# Contradiction lies with all assumptions correct at

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contradiction lies withALLassumptions correct at the start(including,0b d)2.1R1Subtotal4Question Total7
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/2 – JUNE 202012QMarking instructionsAOMarkTypical solution8(a)Eliminates t1.1aM1𝑦𝑦2=𝑡𝑡,𝑥𝑥=𝑦𝑦²4𝑦𝑦² = 4𝑥𝑥Writes the Cartesian equationin the required form1.1bA1Subtotal28(b)(i)Differentiates both𝑑𝑑𝑥𝑥𝑑𝑑𝑡𝑡= 2𝑡𝑡,𝑑𝑑𝑦𝑦𝑑𝑑𝑡𝑡= 2with at least one correctOrDifferentiates their𝑦𝑦² = 4𝑥𝑥toobtainddyyAx=Or rearranges and differentiates2yx=and obtains12ddyAxx=OE3.1aM1𝑑𝑑𝑥𝑥𝑑𝑑𝑡𝑡= 2𝑡𝑡,𝑑𝑑𝑦𝑦𝑑𝑑𝑡𝑡= 2𝑑𝑑𝑦𝑦𝑑𝑑𝑥𝑥=22𝑎𝑎=1𝑎𝑎The gradient of a line is equal tothe tangent of the angle betweenthe line and the horizontal hence1tanaθ=Obtains correct𝑑𝑑𝑦𝑦𝑑𝑑𝑥𝑥att=a1.1bA1Explains that the gradient of aline is the tangent of the anglebetween the line and thehorizontalorshows on right-angled triangleon diagram and links totanθandconcludes1tanaθ=2.4E1Subtotal38(b)(ii)Uses formula for gradient ofstraight line with points A and BMust have21aor21aindenominator1.1aM12220tan121aaaaφ==Obtains correcttanφOE1.1bA1Subtotal2
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/2 – JUNE 2020138(b)(iii)States double angle formula fortan 2θ1.2B12222tantan 21tan121121tanaaaaθθθφ=×===Substitutes1tanaθ=into their22tantan 21tanθθθ=±1.1aM1Simplifies and completesargument to show requiredresult2.1R1Subtotal3Question Total10
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/2 – JUNE 202014QMarking instructionsAOMarksTypical solution9(a)Identifies and clearly definesvariable for radius of cylinder.Can be shown on diagram orcan be implied by use in2Vr hπ=2.5B1Radius of cylinder =r2222hrRVr hπ+==()22Uses Pythagoras to connecth,randR3.1aM1r9(b)Differentiates the expression forvolume w.r.t.hwith at least oneterm correct.2==A1RR,

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Rational number, MARK SCHEME, Kompakt