soalan ramalan add maths+skema [times] 2011

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  • 7/29/2019 Soalan Ramalan ADD MATHS+Skema [Times] 2011

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    NO TOPICSPAPER 1 PAPER 2

    2006 2007 2008 2009 2010 2006 2007 2008 2009 2010

    1 Functions 1,2 1,2,3 1,2,3 1,2,3 1,2,3 2 - - - -

    2QuadraticEquations

    3 4 4 4 5 - - - 2a,2c -

    3QuadraticFunctions

    4,5 5,6 5,6 5,6 4,6 - - 2 2b -

    4SimultaneousEquation

    - - - - - 1 1 1 1 1

    5Indices and

    Logarithms6,7,8 7,8 7,8 7,8 7,8 - - - - -

    6CoordinateGeometry

    12 13,14 13,14 15 13,14 9 2 10 9 5

    7 Statistics 24 22 22 24 22 6 5 5 - 6

    8CircularMeasures

    16 18 18 12 17 10 9 9 10 11

    9 Differentiation 17,18,19 19,20 19,20 19,20 20,21 - 4a,4b 7a 3a,7a 8

    10Solution ofTriangles

    - - - - - 13 15 14 12 13

    11 Index Number - - - - - 15 13 13 13 15

    12 Progressions 9,10 9,10,11 9,10,11 9,10,11 9,10,11 3 6 3 6 313 Linear Law 11 12 12 12 12 7 7 8 8 7

    14 integration 20,21 21 21 18,20,21 19 8 4c,10 7b,7c 3b,7 4

    15 Vectors 15,

    16TrigonometricFunctions

    15 17 17 16,17 18 4 3 4 4 2

    17Permutations

    AndCombinations

    22 22 23 22 23 - - - - -

    18 Probability 23 24 24 23 24 - - - - -

    19ProbabilityDistributions 25 25 25 25 25 11 11 11 11 10

    20Motion Along AStraight Line

    - - - - - 12 12 12 15 12

    21LinearProgramming

    - - - - - 14 14 15 14 14

    TOTAL 25 25 25 25 25 15 15 15 15 15

    Additional Mathematics

    Analysis[3472/1]

    [3472/2]

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    1 Diagram 1 shows he graph o a quadraic uncion :xx2+1 or he domain ax2.

    Find(a) he value o a,(b) he range o (x) corresponding o he given domain. [3 marks]

    2 Given (x)=5x+a and g(x)=3bx.Given g(x)=30x-3, nd he value o a ando b. [3 marks]

    3 Given and 1

    are he roos o he quadraic equaion 2x2+5x+q=0. Find he value o q. [2 marks]

    4 Solve he quadraic equaion (2x+3)2=4. [3 marks]

    5 Find he possible values om i he sraigh line y=x+m is he angen o he curve y=7x-mx2. [3 marks]

    6 Find he range o values o x such ha 4x29 [2 marks]

    7 Diagram 7 shows a graph o quadraic uncion (x)= a(x+2)2+4 such ha A is a maximum poin.

    Find(a) he coordinaes o A,(b) he value o a.

    [3 marks]8 Solve 4log 3 x=64. [2 marks]

    9 Solve he equaion 32(2n-2 )+2n+3-2n= 1 [4 marks]

    10 Given ha log3

    q-log3

    p2 q = log3 o1

    pp +1 , express q in erms o p. [4 marks]

    11 Given he hird erm and he welh erm o an arihmeic progression are - 13 and 14 respecively.Find he common diference o he progression. [3 marks]

    12 Te rs erm o a geomeric progression is our imes is hird erm. Find he common raio o he progression. [2 marks]

    13 Given he second erm and he sum o inniy o a geomeric progression are 4 and 16 respecively. Find(a) he common raio,(b) he rs hree erms

    o he progression. [4 marks]

    Additional Mathematic Paper 1 [3472/1]

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    14 Diagram 15 shows a sraigh line obained by ploting a graph o log10 y agains x. Te wo variables x and y are relaed by heequaion y=10x+h, where h is a consan.

