trial tarc mat1(2011)

8/3/2019 Trial Tarc MAT1(2011)

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Nat exactdecUital m tlwspt:cifilm tM

J I I l f1 A Nn Pt )t l ni siti

STPM 2011

P,\ ER t" 201 1 'ED ESDAY)t3 H o t t ~ )

sh.Jwn clu.ulv

b, gn n correct to three significant figures, or one~ J c . . ~ m degrwtts. u.nius a different level o f accuracy is

a list Malittmllllull formulae andgraph paper are prOVIded

s question paper consists of 4 pnntedpageshttp://edu.joshuatly.com


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By using the laws of the lgebra of -.how th 1t. tor nn y sets B and C{(A - B) l l {A C)} u B I...J C A u B J C {4 mark 1

2 ,. -1Jsing trapezium rule to ob tain an appro imntlon to J.'t ln xdx by w,ing 5 ordmates, e c t UJ 3 deam'

...J .

'places.. . . . . !x- 51+ 1Find the set values ofx whtch snt1sfy the mequnhttes lx_51 1 < 3 (6 mar

d 1 dI fy - (2 + 3x)e 2.r , prove that +4 + 4y =0.dx dx [6 rnarvJ5. (a ) A pol)'gon has sides whose lengths are an Aritmetric Progression. T he lengths of the shofte$t

longest s ides are 1 3cm and 5.7cm respectively. G iven that the perimeter of the polygon 15 42cdeterm ine the number of sides. [2 rnad:s]

(b ) r I I 2rShow that (. ) =- - ( ) . Hence, ( ) .r + I ! r! r + 1 ! r 3 r + 1 ! [5marks]6. The equation of a curve is given by xy = a2 Find the equation of the tangent to the curve

pointP aap,- .p [3marksA liney = mx is perpendicular to the equation of the tangent to the curve at point Q. Find m in terms oand show that the coordinates of point Q is 20P , 20P3l + p4 l+p4 . Hence, find the locus ofQasp varies.

[1 marks]

Sketch 2 suitable graphs to show that the equation 2ln x = _ has only one real root that lies betweenX. of 21n x = ~ c o r r e c t to three decima2 and 3. Use the Newton-Raphson method to detemune the root x

[9marks}places by using 2.5 as the first approximation.http://edu.joshuatly.com


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3.

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lh 1,,m thl' I""' "t the: ,\ltl Vt ,\ t\ l shll\\ th \t , tl'l t\\\\ 'H" Hl ' t" en \., n ,c .-\ \. H \. '-'\

l ht ng lntP(' ' ium ruk h. l1bttun ,m . t p p r ~ ' ' ' m ttton t ~ ' Jn , ~ / : \ b' u ~ m ' ,,,Ju"'h-,, " \H\. , . l t ' I'rind t h ~ 'C;'t '..llll ' !>. of ' whtch ' a 16. 1he equ otion of a curve is given by = a1 Find the equ tion ~ " ' f th tm\g: nt h.' t h ~ ~ \ \ t " l" ,\t

7.

. p apomt ap. - l3 mU'ks lpA line y- m-e is perpendicular to the equation of the tangent to the cun .1t point _'l. Ftnd in t rn\S \, fr

., 2 'd h h h d. f . Q . _ap apan s ow t at t e coor mates o pomt ts 4 4 Hence . ttnd th \ ~ ~ .. "'fQ "r an '.l+ p l+ p

Sketch 2 suitable graphs to show that the equation 2ln x = 2_ has onh o n ~ re .u 1\:..X2 and 3. Use the Newton-Raphson method to detennine the root C'f tn ,,= \;;,.places by using 2.5 as the first approximation.

A .. l" o . , j ) 1\, e ,.. \.) ) \JA( C!\ " ' Vht A \J Q

" \c c } " \)' \\ \I ~ " " tV " A 1\ f ' .( \" f i N ~ ' ' " ' " " A \J ) ' :

'"" ' - :1 .4f ... \)

C m. rk.:l

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http://edu.joshuatly.com


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II. Given that p(x) x,. +ax1 - 7 i - 4ax 1 b, where" und b arc real con tants. Gjven 3 a zero of p(x)and when p(x) is divided by x - 3. the remainder i 60 Jind the values of a and b Solve the equationp(x) 0 and find the set of values ofx such that p(x) 0. [12 marks]

12. (a) Ify x[(ln x)1 - 2 In + 2). ! how dxy

I

1 2

(ln X)l . Hence. evaluate f (ln xf dx .y ln x

X

' ~ ) (b) , On the graph, y = elx andy = In x are two curves and x = 2 is a straight line,

[S marks}

i. calculate the area of the region R bounded by the curves, coordinates axes and x = 2,\.3 mar\(s\

Jl . find the volume o f th e solid formed when R is rotate 360 about th e x-axis

is gjven to the following sources: Past Year papers and other resource materials .http://edu.joshuatly.com

trial tarc mat1(2011)

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