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AUT 1AUT 2SPR 1SPR 2SUM 1SUM 2YEAR 7Rationale: Number is at the heart of our KS3 curriculum as this enables students to be successful in all other strands of Mathematics at KS4 and KS5. In Year 7 the curriculum is strongly linked to the KS2 curriculum to enable students to build on their prior learning and connect their prior knowledge to new concepts. Calculator use is discouraged throughout Year 7 to encourage further fluency with the four basic operations of addition, subtraction, multiplication and division. ADDITION AND SUBRACTIONAdd and subtract negative numbersUse positive and negative numbers in contextSimplify expressions by collecting like termsFind the perimeter of shapesFind equivalent fractionsConvert between mixed numbers and improper fractionsAddition and Subtraction of fractionsMULTIPLICATION AND DIVISIONCompare multiplication and division methodsMultiply and Divide Negative NumbersMultiplication and Division of FractionsFind the area of a rectangle, triangle, parallelogram and trapeziumBIDMAS (New 2020) Use divisibility rulesIdentify prime numbersIdentify factors and HCFANGLESDraw and measure anglesFind angles on a straight line, around a point, vertically opposite, in triangles and quadrilateralsAngles in parallel linesBearings?COORDINATE GEOMETRYPlot and read Cartesian coordinatesUnderstand the equations of vertical and horizontal linesFind simple rules connecting x and y coordinatesReflect, rotate, enlarge and translate shapes on a Cartesian grid?ROUNDING AND ESTIMATIONInvestigate place valueSolve problems involving large numbers.Solve problems that require assumptions to be madeRounding to decimal placesRounding to significant figuresEstimationLimits of AccuracyApplying Limits of Accuracy to problemsINTERPRETING DATASolve problems using averagesRead & interpret pie chartsCompare frequency graphs and pie chartsYEAR 8Rationale: In Year 8 students build on their knowledge and skills gained from Year 7 and KS2 through learning about how to use bar models to understand proportional relationships. Many more algebraic concepts are introduced to enable links to be established between geometry and algebraic manipulation. Calculator use is encouraged in Year 8 alongside regular opportunities for students to practise their mental Maths when appropriate. PROPORTIONAL REASONING Solve problems involving ratioFind percentages of amountsFind percentage increase and decreaseDevelop understanding of ratio tablesUse ratio tables to solve proportional word problemsEXPRESSIONS, EQUATIONS AND INEQUALITIESUse basic index rulesUse algebraic conventionsMultiply single bracketsFactorise single bracketsForm equations and inequalitiesUse different representations for equationsSolve linear equationsSolve linear inequalitiesSolve word problems that lead to linear equationsRatio and Algebra (New 2020) 2D GEOMETRYFind the area of compound shapesSolve word problems involving areasUnderstand the relationship between the circumference and radius of the circleFind the circumference of a circle given a radius or diameterFind the radius of diameter of a circle given the circumferenceFind the length of arcsFind the area of a circle given a radius or diameterFind the radius or diameter of a circle given the areaFind the area and perimeter of compound shapes involving circlesSEQUENCES Find patterns in spatial sequencesFind different ways of describing spatial sequencesFind the nth term of linear sequencesAll about Fibonacci3D GEOMETRY Use isometric paper to draw 3D shapesDraw plans and elevations of 3D shapesFind the volume of cuboidsFind the volume of shapes made from cuboidsUse nets to find the surface Area of cuboidsPyramids and prismsFind the volume of prismsFind the volume of pyramids and cones (New 2020)Find the volumes of spheres and compound shapes (New 2020) STATISTICS AND PROBABILITY Plot Scatter diagramsInterpret scatter diagramsUnderstand correlation and causationSample Space Diagrams (New 2020)Relative Frequency (New 2020) Tree Diagrams (New 2020)Using Tree Diagrams without replacement (New 2020)YEAR 9Rationale:In Year 9 students are introduced to additional algebraic manipulation to enable students to solve coordinate geometry and further 2D/3D geometric problems. ALGEBRAIC MANIPULATION Multiply out two or more bracketsFactorise quadratic expressionsCancel algebraic fractionsMultiply and divide algebraic fractionsAdd and subtract algebraic