MATEMATIK SOALAN KERTAS 1

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1449/1MatematikKertas 1Oktober20061 jamSEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAHKEMENTERIAN PELAJARAN MALAYSIAPEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2006MATEMATIKKertas 1

Satu jam lima belas minitJANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU1.Kertas soalan ini mengandungi 40 soalan.

2.Jawab semua soalan.3.Jawab dengan menghitamkan ruangan yang betul pada kertas jawapan.

4.Bagi setiap soalan hitamkan satu ruangan sahaja.

5.Sekiranya anda hendak menukarkan jawapan, padamkan tanda yang telah dibuat. Kemudian hitamkan jawapan yang baru.

6.Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.

7.Satu senarai rumus disediakan di halaman 2 hingga halaman 3.

8.Buku sifir matematik empat angka boleh digunakan.

9.Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

Kertas soalan ini mengandungi 16 halaman bercetak[Lihat sebelahSULIT

2

MATHEMATICAL FORMULAE

1449/1The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

RELATIONS1.am an = am + n2.am an = am - n3.(am)n = am n4.Distance =

( x2

x ) 2 y

y 25.Midpoint

x x

y y (x, y) = 1 2 , 1 2 226.Average speed =

distance traveled time taken

7.Mean =

sum of data number of data

8.Pythagoras Theoremc2 = a2 + b29.m

y2 y1x2 x11449/1 2006 Hak Cipta Sektor SBPSULITSULIT1Area of trapezium=

3

SHAPE AND SPACE1 sum of parallel sides height2

1449/1=2r4Curved surface area of cylinder= 2rh5Surface area of sphere= 4r26Volume of right prism= cross sectional area length

7Volume of cuboid= length width length

8Volume of cylinder= r2h9Volume of cone=

10Volume of sphere=

11Volume of right pyramid=

1 r2h34 r331 base height3

12Sum of interior angles of a polygon= (n 2) 18013 arc length

=angle subtended at centrecircumference of circle36014area of sector=

angle subtended at centre

area of circle360

15Scale factor, k=

PA'

PA16Area of image=k2 area of object.[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT

4

Answer all questions

1449/11Round off 0.0608 correct to two significant figures.A0.060

B0.061

C0.0610

D0.0600

2The side of a cube is 4.3 cm. The volume, in cm, of the cube correct to three significant figures is

A80.0

B79.5

C79.50

D79.500

3Express 0.0007023 108 as a number in standard form.

A0.7023 1011B7.023 1012C7.023 104D7023 10140.0368

605 50000

A4.89 102B4.89 103C4.89 104D4.89 1055In Diagram 1, AB is a tangent to the circle at point P and ASR is a straight line.RQySB8762PA Find the value of y. A25

B31

C48

D53

DIAGRAM 1

1449/1 2006 Hak Cipta Sektor SBPSULITSULIT5

1449/16The area of a rectangular nursery plot is 1.08 km. Its width is 1 200 m. The length of the nursery plot, in m, is

A9 101B9 102C9 102D9 1047In Diagram 2, O is the centre of the circle. AB and CB are tangents to the circle at A and C respectively.

AE80

Oy

DC

40BFind the value of y.

DIAGRAM 2

A110

B115

C120

D125

8In Diagram 3, PQRST is a pentagon. STU is a straight line.

TUS32yPFind the value of x + y.

x

RQDIAGRAM 3

A212

B362

C384

D392

[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT6

1449/19In Diagram 4, PQRSTU and PVWXQ are regular hexagon and pentagon respectively.

RXSQWTPmV UThe value of m is

DIAGRAM 4

A24

B32

C48

D50

10Diagram 5 shows the graphs of y = sin x and y = cos x.y1

O 1P

360

The x-coordinate of point P is

A270 B225 C215 D180

DIAGRAM 5

11It is given that cos = 0.454 where 180 270, find the value of .A117 B207 C243 D297

1449/1 2006 Hak Cipta Sektor SBPSULITSULIT7

1449/112In Diagram 6, KLMN is a straight line and JK = KM.

JK12 cm

x

L3 cmMNThe value of tan x is

DIAGRAM 6

A 14B 13

C3

D4

13Simplify p (2p1)3 2p 4.

A3pB3p2C4pD4p214Diagram 7 shows a triangle KLM and a shaded triangle, drawn on square grids.LKDIAGRAM 7

Triangle KLM is the image of the shaded triangle under an enlargement. Which of the points, A, B, C or D, is the centre of the enlargement?

