8/12/2019 STPM Trials 2009 Math T Paper 1 (SMJK Tsung Wah, Kuala Kangsar)

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SMJK TSUNG WAH, KUALA KANGSARSTPM TRIAL EXAMINATIONS 2009

MATIIEMArtCS 1Time: 3 hoursAnswer ALL the question.1. Find the square root of -5 + 12i. [5]2. The polynomial x 3 - x2 +ax +b is denoted by p(x). It is given that ( x + 1 ) is afactor ofp x) and that wbenp x) is divided by (x - 2) the remainder is 12(i) Find the values of a and b(ii) When a and b haves 1hesevalues, factories p(x) [7]

E 3r 4. , ~ ~ i f ra H fi d fI 3r 43. xpress m ~ . . . w ctton. ellce In L: , andr r + I) r + 2) r= r r +1) r + 2)f 3r 4r=1 r r + 1) r + 2)

4. Use the binomial theorem to expand + x as a series ofascending powers of x upI xto and including the tenn in r .wherelxl< L By putting x = ~ , show that Jil is10[663approximately equal to 200

X+2 3 35. Find the values ofx i f he matrix A = 3 x + 4 5 is singular.3 5 x 46. The equation of the sides AB, BC and CA ofa triangle ABC are y = 2x, y = 3x and

x + y = 8 respectively. Find the equation of he straight which passes through thepoint C and perpendicular to the line AB.The line cuts the x-axis and the y axis at the points P and Q respectively. Find thePCratio -CQ

7 Sh h ~ X l x+l h . th fi J ~ X + low t at = ence usmg e substItution x = sed} nd xx I dX 1 x I8. The function f and g are defined by

f : x -- - 25 ,1< x ~ 9, x E 913x-2g:x--+-x2 ,1

8/12/2019 STPM Trials 2009 Math T Paper 1 (SMJK Tsung Wah, Kuala Kangsar)

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9. Sketch the graphs y = e -3 , andy = In (x+3) to show that the equation e -In(xt3) = 3has two real roots.By taking x = I.Sas a first p p r o x i m t i o ~ use Newton-Raphson method to find thethe root correct to 3 decimal places. [8]

10 T h e m a m x A i s ~ v e n by ~ : ~ :J(a) Find A2(b) Show that there exist numbers m andn such that A2 :rnA nI, where I is a3x3

identity matrix and find the values of m and n(c) Hence find themverse ofA3x 911.Find the coordinates of he stationary point on the curves y = 2 . Detenmne the

x x 2nature of the stationary points.Sketch the curve and state the equation of asymptotes.Show that the equation of the curve can be written in the fonn yx2- y+3)x -{2y - 9 ) = 0

{12]

and h s no real root if y - 3)(3y - 1) < 0 [16]12. Sketch, on a single diagram, the graphs of =4 - x and =x - I .

Show that area enclosedby the two curves is given by 2 ; J{ and detemline the exactvolume of the solid generated by revolving the region abut the x-axis through 7t radians. [10]

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8/12/2019 STPM Trials 2009 Math T Paper 1 (SMJK Tsung Wah, Kuala Kangsar)

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8/12/2019 STPM Trials 2009 Math T Paper 1 (SMJK Tsung Wah, Kuala Kangsar)

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