe quantities of a and b are given to 1 significant figureas a 300 and b 400.Find the minimum value of8 PageandSelfassessment1 2 3 4 5n/aC1 2 3 4 5n/aB1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aA/B1 2 3 4 5n/a
IGCSE Mathematics NumberTopicSub topicNotes / example questionReferenceGradeN9 StandardFormExpress numbers in the form10 (H)IGCSE 1: p5‐6, 59‐62MEP: Unit 1‐6: p15‐19MyMaths: L1, H1, L2, H2CN9 StandardFormSolve problems involvingstandard form (H)IGCSE 1:MEP: Unit 1‐6: p19‐23MyMaths: L1, H1B1 2 3 4 5n/aN10 ApplyingnumberUse and apply number tosolve practical, day to daytype problemsUse a scientific calculator (F)Write these numbers in standard form:47000, 0.0000463Write these numbers in normal notation:3.6 10 , 5.7 10Calculate:6.2 101.2 101.84 101.92 10Lots of possibilities here C1 2 3 4 5n/aB/C1 2 3 4 5n/aN11ElectroniccalculatorsCalculator checklist (you should be able to do all of thefollowing): Number: standard form, fractions, powers androots, πo Can you use your calculator to convertbetween fractions and decimals?o Could you work out 21 ? 9 PageTrigonometry: sin, cos, tan (and their inversefunctions)o Tip: make sure your calculator is set todegreesMemory buttonCan you reset your calculator in case you haveproblems?IGCSE 1:MEP: Unit 1‐6: p231‐236MyMaths:Selfassessment1 2 3 4 5n/a
IGCSE Mathematics AlgebraRevising AlgebraTopicSub topicNotes / example questionReferenceGradeA1 Use ofSymbolsUse index notation and lawsfor positive integer powers(F)Use index notation involvingfractional powers (H)SimplifyIGCSE 1: p79‐80MEP: Unit 1‐6: p 5‐9MyMaths: L1, H1IGCSE 2: p72‐76MEP: Unit 1‐6: p 13‐15MyMaths: L1, H1IGCSE 1: p11‐12MEP: Unit 7‐12:p187‐189MyMaths: L1, H1, L2, H2IGCSE 1: p12‐13, 268‐270MEP: Unit 7‐12:p187‐189Unit 7‐12:p201‐204MyMaths: L1, H1IGCSE 1: p132‐133MEP: Unit 7‐12:p210‐212MyMaths: L1, H1IGCSE 1: p268‐270MEP: Unit 7‐12:p201‐204MyMaths: L1, H1IGCSE 1: p273‐276MEP: Unit 7‐12:p212‐215MyMaths: L1, H1, L2, H2CA1 Use ofSymbolsSimplifySimplify 64A2 AlgebraicManipulationCollect like terms (F)Simplify 2A2 AlgebraicManipulationMultiply out single anddouble brackets (F)Multiply out the brackets:33A2 AlgebraicManipulationFactorise simple expressions(F)Factorise:A2 AlgebraicManipulationMultiply out harderexpressions (H)A2 AlgebraicManipulationFactorise quadraticexpressions (H)Multiply out the brackets:23 323Factorise:126510 P a g e5244231454Selfassessment1 2 3 4 5n/aA1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aB1 2 3 4 5n/aA/B1 2 3 4 5n/a
IGCSE Mathematics AlgebraTopicSub topicNotes / example questionA2 AlgebraicManipulationSimplify expressions withalgebraic fractions (H)Express as a single fraction:13343124ReferenceGradeSelfassessment1 2 3 4 5n/aIGCSE 1: p 70‐73IGCSE 2: p 269‐274MEP: Unit 7‐12:p224‐227MyMaths: L1, H1, L2, H2, L3,H3A*/AIGCSE 1: p197‐200MEP: Unit 1‐6: p32‐35MyMaths: L1, H1, L2, H2IGCSE 1:MEP:MyMaths:C1 2 3 4 5n/aC1 2 3 4 5n/aA*/A/B1 2 3 4 5n/aC1 2 3 4 5n/aFactorise and simplify:412A3Expressionsand formulaeA3Expressionsand formulaeA3Expressionsand formulaeA4 Linearequations11 P a g eSubstitute numbers intoexpressions and formulae (F)Evaluate 23 whenUse formulae from mathsand other real life contextsexpressed in words. Convertto letters and symbols (F)Change the subject of aformulaLots of possibilities Solve linear equations (F)Solve:242Make s the subject ofMake t the subject of37154222IGCSE 1: p194‐197MEP: Unit 1‐6: p39‐45MyMaths: L1, H1, L2, H2IGCSE 1: p13‐19MEP: Unit 7‐12:p189‐197MyMaths: L1, H1, L2, H2
