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A2 Decision Planner 14-15 WDateThingsTopicset11/9Thur/Fri onlySingle lesson all blocks“A level compared to AS”115/9C3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy. α222/9TT1CWC testC3 Integration as the invers of differentiationFunctions – Domain, Range, Compositeβ329/09C3 Functions – Modulus, Inverse, Transformationsγ46/10C3 Natural logs including derivatives of e^x and lnxδ513/10TT2 (C3 + integration)C3 Rcos(x+a), ε620/10C3 Inverse trig functions including graphs. Numerical MethodsζOctober Half Term / End Term 1 73/11C4 Partial fractions. *Forming Differential Equations.η 910/11Lessons on MondayReading Week – Open Eve, Dept Day, SRs Thurs/Fri ι817/11D1 Algorithms – Bubble sort, Quick sort, Bin packing, Binary search? 1024/11TT3 (C3)**C4 Integration using Trig, Partial FractionsIntegrals of form f1(x)/f(x) (substitution optional here)κ111/12D1 Algorithms on graphs (Dijkstra, Kruskal and Prims)λ128/12C4 Implicit Differentiationμ1315/12No P4 ThursdayNo P5,6 FridayD1 Route inspectionνChristmas / End Term 2 145/1C4 Review of integration so far, trapezium rule and % errorξ1512/1TT4 pure/ appliedC4 Vectors* equation line, intersection, etc ο1619/1D1 Linear programming, ruler and vertex methodsπ1726/1C4 Integration by Substitution/Partsρ182/2C4 Differential Equations & Connected Rates of Changeσ199/2D1 Critical Path Analysis, Precedence tables, activity networks τFebruary Half term / End Term 3 2023/2TT5C4 Parametricsυ212/3D1 Gantt charts, schedulingφ229/3C4 Binomial Expansion, Vol of Revolutionχ2316/3D1 Matchingsψ2423/3C4 MockD1 RevisionωEaster / End Term 42513/4D1 MockEXAM PRACTICE & REMOCKA2620/4C3 MockEXAM PRACTICE & REMOCKB2727/4EXAM PRACTICE & REMOCKC284/5No mondayEXAM PRACTICED2911/5EXAM PRACTICEE3018/5A2 Study LeaveF-JA2 Statistics Planner 14-15 WDateThingsTopicset11/9Thur/Fri onlySingle lesson all blocks“A level compared to AS”115/9C3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy. α222/9TT1CWC testC3 Integration as the invers of differentiationFunctions – Domain, Range, Compositeβ329/09C3 Functions – Modulus, Inverse, Transformationsγ46/10C3 Natural logs including derivatives of e^x and lnxδ513/10TT2 (C3 + integration)C3 Rcos(x+a), ε620/10C3 Inverse trig functions including graphs. Numerical MethodsζOctober Half Term / End Term 1 73/11C4 Partial fractions. *Forming Differential Equations.η 910/11Lessons on MondayReading Week – Open Eve, Dept Day, SRs Thurs/Fri ι817/11S2 Binomial Distribution? 1024/11TT3 (C3)**C4 Integration using Trig, Partial FractionsIntegrals of form f1(x)/f(x) (substitution optional here)κ111/12S2 Poisson Distribution (mean/var), Poisson as approximation to Binomialλ128/12C4 Implicit Differentiationμ1315/12No P4 ThursdayNo P5,6 FridayS2 Binomial to normal approximation Poisson to normal approximationνChristmas / End Term 2 145/1C4 Review of integration so far, trapezium rule and % errorξ1512/1TT4 pure/ appliedC4 Vectors* equation line, intersection, etc ο1619/1S2 CRVs pdf & cdfπ1726/1C4 Integration by Substitution/Partsρ182/2C4 Differential Equations & Connected Rates of Changeσ199/2S2 CRVs E(X),Var(X), median, mode, IQR, τFebruary Half term / End Term 3 2023/2TT5C4 Parametricsυ212/3S2 CRVs Uniform Distribution Sampling, Statistics, Distributionsφ229/3C4 Binomial Expansion, Vol of Revolutionχ2316/3S2 Hypothesis Testingψ2423/3C4 MockS2 Hypothesis TestingωEaster / End Term 42513/4S2 MockEXAM PRACTICE & REMOCKA2620/4C3 MockEXAM PRACTICE & REMOCKB2727/4EXAM PRACTICE & REMOCKC284/5No MondayEXAM PRACTICED2911/5EXAM PRACTICEE3018/5A2 Study LeaveF-JA2 Mechanics Planner14-15WDateThingsTopicset11/9Thur/Fri onlySingle lesson all blocks “A level compared to AS”115/9C3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy. α222/9TT1CWC testC3 Integration as the inverse of diffn Functions – Domain, Range, Compositeβ329/09C3 Functions – Modulus, Inverse, Transformationsγ46/10C3 Natural logs including derivatives of e^x and lnxδ513/10TT2 (C3 + integration)C3 Rcos(x+a),ε620/10C3 Inverse trig functions including graphs. Numerical MethodsζOctober Half Term / End Term 1 73/11C4 Partial fractions. *Forming Differential Equations.