fractionsFURTHER COORDINATE GEOMETRYUse multiple representations of straight linesUnderstanding and using y = mx + cUnderstand the link between parallel and perpendicular linesANGLES, CONSTRUCTION AND CONGRUENCE Know and use angle rules for parallel linesKnow and use angles in polygonsUnderstand when shapes tessellateConstruct trianglesIdentify when triangles are congruentConstruct bisectors and angles using compasses and rulersQUADRATIC EXPRESSIONS, EQUATIONS AND GRAPHS Drawing Quadratic GraphsFinding roots of quadratic equations by factorisingForm and Solve Quadratic Equation by factorising by (a =1)Form and Solve Quadratic Equation by factorising (a>1)Complete the SquareUsing the Quadratic FormulaPYTHAGORAS, SURDS AND SURFACE AREAFinding the hypotenuseFinding a shorted sidePythagoras ProblemsIntroducing SurdsSimplifying SurdsManipulating SurdsExpanding brackets with surds (NEW 2020)Rationalising Surds (NEW 2020)3D PythagorasSurface Area of PyramidsPROBABILITY AND VENN DIAGRAMS Frequency TreesVenn DiagramsFinding probabilities from a Venn DiagramsYEAR 10Rationale: During Year 10 students build on prior learning from subsequent years to learn about Trigonometry and its applications. Additional algebraic techniques are introduced to provide students with more tools for solving complex problems. Links between circles and triangles are investigated and applied to further coordinate geometry problems. Statistical representations are explored with opportunities for students to analyse data in a variety of ways. TRIGONOMETRY Use trigonometric ratios to find missing lengths and angles in trianglesFind exact values for sin theta, cos theta and tan theta for key anglesUse the Sine and Cosine rules to find missing lengths and angles. Bearings (New 2020) Find the area of triangles using trigonometryRecognise and sketch trigonometric functions.CIRCLES AND EQUATIONS Solving and forming simultaneous equations by eliminationSolving and forming simultaneous equations by substitutionCalculate arc lengths, angles and areas of sectorsProof and application of Circle TheoremsEquation of a CircleFinding the equation of a tangentFinding the intersection of lines and curvesSCIENCE SKILLS Rearranging FormulaWork with numbers in Standard FormSUVAT EquationsSolve problems involving measure such as speed, density and pressure.Changing UnitsDraw and interpret graphs of non-standard functions and use them in real-life problems.Index Laws in ContextApproximate the gradient of a curve at a given point and the area under a graph.Interpret these values in real-life problems including kinematic graphsSTATISTICAL REPRESENTATIONSConstruct and Interpret Cumulative Frequency Tables and GraphsConstruct and Interpret BoxPlotsConstruct and Interpret HistogramsUse tables and line graphs to represent time seriesSEQUENCES AND GRAPHS Using iterative methods to generate different types?of?sequencesFinding the nth term of a Quadratic SequenceSolving Equations using Iterative methodsSolving Quadratic InequalitiesSolve Direct and Inverse Proportion ProblemsRecognise graphs showing direct and inverse proportionFunction Notation and Composite Functions (NEW 2020)?Inverse Functions (NEW 2020)Recognise and draw cubic and reciprocal functionsRecognise and draw graphs of exponential functionsRecognise and sketch translations and reflections of graphsFURTHER PROBABILITY AND COMBINATORICS CombinationsCalculating conditional probabilitiesUnderstanding independent eventsYEAR 11Rationale: Tier decisions are made in Year 11 to ensure that students are thoroughly prepared for their GCSE examination in Mathematics. Higher tier students deepen their existing knowledge and skills by exploring further similarity and congruence, vector geometry and loci problems. Foundation students will have an opportunity to further strength and deepen their understanding and knowledge of the most challenging GCSE concepts including working with quadratics and percentage problems. HIGHER Vector Geometry Similar Shapes (BWA)Further TransformationsProofLoci Problems Further RatioFOUNDATION Simultaneous Equations Compound InterestReverse Percentages Further RatioFactorising Quadratics Arcs and Sectors See Bespoke MTPSee Bespoke MTPSee Bespoke MTPSee Bespoke MTPLevel 2 FURTHER MATHS KS4 students are given the opportunity to study Further Mathematics GCSE to help the transition for further learning of Mathematics beyond Year 11. The curriculum has been planned to enable