Higher R Recap (levels 7 & 8); C Core (bold); E .

HigherTierDateR Recap (levels 7 & 8); C Core (bold); E Extension to include AQA Further Maths (italics)Y10 & 11 GCSE SOW forSet 1Teacher support material available here: gcse/allgcse.htmTopicNotesMid-Jun –Jul1. INDICES: STANDARD FORMN1 – N9(Y10)R: Index notationPrime factorsLaws of indicesC: Negative / fractional IndicesStandard formExamplesStudentReferenceResourcesN7: Positive integer powers onlySimplify a5 a3; m4 m2; (p2)5; (2xy2)3;Prime factors Find HCF of 216 and 240Ex 13, 14 p1418 (HCF, LCMetc)Ex 13 p14(roots)There is teacher support material foreach unit, including teaching notes,mental tests, practice book answers,lesson plans, revision tests & activities.The teacher support material isavailable HEREN7: With and without calculatorsimplify 812/3 (without calculator);Ex1,2 p354-355(indices)N9: SFEvaluate 2.762 10 4.97 10 (cal.)Evaluate 2.8 104 7 106 (no cal.)Evaluate 2.8 104 7 106 (no cal.)Clip 44 Factors, Multiples and PrimesClip 95 Product of Prime FactorsClip 96 HCF & LCMClip 99 Four rules of NegativesClip 45 Evaluate PowersClip 46 Understanding Squares, Cubes& RootsClip 111 Index Notation forMultiplication. & DivisionClip 135 Standard Form CalculationsClip 156 Fractional & Negative Indices 1221Ex18,19 p68-71(standard form)Starter:Jul – AugSUMMER HOLIDAYSSeptember(Y10)2. FORMULAE: ALGEBRAICFRACTIONSR: Formation, substitution,change of subject in formulaeMore complex formulae:– substitution– powers and roots– change of subject with subject in morethan 1 termA1 – A7With and without calculatorOpportunity for revision of negativenumbers, decimals, simple fractions.Including denominators with(i) numerical or single term(ii) linear termGiven q – 2, v 21, find the value of v2 q2.𝐿Make L the subject of t 2π 𝐺 More complex formulae: Given u 2 , v 3, find f when1 1 1f u vMake v the subject of1 1 1f u vEx1 p96 (basicof algebra)Ex7 p104(definitions)Ex24 p75-76(substitution)Clip 104 FactorisingClip 107 Changing the subject of theFormulaClip 111 Index Notation for Mult. &DivisionClip 163 Algebraic FractionsClip 164 Rearranging DifficultFormulaeFactorise x3y4 x4y3 x2yCommon term factorisationSimplify𝑥𝑥 1 2𝑥2𝑥 1C: Algebraic fractions – additionand subtractionOctober(Y10)3. ANGLE GEOMETRYG1, 3, 4, 6, 13R: Angle properties of straight lines,points, triangles, quadrilaterals, parallellinesAngle symmetry propertiesof polygonsInclude line and rotational symmetryInclude plane, axis and pointSymmetrySymmetry properties of 3-D shapesEx1 p157-159(angles)Calculate interior angle of a regular octagon/decagonShade in the diagram so that it has rotational symmetry ofOrder 4 but no lines of symmetry.Ex4 p164-166(angles inpolygons)Clip 67 Alternate anglesClip 68 Angle sum of a TriangleClip 69 Properties of Special TrianglesClip 70 Angles of Regular PolygonsClip 150 Circle theorems

