A Level Mtc Paper 1 Pdf

[email protected](AhabChosen) S.5MATHEMATCISPAPERONE CHAPTERONE:DIFFERENTIATION REVISIONQUESTIONS2020 Attemptallquestions 1.Findthegradientfunction foreachofthefollowingfunctions. dy dx a)y= +7x-4 x 2 b)y= -7x+8 6x 2 c)y=3 -7 +6x-8 x 6 x 2 d)y=3x- + 5 x 6 x 2 e) (4x-1) ( +2 x 7 ) 2.Findthegradientsofthefollowinglinesatthepointsindicated. a) +3x-1at(-1,-6) y=2x 3-x 2 b)y= +7x-4at(2, 21) x 2 c)y= -x+ at(2, 8) 2x 2 4 x d)y=3x+ at(1, 4) 1 x e)y= (2x+3)at(2, 21) (x+1) 3.Iff = +4xfind (x) x 3 a)f(1) b) (x) f ' c) (1) f ' d) (x) f ' ' [email protected](AhabChosen) e) (2) f ' ' 4.Iff =3 + find (x) x 2 24 x a)f '(x) b) (-12) f ' 5.Findtheequationofthenormaltothecurve +4x-3atthepointwherethecurve y=x 2 cutsthey-axis. Ans:4y+x+12=0 6.Findtheequationofthetangenttothecurve -3x-4atthepointwherethiscurve y=x 2 cutsthelinex=5. Ans:y=7x-29 7.Findtheequationofthetangenttothecurvey= (x-1)ateachofthepointswhere (2x-3) thiscurvecutsthex-axis.Findthepointofintersectionofthesetangents. Ans:y+x=1,2y=2x-3;(,-) 5 4 1 4 8.Findtheequationofthenormaltothecurve -6x+5ateachofthepointswherethe y=x 2 curvecutsthex-axis. Ans:4y-x+1=0,4y+x-5=0 9.Findtheequationofthetangenttothecurve +5x-3atthepointswheretheline y=x 2 y=x+2crossesthecurve. Ans:y=7x-4,y+5x+28=0 10.Findthecoordinatesofthepointonthecurve atwhichthegradientis8Hence y=2x 2 findtheequationofthetangentto whosegradientis8.Ans:(2,8),y=8x-8 y=2x 2 11.Findthecoordinatesofthepointonthecurve3 -1atwhichthegradientis3.Ans:( x 2 1 2 , -) 1 4 12.Findtheequationofthetangenttothecurvey=2 -2x+1whichhasagradientof0.5 x 2 Ans:2y=x+2 13.Findthevalueofkforwhichy=2x+kisatangenttothecurve y=2 -3.Ansk=- x 2 7 2 14.Findtheequationofthetangenttothecurvey= (2x+1)whichisparalleltothex- (x-5) axis.Ans:8y+121=0 15.Acurvehastheequationy= -px+q.Thetangenttothecurveatthepoint(2,-8)is x 3 paralleltothex-axis.Findthevaluesofpandq.findalsothecoordinatesoftheother pointwherethetangentisparalleltothex-axis.Ansp=12,q=8;(-2,24) [email protected](AhabChosen) 16.Thefunctiona +bx+chasagradientfunction4x+2andastationaryvalueof1.Find x 2 thevaluesofa,bandc.Ansa=2,b=2andc=3 2 17.Findtheseconddifferentialofywithrespecttoxforeachofthefollowing: a)y=6 +7 x 2 b)y=5 +6x-5 x 3 c)y=2+3 x 18.Ify=3 -xshowthaty + -6y+1=6x. x 2 y d 2 dx 2 dy dx 19.Thetangenttothecurvey=a +bx+2at(1,)isparalleltothenormaltothecurve x 2 1 2 y= +6x+10at(-2,2).Findthevaluesofaandb.Ans:1,-2.5 x 2 20.Findthecoordinatesofanystationarypointsonthegivencurvesanddistinguish betweenthem. a)y=2 -8x x 2 b)y= - -x+7 x 3 x 2 c)y=1-3x+x 3 d)y= ( -6x+2) (x-1)x 2 e)y=18x-20-3x 3 f) y= +6 +12x+12 x 3 x 2 g)y= -3 +3x-1 x 3 x 2 21.Findthecoordinatesofthestationarypointsonthefollowingcurvesanddistinguish betweenthem.Hencesketchthecurves. a)y= +2 x 4 x 3 b)y= -4 +4x x 3 x 2 c)y=5 -12 x 6 x 5 [email protected](AhabChosen) d)y= -4 +4 x 4 x 3 x 2 22.Differentiatex2+ fromfirstprinciples. 1 x 23.Differentiatey= withrespecttoxfromfirstprinciples x +1 x 2 24.Findthederivativeof …