soalan set matematik tambahan

SULIT 3472/1

JABATAN PELAJARAN NEGERI JOHORGERAK GEMPUR SPM TAHUN 2010

Kertas soalan ini mengandungi 15 halaman bercetak

[ Lihat sebelah3472/1 SULIT

For examiner’s use only

Question Total Marks

Marks Obtained

1 32 33 44 35 36 37 28 49 210 411 412 313 314 315 316 417 318 319 420 321 222 423 424 225 4

TOTAL 80

MATEMATIK TAMBAHAN

Kertas 1 Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1 This question paper consists of 25 questions. 2. Answer all questions. 3. Give only one answer for each question. 4. Write your answers clearly in the spaces provided in

the question paper. 5. Show your working. It may help you to get marks. 6. If you wish to change your answer, cross out the work

that you have done. Then write down the new answer.

7. The diagrams in the questions provided are not

drawn to scale unless stated. 8. The marks allocated for each question and sub-part

of a question are shown in brackets. 9. A list of formulae is provided on pages 2 to 3. 10. A booklet of four-figure mathematical tables is provided. . 11 You may use a non-programmable scientific calculator. 12 This question paper must be handed in at the end of

the examination .

Name : ………………..……………

Form : ………………………..……

3472/1Matematik TambahanKertas 1Okt 20102 jam

SULIT 3472/1

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

ALGEBRA

1

2 am an = a m + n

3 am an = a m - n

4 (am) n = a nm

5 loga mn = log am + loga n

6 loga = log am - loga n

7 log a mn = n log a m

8 logab =

9 Tn = a + (n-1)d

10 Sn =

11 Tn = ar n-1

12 Sn = , (r 1)

13 , <1

CALCULUS

1 y = uv ,

2 , ,

3

4 Area under a curve

= dx or

= dy

5 Volume generated

= dx or

= dy


5 A point dividing a segment of a line

( x,y) =

6 Area of triangle =

1 Distance =

2 Midpoint

(x , y) = ,

3

4

GEOMETRY

SULIT 3 3472/1

STATISTICS


1 Arc length, s = r

2 Area of sector , L =

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2 A = 1 + cot2 A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A – sin2 A = 2 cos2A - 1 = 1 - 2 sin2A

8 tan 2A =

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosB sinA sinB

11 tan (A B) =

12

13 a2 = b2 + c2 - 2bc cosA

14 Area of triangle =

1 =

2 =

3 = =

4 = =

5 m =

6

7

8

9

10 P(A B) = P(A)+P(B)- P(A B)

11 P (X = r) = , p + q = 1

12 Mean µ = np

13

14 z =

SULIT 3 3472/1

Answer all questions.

1. Diagram 1 shows the function maps to . Rajah 1 menunjukkan fungsi yang memetakan kepada .

State Nyatakan

(a) the value of (b) the type of the relation. nilai bagi jenis hubungan. (i) , (ii) .

[3 marks] [3 markah]

Answer/Jawapan : (a) (i) …………(ii)……......……..

(b) ……………………....................

2. The function is defined as Find

Fungsi ditakrifkan oleh Carikan

(a) ,(b)

[3 marks][3 markah]

Answer/Jawapan : (a) ………………......……..

(b) ……………………............

3. It is given that the functions and the composite function ,

Diberi fungsi dan fungsi gubahan ,

find carikan(a) , (b) the value of .

nilai [4 marks] Answer/Jawapan : (a) ………………......……..

(b) ……………………............


4

3

3

1

3

2

For examiner’s

use only

Diagram 1Rajah 1

SULIT 3 3472/1

4. Given that and are the roots of the quadratic equation where and are constants. If , find the value of and of . Diberi dan adalah punca-punca bagi persamaan kuadratik dengan keadaan dan adalah pemalar. Jika , carikan nilai dan nilai .

[3 marks] [3 markah]

Answer/Jawapan : ………… ……......……..

5. Find the range of the values of for which . Cari julat nilai bagi .

[3 marks][3 markah]

Answer/Jawapan : ………………......……..

