Stpm Trial 2009 Matht&s1 (Smi Ipoh)

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SMK ST.MICHAEL, IPOH STPM TRIAL EXAMINATION 2009 MATHEMATICS sn 9SQ/I,95411 PAPER 1 Thrte hours Instructions: Answer all questions. All working should be shown clearly, Non-exact numerical answers may he given COi ecllo threo significant figures, or ons decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. n _ w . =tn(n+IX 2n + I ), L;r' =tn'(n+I)' ,...1 r _1 . ,...\ ã Trapezi
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  SMK ST.MICHAEL, IPOH STPM TRIAL EXAMINATION 2009 MATHEMATICS sn 9SQ/I,95411 PAPER 1 Thrtehours Instructions: Answer all questions. All neces~ary working should be shown clearly,N on -exact numerical answers may hegiven COi ecllo threosignificant figures, or onsdecimal place in thecase of angles in degrees, unless a different level of accuracy is specified in the question . n_ w. ~:;r=tn(n+l) ,~:;r' =tn(n+IX 2n +I ), L;r' =tn'(n+I)' ,...1 r _1 .,...\ ã TrapeziumRule: ff(x)dr = thlY, + 2(y,+ y, + ..... + y_ ,) + y,] ã 1. Express(i) (3+.fi)' in theform a+bfi (ii)in(2.,Je) - ~I{;)-I{~) in th~ form c + Ind Where a,h,e and d are rational numbers. 2. By letting z = x +Iy ,find the complex number z which satisfiestheequation z + 2z' =2 15 -I [3] (3] where z· denotes the complex conjugate ofz , [5] , 3. Use the trapezium rule toobtainan approximation to !xIn xcaby using 5 ordinates. [6] , xl-2x-9 4. Express (2x -I)(x' + 3) , in partial fractions. Hence, evaluate J , x' -2x-9 ~ ., (2x -l)(x ' + 3) ' gtVlng your answer correct to 2 significant figures. [6] 5. Find the equation· of the circle that touches the line y = -5x +3 at thepoint (2,-7) and itscentre is located on the line x-2y=19 . . [6] {1 X-x'l,x 4 6. Sketch the graph ofthe functionfdefined by f(x) =. x l - 5x+6,x >4 . . Find limf(x) and limf(x) . Hence,show thatfis notcontinuous atx=4.Determine whetherfis ... -+4- ~ ... ... continuous at x = o. [9] 7. Given that y = (2 + 3x)e- ,prove that ~; +4: +4y =0 (6) 8.The polynomial p(x) = x· + ax' -7x' -4ax +b bas. factor x+ 3 and, when divided by x-3, .bas remainder 60.Findthevalues of a and b, andf.ctorise p(x) completely.[9] Using the s u b s t i t u t i o ~ ' y -.! , solve the equation 12y _8 y 3 _7y l + 2y+ 1 = O. x [3]  A=(~ -2 l . The matrix Ais given by -3 -2 (a) Find A'. [3) (b) Given that A' = rnA + nI , where m, values of m and n. n are integers and lis a 3 x 3 identity matrix, find the [3] (0) Hence,or otherwise find tha inverse ofA . [4) 10. (a) Find the sum of he following series: I x 4+2x 7 +3 x 10+ ............ .. ...+ n(Jn+ 1). [6) (b) In a geOmetric progression, the first term is12 and the fourth tenn is -~ .Find the leastvalue 2 ofn for which the magniiude of the difference between S, and S. is less than 0.001.[4] ' 11 .· Expand (1 + x)~ in ascending power of x until the tenn in Xl . By takingx = _1_ , findthe 40 I I I approximation for 32.S; correct to Jour decimal places. If the expansion of +ax and (1 + xl i 1 +bx .. ~ 20 3 are the same until the term in x', find thevalues of a and b. Hence, show th.t 32.8' ~ -. 12] 10112. Sketch in separate diagnuns, the graphs of (a) )I=3x' +4~+2 .1 (b) )I = .-;---'::-----=- 3x' +4.+2 stating, in each case, the coordinates of my turning points, and for (b), show the shape of the curve for Jarge, positive values of x and large ,negative values of x. By sketching an additional graph onone of the above graphs, or otherwise,show that the .equation 3x' + 4x' + 2x = 6 has one, and only one,real root. Show also that thisroot Ues between 0 and 1. END OF THE QUESTION PAPER Prepared by, .. ~ : .... .V.Paul Checked by. .~~ ..: ..!.. Pn.RAtaa Kaur _ ....... -. ... t. MWwol fpoL Endorsed by ã . ~   .. . ... .. .. ..... . .... .... Pn. Cb g Sau Han [12)
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