IGCSE Mathematics AlgebraTopicSub topicNotes / example questionReferenceGradeA4 LinearequationsSolve linear equations (H)Solve:IGCSE 2: p275‐281MEP:MyMaths: L1, H1A/BIGCSE 1:MEP:MyMaths:IGCSE 2: p9‐19MEP: Unit 13‐19:p177‐196MyMaths: L1, H1C1 2 3 4 5n/aA/B1 2 3 4 5n/aIGCSE 1: p137‐138MEP:MyMaths: L1, H1B/C1 2 3 4 5n/aIGCSE 1: p138‐143MEP: Unit 7‐12:p205‐210MyMaths: L1, H1, L2, H2, L3,H3IGCSE 1: p86‐88MEP: Unit 13‐19: p59‐68MyMaths:A/B1 2 3 4 5n/aB1 2 3 4 5n/a1742Set up simple linearequations (F)A5 Proportion Set up problems involvingdirect or inverse 12 P a g eSolve simple simultaneousequations (F)Solve harder simultaneousequations (H)Use graphical methods tosolve simultaneousequations (H)236A4 Linearequations2352The three angles of a triangle are:a, (a 10) and (a 20)Find the value of ais directly proportional to the square of . Ifwhen5, find:‐ A formula for y in terms of x‐when6‐when64Solve:2 ,1214,2Solve:323Draw the graphs ofHence solve2 ,47, 2Selfassessment1 2 3 4 5n/a817, 35182 ,1212100
IGCSE Mathematics AlgebraTopicSub topicNotes / example questionReferenceGradeA7 QuadraticEquationsSolve quadratic equations byfactorising (H)Solve:IGCSE 1: p277‐279IGCSE 2: p77‐83MEP: Unit 7‐12:p216‐219MyMaths: L1, H1IGCSE 2:MEP: Unit 7‐12:p220‐223MyMaths: L1, H1IGCSE 2: p83‐87MEP:MyMaths:IGCSE 2: p188‐195MEP:MyMaths: L1, H1A/BIGCSE 1: p80‐94MEP: Unit 13‐19: p197‐203MyMaths:L1, H1, L2, H2IGCSE 1: p88‐94MEP: Unit 13‐19: p208‐219MyMaths: L1, H1IGCSE 1: p88‐94MEP: Unit 13‐19: p208‐219MyMaths: L1, H1IGCSE 2: p87‐90MEP: Unit 13‐19: p204‐207MyMaths: L1, H171203105202A7 QuadraticEquationsA7 QuadraticEquationsA7 equalitiesA8Inequalities13 P a g eSolve quadratic equations byusing the quadratic formula(H)Form and solve quadraticequations from data given incontext (H)Solve simultaneousequations involving onequadratic (H)Solve simple inequalities andshow solutions on a numberline (F)Show simple inequalities ona graph and interpret graphswith inequalities (F)Show simple inequalities ona graph and interpret graphswith inequalities (F)Solve quadratic inequalities(H)Solve:The sum of the squares of two consecutive integers.Find the integers.Solve:211251125Solve the inequality and show the result on a numberline:32 10Shade the region defined by the inequalities0,1,5Shade the region defined by the inequalities21, 5220Solve the inequalities:2125104,Selfassessment1 2 3 4 5n/aA1 2 3 4 5n/aA*1 2 3 4 5n/aA*1 2 3 4 5n/aC1 2 3 4 5n/aB1 2 3 4 5n/aA/B1 2 3 4 5n/aA*1 2 3 4 5n/a