[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT8

1449/115Express

2u 1 2 w

as a single fraction in its simplest form.uwwA1 uw uwBuw 1uwC2u uw 1uwD2u 1uw13

1632 18 2 2 2 =A36

B54

C108

D1623

2

17

1

(5 2 ) 4188pq (3p + q)2 =

A3p2 + q2 + 5pq B3p2 q2 + 3pq C9p2 q2 + 2pqD9p2 q2 + 10pq1449/1 2006 Hak Cipta Sektor SBPSULITSULIT9

1449/119Diagram 8 shows a right prism with rectangular base KLMN.PQ5 cmNM K6 cm8 cm

LDIAGRAM 8Calculate the angle between the line PL and the base KLMN.

A20 18 B24 16 C24 22 D26 34 20The angle of elevation of the peak of pole P from the peak of pole Q is 60. The two poles are vertically planted in a horizontal ground. Which diagram below represents the situation described?

QAC60

P30

PQQBDP60P

30Q[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT10

1449/121Diagram 9 shows a pole, PR on a horizontal plane.P160

RQDIAGRAM 9

Calculate the angle of depression of Q from vertex P.A70 B60 C30 D20

22Given that v

h , then h =tAvtBvt22Cv2tv 2tD223There are two helicopters X and Y at height 300 m and 340 m above sea level respectively. If the angle of elevation of helicopter Y from helicopter X is 41, calculate the horizontal distance, in m, between the two helicopters.

A26.2

B30.2

C34.2

D46.0

1449/1 2006 Hak Cipta Sektor SBPSULITSULIT11

1449/124Given that

y w1 w

, express w in terms of y.

Aw Bw

y1 y y1 yCw 1 y yDw 1 y y25In Diagram 10, Q is the image of P under a reflection.PKLNM HQDIAGRAM 10

The axis of reflection is the straight line that joins H and

AK BL CMDN26Express

m 1 2m

as a single fraction in its simplest form.n3nA3m 14nB3m 13n 2Cm 13nD5m 13n[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT12

1449/127The solution for 1 k k 3 is2

Ak 4Bk 83Ck 52Dk 53

28The solution for simultaneous linear inequalities 3n + 1 > 11 and 20 8 4n is

A3 < n 4

B4 < n 3

C3 < n < 4

D4 < n 3

29Diagram 11 is a pie chart showing the colours of t-shirts chosen by a number of students.

Red

190 Blue

Yellow

60

DIAGRAM 11

If 18 students chose yellow t-shirts, find the number of students who chose red t-shirts.

A108

B72

C36

D33

1449/1 2006 Hak Cipta Sektor SBPSULITSULIT13

1449/130Table 1 shows the frequency distribution of the scores obtained by a group of pupils in a competition.

Time (min)11 1516 2021 2526 3031 35

Frequency4101295

TABLE 1

Calculate the mean of the distribution.A21.375

B22.875

C23.125

D25.250

31Diagram 12 is a bar chart showing the number of candidates who obtained scores 1 to 5 in a Mathematics test.

Number of

Candidates20

1510

5

12345 Score

DIAGRAM 12If the passing score is the mean score, calculate the percentage of students who pass the test.

A90

B70

C60

D50

[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT14

1449/132It is given that the universal set = {x : 1 x 20, x is an integer}, set P = {2, 3, 6, 7, 9, 11, 13, 17}, set Q = {x : x is a prime number} and set R = {x : x multiple of 3}.

Find n[(P R) Q].A5

B6

C7

D9

33Diagram 13 is a Venn diagram showing the sets P, Q and R such that the universal set = P Q R.

P

Q RDIAGRAM 13

The shaded region represents the set

AP (Q R) BP (Q R) CP (Q R) DP (Q R)

34Diagram 14 is an incomplete Venn diagram showing the elements in sets P, Qand R.PQ.s.c.y.w.m.g.q.kDIAGRAM 14

It is given that the universal set, = P Q R, n(Q) = 6 and n(PR) = 3. Find n(P Q R).

A8

B10

C11

D12

1449/1 2006 Hak Cipta Sektor SBPSULITSULIT15

1449/135Find y-intercept of the straight line

2 x 5 y 3 .36

A 185B 45C185D4536The straight line PQ has gradient 2 and passes through the point (3, 5). It is parallel to the straight line y + mx 4 = 0.

Find the value of m.

A 3

B 2

C2

D3

37Diagram 15 shows two straight lines, OR and QR, on a Cartesian plane.yQR(1, 8)POxDIAGRAM 15

The distance and the x-intercept of PQ is 15 units and 9 respectively. Find the gradient of QR.

A1

B4

C7

D8[Lihat sebelah1449/1 2006 Hak Cipta Sektor SBPSULITSULIT16

1449/138Table 2 shows the distribution of a group of students playing a game.

Form OneForm Two

Girlsx12

Boys86

TABLE 2

A student is chosen at random from the group to start the game. The probabilitythat a girl from Form One will be chosen is

2 . Find the value of x.15

A2

B4