sabah add math p2 & ans 2

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SULIT

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MATHEMATICS

PAPER 2AUGUST 2008

2 HOURS

JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA TAHUN 2008

EXCEL 2

___________________________________________________________________________

TWO HOURS THIRTY MINUTES (DUA JAM TIGA PULUH MINIT)

___________________________________________________________________________

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. This question paper consists of three sections: Section A, Section B and Section C.

2. Answer allquestions in Section A, fourquestions from Section Band twoquestions

from Section C.

3. Give only one answer / solution for each question.

5. The diagrams in the questions provided are not drawn to scale unless stated.

6. The marks allocated for each question and sub-part of a question are shown inbrackets.

7. A list of formulae is provided on pages 2 to 4.

8. A booklet of four-figure mathematical tables is provided.

9. You may use a non-programmable scientific calculator.

___________________________________________________________________________This question paper consists of 13 printed pages.

(Kertas soalan ini terdiri daripada 13 halaman bercetak.)[Turn over (Lihat sebelah)

The following formulae may be helpful in answering the questions. The symbols given are theones commonly used.

NAMA : _____________________

KELAS : _____________________

NO K.P : _____________________

A. GILIRAN : _________________-

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3

1.x

xN

2.fx

x

f

3.

2 2

2( )x x x

xN N

4.

2 2

2( )f x x fx

xf f

5.

1

2

m

N F

m L cf

6. 1 100o

QI

Q

7.i i

i

W I

I

W

8.

!

!r

nnn rP

9.

!

! !r

nnn r rC

10. P A B P A P B P A B

11. , 1n r n r

rP X r C p q p q

12. Mean, = np

13. npq

14.x

Z

GEOMETRY

1. Distance

= 2 2

1 2 1 2x x y y

2. Midpoint

1 2 1 2, ,2 2

x x y yx y

3. A point dividing a segment of a

line

1 2 1 2, ,nx mx ny my

x ym n m n

4. Area of triangle =

1 2 2 3 3 1 2 1 3 2 1 3

1( ) ( )

2x y x y x y x y x y x y

5. 2 2r x y

6.2 2

xi yj

rx y

TRIGONOMETRY

1.

Arc length, s r 8. sin ( ) sin cos cos sinA B A B A B

9. cos( ) os os sin sinA B c Ac B A B

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4

2.

Area of sector, 21

2A r

3.

2 2sin cos 1A A

4.

2 2sec 1 tanA A

5. 2 2cosec 1 cotA A

6. sin 2 2 sin cosA A A

7.

2 2cos 2 cos sinA A A

2

2

2 os 1

1 2 sin

c A

A

10.tan tan

tan ( )1 tan tan

A BA B

A B

11.2

2tantan 2

1 tan

AA

A

12.sin sin sin

a b c

A B C

13. 2 2 2 2 cosa b c bc A

14. Area of triangle 1

sin2

ab C

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Section A

[40 marks]

1 Solve the simultaneous equations 24 3x y x x y . [5 marks]

2 Diagram 1 shows a straight line CDwhich meets a straight lineABat pointD. The

point C lies on they-axis.

Diagram 1

(a) State the equation ofABin the intercept form. [1 mark]

(b) Given that 2AD =DB, find the coordinates ofD. [3 marks]

(c) Given that CD is perpendicular toAB, find they-intercept of CD. [3 marks]

3 (a) Sketch the graph of 3sin 2 for 0 2y x x . [4 marks]

(b) Hence, using the same axes, sketch a suitable straight line to find the number

of solutions for the equation 3sin 2 =1 for 0 2x

x x

. State the number

of solutions. [3 marks]

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4 Given that the gradient of the tangent to the curve 3 22 6 9 1y x x x at pointP is

3, find

(a) the coordinates ofP, [2 marks]

(b) the equation of the tangent and normal to the curve atP. [4 marks]

5 Table 1 shows the distribution of the ages of 100 teachers in a secondary school.

Age

(years)

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Section B

[40 marks]

7 Use graph paper to answer this question.

Table 3 shows the values of two variables,xandy, obtained from an experiment.

Variablesxandyare related by the equation xy ab , where aand bare constants.

x 1 2 3 4 5 6

y 41.7 34.7 28.9 27.5 20.1 16.7

Table 3

(a) Plot 10log y againstxby using a scale of 2 cm to 1 unit on thex-axis and 2 cm

to 0.2 unit on the 10log y -axis.

Hence, draw the line of best fit. [4 marks]

(b) Use your graph from (a) to find

(i) the value ofywhich was wrongly recorded, and estimate a more

accurate value of it,

(ii) the value of aand of b,(iii) the value ofywhenx= 3.5. [6 marks]

8 Diagram 2 shows a trapeziumPQRS. Uis the midpoint ofPQand 2PU SV

.PVand

TUare two straight lines intersecting at Wwhere TW: WU= 1 : 3 andPW= WV.

Diagram 2

It is given that 12 , 18 and QR 18 5PQ a PS b b a

.

(a) Express in terms of and/ora b

,

S R

P Q

V

TW

U

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8

(i) SR

,

(ii) PV

,

(iii) PW

. [5 marks]

(b) UsingPT: TS= h: 1, where his a constant, express PW

in terms of h,

and/ora b

and find the value of h. [5 marks]

9 Diagram 3 shows a circle with centre Cand of radius rcm inscribed in a sector OAB

of a circle with centre Oand of radius 42 cm. [Use = 3.142]

Diagram 3

, find

(a) the value of r, [2 marks]

(b) the perimeter, in cm, of the shaded region, [4 marks]

(c) the area, in cm2, of the shaded region. [4 marks]

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10 Diagram 4 shows part of the curve 1y x .

Diagram 4

The curve intersects the straight liney= kat pointA, where kis a constant. The

gradient of the curve at the pointAis1

4.

(a) Find the value of k. [3 marks]

(b) Hence, calculate

(i) area of the shaded regionR: area of the shaded region S.

(ii) the volume generated, in terms of , when the regionRwhich is

bounded by the curve, thex-axis and they-axis, is revolved through

11 (a) A committee of three people is to be chosen from four married couples. Find

how many ways this committee can be chosen

(i) if the committee must consist of one woman and two men,

(ii) if all are equally eligible except that a husband and wife cannot both

serve on the committee. [5 marks](b) The mass of mango fruits from a farm is normally distributed with a mean of

820 g and standard deviation of 100 g.

(i) Find the probability that a mango fruit chosen randomly has a

minimum mass of 700 g.

(ii) Find the expected number of mango fruits from a basket containing

200 fruits that have a mass of less than 700 g. [5 marks]

Section C

y

Ox

1y x y= k

A

R S

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[20 marks]

12 A particle moves along a straight line and passes through a fixed point O. Its velocity,

v m s1, is given by 2 16v pt qt , where t is the time, in seconds, after passing

through O, pand qare constants. The particle stops momentarily at a point 64 m to

the left of Owhen t= 4.

[Assume motion to the right is positive.]

Find

(a) the initial velocity of the particle, [1 mark]

(b) the value ofpand of q, [4 marks]

(c) the acceleration of the particle when it stops momentarily, [2 marks]

(d) the total distance traveled in the third second. [3 marks]

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13 Table 4 shows