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PAGE 16SULIT 1449/1

NAMA :.........................................................

SULIT

KELAS : .......................................................

JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA

1449/1

EXCEL 1 TINGKATAN 4 (SPM 2010)

MATHEMATICS

Paper 1

Oktober 2009

1 hour 15 minutes One hour fifteen minutes

MATHEMATICS (MATEMATIK)

PAPER 1 (KERTAS 1)ONE HOUR FIFTEEN MINUTES (SATU JAM LIMA BELAS MINIT) ________________________________________________________________________

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Calon dikehendaki membaca maklumat di halaman 2

________________________________________________________________________

This question paper consists of 16 printed pages.

(Kertas soalan ini terdiri daripada 16 halaman bercetak.)INFORMATION FOR CANDIDATES

1. This question paper consists of 40 questions.2. Answer all questions.3. Answer each question by blackening the correct space on the answer sheet.4. Blacken only one space for each question.5. If you wish to change your answer, erase the blackened mark that you have done. Then blacken the space for the new answer.6. The diagram in the questions provided are not drawn to scale unless stated.7. A list of formulae is provided on page 3.8. A booklet of four-figure mathematical tables is provided.9. You may use a non-programmable scientific calculator.

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

1.

2.

3.

4.

5.

6.

7. Distance =

8.Midpoint,

9. Average Speed =

10. Mean =

11. Mean = 12. Pythagoras Theorem

c2 = a2 + b213.

14. m =

1.Area of trapezium

=

2.Circumference of circle = d = 2r3. Area of circle = r24. Curved surface area of cylinder = 2rh

5. Surface area of sphere = 4r26. Volume of right prism =

Cross sectional area length7. Volume of cylinder = r2h

8. Volume of cone = r2h

9. Volume of sphere = r310.Volume of right pyramid

= base area height11. Sum of interior angles of a polygon

= (n - 2) 180o12.

13.

14. Scale factor , k =

15. Area of image = k2 area of object.

1Round off 0.00497 correct to two significant figures.

Bundarkan 0.00497 betul kepada dua angka bererti.

A0.0040C0.0050

B0.0049D0.00050

2Express 1.28 105 as a single number.

Ungkapkan 1.28 105 sebagai satu nombor tunggal.

A0.000128C128 000

B0.0000128D12 800 000

34.31 10 5 2.5 106 =

A1.81 106 C4.06 106

B1.81 105 D4.06 105

4A factory consumed 3.6 105 m3 of water in a certain year. Calculate its average monthly consumption of water, in m3, for that year.

Sebuah kilang menggunakan 3.6 105 m3 dalam suatu tahun tertentu. Hitungkan penggunaan purata air sebulan, dalam m3, untuk tahun itu.

A3 104C0.3 104

B3 105D4.32 106

5In Diagram 1, PQRSWX is a regular hexagon. SV is parallel to TU. Dalam Rajah 1, PQRSWX merupakan heksagon sekata. SV adalah selari dengan TU.

Find the value of x + y.

Cari nilai x + y.

A184C204

B192D212

6In Diagram 2, O is the centre of a circle and PQR is a tangent to the circle at Q.Dalam Rajah 2, O adalah pusat bulatan dan PQR adalah tangen kepada bulatan pada titik Q.

Find the value of x.Cari nilai x.

A45C115

B90D220

7In Diagram 3, ABC is the tangent to the circle BDEF at the point B.

Dalam Rajah 3, ABC merupakan tangen kepada bulatan BDEF pada titik B.

The value of x is

Nilai x ialah

A48C56

B54D59

8In Diagram 4, Q is the image of P under an clockwise rotation of 90o. Which of the points A, B, C or D, is the centre of the rotation?

Dalam Rajah 4, Q ialah imej bagi P di bawah suatu putaran 90o ikut arah jam. Antara titik A, B, C dan D, yang manakah pusat putaran itu?

9In Diagram 5, the triangle UVW is the image of the triangle RST under an enlargement.

Dalam Rajah 5, segitiga UVW ialah imej bagi segitiga RST di bawah satu pembesaran tertentu.