this to be taught alongside the Year 10 programme of study. For example, Autumn 1 concepts only require pre-requisite knowledge from the Year 9 concepts. Expanding brackets using Pascal’s TriangleDifferentiating polynomials Equation of Tangent and Normal at any point on the curveIncreasing and Decreasing Functions Stationary PointsThe second derivative Using Trigonometric identities to simplify expressions and proof further identities Using Trigonometric identities to solve trigonometric equations in given intervals Solving linear equations in three unknownsEquation of a Circle with centre (a, b) Limiting Value of a sequence Multiplying Matrices Transformation MatricesCombinations of Transformations The Factor Theorem Factorising cubic expressions Y12 CORE MATHS This course prepares students for the varied contexts they are likely to encounter in vocational and academic study and in future employment and life. FERMI ESTIMATIONEstimate answers to calculations in unfamiliar contextsPERCENTAGESPercentages of an amountInterpret percentages as a fraction or decimalCompare two quantities Understand and use percentages greater than 100%Reverse percentagesSolve problems involving percentage increase and decreaseSimple interestCompound interest and depreciationINCOME TAX AND NATIONAL INSURANCECalculate tax, NI, Student Loan and pension paymentsDATA ANALYSISPrimary, secondary, qualitative and quantitative dataREPRESENTING DATACumulative Frequency and box plotsStem and leaf diagrams (including back to back)SPREADSHEETSUse of simple formulaeVOLUME AND SURFACE AREASurface area and volume of cones, spheres, pyramids and compound shapesSolve problems involving similar shapesAERPerform AER calculationsSolve problems involving savings and investments and AER calculationsEQUATION OF A STRAIGHT LINEGradient of a line connecting 2 pointsUnderstand and use y=mx+cREPRESENTING DATACalculate and interpret the mean, median and mode of a data setCalculate and interpret quartiles, percentiles, range, interquartile range and standard deviation of a data setAPRPerform APR calculationsSolve problems involving debt and APR calculationsPayday LoansOPTIONAL CONTENTFINANCIAL PROBLEMSUnderstand the effect of inflationUse iterative formulaeExchange ratesUnderstand how to budgetOPTIONAL CONTENTCRITICAL ANALYSISCritically analyse data used in the mediaLIMITS OF ACCURACYApply and interpret limits of accuracyAppreciate errors due to roundingOPTIONAL CONTENTBESPOKE REVISION / MOCK EXAMS Y12 AS Mechanics routeAS Mathematics extends students experience of mathematical techniques significantly, developing advanced analysis of mathematical problems and construction of related arguments and methods of proof. The Mechanics route ensures that students have the pre-requisite knowledge and understanding of calculus to be successful when solving problems involving kinematics. STRAIGHT LINES AND CIRCLESDistance between two points and midpointsThe equation of a straight lineParallel and perpendicular linesThe equation of a circleSolving problems with lines and circlesPROOFMathematical arguments and notationProof by deduction, exhaustion and counter-exampleBINOMIAL EXPANSIONUnderstanding the Binomial TheoremSolving problems involving binomial coefficientsApplications of the Binomial TheoremDIFFERENTIATIONSketching derivativesDifferentiation from first principalsRules of differentiationInterpreting derivatives and second derivativesSolving problems involving tangents, normal and stationary pointsOptimisationINTEGRATIONRules for integrationFinding the equation of a curveDefinite integralsCalculate the area between a curve and a lineVECTORSDescribe vectors using magnitude and directionAddition and subtraction of vectorsProblems involving equal and parallel vectorsUnderstand position and displacement vectorsUse vectors to solve geometrical problemsKINEMATICS IN ONE DIMENSIONDisplacement, velocity and accelerationCalculus and kinematicsDisplacement-time graphsVelocity-time graphsProblems involving kinematicsFORCES AND NEWTONS LAWSDeriving the constant acceleration formulaSolving problems involving the constant acceleration formula and vertical motionNewton’s Laws of motionProblems involving gravity and resultant forcesTypes of forces, gravity and weightForces in equilibriumFORCES AND NEWTONS LAWSNewton’s third lawNormal reaction forceSolving complex problems in involving equilibriumConnected particlesProblems involving pulleysBESPOKE REVISION / MOCK EXAMSSEQUENCES AND SERIESTerm-to-term and position-to-term rulesSigma notationArithmetic sequences and seriesGeometric sequences and seriesInfinite geometric seriesMixed arithmetic and geometric problemsStatistics routeALGEBRAIC MANIPULATIONLaws of indicesSurdsQUADRATIC EQUATIONSSolving quadratic equationsGraphs of quadratic equationsCompleting the squareQuadratic inequalitiesThe discriminantDisguised quadraticsPOLYNOMIALSPolynomial divisionThe factor theoremSketching polynomial functionsGRAPHS, LINEAR AND QUADRATIC INEQUALITIESIntersections of graphsTransforming graphsReciprocal GraphsSketching inequalitiesTRIGONOMETRYGraphs of sine, cosine and tangent functionsTrigonometric identitiesSolving trigonometric equations in degreesTransformations of trigonometric graphsPROBABILITY AND STATISTICAL DISTRIBUTIONSMutually exclusive and independent probabilitiesProbability distributionsThe binomial distributionSTATISTICAL SAMPLING AND HYPOTHESIS TESTINGMethods of samplingHypothesis testing for the binomial distributionUnderstand critical regions for hypothesis testing. LOGARITHMSUnderstand the relationship between logarithms and indicesUnderstand the laws of logarithmsSolve exponential equations including disguised quadraticsEXPONENTIALSGraphs of exponential and logarithmic functionsSolve problems involving exponential functionsApproximate an exponential model as a straight lineDATA PRESENTATION AND REPRESENTATIONDraw and interpret statistical diagrams including histograms, cumulative frequency diagrams and box and whisker plotsStandard deviationCalculate and interpret the mean, standard deviation and variance from frequency tables. Interpret correlation coefficients and regression linesCalculate and determine outliersBESPOKE REVISION / MOCK EXAMSFUNCTIONSMappings and functionsDomain and rangeComposite functionsInverse functionsFURTHER TRANSFORMATIONS OF GRAPHSCombined graph transformationsThe modulus functionSolving modulus equations and inequalitiesY13 A2Mechanics route RADIAN MEASUREUnderstanding radians as an angle measureInverse trigonometric functionsSolving trigonometric equations in radiansModelling with trigonometric functionsArc length and sector areaSmall angle approximationsPROOFProof by contradictionCriticising proofBINOMIAL THEROEMBinomial theorem for fractional and negative powersExpansion of compound expressionsFURTHER DIFFERENTIATIONThe chain ruleThe product ruleThe quotient ruleImplicit differentiationDifferentiation of inverse functionsFURTHER APPLICATIONS OF CALCULUSConcave and convex curvesPoints of inflectionParametric equationsDifferentiating parametric equationsIntegrating parametric equationsConnected rates of changeFinding complex areas e.g. between 2 curves, between a curve and the y-axis. DIFFERNETIAL EQUATIONSSolving differential equations with 1 or 2 variablesModelling with differential equationsAPPLICATIONS OF VECTORSDescribing motion in two dimensionsConstant acceleration equationsCalculus with vectorsVectors in three dimensionsSolving geometrical problemsPROJECTILESModelling projectile motionThe trajectory of a projectileFORCES IN CONTEXTResolving forcesCoefficient of frictionMotion on a slopeMOMENTSThe turning effect of a forceEquilibriumBESPOKE REVISION / MOCK EXAMSStatistics RoutePARTIAL FRACTIONSSolving problems involving the factor theoremSimplifying rational functionsPartial fractions with distinct and repeated factorsTRIGNOMETRYCompound angle identitiesDouble angle identitiesFunctions in the form a sin x + b cos xReciprocal trigonometric functionsCALCULUS OF EXPONENTIAL AND TRIGONOMETRIC FUNCTIONSDifferentiationIntegrationFURTHER INTEGRATIONIntegration of secx, cosec x and cotxIntegration by substitutionIntegration by partsUsing trigonometric identities in integrationIntegration rational functionsNUMERICAL METHODSLocating roots of a functionThe Newton-Raphson method and its limitationsFixed-point iteration and its limitationsThe trapezium ruleFURTHER PROBABILITYSet notationVenn diagramsTwo-way tablesTree diagramsTHE NORMAL DISTRIBUTIONThe normal distributionThe inverse normal distributionFinding unknown μ or σModelling with the normal distributionFURTHER HYPOTHESIS TESTINGCalculating and interpreting probabilities using the normal distribution for a sampleHypothesis testing for the normal distributionHypothesis testing for correlation coefficientsBESPOKE REVISION / MOCK EXAMS ................
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