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 thethe 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 whereh 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+2rlr l . i t u LrJci-rrg * = $, find f;6 correcl ro y- d"rgsalil--eg

I i t ^l5 S,.ive the equalion 3 lrl = lx-zl',il:rrb-es:s"r:..,',rrdinateaxes,sketchthegraphs atg=gl riand37 =1*-2 |Henceisc,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 lj_,.F'9.

,.,,1,i,.,,1 ,,,,

Sketch the graph of y = s:'2. ghow clearly the turning point and state the equatio" "t '1"f,, *ltlie 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 reall3 rnwksl

values of r.

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I 0. R. is the region bounded by the axes and the part ofthe curvey2-4a(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 that8_.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

624V : r-r

-Y-3 x+3A^\

(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.

[3 marks]

[4 marks]

[2 marks]

[5 marks]

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