The centre of the enlargement and its scale factor are

Pusat pembesaran dan faktor skala bagi pembesaran itu ialah

Centre of Enlargement

Pusat PembesaranScale Factor

Faktor Skala

AP

BP2

CS

DS4

10Which of the following represents the graph of y = cos x for ?Di antara berikut, yang manakah mewakili graf y = kos x untuk ?

A

C

B

D

11Given that cos xo = where , find the value of tan xo.

Diberi bahawa kos xo = dengan keadaan , cari nilai tan xo.

A

C

B

D

12In Diagram 6, PQS is a right angled triangle.

Dalam Rajah 6, PQS ialah sebuah segitiga bersudut tegak.

It is given that PS = 25 cm, PQ =15 cm, and RS = 12cm. Find the value of cos xo.

Diberi bahawa PS = 25 cm,PQ = 15 cm, dan RS = 12 cm. Carikan nilai kos xo.

A

C

B

D

13Diagram 7 shows a right-angled triangular prism with the horizontal base ABCD. Points L, M and N are the midpoint of the side AD, EF and BC respectively. Rajah 7 menunjukkan sebuah prisma segitiga tegak dengan tapak mengufuk ABCD. Titik L, M dan N adalah titik tengah bagi sisi AD, EF and BC masing-masing.What is the angle between the plane BMC and the base ABCD?

Apakah sudut di antara satah BMC dengan tapak ABCD?

A

C

B

D

14Diagram 8 shows a cuboid with the horizontal base PQRS.

Rajah 8 menunjukkan sebuah kuboid dengan tapak mengufuk PQRS.

Name the angle between the line UV and the plane QUR?

Namakan sudut di antara garis UV dengan satah QUR?

A

C

B

D

15Diagram 9 shows a right pyramid with quadrilateral base EFGH. M and N are the midpoint of the side EH and FG respectively. What is the angle between the plane VFG and the base EFGH?Rajah 9 menunjukkan sebuah pyramid tegak dengan tapak segiempat tepat EFGH. M dan N adalah titik tengah bagi sisi EH dan FG. Apakah sudut antara satah VFG dengan tapak EFGH?

A

C

B

D

16Diagram 10 shows two blocks of flats PQ and ST, on a horizontal ground. It is given that Q and S have the same height.

Rajah 10 menunjukkan dua blok pangsa PQ dan ST yang terletak pada tanah rata. Tinggi Q dan S adalah sama.

State the angle of depression of R from S.

Nyatakan sudut tunduk R dari S.

A( PSQC( RSQ

B( SPQD( PSQ

17Diagram 11 shows a pole on a horizontal plane.Rajah 11 menunjukkan sebatang tiang tegak pada satu permukaan mengufuk.

Given that the angle of elevation of the top of the pole, P from Q is . Calculate the height, in m, from P to R.

Diberi bahawa sudut dongakan puncak P dari Q ialah . Hitung panjang dalam unit m dari P ke R.

A6.25C8.22

B7.14D10.12

18In Diagram 12, PR is a vertical pole standing on a horizontal plane. The angle of elevation of Q and P from S is 35o and 45o respectively.Dalam Rajah 12, PR ialah sebatang tiang tegak yang terletak pada satu permukaan mengufuk. Sudut dongakan Q dan P dari S ialah masing-masing 35o and 45o.

Calculate the length, in m , of PQ.

Hitung panjang bagi PQ dalam unit m.

A3C7

B5D10

19In Diagram 13, PQ and RS are two vertical poles on a horizontal plane. The height of PQ is 16 m and the height of RS is 10 m. The angle of depression of R from vertex P is .

Dalam Rajah 13, PQ dan RS ialah dua batang tiang tegak pada satah mengufuk. Tinggi PQ ialah 16 m dan tinggi RS ialah 10 m. Sudut tunduk R dari puncak P ialah .

Calculate the distance between Q and S.Hitung jarak di antara Q dengan S.

