Edexcel International Advanced Level - Insworld

Tiered papers – Provided at two tiers of entry (Higher and Foundation) that allow studentsto be entered for a level appropriate to them with questions in each tier that are accessibleto students of all abilities within that tier.Clear and straightforward question papers – Our question papers are clear andaccessible for all students of all ability ranges and learning style. Our mark schemes arestraightforward, so that the assessment requirements are clear.Broaden and deepen students’ skills – We have designed the International GCSE toextend students’ knowledge by broadening and deepening skills, for example: Students develop their problem-solving skills by translating problems in mathematical ornon-mathematical contexts at both Higher and Foundation tiers Students will develop reasoning skills through exercises such as presenting argumentsand proofs, and making deductions and drawing conclusions from mathematicalinformation.Comparable to GCSE – We have designed our International GCSE qualification to be ofequivalent standard to Pearson’s regulated GCSE qualification. This ensures thatInternational GCSEs are recognised globally and provide learners with the same progressionroutes.Supports progression to A Level – Our qualifications enable successful progression toA Level and beyond. Through our world-class qualification development process, we haveconsulted with International A Level and GCE A Level teachers, as well as universityprofessors to validate the appropriacy of this qualification including the content, skills andassessment structure.Centres wishing to teach mathematics using a different approach to meet their students’needs can use our Pearson Edexcel International GCSE in Mathematics (Specification B) orextend students’ study with Pearson Edexcel International GCSE in Further PureMathematics. More information about all of our qualifications can be found on our EdexcelInternational GCSE pages at: qualifications.pearson.comSupporting you in planning and implementing thisqualificationPlanning Our Getting Started Guide gives you an overview of the Pearson Edexcel InternationalGCSE in Mathematics (Specification A) to help you understand the changes to contentand assessment, and to help you understand what these changes mean for you and yourstudents. We will provide you with a course planner and editable schemes of work. Our mapping documents highlight key differences between the new and 2009 legacyqualifications.Teaching and learning Our skills maps will highlight skills areas that are naturally developed through the studyof mathematics, showing connections between areas and opportunities for furtherdevelopment. Print and digital learning and teaching resources – promotes any time, any place learningto improve student motivation and encourage new ways of working.Pearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 20173

Preparing for examsWe will also provide a range of resources to help you prepare your students for theassessments, including: specimen papers to support formative assessments and mock exams examiner commentaries following each examination series.ResultsPlusResultsPlus provides the most detailed analysis available of your students’ examperformance. It can help you identify the topics and skills where further learning wouldbenefit your students.examWizardA free online resource designed to support students and teachers with exam preparation andassessment.Training eventsIn addition to online training, we host a series of training events each year for teachers todeepen their understanding of our qualifications.Get help and supportOur subject advisor service will ensure you receive help and guidance from us. You can signup to receive the Edexcel newsletter to keep up to date with qualification updates andproduct and service news.4Pearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

Qualification at a glanceFoundation Tier Externally assessed Availability: January and June First assessment: June 2018 Two papers: 1F and 2F*Component/papercode 4MA1/1F and4MA1/2FEach paper is 50% ofthe total InternationalGCSEContent summary Number Algebra Geometry StatisticsAssessment Each paper is assessed through a 2-hour examination set and marked by Pearson. The total number of marks for each paper is 100. Each paper will assess the full range of targeted grades at Foundation Tier (5–1). Each paper will have approximately equal marks available for each of the targetedgrades. There will be approximately 40% of questions targeted at grades 5 and 4, across papers1F and 1H to aid standardisation and comparability of award between tiers. A Foundation Tier formulae sheet (Appendix 4) will be included in the writtenexaminations. A calculator may be used in the examinations (please see page 42 for furtherinformation).Pearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 20175