η910/11Lessons on MondayReading Week – Open Eve, Dept Day, SRs Thurs/Fri ι817/11M2 Projectiles?1024/11TT3 (C3)**Integration using Trig & Partial Fractionsκ111/12Motion in a straight line & on plane/vectorsλ128/12Implicit Differentiationμ1315/12No P4 ThursdayNo P5,6 FridayCentres of mass (discrete masses, frameworks, laminas,)νChristmas / End Term 2 145/1TT4 pure/appC4 Review of integration so far, trapezium rule and % errorξ1512/1C4 Vectors* equation line, intersection, etcο1619/1M2 Work, Energy& Powerπ1726/1C4 Integration by Substitution/Partsρ182/2C4 Differential Equations & Connected Rates of Changeσ199/2M2 Centre of mass suspension, tiltingτFebruary Half term / End Term 3 2023/2TT5C4 Parametricsυ212/3M2 Collisionsφ229/3C4 Binomial Expansion, Vol of Revol’nχ2316/3M2 Staticsψ2423/3C4 MockM2 StaticsωEaster / End Term 42513/4M2 MockEXAM PRACTICE & REMOCKA2620/4C3 MockEXAM PRACTICE & REMOCKB2727/4EXAM PRACTICE& REMOCKC284/5No MondayEXAM PRACTICED2911/5EXAM PRACTICEE3018/5A2 Study LeaveF-JC3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy. Application of the chain rule, product rule and quotient ruleC3 Integration as the inverse of differentiationEmphasis on correct notation for integration.Make sure they understand the importance of dx in the integrationGood to do some definite integrations and insist on correct notationC3 Functions – Domain, Range, CompositeThey find domain and range difficult.Emphasise two methods – graph sketching: domain is x axis, range is y axis – good use of graphical calculatorslook at domain and use algebra to work out domainHowever, beware of thisy=9-x2 domain -3<x<2 x=-3, y=0; x=2, y=√5, so domain is 0<y<√5 whereas the correct answer is 0<y<9Emphasise correct notation – e.g. domain -3<x<2 and range is 0<y<9 or 0<f(x)<9; not 0<x<9Emphaise care with < and ≤ Functions – Modulus, Inverse, TransformationsModulus graphs can be easily drawn with graphical calculators – sometimes this is abs (absolute)Inverse functions can be found by swapping x and y which is the same as reflecting the graph in the line y=x Natural logs including derivatives of e^x and lnxDraw the graphs of y=2 x, y=3 x, y=2.5 x, y=2.7x and use Autograph to plot the gradient function. Show that y=ex is the same as its gradient function. Rcos(x+a), Beware of using tan because they often invert to mistakenly get cot.I prefer to find R using Pythagoras and then equatee.g. express 3 cos x + 4 sin x in the form Rcos(x-a)R= 5 (Pythagoras)R cos (x-a) = 5(cos x cos a + sin x sin a)3 cos x + 4 sin x = 5(cos x 3/5 + sin x 4/5)Then equate to get cos a = 3/5 or sin a = 4/5 Inverse trig functions including graphs. Numerical MethodsMake sure they put in the correct words for Numerical solutions.“Because there is a change of sign and the graph is continuous, there is a solution between x = 1.65 and x = 1.66” or “Because there is a change of sign and the graph is continuous, x = 2.71 to 2 decimal places” – in the last example they should have shown that x = 2.705 and 2.715 produce a different sign Partial fractions. *Forming Differential Equations.Three types to considerAx+B(x+a)(x+b)2) Ax+B(x+a)(x+a)(x+b)3) Ax2+Bx+C(x+a)(x+b) Algorithms – Bubble sort, Quick sort, Bin packing, Binary searchAt some point, students will need to memorise the definitions that are listed in the syllabus on page 100. Don’t be tempted into getting them to memorise all definitions in the textbook as there are lots of extra ones in the textbook. Bubble Sort: Packing: Sort: Search includes flow charts and algorithmsSome teachers don’t normally bother teaching