jawab semua soalan · web viewsoalan. 1 the relation which maps set to setis defined by the ordered...

NAMA : _____________________________ KELAS : _____________________________SULIT

JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA 2009 3472/1 EXCEL 1ADDITIONAL MATHEMAATICSKertas 1 Januari 2009

2 Jam Dua jam

ADDITIONAL MATHEMATICS

Paper 1Two hours

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tuliskan angka giliran dan nombor kad pengenalan anda pada ruang yang disediakan.

2. Calon dikehendaki membaca arahan di halaman 2 .

Question FullMarks

MarksObtained

1 22 23 34 35 36 37 38 39 210 411 312 313 414 315 316 417 318 319 420 321 422 423 324 425 4

3472/1 @ 2009 Hak Cipta Jabatan Pelajaran Sabah [Lihat sebelah SULIT

SULIT 2 3472/1Total 80

__________________________________________________________________________This paper consists of 19 printed pages.

INFORMATION FOR CANDIDATES

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 space 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 are shown in brackets.

9. A list of formulae is provided on pages 3 to 5.

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.

SULIT 3 3472/1

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

ALGEBRA

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

CALCULUS

1.

2.

3.

4. Area under a curve

= or

=

5. Volume generated

= or

SULIT 4 3472/1

=

STATISTICS

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. Mean, μ = np

13.

14.

GEOMETRY

1. Distance

=

2. Midpoint

3. A point dividing a segment of a line

4. Area of triangle =

5.

6.

SULIT 5 3472/1

TRIGONOMETRY

1. Arc length,

2. Area of sector,

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14. Area of triangle

SULIT 6 3472/1

Answer all questions.Jawab semua soalan.

1 The relation which maps set to set is defined by the ordered pairs . State

Hubungan yang memetakan set kepada set diwakilkan oleh pasangan bertertib . Nyatakan

(a) the images of 2,

imej bagi 2,

(b) the object of 4.

objek bagi 4.

[2 marks]

[2 markah]

Answer / Jawapan: (a) ……………………

(b) …….……………..

2 Given that [2 marks]

Diberi cari [2 markah]

ForExaminer’s

Use

1

2

2

2

SULIT 7 3472/1

Answer / Jawapan : ……………………

3 Given that

Diberi cari

(a) the value of k ,

nilai k ,

(b) the value of .

nilai .

[3 marks]

[3 markah]

Answer /Jawapan: (a) ……………………

(b) …….……………..

4 Given that Find the value of a and of b.

[3 marks]

Diberi Cari nilai a dan nilai b.

[3 markah]

3

3

4

3

ForExaminer’s

Use

SULIT 8 3472/1

Answer /Jawapan: a = ……………………

b = …….……………..

5 Find the values of p, given the quadratic equation has

two real and equal roots.[3 marks]

Cari nilai-nilai p, diberi persamaan kuadratik

mempunyai dua punca nyata dan sama. [3 markah]

Answer / Jawapan : ……………………

6 Solve the quadratic equation .

Give your answer correct to four significant figures. [3 marks]

Selesaikan persamaan kuadratik .

Beri jawapan anda betul kepada empat angka bererti. [3 markah]

5

3

ForExaminer’s

Use

6

3

SULIT 9 3472/1

Answer / Jawapan: ….………….……………7 Given that quadratic equation has no roots, find the range

of values of p. [3 marks]

Diberi persamaan kuadratik tidak mempunyai punca, cari julat nilai bagi p. [3 markah]

Answer / Jawapan: ….………….……………

8 Find the range of values of x for which . [3 marks]

Cari julat nilai x bagi . [3 markah]

7

3

8

3

ForExaminer’s

Use

SULIT 10 3472/1

Answer / Jawapan : ….………….……………9 Given . Determine whether has maximum or minimum value

and state its value. [2 marks]

Diberi . Tentukan samada mempunyai nilai maksimum atau minimum dan nyatakan nilainya. [2 markah]

Answer / Jawapan : ….………………………

10 Find the range of values of k if is always positive. [4 marks]

Cari julat nilai k jika fungsi sentiasa bernilai positif. [4 markah]


9

2

ForExaminer’s

Use

10

4

11

3

SULIT 11 3472/1

11 Solve the equation . [3

marks]

Selesaikan persamaan . [3

markah]


12 Solve the equation . [3 marks]

Selesaikan persamaan . [3 markah]

Answer / Jawapan: .…………….…….………

13 Given that and , express in terms of m and n.

[4 marks]

Diberi dan , ungkapkan dalam sebutan m dan n.