6. Diagram 6 shows the graph of a funcion . The straight line is a tangent to the curve . Rajah 6 menunjukkan graf bagi fungsi kuadratik . Garis lurus merupakan garis tangen kepada lengkung .

(a) Find Carikan

(i) the coordinate of the maximum point , koordinat titik maksimum,

(ii) the equation of the axis of symmetry. persamaan paksi simetri .

(b) Express in the form of , where , and are constants.


For examiner’s

use only

3

4

3

5

y

3

6

O

Diagram 6Rajah 6

SULIT 3 3472/1

Ungkapkan dalam bentuk , dimana , dan adalah pemalar. [3 marks][3 markah]

Answer/Jawapan : (a)…………….…………….

(b)………….………………..

(c )………….…………….…

7. Solve the equation . Selesaikan persamaan .

[3 marks]

[3 markah]

Answer/Jawapan : ………………………...

8. Given and , express in terms of and . Diberi dan , ungkapkan dalam sebutan dan .

[4 marks][4 markah]

Answer/Jawapan :: ……..……...……….....

9. Given the three first terms of arithmetic progression are and , find the value of . Diberi tiga sebutan pertama satu janjang aritmetik ialah dan , carikan nilai .

[2 marks][2 markah]

Answer/Jawapan : ……………...………................

10. The sum of the first terms in a arithmetic progression is given as .[ Lihat sebelah

3472/1 SULIT

For examiner’s

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4

8

2

9

2

7

For examiner’s

use only

SULIT 3 3472/1

Hasil tambah bagi sebutan pertama suatu janjang aritmetik diberikan oleh .

Find Carikan (a) the fourth term , (b) the common difference of the

progression. sebutan keempat , beza sepunya janjang ini.

[4 marks]

[4 markah]

Answer/Jawapan : ………......……...……….....

11. The first three terms of a geometric progression are Tiga sebutan pertama suatu janjang geometri ialah Find Carikan (a) the common ratio of the progression, nisbah sepunya janjang ini , (b) the sum to infinity of the progression. hasiltambah sebutan-sebutan janjang itu hingga ketakterhinggaan.

[ 4 marks ][4 markah]

Answer/Jawapan : (a) ……….…………………….(b)………………………………

12. The price of a house in a certain area is . Its price increases by 6 % each year. Harga sebuah rumah dalam suatu masa tertentu ialah . Harganya bertambah sebanyak 6 % setiap tahun. Find the price of the house after 8 years. Carikan harga rumah tersebut selepas 8 tahun.

[3 marks][3 markah]

.

Answer/Jawapan : ………..………..................


For examiner’s

use only

3

101

3

12

4

11

SULIT 3 3472/1

13. Diagram 13 shows a straight line graph of against .

Rajah 13 menunjukkan graf garis lurus melawan .

Given that , where and are contansts.

Diberikan , dimana dan adalah merupakan pemalar.

Find the value of and of . Carikan nilai dan nilai .

[3 marks][3 markah]

Answer/Jawapan : ………..………..................

14. Diagram 14 shows a straight line with the equation .

Rajah 14 menunjukkan garis lurus yang mempunyai persamaan .

Diagram 14 Rajah 14

A point lies on the -axis and the point lies on the -axis. Find the equation of the straight line which is perpendicular to and passes through the point .Titik terletak pada paksi- dan titik terletak pada paksi- . Carikan persamaan garis lurus yang berserenjang dengan garis lurus dan melalui titik .

[3 marks][3 markah]

Answer/Jawapan : ………..………..................15. Given point and point is a diameter of a circle and is

a points moves along the circumference, find the locus of . [ Lihat sebelah

3472/1 SULIT

For examiner’s

use only

3

13

34

14

)7,2(

)1,2(

y

0Diagram 13Rajah 13

MO

y

x

)7,2(

)1,2(

y

0Diagram 13

SULIT 3 3472/1

Diberi titik dan titik ialah diameter bagi sebuah bulatan dan titikadalah satu titik yang bergerak di sepanjang lilitan bulatan tersebut,carikan persamaan lokus bagi titk .

