trial stpm mathematics t2 pahang

8/8/2019 Trial STPM Mathematics T2 PAHANG

1/7

CONFIDENTIAL*

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PERCUBAAN JPNP PEPERIKSAAN PERCUBAAN JPNP PEPERIKSAAN PERCUBAAN JPNP PEPERIKSAAN PERCUBAAN

JPNP PEPERIKSAAN PERCUBAAN JPNP PEPERIKSAAN PERCUBAAN JPNP

PEPERIKSAAN PERCUBAAN

SIJIL TINGGI PERSEKOLAHAN MALAYSIA

NEGERI PAHANG DARUL MAKMUR 2010

Instructions to candidates:

Answerall questions. Answers may be written in either English or Malay.

All necessary working should be shown clearly.

Non-exact numerical answers may be given correct 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.

Mathematical tables, a list of mathematical formulae and graph paper are provided.

This question paper consists of 7 printed pages.

954/2 STPM 2010

Three hours

MATHEMATICS T

PAPER 2


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CONFIDENTIAL* 2

Mathematical Formulae for Paper 2 Mathematics T :

Logarithms :

a

xx

b

b

alog

loglog

Series :

)1(2

1

1

nnrn

r

)12)(1(6

1

1

2

nnnrn

r

22

1

3)1(

4

1

nnrn

r

Integration :

dxdx

du

vuvdxdx

dv

u

cxfdxxf

xf )(ln)(

)('

ca

x

adx

xa

1

22tan

11

c

a

xdx

xa

1

22sin

1

Series:

Nnwhere

,

21)(

221 nrrnnnnnbba

r

nba

nba

naba

Coordinate Geometry :

The coordinates of the point which divides the line joining (x1 ,y1) and (x2 ,y2) in

the ratiom :n is

nm

myny

nm

mxnx 2121 ,

The distance from ),( 11 yx to 0 cbyax is

22

11

ba

cbyax

Maclaurin expansions

1,!

)1()1(!2

)1(1)1(2 xx

rrnnnxnnnxx rn where

...!

...!2

12

r

xxxe

rx

11...,1

...32

1ln

132

xr

xxxxx

rr


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CONFIDENTIAL* 3

Mathematical Formulae for Paper 2 Mathematics T :

Numerical Methods :

Newton-Raphson iteration for 0)( xf :

)('

)(1

n

n

nnxf

xfxx

Trapezium rule :

b

ann yyyyyhdxxf ])(2[

2

1)( 1210

n

abhrhafyr

andwhere )(

Correlation and regression :

Pearson correlation coefficient:

22

yyxx

yyxxr

ii

ii

Regression line ofy onx :

y =a +bx

where 2i ii xx yyxxb

xbya

Trigonometry

BAAABA sincoscossin)sin( BABABA sinsincoscos)cos(

BA

BABA

tantan1

tantan)tan(

AAAAA 2222 sin211cos2sincos2cos AAA 3sin4sin33sin AAA cos3cos43cos 3

2

BAcos

2

BAsin2BsinAsin

2

BAsin

2

BAcos2BsinAsin

2

BAcos

2

BAcos2BcosAcos

2

BAsin

2

BAsin2BcosAcos


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CONFIDENTIAL* 4

1. (a) Solve the equation

for 0 180 [3](b) Express in the form ,

wherea ,b andc are constants. [4]

2. (a) Express in the form , where R is a

positive constant and an acute angle. [2](b) Hence, find the maximum and minimum values for

and their corresponding angles.

Sketch of the graph in the interval 0 360 . [4]Hence, find the set of values of , with 0 360 , which

0 . [4]

3. The diagram given shows two intersecting circles ABC and CDEF, XY is a tangent to

the circle ABC at C, while BC is a tangent to CDEF at C.

Prove that , ABC is similar to DCF. [6]

4. The position vectors of three points A , B and C relative to the origin O

are , and respectively.

(a) Find the scalar product of . [2]

(b) Hence , find the ABC and the area of triangle ABC. [4]


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CONFIDENTIAL* 5

5. When a valve is released, water flowed into a large tank that is initially empty.

The volume, v litres , in the tank increase at the rate

where t is measured in hours from the time the valve is released.