IGCSE Mathematics AlgebraTopicSub topicNotes / example questionReferenceGradeA9 SequencesFind terms in a sequence andcontinue a sequence (F)IGCSE 1: p283‐286MEP: Unit 7‐12: p262‐264MyMaths: L1, H1CA9 SequencesDescribe the nth term in anarithmetic sequence (H)Find the next three terms in the sequence:3, 7, 11, 15, Find the first four terms in the sequence:nth term 4n‐3Find an expression for the nth term in the sequence 3,7, 11, 15, B/C1 2 3 4 5n/aA10 FunctionnotationUnderstand simple functions(H)IGCSE 1: p288‐293MEP: Unit 7‐12: p273‐279MyMaths: L1, H1IGCSE 2: p196‐199MEP:MyMaths:B1 2 3 4 5n/aIGCSE 2: p200‐203MEP:MyMaths:A1 2 3 4 5n/aIGCSE 2: p204‐211MEP:MyMaths:IGCSE 1: p21‐24MEP: Unit 13‐19: p25‐30MyMaths:A*1 2 3 4 5n/aC1 2 3 4 5n/a3If4 ,3IfA10 FunctionnotationFind the domain and rangeof a function (H)A10 FunctionnotationUse composite functionsand inverse functions(H)Find the gradient of a line (F)A11 Graphs2, find:,2 ,2 and225, findWhich values cannot be included in the domain of thefollowing functions:112 If2, find1, find 3If4 yFind the gradientof the line.321x 6 4 22 1 2 3 414 P a g e46Selfassessment1 2 3 4 5n/a
IGCSE Mathematics AlgebraTopicSub topicNotes / example questionReferenceGradeA11 GraphsFind the gradient of a linegiven two points (H)Find the gradient of the straight line joining A(6,4) to D(12,1)BA11 GraphsRecognise that m is thegradient, c is the y interceptand find parallel lines (H)Plot straight line andquadratic graphs (F)Find the gradient and y intercept of the equation35IGCSE 1: p21‐24MEP: Unit 13‐19: p25‐30MyMaths:IGCSE 1: p24‐29MEP: Unit 13‐19: p49‐56MyMaths: L1, H1IGCSE 1: p24‐29MEP: Unit 13‐19: p9‐24MyMaths: L1, H1Plot and draw morecomplicated graphs (H)Draw a graph of:A11 GraphsDraw a graph of:2433123A11 Graphs13A11 GraphsInterpret graphs includingdistance‐time, speed‐timeand currency conversion (F)125354Distance, m642Find the speed between(a) 0 and 2 seconds(b) 4 and 10 seconds215 P a g e246Time, s810Selfassessment1 2 3 4 5n/aC1 2 3 4 5n/aB/C1 2 3 4 5n/aIGCSE 2: p21‐29MEP: Unit 13‐19: p69‐73MyMaths: L1, H1, L2, H2A/B1 2 3 4 5n/aIGCSE 1: p146‐153MEP: Unit 13‐19: p30‐39MyMaths: L1, H1, L2, H2C1 2 3 4 5n/a
IGCSE Mathematics AlgebraTopicSub topicA11 GraphsFind the gradient of a graphby drawing a tangent (H)A11 GraphsFind the intersection of twographs by graphical andalgebraic methodsDifferentiate powers of xA12 CalculusNotes / example questionFind the x values of the co‐ordinates of intersection of21 and3Differentiate:2A12 CalculusA12 Calculus16 P a g eDetermine gradients andturning points bydifferentiation. Distinguishbetween maximum andminimum points.Use differentiation to solveproblems involvingdisplacement, velocity andacceleration452Find and classify the turning points on the curve397The displacement, s metres of a particle after t secondsis given by100 5Find an expression for the velocity.Find the accelerationReferenceGradeSelfassessment1 2 3 4 5n/aIGCSE 2: p212‐223MEP:MyMaths:AIGCSE 2: p91‐103MEP: Unit 13‐19: p74‐78MyMaths: L1, H1IGCSE 2: p284‐287MEP:MyMaths:A*/A1 2 3 4 5n/aA1 2 3 4 5n/aIGCSE 2: p288‐295MEP:MyMaths:A*1 2 3 4 5n/aIGCSE 2: p296‐301MEP:MyMaths:A*1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresRevising Shape, Space and MeasuresTopicSub topicS1 Angles andtrianglesUse angle properties (anglesat a point, vertically oppositeangles, alternate angles andcorresponding angles) andunderstand differencebetween acute, obtuse andreflex angles (F)S1 Angles andtrianglesUse angle properties oftriangles to include isosceles,equilateral and right angled.Find exterior angles andangle sum in a triangle. (F)Recognise