[4 markah]

Answer / Jawapan: …………………………...

ForExaminer’s

Use

12

3

14

3

13

4

SULIT 12 3472/114 Point Q(2, 7) divides the line joining P(2, 1) and R(4, 10) internally in the ratio

m : n. Find the ratio m : n. [3 marks]

Titik Q(2, 7) membahagi dalam garis yang menyambung P(2, 1) dan R(4, 10)

dengan nisbah m : n. Cari nisbah m : n. [3 markah]

Answer / Jawapan: …………………………...15 The vertices of a triangle are P(2, 5), Q(k, 1) and R(3, 4). Given that the area

of the triangle is 6 unit2, find the values of k. [3 marks]

Bucu bagi sebuah segitiga ialah P(2,5), Q(k, 1) dan R(3, 4). Diberi bahawa luas segitiga itu ialah 6 unit2, cari nilai-nilai k. [3 markah]

Answer / Jawapan : ………………………..

16 Given points P, Q(0, 3), R(4, 1) and S(6, 3), where P is the midpoint of RS. Find the

equation of a straight line which passes through P and is parallel to the straight line

QR.

[4 marks]

ForExaminer’s

Use

15

3

16

4

SULIT 13 3472/1Diberi titi-titik P, Q(0, 3), R(4, 1) dan S(6, 3), di mana P ialah titik tengah bagi RS.

Cari persamaan garis lurus yang melalui titik P dan selari dengan garis lurus QR.

[4 markah]

Answer / Jawapan : ………………………..

17 A set of data consists of five numbers. The sum of the number is 95 and the sum of the

squares of the numbers is 1845.

Satu set data mengandungi lima nombor. Hasil tambah bagi nombor-nombor itu ialah 95

dan hasil tambah bagi kuasa dua nombor-nombor itu ialah 1845.

Find,

Cari,

(a) the mean,

min,

(b) the standard deviation.

sisihan piawai.

[3 marks]

[3 markah]


ForExaminer’s

Use

17

3

18

3

SULIT 14 3472/1(b) …….……………..

18 A set of five numbers has a mean of 15. When a number, m is added to the data,

the new mean is 18. Find the value of m. [3 marks]

Satu set yang mengandungi lima nombor mempunyai min 15. Apabila satu nombor, m

ditambah ke data itu, min baru ialah 18. Cari nilai m. [3 markah]

Answer / Jawapan : m =…………………..19 Given that the mean of a set of data 4, 5, 7, 3, 7 and m is 5.

Diberi min untuk set data 4, 5, 7, 3, 7 dan m ialah 5.

Find,

Cari,

(a) the value of m,

nilai m,

(b) the variance of the set of data.

varians bagi set data itu.

[4 marks]

[4 markah]

ForExaminer’s

Use

19

4

SULIT 15 3472/1


(b) …….……………..

20 Diagram 1 shows two sectors with center O. Given that OAB and ODC are two straight lines. OD = 5 cm , DC = 2 cm and , find the area, in , of the shaded region. [3 marks]

Rajah 1 menunjukkan dua sektor berpusat O. Diberi OAB dan ODC ialah dua garis lurus. OD = 5 cm, DC = 2 cm dan , cari luas, dalam

, kawasan berlorek . [3 markah]

Diagram 1

Rajah 1

ForExaminer’s

Use

20

3

O

A Given that OAB and ODC are two straight lines. OD = 5cm , DC = 2 cm and

, find the area of the shaded region.

[3 marks]

B

DA C

A2cm

5 cm

0.6 rad

SULIT 16 3472/1

Answer / Jawapan: …..………………

21 Diagram 2 shows a right-angled triangle OAT and a sector AOB.

Rajah 2 menunjukkan segitiga bersudut tegak OAT dan sektor AOB.

Diagram 2

Rajah 2

[Use / Guna ]

Calculate the area, in cm2, of the shaded region.

Hitungkan luas, dalam cm2, kawasan berlorek.

[4 marks]

[4 markah]

ForExaminer’s

Use

21

4

10 cm

1.2 rad

A

O B T

SULIT 17 3472/1

Answer / Jawapan: …..………………22 Diagram 3 shows a sector BOC with centre O.

Rajah 3 menunjukkan sektor BOC berpusat O.

