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QSchemeMarksAOsPearson Progression Step and Progress descriptor1aStates M13.1b5thDifferentiate simple trigonometric functions.Makes correct substitutions:M11.1bUses the appropriate trigonometric addition formula to writeM12.2aGroups the terms appropriatelyA12.2a(4)1bExplains that as h → 0,andM13.2b5thDifferentiate simple trigonometric functions.Concludes that this leaves So if A13.2b(2)(6 marks)NotesQSchemeMarksAOsPearson Progression Step and Progress descriptor2aDifferentiates obtaining and differentiates obtainingM11.1b6thDifferentiate using the product rule.Makes an attempt to substitute the above values into the product rule formula:M12.2aFindsM11.1bFully simplfies using correct algebra to obtain A12.4(4)2bMakes an attempt to substitute t = 2 into M1 ft1.1b6thDifferentiate using the product rule.Correctly findsand concludes that asthe toy soldier was decreasing in height after 2 seconds.B1 ft*3.5a(2)2c= 0 or at a turning point.M1 ft1.1b6thDifferentiate using the product rule.Solvesto findCan also stateA1 ft1.1b(2)(8 marks)Notes2bAward ft marks for a correct answer using an incorrect answer from part a.B1: Can also stateas the numerator ofis negative and the denominator is positive.2bAward ft marks for a correct answer using an incorrect answer from part a.QSchemeMarksAOsPearson Progression Step and Progress descriptor3Makes an attempt to differentiate y = ln?3x using the chain rule, or otherwise.M12.2a6thDifferentiate sums and differences of functions involving trigonometric, logarithmic and exponential functions.Differentiatesto obtainA11.1bEvaluates at A11.1bEvaluates at x = 1M11.1bAttempts to substitute values intoFor example, is seen.M1 ft2.2aShows logical progression to simplify algebra, arriving at:A12.4(6 marks)NotesAward ft marks for a correct attempt to substitute into the formula using incorrect values.QSchemeMarksAOsPearson Progression Step and Progress descriptor4aDifferentiatesto obtainM11.1b6thDifferentiate reciprocal and inverse trigonometric functions.WritesA11.1b(2)4bUse the identityto write M12.2a6thDifferentiate reciprocal and inverse trigonometric functions.Attempts to substituteandinto M12.2aCorrectly substitutes to findand statesA11.1b(3)(5 marks)NotesQSchemeMarksAOsPearson Progression Step and Progress descriptor5Differentiates 4x to obtain 4x?ln?4M11.1b7thDifferentiate simple functions defined implicitly.Differentiates 2xy to obtainM12.2aRearrangesto obtainA11.1bMakes an attempt to substitute (2, 4)M11.1bStates fully correct final answer:AcceptA11.1b(5 marks)NotesQSchemeMarksAOsPearson Progression Step and Progress descriptor6aFindsandM11.1b6thDifferentiate simple functions defined parametrically including application to tangents and normals.Writes ?2sin?2t = ? 4sin?t?cos?tM12.2aCalculatesA11.1b(3)6bEvaluatesatA1 ft1.1b6thDifferentiate simple functions defined parametrically including application to tangents and normals.Understands that the gradient of the tangent is, and then the gradient of the normal is ?2.M1 ft1.1bFinds the values of x and y atandM1 ft1.1bAttempts to substitute values intoFor example, is seen.M1 ft2.2aShows logical progression to simplify algebra, arriving at: orA12.4(5)(8 marks)Notes6bAward ft marks for a correct answer using an incorrect answer from part a.QSchemeMarksAOsPearson Progression Step and Progress descriptor7aFindsM11.1b7thUse second derivatives to solve problems of concavity, convexity and points of inflection.FindsM11.1bStates thatfor alland concludes this implies C is concave over the given interval.B13.2a(3)7bStates or implies that a point of inflection occurs whenM13.1a7thUse second derivatives to solve problems of concavity, convexity and points of inflection.Finds x = ?2A11.1bSubstitutes x = ?2 into, obtaining y = 46A11.1b(3)(6 marks)NotesQSchemeMarksAOsPearson Progression Step and Progress descriptor8Attempts to write a differential equation.For example,oris seen.M13.1a7thConstruct simple differential equations.StatesA13.1a(2 marks)NotesQSchemeMarksAOsPearson Progression Step and Progress descriptor9Recognises the need to use the chain rule to findFor exampleis seen.M13.1a8thConstruct differential equations in a range of contexts.FindsandM12.2aMakes an attempt to substitute known values. For example,M11.1bSimplifies and statesA11.1b(4 marks)Notes ................
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