Describe fully the symmetriesof this shape.Compass bearings8 compass points and 3 figurebearingsScale drawings of 2-stage journeysC: Angle in a semi-circleRadius is perpendicular to the tangentRadius is perpendicular bisector ofchordAngles in the same segment are equalAngle at the centre is twice the angle atthe circumference.Opposite angles of a cyclicquadrilateral add up to 180 .Alternate segment theorem.Tangents from an external point areequal.Intersecting chordsTangent/secant(Y10)Application of Pythagoras and Trig.G9: identify and apply circledefinitions and properties, including:centre, radius, chord, diameter,circumference, tangent, arc, sector andsegmentAX.BX CX.DXPT2 PA.PB4. TRIGONOMETRYG20 – G23R: Trigonometry (sin, cos, tan)Angles of elevation and depressionBearings2-D with right-angled triangles onlyIncluding case with two solutionsAngles of any sizeG21: know the exact values of sin θand cos θ for θ 0 , 30 , 45 , 60 and90 ; know the exact value of tan θ forθ 0 , 30 , 45 and 60 C: Sine and cosine rulesEx23-25 p337343 (circletheorems)Calculate angles: BDA, BOD, BAD & DBOShip goes from A to B on a bearing 040 Bearings for 20 km. How far north has it travelled?Ex6-7 p294(finding thelength)Ex8 p297(finding angles)Ex9 p299 (trig &bearing)Clip 147 TrigonometryExact Trig Values resourcesEx19-20 p328(sine rule)Ex21 p331(cosine rule)Clip 173 (sine & cosine)

Ex22 (problemsolving with sine& cosine rules)find length CB1Solve sin x or all x in range 0 x 720o.E: Graphs of sin, cos, tan.Solutions of trig equationsOct –NovNovember(Y10)2Ex17 p232(graphs of trigfns)Ex18 p325(solutions of trigequations)Clip 168 Graphs of trig fns. (A/A*)OCTOBER HALF TERM5. PROBABILITYP1 – 9R: Relative frequency experimentalprobability and expected resultsAppropriate methods of determiningprobabilitiesKnow that a better estimate for aprobability is achieved by increasingthe number of trialsUsing symmetry, experimentSimple tree diagramsProbability of 2 eventsBy listing, tabulation or tree diagramsRayner: Ch9p445Experiment to find probability of drawing pin landing point up.p ace 4/52 1/13There are 5 green, 3 red and 2 white balls in a bag. What is the probability ofobtaining(a) a green ball (b) a red ball(c) a non-white ball?Multiplication law for independent eventsC: Addition law for mutuallyexclusive (ME) eventsMEP StudentbookUnit 5 Teachers NotesMEP Text BookLast One Standing Mathsland National Lottery Same Number! Who’s the Winner? Chances Are The Better BetClip 154 Tree Diagrams (Grade B)Clip 182 Probability – And & Orquestions (Grade A* - A)ME means both events cannot happenat the same timeResources for Venn DiagramsAddition Law for nonmutually exclusive eventsNon ME mean independent events both can happen at same time.Find the probability of obtaining a head on a coin and a 6 on a dice.Conditional probability;dependent eventsSampling without replacementUsing Venn diagrams (optional)Calculate the probability of obtaining 3 aces when dealt 3 cards from a deck of 52.Using Venn diagramsExamples of what pupils should know and be able to do for VennDiagrams:C: Sets & Venn DiagramsEnumerate sets and combinations of setssystematically, using tables, grids, Venndiagrams and tree diagrams.""Calculate and interpret conditionalprobabilities through representation usingEnumerate sets and unions /intersections of sets systematically, usingtables, grids and Venn Diagrams. Very simple Venn diagrams previouslyKS2 content.Post on Frequency TreesResources for Frequency TreesPrize Giving (NRich)

expected frequencies with two-waytables, tree diagrams and Venn diagramsInvestigate – Venn Diagrams:ξ {numbers from 1- 15}; A {odd numbers}; B {multiples of 3}and C {square numbers}(a) Draw a Venn diagram to show sets A, B & C. You’ll need 3circles(b) Which elements go in the overlap of A&B A&C B&C A, B & C(c) Try and come up with three different sets where not all of thecircles overlap. How many different Venn diagrams with threecircles that overlap in different ways can you find?Example:X is the set of students who enjoy science fictionY is the set of students who enjoy comedy filmsThe Venn diagrams shows the number of students in each set, work out:(i)P(X Y)(ii)P(X U Y)Example:One of these 80 students is selected at random.(b) Find the probability that this student speaks German but not Spanish.Given that the student speaks German,(c) Find the probability that this student also speaks French