(a) What is the initial rate of the water entering the tank ? [1]

(b) Find an expression for v in terms of t . [4]

(c) Determine the value of v when t is 40 minutes. [2]

(d) Find the time taken, to the nearest minute, for the volume of water in the

tank to be 4 litres. [4]

6. Two cyclist, A and B are initially 25 km apart with B on a bearing of N 67 E from A.A is moving at 18 km/h in a direction S 20 E and B is moving at 12 km/h due south.The velocities of A and B remain unchanged.

(a) Find the velocity of A relative to B. [5]

(b) Find the nearest distance between the two cyclists. [3]

(c) Find the time when the distance between the two cyclists is the nearest. [2]

7. The eventsA andB are such that P(A) =5

2, P(B) =

2

1and P(AB) =

5

4.

(a) Find (i) P(AB), (ii) P(AB), (iii) P(AB). [5 marks](b) State, with a reason, whether or notA andB are independent. [2 marks]

8. A study of the number of male and female children in families of inhabitants on an

isolated island reveals that the probability that a baby girl is born is 0.995. 500 babies

are chosen at random. Use a suitable approximation to find the probability that at most

495 of them are girls. [5marks]


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CONFIDENTIAL* 6

9 The Pre-University Students Council of a Premier School is in charge of selling

the schools tee shirt. Based on the sales record of the club, it was found that the

monthly demand for tee shirt size M has a Poisson distribution with mean 2 and the

monthly demand for tee shirt size L has a Poisson distribution with mean 3. The club

kept a monthly stock of 3 and 4 for tee shirt sizes M and L respectively.

(a) Show that the probability the club will not meet the demand for either M or L

size tee shirts in a month is 0.301. [4marks]

(b) Let L be the number of L size t-shirts sold in a month. Copy and complete theprobability distribution for L size t-shirts sold in a month.

No. Sold (l) P(L=l)

0

1 0.1494

2 0. 2240

3 0. 2240

4

Hence, find the most probable number of L size tee shirts sold in a month. [3marks]

(c) The club earns a profit of RM5 for every tee shirt sold regardless of the size of

the tee shirt. Assuming there is enough supply to meet all demand, use a suitable

approximation to calculate the probability that the club will earn a profit of more than

RM200 from the sales of the M and L size tee shirts in half a yea r. [5marks]

10. A random variableXhas probability density function given by

f(x) =3

1, 0 1,

3

8, 1 2,

45

0, otherwise.

x

xx

(a) Calculate the mean ofX. [5 marks]

(b) Specify fully the cumulative distribution function F(x). [6 marks]


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CONFIDENTIAL* 7

11. The ages of 300 houses in a historic village are recorded giving the following table

of results. 200 means 200 x < 300 .

Age x (years) Number of houses

0 - 36

20- 9240 - 74

60 - 39

100 - 14

200 - 27

300 - 500 18

Use linear interpolation to estimate the limits of the age between which the middle 80%

of houses lie. Give your final answer to the nearest integer. [5 marks]

12. The number of tents rented out on Pantai Sepat camping site each night in Augustlast year is summarised in the following stem and leaf diagram.

No of tents Totals

1 0 5 (2)

2 1 2 4 8 (4)

3 0 3 3 3 4 7 8 8 (8)

4 1 1 3 5 8 8 8 9 9 (9)

5 2 3 6 6 7 (5)6 2 3 4 (3)

Key 10 means 10(a) Find the three quartiles of these data. [3marks]

During the same month, the least number of tents rented out on Balok Beach camping

site was 31. The maximum number of tents on this site on any night that month was 72.

The three quartiles for this site were 38, 45 and 52 respectively.

(b) On graph paper and using the same scale, draw box plots to represent the data forboth camping sites. You may assume that there are no outliers. [4marks]

(c) Compare and contrast these two box plots. [3marks]

END OF QUESTION PAPER

trial stpm mathematics t2 pahang

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