    Find he value o h and k. [4 marks]

    15 Given hree poins A (-3, -2), B (7 , 3) and P(1,k) . Poin Plies on he sraigh line AB and divides AB in he raio m: n. Find(a) he raio m :n ,(b) he value o k . [4 marks]

    16 Diagram 16 shows a sraigh line PQ which is perpendicular o a sraigh line QR a poin Q.

    Given he equaion o he sraigh line PQ is 2y = -x + 4 , nd(a) he equaion o he sraigh line RQ ,(b) he coordinaes o poin Q. [4 marks]

    17 Given vecor a=2 i j and b = -i +3 j, nd he value o p i 2p a + 3 b is parallel o he y- axis. [2 marks]

    18 Poin M is (4,-5) and poin N is ( -6, -3). Find he uni vecor in he direcion o MN. [3 marks]

    19 Solve he equaion 4 sin x cos x =1 or 00 x 3600 . [3 marks]

    20 Diagram 20 shows he semicircle wih cenre O and radius 8 cm.

    Given he lengh o arc BC is 5 cm, nd he area o secor OAC.

    (Use = 3.142) [ 4 marks]

    21 Te sraigh line y =5x 7 is he angen o he curve wih gradien uncion kx2 x a poin (1, -2).Find he value o k. [2 marks]

    ~ ~~ ~ ~ ~ ~ ~

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    22 Diagram 22 shows he graph o y=(x). Given he area o he shaded region is 12 uni2.

    Find[4 marks]

    23 Given a se o ve posiive inegers wih mode 3, median 4 and mean 5.(a) Find one possible se o posiive inegers wih he value o mode, median and mean given.(b) I each o he inegers is increased by 2, nd he new mode, he new median and he new mean o he

    new se o posiive inegers. [4 marks]

    24

    A code is ormed by arranging hree alphabes rom se X ollowed by wo digis rom se Y. Find(a) he number o possible arrangemens or he code,(b) he probabiliy ha hese arrangemens ends wih he digi 2. [3 marks]

    25 Te marks o a group o sudens in Addiional Mahemaics es is normally disribued wih mean 55 andsandard deviaion 6. I 70% o he sudens have marks more han , nd he value o . [3 marks]

    END OF QUESION PAPER

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    Additional Mathematic Paper 2 [3472/2]

    Secion A[40 marks]

    Answer all quesions in his secion

    1. Solve he ollowing simulaneous equaions:2x-y-2=02x2+y-10x+8=0 [5 marks]

    2. Te quadraic uncion (x)=ax2+bx+16 is negaive when 2

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    6. Diagram 6 shows he arrangemen o he rs our o he innie series ocircles. Te radiuso he rs circle is xcm.Te radius o each subsequen circle is hal o he radius o he previous circle.

    [Use = 3.142](a) Show ha he areas o he circles orm a geomeric progression. [2 marks](b) Given he area o he ourh circles is 4 cm2, nd he value o x . [2 marks](c) Hence, nd he sum o inniy o he areas ohe series o circles. [2 marks]

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    Secion B[40 marks]

    Answer any ourquesions rom his secion.

    7 Use graph paper o answer his quesion.able 7 shows he experimenal values o wo variables x and y known o be relaed by he equaion y = (p+q) xp.

    x 1.2 1.6 2.5 4.0 6.3 8.0y 1.5 1.8 2.6 3.6 5.0 5.8

    able 7

    (a) Plo log10

    y agains log10

    x , by using a scale o 2 cm o 0.1 uni on boh axes .Hence, draw he line o bes . [5 marks]

    (b) Use your graph in 7(a) o nd he value oi) p,ii) q. [5 marks]

    8. Diagram 8 shows a graph o he sraigh lines y + 3x = 5, y - 3x = -5 and he curve y2=4x.

    Find

    [Use = 3.142](a) he coordinaes o P and Q, [3 marks](b) he area o he shaded region, [5marks](c) he volume generaed when he area bounded by he curve and he line x = 1 is revolved

    180O around he x-axis. [2marks]

    9. Diagram 9 shows he secor ABC wih cenre A and he secor OMN wih cenre O.Poin A is he midpoin o OB and poin N is he midpoin o AC .

    Given OB = 12 cm. Find[Use = 3.142]

    (a) AON in radian, [1 marks]

    (b) he perimeer o he shaded region, [5 marks](c) he area o he shaded region. [4 marks]

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    10. Soluion by scale drawing is no acceped.Diagram 10 shows a righ- angled riangle PQR. Te coordinaes o P is (4,9) and poin R lies on he y-axis.