Frequency TreesRecord describe and analyse thefrequency of outcomes of probabilityexperiments using tables and frequencytrees(Y10)6. NUMBER SYSTEMN13 – N16R: Estimating answersUse of brackets and memory on acalculatorUse of ( ) button29.4 61.230 60 614.815N10: Recurring decimalsList some irrational numbers between 5 and 6.Show that (i) 0.0 9 (ii) 0.16 are rational.N8: Surd form of sin, cos, tan of 30 45 60 N8: Division of surds usingconjugatesRationalise the denominator;Addition, subtraction, multiplication ofsurdsExpansion of two bracketsexpand 1 2 1 2 If p and q are different irrational numbers, is(i) p q (ii) p qRational / Irrational / Could be both?7. MENSURATIONR: Difference between discreteand continuous measuresG14: To include estimation ofmeasuresSurds1 3;21Clip 157 Surds (A)Clip 158 Rationalising the Denominator(A)Ex1 p49-50Q21,22(decimals tofractions)Ex3 p357(surds) 7Illustrate current postal rates; shoe sizesG16: Find the area of this kite.Areas of parallelograms, trapezia, kites,rhombusesand composite shapesVolumes of prisms and composite solidsClip 98 & 155 Recurring Decimals toFractions2.5 14.3 3.32558 (𝑡𝑜 5. 𝑑. 𝑝)7.8 2.959.7 means 9.65 x 9.75100 metres (to nearest m) is run in 9.8 s (to nearest 0.1 s). Give the range ofvalues within which the runner's speed must lie.Irrational / rational numbersEx20 p28-29(estimatingmeasures)Ex13-15 p185193 (area &perimeter)Ex23-25 p211217 (Volume &surface area)G16: Area of cross-section x length ofprismSurface area of simple solids:cubes, cuboids, cylindersVolume/capacity problemsG17: Include compound measuressuch as density.Clip 101 Estimating (grade C)Clip 125 & 160 Upper & lower boundsIncluding area, density, speedC: Upper and lower bounds includinguse in formulaeDecember(Y10)Ex19 p26-31(estimating)G17: Find the mass of water to fill this swimming pool.Ex27-28 p79-82(compoundmeasures)Clip 71 & 72 CirclesClip 73 Area of compound shapesClip 120 & 121 surface areaClip 122 & 177 VolumeClip 178 Segments & FrustumsClip 124 metric unitsClip 126 compound measuresClip 176 Area of a triangle using Sinerule

2-D representations of 3-D objectsC: UnitsAppropriate degree of accuracyUse of isometric paperN13: Conversion between m and cm,m2 and cm2, m3 and cm3.Given the plan and side elevation, draw a 3D isometric diagram of the object.Ex25-26 p77-78(metric &imperial)N15: Rounding sensibly for thecontext and the range of measuresusedUpper and lower boundsN16: apply and interpret limits ofaccuracy including UB & LBl 9.57 m 9.565 l 9.575Calculate the radius of a sphere which has the same volume as a solid cylinderof base radius 5 cm and height 12 cm.Volume and surface area pyramid,cone and sphere and combinations ofthese (composite solids)G18: arcs & sectorsLength of circular arc, areas of sectorsand segments of a circleG18: Calculate the shaded area given a 5Notation [L] [T] [M] for basicdimensionsDimensionsWhich of the following could be volumes? rl, x3, ab cd,1Area of triangle a b sinC(𝑎𝑏)27𝑏; where (r, l, x, a, b, c, d, are lengths)2E: Area of triangle s s a s b s c 1where s a b c Heron's formula2Find the area of thesetrianglesDec – JanCHRISTMAS HOLIDAYSJanuary(Y10)8. DATA HANDLINGR: Two-way tables including timetablesand mileage chartsFrequency graphsp386-44412 hour and 24 hour clockIf a train arrives at a station at 13:26 and the connection leaves at 14:12, howlong do you have to wait?Unit 8 Teachers notesClip 85 Two-Way Tables (Grade D)Clip 84 Questionnaires and DataCollection (Grade D)