A4.00 mC5.68 m

B4.86 mD7.41 m

20Express as a single fraction in its simplest form.Nyatakan sebagai satu pecahan tunggal dalam sebutan terendah.

A

C

B

D

21 =

A 2xy + 1C 42xy + 48

B 2xy 7D 42xy 48

22Given that , express in terms of .Diberi bahawa , nyatakan n dalam sebutan m.

A

C

B

D

23Given that , express in terms of .

Diberi bahawa , nyatakan dalam sebutan .

A

C

B

D

24Simplify (m3)2 m4.

Ringkaskan (m3)2 m4.

AmCm9

Bm2Dm10

25Given that 3125 = 5n, find the value of n.

Diberi 3125 = 5n, cari nilai n

A4C5

B6D7

26Find the solution of the simultaneous inequalities and .

Selesaikan ketaksamaan serentak and .

A

C

B

D

27List all the integers x that satisfy the inequality 3x 8 < x 5 + 4xSenaraikan semua integer x yang memenuhi ketaksamaan 3x 8 < x 5 + 4x

A0 , 1 , 2 , 3C1 , 0 , 1 , 2 , 3

B1 , 0 , 1 , 2 , 3 , 4D2 , 1 , 0 , 1 , 2 , 3 , 4

28Table 1 shows the Mathematics marks for a group of students.

Jadual 1 menunjukkan markah Matematik untuk sekumpulan pelajar.

Marks

Markah

45

63

76

81

Frequency

Kekerapan

6

12

8

5

Calculate the mean mark.Hitungkan markah min.

A50C65.77

B60D75.21

29Diagram 14 below is a pictograph showing the number of articles read by a student in January and March. The number of articles read in February and April are not shown. Rajah 14 di bawah menunjukkan bilangan artikel yang dibaca oleh seorang pelajar dalam bulan Januari dan Mac. Bilangan artikel yang dibaca dalam bulan Februari dan April tidak ditunjukkan.January

Januari

February

Februari

March

Mac

April

April

Represent 5 articles

Mewakili 5 artikel

A total of 100 articles are read in those four months. The number of articles read in April was three times the number of articles read in February. The number of articles read in April was

Sejumlah 100 artikel telah dibaca dalam empat bulan tersebut. Bilangan artikel yang dibaca dalam bulan April adalah tiga kali ganda bilangan yang dibaca dalam bulan Februari. Bilangan artikel yang dibaca dalam bulan April ialah

A9C45

B15D60

30Diagram 15 is a Venn diagram showing the universal set , set R and set S.

Rajah 15 ialah gambar rajah Venn yang menunjukkan set semesta , set R and Set S.

The region R ( S is equivalent to the region

Rantau R ( S setara dengan rantau

AR ( SCR S

BR SD( R S)

31Diagram 16 is a Venn diagram showing the elements of universal set , set A and Set B.Rajah 16 ialah gambar rajah Venn yang menunjukkan unsure-unsur set semesta , set A and Set B.

List all elements of set ( A B )

Senaraikan unsure-unsur bagi set (A B).

A{p, q, u, v, w }C{r, s, t}

B{p, q, v, w}D{p, q, u}

32It is given that set W = { x : x is factor of 6, 0 < x < 10}. Find the number of subset of set W.

Diberi bahawa set W = { x : x ialah faktor bagi 6, 0 < x < 10}. Cari bilangan subset bagi set W.

A4C12

B8D16

33Table 2 shows data obtained from a survey of 100 students. Diagram 17 is a Venn diagram that represents part of the information in Table 2.Jadual 2 menunjukkan data yang diperolehi daripada satu kaji selidik ke atas 100 orang pelajar. Rajah 17 adalah gambarajah Venn yang mewakili sebahagian maklumat di dalam Jadual 2. Hobbies

Hobi

Number of students

Bilangan pelajar

Reading

Membaca

55

Playing sports

Bersukan

61

Reading and playing sport only

Membaca dan Bersukan sahaja

12

Reading and Listening music only

Membaca dan Mendengar muzik sahaja

5

Reading only

Membaca sahaja

25

Playing sports only

Bersukan sahaja

28

Find the number of students who does not like reading.