the names andproperties of the followingpolygons:Parallelogram, rectangle,square, rhombus, trapezium,kite, pentagon, hexagon andoctagon (F)Calculate interior andexterior angles for regularpolygons (F)S2 PolygonsS2 Polygons17 P a g eNotes / example questionReferenceGradeSelfassessment1 2 3 4 5n/aIGCSE 1: p31‐36MEP: Unit 1‐6: p73‐79MyMaths: L1, H1CThe largest angle in an isosceles triangle is 100 degrees.Find the other two angles.IGCSE 1: p31‐36MEP: Unit 1‐6: p66‐73MyMaths: L1, H1C1 2 3 4 5n/aState similarities and differences between aparallelogram and a rhombus.IGCSE 1: p31MEP:MyMaths: L1, H1C1 2 3 4 5n/aThe interior angle of a regular polygon is 150 degrees.How many sides does it have?IGCSE1: p32‐36MEP: Unit 1‐3: p80‐84MyMaths: L1, H1B/C1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicNotes / example questionReferenceGradeS2 PolygonsUnderstand congruence asmeaning the same size andshape (F)Are the shapes congruent?IGCSE1: p31‐36MEP:MyMaths: L1, H1CS3 SymmetryRecognise line and rotationalsymmetry and state order ofrotational symmetry (F)How many lines of symmetry does the shape have?IGCSE1: p31‐36MEP: Unit 1‐3: p61‐66MyMaths: L1, H1, L2, H2C1 2 3 4 5n/aS4 MeasuresInterpret a range ofmeasures: Scales Time intervals for 12and 24 hour clocks Measure angles Find bearings Use relationshipbetween speed,distance and time (F)Construct triangles and other2d shapes using a ruler,protractor and/or compass.Construct the perpendicularbisector of a line and thebisector of an angle (F)The bearing of B from A is 130 degrees. Find thebearing of A from B.IGCSE 1: p97, p146,153MEP:MyMaths:C1 2 3 4 5n/aConstruct triangle ABC, where AB 8cm, angle BAC 60degrees and angle ABC 45 degreesIGCSE 1: p36‐42MEP: Unit 13‐19: p90‐96Unit 13‐19: p109‐111MyMaths: L1, H1, L2, H2B/C1 2 3 4 5n/aS5Construction18 P a g eSelfassessment1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicNotes / example questionReferenceGradeS5ConstructionSolve problems using scaledrawings (F)A room measures 8m by 6m. Construct a scale drawingwhere 1cm represents 50cm.CS6 CirclepropertiesKnow circle definitionsincluding: centre, radius,chord, diameter,circumference, tangent, arc,sector and segment.Use chord and tangentproperties of circles (F)Use angle properties ofFind the missing anglescircles including: Angle at centre istwice angle atcircumference (soangle in semi‐circle isright angle) Angles in the samesegment are equal Sum of oppositeangles in cyclicquadrilateral is 180degrees Alternate segmenttheorem (H)IGCSE 1:MEP:MyMaths:IGCSE 1: p214MEP: Unit 1‐6: p96MyMaths:S6 Circleproperties19 P a g eIGCSE 1: p214‐225IGCSE 2: p38‐48MEP: Unit 1‐6: p96‐109MyMaths: L1, H1Selfassessment1 2 3 4 5n/aC1 2 3 4 5n/aA/B1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicS6 CirclepropertiesUse the internal and externalintersection chord properties(H)S7GeometricalreasoningProvide reasons to supportnumerical answers given inquestions relating to anglesand circles (H)Use Pythagoras’ Theorem etryandPythagoras’Theorem20 P a g eUse sine, cosine and tangentrules to find missing lengthsand angles in right angledtriangles (F)Notes / example questionReferenceGradeSelfassessment1 2 3 4 5n/aIGCSE 2: p49‐56MEP: Unit 1‐6: p110‐115MyMaths:A*No links or examples here just remember to give areason when answering these sorts of questionsIGCSE 1:MEP:MyMaths:A1 2 3 4 5n/aFind x in each of the trianglesIGCSE 1: p234‐239MEP: Unit 1‐6: p118‐126MyMaths: L1, H1C1 2 3 4 5n/aFind the missing angle and missing sideIGCSE 1: p95‐103,p154‐167MEP: Unit 1‐6: p126‐141MyMaths: L1, H1, L2, H2B/C1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicNotes / example ��TheoremUse sine and cosine rules tofind missing angles in anytriangle (H)Find the unknown angles and sideIGCSE 2: p305‐317MEP: Unit 1‐6: p142‐148MyMaths: L1, H1, L2, H2,L3, etryandPythagoras’TheoremUse the formulatofind the area of a triangleCalculate the area of the triangle in the box aboveIGCSE 2: p318‐319MEP:MyMaths: L1, H1B1 2 3 4 5n/aUse Pythagoras andtrigonometry to solveproblems in 3 dimensionsFind the length of the longest rod that will fit in the boxIGCSE 2: p320‐328MEP: Unit 13‐19: p244‐255MyMaths: L1, H1, L2, H2A1 2 3 4 5n/aConvert measurementswithin the metric systemincluding area and volume(F)Convert between volumemeasures (H)A rectangle measures 3m by 4m. Find its area inA bottle has a capacity of 2 litres. Find the volume inIGCSE 1:MEP: Unit 7‐12: p1‐5MyMaths:C1 2 3 4 5n/aA cuboid measures 1m by 2m by 3m. Find the volume inIGCSE 2: p104‐109MEP:MyMaths:B1 2 3 4 5n/aS9MensurationS9Mensuration21 P a g eSelfassessment1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicNotes / example questionReferenceGradeS9MensurationFind areas and perimetersfor triangles and rectangles(F)Find the area of aparallelogram and atrapezium (F)Find the area and perimeter of a right angled trianglethat has sides of 3m, 4m and 5mIGCSE 1: p75‐76MEP: Unit 7‐12: p24‐31MyMaths: L1, H1, L2, H2IGCSE 1: p75‐76MEP: Unit 7‐12: p57‐61MyMaths: L1, H1, L2, H2CC1 2 3 4 5n/aIGCSE 1: p75‐76MEP: Unit 7‐12: p32‐37MyMaths: L1, H1, L2, H2IGCSE 2: p124‐135MEP: Unit 7‐12: p62‐68MyMaths: L1, H1IGCSE 2: p124‐129MEP: Unit 7‐12: p38‐45MyMaths: L1, H1, L2, H2, L3,H3C1 2 3 4 5n/aC1 2 3 4 5n/aC1 2 3 4 5n/aS9MensurationFind the area of each shapeS9MensurationFind the circumference andarea of a circle (F)A circle has a radius of 4cm. Find its circumference andareaS9MensurationFind the surface area ofsimple shapes (F)A cube has sides of 3cm. What is its surface area?S9MensurationFind the volume of prismsincluding cuboids andcylinders (F)Find the volume of the cylinder22 P a g eSelfassessment1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicNotes / example questionReferenceGradeS9MensurationFind perimeters and areas ofsectors of circles (H)Find the shaded areaIGCSE 2: p110‐123MEP: Unit 7‐12: p72‐80MyMaths: L1, H1AS9MensurationFind the surface areas andvolumes of spheres andcones (H)A sphere has a volume of 4000Find its radius and surface areaIGCSE 2: p129‐135MEP: Unit 7‐12: p72‐80MyMaths: L1, H1, L2, H2A/B1 2 3 4 5n/aIGCSE 1: p226‐234MEP:MyMaths: L1, H1C1 2 3 4 5n/aIGCSE 2: p135‐141MEP: Unit 13‐19: p145‐155MyMaths: L1, H1A1 2 3 4 5n/aS10 SimilarityUnderstand that angles staythe same in similar shapes(F)S10 SimilarityFind missing lengths andareas of similar shapes (H)23 P a g e.Note: MEP and My Maths link also includes volumes ofpyramids – this is NOT in IGCSE syllabusAre the triangles similar? Give a reasonSelfassessment1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicS10 SimilarityReferenceGradeFind missing lengths and.AA can has a height of 10 cm and a volume of 200volumes of similar shapes (H) can with a similar shape has a height of 12cm.a) Find the volume of the larger can.b) Find the height of a similar can with a volume of 675IGCSE 2: p142‐151MEP: Unit 13‐19: p145‐155MyMaths: L1, H1AS11 VectorsUse vector notation and usesimple vector arithmetic (H)A1 2 3 4 5n/aS11 VectorsFind the resultant of two ormore vectors (H)IGCSE 2: p224‐239MEP: Unit 13‐19: p256‐259,266‐273MyMaths:IGCSE 2: p224‐239MEP: Unit 13‐19: p256‐259,266‐273MyMaths:A1 2 3 4 5n/aS11 VectorsFind the modulus(magnitude) of a vector (H)IfA1 2 3 4 5n/aS11 VectorsApply vector methods tosimple geometrical proofs(H)If,parallel to cA*1 2 3 4 5n/a24 P a g eNotes / example questionIfandFind (i) a b (ii) 5a (iii) 3a – 5b, find the magnitude of the vector aand, show that a b isIGCSE 2: p224‐239MEP: Unit 13‐19: p256‐259,266‐273MyMaths:IGCSE 2: p224‐239MEP: Unit 13‐19: p256‐259,266‐273MyMaths:Selfassessment1 2 3 4 5n/a
IGCSE Mathematics Shape, Spaceand MeasuresTopicSub topicNotes / example questionReferenceGradeS12Rotate, reflect and translateshapes (F)Note – for higher tier onlyneed to be able to translateusing vector notationDescribe the transformation from A to BIGCSE 1: p295‐302MEP: Unit 13‐19: p118‐134MyMaths: L1, H1, L2, H2, L3,H3CCombine transformations (F)Describe the transformation from A to C (in the diagramabove) by using more than one transformationC1 2 3 4 5n/aEnlarge a shape using centreof enlargement and scalefactor (F)Describe the transformation from A to B (in the diagramabove)IGCSE 1: p303‐304MEP: Unit 13‐19: p135‐138MyMaths: L1, H1IGCSE 1: p305‐312MEP: Unit 13‐19: p96‐103MyMaths: L1, H1C1 2 3 4 yS12Transformationgeometry25 P a g eSelfassessment1 2 3 4 5n/a
IGCSE Mathematics Handling DataRevising Handling dataTopicSub topicNotes / example questionReferenceGradeHD1 GraphicalUse and interpret bar chartsand pie charts (F)The bar charts shows the number of visits made to asupermarket by different people. How many visits weremade in total?IGCSE 1: p108‐112MEP: Unit 7‐12: p98‐110MyMaths: L1, H1, L2, H2, L3,H3CConstruct and interprethistograms (H)Construct a histogram from the information belowIGCSE 2: p240‐249MEP: Unit 7‐12: p132‐139MyMaths: L1, H1A1 2 3 4 5n/aCalculate the mean, medianand mode for a discrete dataset (F)Calculate the mean, median and mode for the followingdata set:1, 3, 3, 3, 4, 6, 9IGCSE 1: p106‐107MEP: Unit 7‐12: p145‐149MyMaths: L1, H1, L2, H2, L3,H3C1 2 3 4 5n/arepresentationof dataHD1 Graphicalrepresentationof dataHD2Statisticalmeasures26 P a g eSelfassessment1 2 3 4 5n/a
IGCSE Mathematics Handling DataTopicSub topicNotes / example ate the mean andmodal class from groupeddata (F)Calculate the mean time to complete a snooker framefrom the table belowIGCSE 1: p168‐175MEP: Unit 7‐12: p157‐163MyMaths: L1, H1CHD2StatisticalmeasuresConstruct a cumulativefrequency diagram and useit to calculate the medianand interquartile range(H)Understand the language ofprobability and theprobability scale (F)Construct a cumulative frequency from the table above.Hence find the median time taken to complete a frame.IGCSE 1: p314‐326MEP: Unit 7‐12: p164‐174MyMaths: L1, H1B1 2 3 4 5n/aIGCSE 1:MEP: Unit 1‐6: p159‐163MyMaths: L1, H1C1 2 3 4 5n/aIGCSE 1: p240‐242MEP: Unit 1‐6: p167‐170MyMaths: L1, H1C1 2 3 4 5n/aI