[3 marks ][3 markah]

Answer/Jawapan :.................................................

16. Given that , and , find in terms of unit vectors , and

Diberi , dan , carikan dalam sebutan unit vektor , dan

(a) (b) the unit vector in the direction of . vector unit dalam arah

[4 marks][4 markah]

Answer/Jawapan : (a)………..……….………

(b)………………..…........

17. It is given that and , where is a constant and the

three points , and are collinear. Find the value of .

Diberi dan , dimana adalah pemalar dan tiga titik

, dan adalah segaris. Carikan nilai .[ 3 marks ][3 markah]

Answer/Jawapan : ………..………..........18. Solve the equation for .


4

16

3

17

3

15

SULIT 3 3472/1

Selesaikan persamaan bagi .

[4 marks][4 markah]

Answer/Jawapan : ……............…..……….........

19. Diagram 19 shows a semicircle with centre O and radius 9 cm. Rajah 19 menunjukkan sebuah semibulatan berpusat O dan berjejari 9 cm.

Diagram 19

Given that the area of the sector is 40 cm . Diberi luas sektor ialah 40 cm . By using = 3.142 , findDengan menggunakan = 3.142, carikan

(a) the value of , in radian, nilai , dalam radian,(b) the perimeter , in cm , of sector perimeter , dalam cm , sektor

[4 marks]

[4 markah]

Answer/Jawapan : (a) …...…………..……..…... (b) ........................................

20. Given that , evaluate .


For examiner’s

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4

19

For examiner’s

use only

Rajah 19

SULIT 3 3472/1

Diberi , hitungkan .

[3 marks][3 markah]

Answer/Jawapan :…...…………..……..…...

21. Find the value of .

Carikan nilai bagi .

[2 marks][2 markah]

Answer/Jawapan :…...…………..……..…...

22. Given that , find the value of

Diberikan , carikan nilai bagi

(a) (b) if

jika

[4 marks][4 markah]

Answer/Jawapan: (a) ...…..……..……..…........ (b) ...……….……..….......

[ Lihat sebelah

3472/1 SULIT

3

20

2

21

4

22

SULIT 3 3472/1

23. Diagram 23 shows six cards of different letters.

Rajah 23 menunjukkan enam kad huruf yang berlainan.

S E N Y U M

Diagram 23

Rajah 23

(a) Find the number of posibble arrangments, in a row, of all cards.

Carikan bilangan cara susunan yang mungkin, dalam satu baris, semua kad itu.

(b) Find the number of these arrangments in which the letters of vowels are side by side.

Carikan bilangan cara susunan itu dengan keadaan huruf-huruf vokal bersebelahan.

[4 marks][4 markah]

Answer/Jawapan : (a) ...…..……..……..….....

(b) ...…………..……..…...

24. A box contains 12 red marbles and yellow marbels. If a marble is picked at random

from the box , the probabity of getting a yellow marble is .

Sebuah kotak mengandungi 12 guli merah dan guli kuning.. Jika sebiji guli diambil secara rawak dari

kotak itu, kebarangkalian mendapatkan guli kuning ialah .

Find the value of . Carikan nilai .

[2 marks][2 markah]


For examiner’s

use only

4

23

2

24

SULIT 3 3472/1

Answer/Jawapan : …...…………..……..…........

25. Diagram 25 shows a standard normal distribution graph.

Rajah 25 menunjukkan satu graf taburan normal piawai.

It is given

Diberi

(a) find the value of

carikan nilai bagi

(b) is a continous variable which is normally distributed with a mean of 80 and a

standard deviation of 5. Find the value of when the -score is .

ialah satu taburan normal selanjar dengan pembolehubah minnya 80 dan sisihan

piawainya 5. Carikan nilai bagi apabila skor- nya ialah .

Answer/Jawapan : (a) ......……...…..……..…...

(b) ...…………..……..…...


4

25

0

SULIT 3 3472/1

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