    Given he equaion o he sraigh line QR is2y-x+6=0.(a) Find

    (i) he equaion o he sraigh line PQ,

    (ii) he coordinaes o Q,(iii) he area o riangle PQR. [7marks]

    (b) Te poin A moves such ha is disance rom P is always 5 unis. Find he locus o A. [3 marks]11 (a) Te probabiliy o buying a good compac disc rom a paricular shop is 0.85.

    (i) Find he probabiliy ha a leas 4 compac disc are good i 6 compac discs are bough.(ii) Calculae he mean and he sandard deviaion o geting a good compac disc i

    6 compac discs are bough. [4 marks]

    (b) Te mass o each o he sh rom a pond ollows a normal disribuion wih a mean o 720 gram

    and a sandard deviaion o k gram.

    Te probabiliy ha a sh caugh a random rom he pond has a mass more han 745.5 gram is 0.0539.Find he value o k.I 200 sh has a mass beween 700 gram and 740 gram, esimae he oal number o sh in he pond. [6 marks]

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    Secion C[20 marks]

    Answer any WO quesions rom his secion

    12. A paricle moves in a sraigh line and passes hrough a xed poin O. Is velociy, vms-1,is given by v= 27 + k, where is he ime in seconds aer leaving O and k is a consan.

    [ake he moion o he righ as he posiive direcion]

    (a) Given he iniial velociy o he paricle is 10 ms-1, nd(i) he value o k,(ii) he range o values o during which he paricle moves o he le,(iii) he range o values o during which he paricle acceleraes. [5 marks]

    (b) (i) Skech he velociyime graph o he moion o he paricle or 05.(ii) Hence, or oherwise , calculae he oal disance ravelled by he paricle in

    he rs 4 second aer leaving O. [5 marks]

    13. able 13 shows he prices and weighages o our ypes o iems A, B , C and D.

    IemPrice(RM) Price(RM)

    Price Index WeighageYear 2006 Year 2008

    A 7.00 8.40 w 10

    B 13.50 x 130 8

    C y 13.00 115 7

    D 11.00 12.10 110 zABLE 3

    (a) Calculae he value o w, x and y. [4 marks]

    (b) Te composie index o hese iems or he year 2008 based on he year 2006 is 120.Calculae he value o z. [3 marks]

    (c) Te oal cos o all hese iems is expeced o increase by 10% rom he year 2008 o he year 2009.Find he expeced composie index or he year 2009 based on he year 2006. [3 marks]

    14. Diagram 14 shows wo riangles ABCand CDE. Te wo riangles are joined a C such ha AE and BD are sraigh lines.

    Given ha DCE = 34.050 and CED is an obuse angle.(a) Calculae

    (i) CED(ii) he lengh o AB. [5 marks]

    (b) Te sraigh line CE is exended o F such ha DE = DF.Find he area o riangle CDF. [5 marks]

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    15. Use graph paper o answer his quesion.

    Perdana Youh Club wans o send a number o is members o paricipae in a moivaion course. Given he number omale paricipans is x and he number o emale paricipans is y. Te paricipaion o he members is based on he ollowingconsrains:I : Te oal number o he paricipans is a leas 100.II : Te number o emale paricipans is a mos wice ha o he male paricipans.III : Te ee or each male paricipan is RM 60 while he ee or each emale paricipan is RM 120. Te maximum allocaion

    or he course is RM 12,000.

    (a) Wrie hree inequaliies, oher han x0 andy0 , which saisy all he above consrains. [3 marks]

    b) By using a scale o 2 cm o 20 paricipans on he x- axis and 2cm o 10 paricipans on he y-axis ,consruc and shade he region R ha saises all he above consrains. [3 marks]

    (c) By using your graph rom (b), nd

    (i) he range o he number o male paricipans i he number o emale paricipans is 60.

    (ii) he minimum allocaion needed by he club or is members o paricipae in he course. [4 marks]

    END OF QUESION PAPER

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    Additional Mathematics

    Jawapan

    Additional Mathematics Paper 1

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    Additional Mathematics Paper 2

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