The Revision Guide provides links to three main resources. IGCSE Book 1 and Book 2 You should have a copy of IGCSE Book 2. Copies of IGCSE Book 1 are available in the Maths Department. When working through e
IGCSE First Language English 12 IGCSE World Literature 13 IGCSE English as a Second Language 14 . IGCSE Business Studies 19 IGCSE Global Perspectives 21 IGCSE Geography 22 IGCSE History 23 IGCSE Sciences 24 IGCSE Cambridge Mathematics Extended & Core 26 . At BISP, Year 12 and 13 (Key Stage Five) students study the IB Diploma Programme (IBDP .
IGCSE ARABIC for Native Arabic Speakers - Edexcel 11 GCSE ART & DESIGN - Edexcel 13 IGCSE BUSINESS STUDIES - Cambridge 15 IGCSE ECONOMICS - Cambridge 17 IGCSE COMPUTER SCIENCE - Cambridge 19 GCSE DRAMA - Edexcel 20 IGCSE ENGLISH LANGUAGE - Cambridge 22 IGCSE ENGLISH LITERATURE - Edexcel 22 IGCSE GEOGRAPHY - Edexcel 25
University of Cambridge International Examinations London GCE AS/A-Level / IGCSE / GCSE Edexcel International. 6 Examination Date in 2011 Cambridge IGCSE Oct/Nov X 9 Cambridge GCE / May/Jun 9 9 London GCE London GCSE May/Jun 9 X Chinese London IGCSE Jan X 9 Cambridge IGCSE / May/Jun 9 9 London IGCSE London GCE Jan 9 9 Cambridge GCE Oct/Nov X 9 Private Candidates School Candidates Exam Date. 7 .
Mathematics for Cambridge IGCSE Complete Science for Cambridge IGCSE Complete Business Studies for Cambridge IGCSE & O Level Trusted by teachers and students around the world, our popular Core and Extended Mathematics books have been fully updated for the latest Cambridge IGCSE syllabus
Upcoming Cambridge IGCSE training in Rome 05-06 April 2017 Introductory Cambridge IGCSE English as a Second Language (0510) Introductory Cambridge IGCSE International Mathematics (0607) Introductory Cambridge IGCSE Art and Design (0400) Extension Cambridge IGCSE Geography (0460) 07-08 April 2017
They risk their own resources in business ventures. They also organise the other 3 factors of production. StudyGuide.PK O-Level/IGCSE Economics Revision Notes Page 7 igcse economics - types of production . StudyGuide.PK O-Level/IGCSE Economics Revision Notes Page 11 3 MIXED ECONOMY In this case some decisions are made by private individuals .
IGCSE English Literature and IGCSE First Language English Students begin a two-year course, covering two IGCSE subjects: 1) English Literature, and 2) First Language English. The study culminates in the examinations of the IGCSE papers set by the Cambridge International Examinat
Introduction to Takaful Prepared by: Dr. Khalid Al Amri 6 Conventional Insurance (non-mutual) Takaful Insurance Five Key Elements Speculation Uncertainty Prohibited activities Mutual Guarantee: The basic objective of Takaful is to pay a defined loss from a defined fund. Liability and all losses are divided between policyholders. The policyholders are both the insurer and the insured Ownership .