C

B

O 0.45 rad

Given the perimeter of the sector BOC is 24.5 cm, calculate

Diberi perimeter sektor BOC ialah 24.5 cm, hitungkan

(a) the radius, in cm, of the sector,

jejari, dalam cm, sektor,

(b) the area, in cm2, of the sector.

Diagram 3

Rajah 3

ForExaminer’s

Use

22

44

SULIT 18 3472/1 luas, dalam cm2, sektor itu.

[4 marks]

[4 markah]


(b) …….……………..

23 Two variables, A and r, are related by the equation .

Given that r increases at a constant rate of 0.1 unit per second, find the rate of change of A when r = 2. [3 marks]

Dua pembolehubah, A dan r, dihubungkan oleh persamaan .

Diberi bahawa r bertambah dengan kadar malar 0.1 unit sesaat, cari kadar perubahan A apabila r = 2. [3 markah]

Answer / Jawapan: …..………………

24 Given that , evaluate . [4 marks]

ForExaminer’s

Use

24

4

23

3

SULIT 19 3472/1

Diberi , nilaikan . [4 markah]

Answer / Jawapan: …..………………25 Given that ,

Diberi ,

(a) find the value of when x = 1.

cari nilai apabila x = 1. [4 marks]

(b) express the approximate change in y, in terms of p, when x changes from1 to 1 + p, where p is a small value.

ungkapkan perubahan kecil bagi y, dalam sebutan p, apabila x berubah daripada 1 kepada 1 + p, dengan keadaan p ialah nilai yang kecil. [4 markah]

22

3

ForExaminer’s

Use

25

4

SULIT 20 3472/1


(b) …….……………..

END OF QUESTION PAPERKERTAS SOALAN TAMAT

Number Solution and Marking Scheme Sub Marks

Full Marks

1 (a)

(b)

8 , 12

1

1

12

2 2

2

B12

3 (a)

(b)

2 1

2

B1

3

4 3

B2

B1

3

5 3

B2

B13

Both

SULIT 21 3472/1


Full Marks

6 3

B2

B1

3

7

3

B2

B1

3

83

B2 B1

3

9Minimum Value = 5

Minimum Value or 5

2B1 2

10 4

B3

B2

B1

4

11 3

B2

B13

12 3

B2

B1 3

13 4

B3

B2

B1

4

8 4

x

-4 4

SULIT 22 3472/1


Full Marks

14 2 : 1

4n = 2m or 6n = 3m

3

B2

B1

3

15 k = 6, 18 bot h

6 – k = 12 or 6 – k = 12 both

3

B2

B1

3

16y = or 2y = x – 3 or 2y – x + 3 = 0

Point P = (5, 1) and gradient QR =

Point P = (5, 1) or gradient QR =

4

B3

B2

B1

4

17. (a)

(b)

19

2.828

1

2

B1

3

18 m = 33 3

B2

B1

3

SULIT 23 3472/1


Full Marks

19 (a)

(b)

m = 4

2.333 or

2

B1

2

B1

4

20 7.2 3

B2

B1

3

21 68.60 cm2

128.60 – 60

10 25.72 or (102)(1.2)

AT= 10 tan(1.2 rad)

4

B3

B2

B1

4

22 (a)

(b)

10

2r + 0.45r = 24.5

22.5

(102)(0.45)

2

B1

2

B1

4

23 3

B2

B13

24 4

B3

SULIT 24 3472/1


Full Marks

B2

B1

4

25 (a)

(b)

2

B1

2

B1

4

CO-ORDINATOR

UNIT MATEMATIK MENENGAH

SEKTOR PENGURUSAN AKADEMIK

LIST OF PANEL MEMBERS

BIL NAMA GURU SEKOLAH

1 SHIRNEY CHUA (Ketua) SMK KOLOMBONG, INANAM

2 SUDIRMAN DARISE SMK BONGAWAN, MEMBAKUT

3 AILEEN BEH CHIK HEANG SMK DATUK PETER MOJUNTIN, PENAMPANG

4 PHOON CHIEW FUN SMK CHUNG HWA, TENOM

5 TING KAI CHU MAKTAB SABAH KOTA KINABALU

6 SURIANIH SEWAN SMK SRI NANGKA, TUARAN

7 SEAK SAIN YON SMK KONVEN ST. URSULA, TAWAU

SULIT 25 3472/1

8 FARAH IBRAHIM SMK AGAMA, KK

9 ONG KHYE CHING SM KEN HWA, KENINGAU

jawab semua soalan · web viewsoalan. 1 the relation which maps set to setis defined by the ordered...

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