flow charts, just set one in homework although others feel that students find it hard to blindly follow the rules of a flow chart and do exactly what they are told to! Well, they are mon Mistakes; Not packing all the items in the original listFinding ‘H’ and thinking it’s Hugo when actually it’s Hannah and Hugo isn’t in the listNot copying the whole list down They find bubble sort harder than quick sort. They find alphabets and decimals harder than integersCommon mistakes with sorting: Not writing ‘sort complete’ at the endNumbers changing from one line to the nextS2 Binomial DistributionM2 ProjectilesC4 Integration using Trig, Partial FractionsIntegrals of form f1(x)/f(x) (substitution optional here)They need constant reminders of all this stuff. Regular testing of easy work is recommended, e.g. a weekly five minute test asking them to integratesin xcos xtan xcot xsin2xsin2xcos2xcos2xsec2xcosec2xcosec x cot xsec x tan x1x+12xx2+3 Algorithms on graphs (Dijkstra, Kruskal and Prims)Dijkstra: along the arcs as you update helps accuracyMust show method for route TROLL pneumonic (top label, remove row, O round the smallest, LIST! LIST! – ie list the order the arcs were chosen in)Common mistakes: Adding wrongMissing an arc to updateDoubling up on the ‘order’ so having two 6th verticesUnits missing S2 Poisson Distribution (mean/var), Poisson as approximation to BinomialM2 Motion in a straight line and on plane/vectorsC4 Implicit DifferentiationI always make them write differentiate b.s.w.r.t.x (both sides with respect to)e.g.Find dydx if sin x + 6y2 = 2xyDifferentiate b.s.w.r.t.xddx(sin x) + ddx(6y2) = ddx (2xy)ddx(sin x) + ddy(6y2) dydx = y ddx (2x) + 2x ddx(y)cos x + 12ydydx = 2y + 2xdydxdydx(12y – 2x) = 2y – cos xdydx = 2y-cosx12y-2x Route inspection mistakes; Thinking AB direct is the best link of A and BWriting ‘repeat AB’ when you mean ‘repeat AC, CB’Units missing S2 Binomial to normal approximation Poisson to normal approximationM2 Centre of mass suspension, tiltingC4 Review of integration so far, trapezium rule and % errorAlthough they have done the trapezium rule in C2, don’t assume that they remember how to do it.Beware complex methods and formulae for working out he.g.x6.46.66.877.27.4yDon’t use h = (b-a)/(n-1)Do use h=0.2 because the x numbers are increasing by 0.2 each time large number of videos at Vectors* equation line, intersection, etc Vectors are traditionally hard for students to understand.A large number of videos at Linear programming, ruler and vertex methods mistakes: Mistakes using simultaneous equationsTwisting ruler en route and getting wrong vertexWrong integer solutionShading y<mxNot labelling linesAt least twice as many x as y as an inequality S2 CRVs pdf & cdfM2 Work, Energy and PowerC4 Integration by Substitution/PartsIt’s very important to insist that students set their work out carefully and methodically in this topic. It’s always important for every topic, obviously, but it’s very easy for their work to become excessively muddled in these topics.For substitution, I insist that they draw a vertical line with the main working on the left and the substitution and limit replacement on the right. Differential Equations & Connected Rates of Change Critical Path Analysis, Precedence tables, activity networks CRVs E(X),Var(X), median, mode, IQR,M2 Centre of Mass suspension, tilingC4 Parametrics Gantt charts, schedulingImportant to emphasise the difference between a scheduling diagram and a Gantt chart. CRVs Uniform Distribution Sampling, Statistics, DistributionsM2 CollisionsC4 Binomial Expansion, Vol of RevolutionReview of all integration at lot of videos at Matchings mistakes; Thinking that ‘because C and D can only do M P and Q’ is the same as ‘because M, P and Q can only do C and D’S2 Hypothesis TestingM2 Statics ................
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