Higher Tier*Component/papercode 4MA1/1H and4MA1/2H Externally assessed Availability: January and June First assessment: June 2018 Two papers: 1H and 2HEach paper is 50% ofthe total InternationalGCSEContent summary Number Algebra Geometry StatisticsAssessment Each paper is assessed through a 2-hour examination set and marked by Pearson. The total number of marks for each paper is 100. Questions will assume knowledge from the Foundation Tier subject content. Each paper will assess the full range of targeted grades at Higher Tier (9–4). Each paper will have approximately 40% of the marks distributed evenly over grades4 and 5 and approximately 60% of the marks distributed evenly over grades 6, 7, 8and 9. There will be approximately 40% of questions targeted at grades 5 and 4, across papers2F and 2H, to aid standardisation and comparability of award between tiers. A Higher Tier formulae sheet (Appendix 5) will be included in the written examinations. A calculator may be used in the examinations (please see page 42 for furtherinformation).* See Appendix 1 for a description of these code and all the other codes relevant to thisqualification.6Pearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

2 Mathematics (Specification A) contentFoundation Tier1: Numbers and the number system112: Equations, formulae and identities153: Sequences, functions and graphs174: Geometry and trigonometry195: Vectors and transformation geometry236: Statistics and probability24Higher Tier1: Numbers and the number system292: Equations, formulae and identities313: Sequences, functions and graphs334: Geometry and trigonometry365: Vectors and transformation geometry386: Statistics and probability39Pearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 20177

8Pearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

Foundation TierExternally assessedDescriptionThe Pearson Edexcel International GCSE in Mathematics (Specification A) requires studentsto demonstrate application and understanding of the following.Number Use numerical skills in a purely mathematical way and in real-life situations.Algebra Use letters as equivalent to numbers and as variables. Understand the distinction between expressions, equations and formulae. Use algebra to set up and solve problems. Demonstrate manipulative skills. Construct and use graphs.Geometry Use properties of angles. Understand a range of transformations. Work within the metric system. Understand ideas of space and shape. Use ruler, compasses and protractor appropriately.Statistics Understand basic ideas of statistical averages. Use a range of statistical techniques. Use basic ideas of probability.Students should be able to demonstrate problem-solving skills by translating problems inmathematical or non-mathematical contexts into a process or a series of mathematicalprocesses.Students should be able to demonstrate mathematical reasoning skills by: making deductions and drawing conclusions from mathematical information constructing chains of reasoning presenting arguments and proofs interpreting and communicating information accurately.Pearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 20179

Assessment informationEach paper is assessed through a 2-hour examination set and marked by Pearson.The total number of marks for each paper is 100.Each paper will assess the full range of targeted grades at Foundation Tier (5–1).Each paper will have approximately equal marks available for each of the targeted grades.There will be approximately 40% of questions targeted at grades 5 and 4, across papers1F and 1H to aid standardisation and comparability of award between tiers.Diagrams will not necessarily be drawn to scale and measurements should not be taken fromdiagrams unless instructions to this effect are given.Each student may be required to use mathematical instruments, e.g. pair of compasses,ruler, protractor.A Foundation Tier formulae sheet (Appendix 4) will be included in the written examinations.Tracing paper may be used in the examinations.A calculator may be used in the examinations (please see page 42 for further information).Questions will be set in SI units (international system of units).10Pearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

AO1 Numbers and algebra1Numbers and the number systemStudents should be taught to:1.1IntegersNotesAunderstand and use integers (positive,negative and zero)Bunderstand place valueCuse directed numbers in practical situationse.g. temperaturesD order integersEuse the four rules of addition, subtraction,multiplication and divisionFuse brackets and the hierarchy of operationsG use the terms ‘odd’, ‘even’, ’prime numbers’,‘factors’ and ‘multiples’H identify prime factors, common factors andcommon multiples1.2FractionsAunderstand and use equivalent fractions,simplifying a fraction by cancelling commonfactorsBunderstand and use mixed numbers andvulgar fractionsCidentify common denominators82 60 15in its simplest form(lowest terms)D order fractions and calculate a given fractionof a given quantityEexpress a given number as a fraction ofanother numberFuse common denominators to add andsubtract fractions and mixed numbersG convert a fraction to a decimal or apercentageH understand and use unit fractions asmultiplicative inversesImultiply and divide fractions and mixednumbersPearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 20172 5 ,3 7123 2533 0.6 60%54 0.4444. 44.4.%93 5 3 2 5 ,3 715123 25311

