Trial P2 CHC (1)

SIITIJK GHUNG HWA CONFUCIAN, PULAU PINANGTRIAL STPTII (2013}

954'2 i'ATHEITIATICS T PAPER 2 (UPPER 6}

ffime: 1] hours)

Prepared by : Mdm Low Yee Yean

Checked by:Mdm Hoe Swee Yoke -)Approved by: Mr Chew Yoon Seng ,1"/

lnstrucfiont to candidates:1. This question paper consists of 2 printed pages.2. Answer all questions in Section A and any one guestion in Section B.

3. All necessary working should be shown clearly.4. Non-exact numerical answers may be given conect to three significant figures, or one decimal place in the

case of angles in degrees, unless a different level of accuracy is specified in the question.

Section A[45marksl

Answer all questions in this section.

1. The func{.ion/is defined by

r'lt-sl , x.-3/(r) = l1 |

t5r-12 , x23(a) Without sketching the graph, determine whether/is continuous at x=3.

(b) Sketch the graph oflin the domain [0,5] and state the range ofl

2. Given that y = ae-2xsin(x * p), where a dan $ areconstants. Shor tnatfr* 4X* 5y = g. [6ml

[4m][3m]

3. A curve is defined by the parametric equations x = t -f and ! = 3t+f, where t#0.

(a) Show that fr = J - fi "nO hen@, deduce that -1< H.,

(b) Find the coordinates of the points where H= t'

el4.(a) (i) J

-clxv'>!ffidx(iii) Jrs lruc dx

, gx-l(iv) J

-dx

Snt[3ml

[1m]

[1ml

[2m]

[2m]

(b) The trapezium rule, wilth 2 intervals of equalwidth, is to be used to find an approximate value

for Jo1 e-x dx.

(i) Expfain, wfth the aid of a sketcfr, why the approximation will be greater than the exact value of the

integral. [2m](ii) Calculate the approximate value and the exact value, giving eacfi answer conect to 3 decimal

places. [3ml

Under certain conditions, the rate of cooling of a liquid is proportional to the difference between its

temperature and its surrounding temperature. The liquid is placed in a room of temperature 30oC and thetemperature of the liquid at time (minutes) is r.(a) Form a differential eguation to describe this phenomenon. [2m](b) lf the liquid cools from 100oC to 70 oC in 8 minutes, find the further time taken for the liquid to reach a

temperature of 31"C . lsml(c) Find also the temperature of the liquid after it has been in the room for 10 minutes. [2ml

6. Use appropriate Maclaurin series to evaluater. x-sittxlllllr-+0 x\er4)

Section B[1Smarks]

Answer any one question in this section.

7. Given a curvey ="i*7.er-2'(a) Show tnei. zff = L - !2(b) Show that # < otor all values of ;r.

(c) Find lima--*y and [im*-*I

(d) Sketch the gnapfr of y = #Explain how the number of roots of the equation k(Zx-ll=#

8. For the curve y = {?*:af-4x(L-x)

(a) Find the equation of the three asymptotes.(b) Find the coordrnates of the tuming points.

(c) Sketch the curve.(d) Find the set values of y.

(e) Deduce and sketch the graph of y = r.!('-,!).(2x+t1z'

[3m]

[5ml

t3ml

[2ml

[3ml

[2ml

[2ml[3ml[3ml

ISrtfI I

[4ml

END OF QUESTION PAPER

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