Cari bilangan pelajar yang tidak suka membaca.

A17C62

B45D89

34The equation of a straight line is given as 3x + 4y = 9. The gradient of the straight line is

Persamaan bagi suatu gais lurus adalah 3x + 4y = 9. Kecerunan bagi garis lurus itu ialah

A

C

B

D3

35Diagram 18 shows that the straight line PQ is parallel to straight line RS. The gradient of straight line PQ is 2 and the y-intercept of straight line RS is 16.

Rajah 18 menunjukkan garis lurus PQ selari dengan garis lurus RS. Diberi kecerunan garis lurus PQ ialah 2 dan pintasan-y garis lurus RS ialah 16.

Find the x-intercept of RS.

Cari pintasan-x RS.

A32C2

B8D8

36If the gradient of a straight line is (4 and its y-intercept is 2, state the equation of that straight line.Jika kecerunan suatu garis lurus ialah (4 dan pintasan-y ialah 2, nyatakan persamaan bagi garis lurus tersebut.

Ay = (4x + 2Cy = 2x ( 4

By = (4x + 8Dy = 8x ( 4

37Diagram 19 shows 9 cards in a box.

Rajah 19 menunjukkan 9 keping kad dalam sebuah kotak.

A card is chosen at random. State the probability that the card chosen is labelled `L.

Sekeping kad dipilih secara rawak. Nyatakan kebarangkalian bahawa kad yang dipilih itu berlabel `L.

A

C

B

D

38Diagram 20 shows some number cards. A card is picked at random, state the probability that a prime number is picked.

Rajah 20 menunjukkan beberapa kad nombor. Sekeping kad diambil secara rawak. Nyatakan kebarangkalian bahawa kad nombor perdana terpilih.

A

C

B

D

39A container holds 24 blue marbles and a number of yellow marbles. A marble is picked at random from the container. The probability of picking a blue marble is . How many marbles are there in the container?

Sebuah bekas mengandungi 24 biji guli biru dan beberapa biji guli kuning.

Sebiji guli diambil secara rawak daripada bekas itu. Kebarangkalian mendapat guli biru ialah . Berapakah jumlah bilangan guli dalam bekas itu?

A24C48

B36D60

40 =

A2k2 6k + 15C2k2 12k + 6

B2k2 6k + 6

D2k2 14k + 18

X

P

W

V

U

T

S

R

Q

70o

34o

102o

yo

xo

Diagram 1

Rajah 1

P

Q

R

xo

45o

O

110o

S

Diagram 2

Rajah 2

F

E

D

B

A

C

xo

65o

56o

Diagram 3

Rajah 3

Diagram 4

Rajah 4

Diagram 5

Rajah 5

Diagram 6

Rajah 6

P

Q

R

x

S

Diagram 7

Rajah 7

E

A

B

C

D

F

M

N

L

Diagram 8

Rajah 8

P

Q

S

T

V

U

R

W

E

F

G

V

H

N

M

Diagram 9

Rajah 9

P

Q

R

S

T

Diagram 10

Rajah 10

W

Diagram 11

Rajah 11

P

R

Q

*

5 m

Diagram 12

Rajah 12

P

Q

S

10 m

R

Diagram 13

Rajah 13

P

Q

S

R

Table 1

Jadual 1

Diagram 14

Rajah 14

R

S

EMBED Equation.3

Diagram 15

Rajah 15

Diagram 16

Rajah 16

( p

( q

( r

( s

( t

( u

( v

( w

A

B

EMBED Equation.3

Table 2

Jadual 2

Set R = Reading

Membaca

Set S = Playing sports

Bersukan

Set M = Listening Music

Mendengar muzik

R

M

S

12

5

28

Diagram 17

Rajah 17

R

P

Q

S

x

0

16

2

y

Diagram 18

Rajah 18

E

X

C

E

L

L

E

N

T

Diagram 19

Rajah 19

13

15

17

19

21

23

25

Diagram 20

Rajah 20

1499/1

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