Students should be taught to:1.3DecimalsAuse decimal notationBunderstand place valueCorder decimalsD convert a decimal to a fraction or apercentage1.4Powers androotsErecognise that a terminating decimal is afractionAidentify square numbers and cube numbersBcalculate squares, square roots, cubes andcube rootsCuse index notation and index laws formultiplication and division of positive andnegative integer powers including zeroD express integers as a product of powers ofprime factors1.5Set languageand notationEfind highest common factors (HCF) andlowest common multiples (LCM)Aunderstand the definition of a setBuse the set notation , and and NotesTerminating decimalsonly 0.6565 13 100 20720 24 32 5E universal set empty setCunderstand the concept of the universal setand the empty set and the symbols forthese setsD understand and use the complement of asetE12Use the notation A'use Venn diagrams to represent setsPearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

Students should be taught to:1.6PercentagesAunderstand that ‘percentage’ means‘number of parts per 100’Bexpress a given number as a percentage ofanother numberCexpress a percentage as a fraction and as adecimalD understand the multiplicative nature ofpercentages as operatorsEsolve simple percentage problems,including percentage increase and decreaseFuse reverse percentagesNotes15% of 120 15 120100In a sale, prices werereduced by 30%. Thesale price of an itemwas 17.50Calculate the originalprice of the itemG use compound interest and depreciation1.7Ratio andproportion1.8Degree ofaccuracy1.9StandardformAuse ratio notation, including reduction to itssimplest form and its various links tofraction notationExpress in the formBdivide a quantity in a given ratio or ratiosShare 416 in theratio 5 : 3 or 4 : 3 : 1Cuse the process of proportionality toevaluate unknown quantities1:nD calculate an unknown quantity fromquantities that vary in direct proportions varies directly as tEsolve word problems about ratio andproportionIncluding maps andscale diagramsAround integers to a given power of 10Bround to a given number of significantfigures or decimal placesCidentify upper and lower bounds wherevalues are given to a degree of accuracyFind the missing valuein a tableD use estimation to evaluate approximationsto numerical calculationsBy rounding values to1 significant figureA150 000 000 1.5 108calculate with and interpret numbers inthe form a 10n where n is an integerand 1 a 10Pearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 201713

Students should be taught se and apply number in everydaypersonal, domestic or community lifeBcarry out calculations using standard unitsof mass, length, area, volume and capacityCunderstand and carry out calculations usingtime, and carry out calculations usingmoney, including converting betweencurrenciesAuse a scientific electronic calculator todetermine numerical resultsNotesMetric units onlyPearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

2Equations, formulae and identitiesStudents should be taught to:2.1Use ofsymbolsAunderstand that symbols may be used torepresent numbers in equations orvariables in expressions and formulaeBunderstand that algebraic expressionsfollow the generalised rules of arithmeticCuse index notation for positive andnegative integer powers (including zero)Notesa a a a3a 5 D use index laws in simple cases1; a0 1 5axm xn x m nxm xn x m n( x m ) n x mn2.2AlgebraicmanipulationAevaluate expressions by substitutingnumerical values for lettersBcollect like termsCmultiply a single term over a bracketD take out common factorsFactorise fullyEexpand the product of two simple linearexpressionsExpand and simplifyunderstand the concept of a quadraticexpression and be able to factorise suchexpressions (limited to x2 bx c)FactoriseF2.3Expressionsand formulae3 x (2 x 5)Aunderstand that a letter may represent anunknown number or a variableBuse correct notational conventions foralgebraic expressions and formulaeCsubstitute positive and negative integers,decimals and fractions for words andletters in expressions and formulae8 xy 12 y 2( x 8)( x 5)x2 10x 24Evaluate 2x – 3ywhen x 4 andy 5D use formulae from mathematics and otherreal-life contexts expressed initially inwords or diagrammatic form and convert toletters and symbolsEderive a formula or expressionFchange the subject of a formula where thesubject appears oncer the subject ofA π r2Maket the subject ofv u atMakePearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 201715

