[Edu.joshuatly.com] Perak STPM Trial 2010 Maths TS Paper 1 [DDB78BD4]
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SMJK TSLING WAH, KUALA KANGSARPEPERIKSAAN PERCUBAAN STPM MATHEMATICS T I Strowthar [(A n B)' nA] U IG{ n B)' n A : (A-B) U [B-A), where, andB are arr.y two sels. S liitd the the culve intersects the 2 Gi'ren that 1og, r + Zlogny = 3, show that xg = 8' Henj&>solve for x and 3a which satisfirthesirnultaneouseqlationslogro (2r+D = 1ald-log, x +ZLagug =]' 16nzarksl to tlie curverz -y' n 6rg4attnepoints where h t----:- t $mnrksl )+^ t/ - y1,o / l5 marksl ['1,mu*s] L3 mwksl 4 trpress + as a series of ascending powers of r uniil ltre term 13, where lL+2r lr l . i t u LrJci-rrg * = $, find f;6 correcl ro y- d"rgsalil--eg I i t ^l 5 S,.ive the equalion 3 lrl = lx-zl' ,il:rrb-es:s"r:..,',rrdinateaxes,sketchthegraphs atg=gl riand37 =1*-2 |Hencei sc,lrre{fieinequality l"ltl*-21. -t - ,-ttt'=.1t,ea'rk"$}- ,t t * , The points -1o(4, 3), Q{3, -2),]?(-3, 8) ?nd s(0,, B1 ate vertices of a paralleloertio j,j ' fgns.Determine tire vatues' of'aand, p' -\-'r r' - - l":14'nark4 on-a ffnd tlre aree nf 'l l-',t ' F'ind the.shortest disrance fromP tCI QS- Ilence, find the alea of ,the n***r"gtd"l!-,.ji-**-k l j_,.F'9. ,.,,1,i,.,,1 ,,,, Sketch the graph of y = s:'2. ghow clearly the turning point and state the equatio" "t '1"f,, *l tlie asynrptote- '=': l, i-;sc thc trapczium rule witlr six ordinales to estimate the'arear bounded. by, the ;,;'. - r.i ir.l/e, the r-axis and the tinesFT-and r = 2, #'dtng your ans*er correct [o lhfee : ' 'jj ,r*rUrl r' 'r:irnal places" i l2 I -L\ jri*dtlieinversematrixofa=t r :1 g l ,,,,t!-',i+m'u'rks), \4 3 1/ ',,:.";:,.'' .]'r]nce,soivc|hesimultancousequations2r,+x,_fiz=15,r,-rz=2anr1 ,:.:'.,';: 14 fnarksl ''i;.r+3rr+rr='!J- Given tlrat the polynomial p (r) - :t" + uffz + br + 10 has a factor of {r -r 2) and that r"".hen c{ivideil by (c - 3), the remainder is 10' ir) Find tire values of a and b' 14 marhsl { .r) F ind t}rc other r:eal factor of p{x} and show that this factor is pcsifive for ail real l3 rnwksl values of r. http://edu.joshuatly.com/ http://www.joshuatly.com/ I 0. R. is the region bounded by the axes and the part ofthe curve y2-4a(a-x)inthefirstquadrant !.-_tata,x) \f^L_ V' Findintermsofa | - ' \rr'- 1 (a) the area of R t 3 marks l (b) the volume 11, " of the solid formed when R is rotated cornpletetry abou€ thex-a,r11 [-a marks ] "lThe volume of the solid formed rr&en R is rotated about the y-axis is F " lg 3 nta.rks ] [ 2 marks J tt Show that 8_. V..=-V- / lq ^ The region S , l$ng in theSrst quadrant, is bounded by the curve f=ie$j 1 unJ &" lini* * : * and v = E- Enilinlerhsof a, the volume ofthe solid formed when S is rotated completely about the y*axis. The equation of a curve C is 624 V : r-r -Y-3 x+3 A^\ (a) Write down the equatio{5 pf the asymptot$ (b) Find the coordinates of thepoint$where C meets the €fes-) ;\- (c) Find the coordinates of the stationary poinQJof C - (d) Sketch C [ 2 marks J I / ff^rre I [4 rnarks ] [ 3 rnarks ] i 2.The function f is defined as f(x\:{ s-lx+tl ,-6<x<1 [x'-6x+8, 1<x<4 (a).Find lim f(x) and lim f(x). (b) (c) (d) Hence, determine whether f is continuous at X = 1 . Sketch the graph of f. Determine the range of f . Determine the set of values of x so that./(x) > 2 - x. 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