Overview

These are the Paper 1 Topics that are coved in this course:Multiples, factors, LCM and HCF and prime factor decompositionFractions and ratio problemsStandard constructions using a compass (including triangles)Bearings with geometrical problemAverages and range, problems and comparing distributionsSimplify algebraic indicesExpand single and double bracketsUse a cumulative frequency graph to compare distributions (median and IQR)Probability tree for independent eventsSimplify algebraic indicesAlgebraic fractionsFactorising quadratic expressions, including difficult where a > 1Perimeter and area of triangles and quadrilaterals, including trapeziumRecurring decimal to fraction (prove)Simplify and manipulate surdsSurface area and volume of cylindersCompleting the Square and turning pointsComposite and inverse functionsDraw transformations and combination of transformationsGraphical solution to equations, including quadratic rootsGeometrical problems, alternate /corresponding angles and angles in a segment Graphs of trigonometric functions Translations and reflections of a functionThese are the complete list of topics that will be covered in the higher GCSE course:NumberBIDMAS (brackets)Interpret calculator displaysRounding and estimation, error intervalsCompare fractions, decimals and percentagesFractions and ratio problemsRecurring decimal to fraction (prove)Index Laws (division, negative and fractional)Multiples, factors, LCM and HCF and prime factor decompositionFractions and ratio problems Adding, subtracting, multipling and dividing fractions (problem)Changing from standard form into an ordinary numberCalculating with standard form (calculator)Upper and lower bounds (including calculations)Simplify and manipulate surdsAlgebraForming expression, formulae and equations (then solving)SubstitutionMid-point and distance between two coordinatesSimplify algebraic indicesExpand single and double bracketsnth term of a linear sequenceLinear equations (including variable on both sides)Drawing graphs of linear functionsFinding the equation of a line, and parallel and perpendicular linesSimultaneous equations (linear) problemFactorise single bracketFactorising quadratic expressions, including where a > 1Quadratic equations (including when needs re-arrangement)Recognise Fibonacci and quadratic sequencesnth term of a quadratic sequenceDrawing quadratic graphsRearranging Formulae (including when subject appears twice / factorising)Represent linear inequalities on number line and graphicallySolving linear inequalities and represent on number line and graphicallyRepresent quadratic inequalities graphicallySolving quadratic inequalitiesThe Quadratic FormulaCompleting the Square and turning pointsSimultaneous equations (linear/quadratic)Draw and recognise reciprocal and cubic graphsGraphs of exponential functions and growth and decayGraphical solution to equations, including quadratic rootsComposite and inverse functionsGeneral iterative processesAlgebraic fractionsAlgebra proofGraphs of trigonometric functions Translations and reflections of a functionRatio, Proportion and Rates of ChangeRatio and proportion problems Comparing quantities as a ratio and division of a quantity as a ratioDivision of a quantity as a ratioProblems involving ratioConverting metric unitsScale drawingsExpress one quantity as the percentage of anotherCompound interest and financial mathsReverse percentages and reverse percentage changeCompare lengths, area, volumeProblems involving compound units (including pressure)Direct and inverse proportionNon-standard real life graphsReciprocal real-life graphsGradient of graphsDistance-time graphsArea under a graph (compare estimate with actual)Geometry and MeasuresProperties of 2D ShapesGeometrical problems, alternate /corresponding angles and angles in polygonsPerimeter and area of triangles and quadrilaterals, including trapeziumArea of a triangle using Area = ½absin CPerimeter and area of composite shapesCircumference of a circle, arc length and perimeter and area of a sectorProperties of 3D Shapes and plans and elevationsSurface area and volume of prisms, pyramids, cones and spheresDraw transformations and combination of transformationsPythagoras' Theorem, including in 3DTrigonometry (SOH CAH TOA), including in 3DStandard constructions using a compass (including triangles)LociBearings (possibly with trigonometry or a geometrical problem)Scale factors and similarityCircle theoremsSine RuleCosine RuleVectorsProbabilityRelative frequencySampling and unbiased samplesVenn diagramsProbability trees for both independent events and conditional probability Frequency treesStatisticsAverages and range, problems and comparing distributionsComparing data on statistical diagrams, including time series graphsMean from a discrete frequency tableScatter graphs and correlationConstructing and interpreting a boxplotUse a cumulative frequency graph to compare distributions (median and IQR)Histograms

Skills

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