Math f4 p2 Final 08

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SEKOLAH MENENGAH KEBANGSAAN

KOTA SAMARAHAN

PEPERIKSAAN AKHIR TAHUN 2008

MATEMATIK

TINGKATAN 4

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian SoalanMarkah

Penuh

Markah

Diperoleh

A

1 4

2 4

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1.Kertas soalan ini mengandungi satu bahagian :Jawab semua soalan.

2.Jawapan hendaklah ditulis dengan jelas dalamruang yang disediakan dalam kertas soalan.

Tunjukkan langkah-langkah penting. Ini bolehmembantu anda untuk mendapatkan markah.

3.Rajah yang mengiringi soalan tidak dilukis

mengikut skala kecuali dinyatakan.

4.Satu senarai rumus disediakan di halaman

2.

5.Anda dibenarkan menggunakan kalkulator

saintifik yang tidak boleh diprogram.

3 4

4 5

5 4

6 6

7 6

8 3

9 12

10 12

Jumlah

Kertas soalan ini mengandungi 14 halaman bercetak

SULIT

1449/2

Matematik

Kertas 2

Oktober2008

2

12 jam

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[Lihat sebelah

SULIT

NAMA :

TINGKATAN :

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MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols given are the ones

commonly used.RELATIONS

1 am x an = a m+ n

2 am an = a m n

3 ( am )n = a mn

4 A-1 =bcad

1

ac

bd

5 P ( A ) =)(

)(

Sn

An

6 P ( A ) = 1 P(A)

7 Distance = 2 21 2 1 2( ) ( ) x x y y +

8 Midpoint, (x, y ) =

++

2,

2

2121 yyxx

9 Average speed =

10 Mean =

11 Mean =

12 Pythagoras Theorem

c2 = a2 + b2

13 m =12

12

xx

yy

14-intercept

-intercept

ym

x=

Answerall questions in this section.

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distance travelled

time takensum of data

number of data

sum of (class mark frequency)

sum of frequencies

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1 Solve the quadratic equation3

5 4 22

x

x

= . [4 marks]

Answer:

2 The Venn diagram shows set P, set Q and set R. Given that the universal set = P Q R,

shade the region which represents the set.

(a) Q R P

[4 marks]

P Q

R

(b) P Q R

P Q

R

3. Diagram 1 shows a right prism with a horizontal rectangular baseJKLM. TrapeziumJKQP

is the uniform cross-section of the prism. The rectangular surface QRLKis inclined.

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3

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Calculate the angle between the planeRSJand the vertical planeRSML.[4 marks]

Answer:

4. In Diagram 2, O is the origin.JK,KL andLMare straight lines.JKis parallel toLMandKL is

parallel to the x-axis.

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DIAGRAM 1

5 cmSR

Q

P

ML

KJ

8 cm

12 cm

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The equation ofLMis 2y =x + 4.

(a) State the equation of the straight lineKL.

(b) Find the equation of the straight lineJKand hence, state itsy-intercept.[5 marks]

Answer:

(a)

(b)


SULIT

5

DIAGRAM 2

2

L K

M

Ox

J(3, 2)

y

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5. Diagram 3 shows a solid that is a combination of a pyramid VPQRSand a semi cylinder

with diameter 7 cm. VS= 8 cm,PS= QR = 6 cm. Using7

22= , find the volume, in cm 3

of the solid.

[4 marks]

Answer:

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V

P

R

S

Q

DIAGRAM 3

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6. Diagram 4 shows two semicirlesAOBCEand OBCD, with the centre O andB respectively.

BFCis a sector with the centreB. AOBCis a straight line andAO = 2OB.

BC= 3.5 cm and FBC= AOE= 60. Using =7

22, calculate

(a) the perimeter, in cm, of the whole diagram,

(b) the area, in cm2

, of the shaded region. [6 marks]

Answer:

(a)

(b)


SULIT

7

A O B

F

C

D

E

DIAGRAM 4

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7. (a) Determine whether the following sentence is a statement.

9 is not a factor of 40

(b) Write two implications from the following statement.

R3 = 64 if and only ifR = 4

(c) Write down the conclusion in the following argument.

Premise 1 : If m = 7 , then 3m = 21Premise 2 : 3m 21

(d) 2 =(0)2 + 2

3 =(1)2 + 2

6 =(2)2 + 2

11=(3)2 + 2

[6 marks]

Answer:

a) ..

b) Implication 1 : ..

Implication 2 : .

(c) Conclusion :

(d) Conclusion :

8. Table 1 shows the results of a survey. The survey is on the mode of transport to SMK

Shahbandar on a particular day involving 200 students.

Boys Girls

Bus 60 30

Car 28 36

Bicycle 32 14

If a student is picked at random, find the probability that the student went to school by car.

[3 marks]

Answer:

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TABLE 1

Make a general conclusion by induction

based on the following number pattern.

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9. The data in Diagram 5 shows the number of telephone calls made by 40 students in a

month.

28 22 34 26 22 37 35 38

23 20 22 33 39 17 45 28

21 39 35 14 38 24 27 35

19 34 31 26 40 32 28 44

30 32 29 27 32 40 33 30

(a) Using data in Diagram 5 and a class interval of 5 telephone calls, complete Table 3

in the answer space.

[4 marks]

(b) For this part of the question, use the graph paper provided on page 11.

By using a scale of 2 cm to 5 telephone calls on the horizontal axis and 2 cm to

5 students on the vertical axis, draw an ogive based on Table 3.

[5 marks]

(c) Find the interquartile range from your ogive in (b), [3 marks]


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9

DIAGRAM 5

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Answer :

9.

(a)

TABLE 3

(b) Refer graph on page 12

(c)

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Number of telephone

calls

Upper

Boundary

Frequency CumulativeFrequency

6 10 10.5 0 0

11 15

16 20

10

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11

Graph for Question 9G

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10. You are not allowed to use graph paper to answer this question.

(a) Diagram 6(i) shows a solid right prism with rectangular base PQMN on a

horizontal table.The surfacePSTNis its uniform cross-section.The rectangle RSTU is an inclined plane. The edges UM, TN , SP and RQ arevertical edges.

Draw to full scale, the elevation of the solid on a vertical plane parallel to MNas

viewed from X.[4 marks]

Answers :

10 (a)

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P

S

N

T

M

Q

U R

3 cm

3 cm

5 cm

6 cm

X DIAGRAM 6(i)

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(b) Another solid right prism is joined to the solid in the Diagram 6 (i) at the vertical plane

MNWVUto form a combined solid as shown in Diagram 6 (ii).

The surfaceDEFGJis its uniform cross-section and GFNWis an inclined plane.

The rectangleDJKL is a horizontal plane.The baseEFNPQMis on a horizontal plane.

DEandJG are vertical.

JG =KW= 5 cm.

Draw to full scale,

(i) the elevation of the combined solid on a vertical plane parallel to FPas viewed

from Y,

[4 marks](ii) the plan of the combined solid. [4 marks]


SULIT

13

3 cm

P

S

N

T

M

Q

U R

3 cm

D

E

F

G

5 cm

6 cm

7 cm

3 cm

L

K

DIAGRAM 6 (ii)

Y

W

V

J

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Answer:

10.

(b) (i)

(ii)

END OF QUESTION PAPER

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Math f4 p2 Final 08

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