2.4LinearequationsStudents should be taught to:NotesAsolve linear equations, with integer orfractional coefficients, in one unknown inwhich the unknown appears on either sideor both sides of the equation5x 8 12set up simple linear equations from givendataThe three angles of atriangle are a ,B7( x 3) 5 x 84x 5 32(a 10) , (a 20) .Find the value of a2.5ProportionHigher Tier ationsAsolve quadratic equations by factorisation(limited to x2 bx c 0)2.8InequalitiesAunderstand and use the symbolsand calculate the exact solution of twosimultaneous equations in two unknownsx y 14, x – y 22a 5b 12,3a b 5 , , Bunderstand and use the convention foropen and closed intervals on a number lineCsolve simple linear inequalities in onevariable and represent the solution set on anumber lineD represent simple linear inequalities onrectangular Cartesian graphsSolve x2 x – 30 0To include doubleended inequalitiese.g.1 x 53x – 2 10, so x 47 x 5, so x 23 x 2 5so 1 x 3Shade the regiondefined by theinequalities x 0,y 1, x y 5E16identify regions on rectangular Cartesiangraphs defined by simple linear inequalitiesConventions for theinclusion of boundariesare not requiredPearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

3Sequences, functions and graphs3.1SequencesStudents should be taught to:NotesAgenerate terms of a sequence usingterm-to-term and position-to-termdefinitions of the sequenceIncluding odd, even,squares, multiples andpowersBfind subsequent terms of an integersequence and the rule for generating it5, 9, 13, 17, (add 4)1, 2, 4, 8, (multiply by 2)Cuse linear expressions to describe thenth term of arithmetic sequences1, 3, 5, 7, 9, nth term is 2n – 1nth term is 4n 3,write down the first 3terms of the sequence3.2FunctionnotationHigher Tier only3.3GraphsAinterpret information presented in a rangeof linear and non-linear graphsBunderstand and use conventions forrectangular Cartesian coordinatesCplot points (x, y) in any of the fourquadrants or locate points with givencoordinatesTo include speed/timeand distance/timegraphsD determine the coordinates of pointsidentified by geometrical informationEdetermine the coordinates of the midpointof a line segment, given the coordinatesof the two end pointsFdraw and interpret straight lineconversion graphsG find the gradient of a straight linePearson Edexcel International GCSE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017To include currencyconversion graphsgradient (increase in y) (increase in x)17

Students should be taught to:NotesH recognise that equations of the formy mx c are straight line graphs withgradient m and intercept on they-axis at the point (0, c)Write down thegradient andcoordinates of theintercept ofy 3x 5;yWrite down theequation of thestraight line withgradient 6 that passesthrough the point (0, 2)Irecognise, generate points and plotgraphs of linear and quadratic functionsTo include x k,y c, y x, y x 0Including completion ofvalues in tables andequations of the formax by c3.4Calculus18Higher Tier onlyPearson Edexcel International GCE in Mathematics (Specification A) –Specification – Issue 2 – November 2017 Pearson Education Limited 2017

AO2 Shape, space and measure4GeometryStudents should be taught to:4.1Angles, linesand trianglesAdistinguish between acute, obtuse, reflexand right anglesBuse angle properties of intersecting lines,parallel lines and angles on a straight lineCunderstand the exterior angle of a triangleproperty and the angle sum of a trianglepropertyNotesAngles at a point,vertically oppositeangles, alternateangles, correspondingangles, allied anglesD understand the terms ‘isosceles’,‘equilateral’ and ‘right-angled triangles’and the angle properties of these triangles4.2PolygonsArecognise and give the names of polygonsTo includeparallelogram,rectangle, square,rhombus, trapezium,kite, pentagon,hexagon and octagonBunderstand and use the term‘quadrilateral’ and the angle sum propertyof quadrilateralsThe four angles of aquadrilateral are 90 ,(x 15) , (x 25) and(x 35) Find the value of xCunderstand and use the properties of theparallelogram, rectangle, square,rhombus, trapezium and kiteD understand the term ‘regular polygon’ andcalculate interior and exterior angles ofregular polygonsEunderstand and use the angle sum ofpolygonsFunderstand congruence as meaning thesame shape and sizeFor a polygon with nsides, the sum of theinterior angles is(2n – 4) right anglesG un

Pearson Edexcel International GCSE in Mathematics (Specifi cation A) (4MA1) For fi rst teaching September 2016 First examination June 2018 . a solid basis for students wishing to progress to Edexcel AS and Advanced GCE Level