of 32 /32
1449/1 Matematik Kertas 1 Oktober 2006 1 ¼ jam SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2006 MATEMATIK Kertas 1 Satu jam lima belas minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. 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

# MATEMATIK SOALAN KERTAS 1

Embed Size (px)

### Text of MATEMATIK SOALAN KERTAS 1 1449/1MatematikKertas 1Oktober20061 ¼ jam

SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2006

MATEMATIK

Kertas 1

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. 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 sebelah 11

2

S U L IT 2

MATHEMATICAL FORMULAE

1449/1

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

RELATIONS

1. am an = am + n

2. am an = am - n

3. (am)n = am n

4. Distance = ( x2 x ) 2 y

y 2

5. Midpoint x x y y (x, y) = 1 2 , 1 2 2 2

6. Average speed =distance traveled

time taken

7. Mean =sum of data

number of data

8. Pythagoras Theoremc2 = a2 + b2

9. m y2 y1

x2 x1 1449/1 © 2006 Hak Cipta Sektor SBP S UL I T 2 Circumference of circle = d

3 Area of circle = r2

S U L IT

1 Area of trapezium =

3

SHAPE AND SPACE

1 sum of parallel sides

height2

1449/1

= 2r

4 Curved surface area of cylinder = 2rh

5 Surface area of sphere = 4r2

6 Volume of right prism = cross sectional area length

7 Volume of cuboid = length width length

8 Volume of cylinder = r2h

9 Volume of cone =

10 Volume of sphere =

11 Volume of right pyramid =

1 r2h

3

4 r3

3

1 base height

3

12 Sum of interior angles of a polygon = (n – 2) 180°

13 arc length

= angle subtended at centre

circumference of circle 360°

14area of sector

=angle subtended at centre

area of circle 360°

15 Scale factor, k = PA'PA

16 Area of image = k2 area of object.

[Lihat sebelah 1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S U L IT 4

1449/1

1 Round off 0.0608 correct to two significant figures.A 0.060B 0.061C 0.0610D 0.0600

2 The side of a cube is 4.3 cm. The volume, in cm³, of the cube correct to three significant figures is

A 80.0B 79.5C 79.50D 79.500

3 Express 0.0007023 108 as a number in standard form.

A 0.7023 1011

B 7.023 1012

C 7.023 104

D 7023 101

4 0.0368 605

50000A 4.89 10–2

B 4.89 10–3

C 4.89 10–4

D 4.89 10–5

5 In Diagram 1, AB is a tangent to the circle at point P and ASR is a straight line.

R Qy°

S B

87° 62°P

A Find the value of y. A 25B 31C 48D 53

DIAGRAM 1

1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 5 1449/1

6 The area of a rectangular nursery plot is 1.08 km². Its width is 1 200 m. The length of the nursery plot, in m, is

A 9 10–1

B 9 10–2

C 9 102

D 9 104

7 In Diagram 2, O is the centre of the circle. AB and CB are tangents to the circle at A and C respectively.

A

E 80°

Oy°

D C

40° B

Find the value of y.DIAGRAM 2

A 110B 115C 120D 125

8 In Diagram 3, PQRST is a pentagon. STU is a straight line.T US 32°

y° P

Find the value of x + y.

R Q

DIAGRAM 3

A 212B 362C 384D 392

[Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 6 1449/1

9 In Diagram 4, PQRSTU and PVWXQ are regular hexagon and pentagon respectively.

RX

SQ

W

T P

m° V U

The value of m isDIAGRAM 4

A 24B 32C 48D 50

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

y1

O

– 1 P

360°

The x-coordinate of point P isA 270° B 225° C 215° D 180°

DIAGRAM 5

11 It is given that cos = –0.454 where 180° ≤ ≤ 270°, find the value of .

A 117° B 207° C 243° D 297°

1449/1 © 2006 Hak Cipta Sektor SBP S UL I T M

D C

A

B

S UL IT 7 1449/1

12 In Diagram 6, KLMN is a straight line and JK = KM.J

K12 cm

L 3 cm M N

The value of tan x isDIAGRAM 6

A 14

B 13

C –3D –4

13 Simplify p (2p–1)3 ÷ 2p –4.

A 3pB 3p2

C 4pD 4p2

14 Diagram 7 shows a triangle KLM and a shaded triangle, drawn on square grids.

L

K

DIAGRAM 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 SBP S UL I T 4

A 2B 5C 37.5D 50

4

S UL IT 8 1449/1

15 Express2u 1

2 w as a single fraction in its simplest form.

uw w

A1 uw

uw

Buw 1

uw

C2u uw 1

uw

D2u 1

uw

1 3

16 32 18 2 2 2 =

A 36B 54C 108D 162

32

171

(5 2 ) 4

18 8pq – (3p + q)2 =

A 3p2 + q2 + 5pq B 3p2 – q2 + 3pq C –9p2 – q2 + 2pqD –9p2 – q2 + 10pq

1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 9 1449/1

19 Diagram 8 shows a right prism with rectangular base KLMN.P

Q

5 cm N

M K 6 cm 8 cm

L

DIAGRAM 8

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

A 20° 18 B 24° 16 C 24° 22 D 26° 34

20 The 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?

Q

A C60°

P

30°

P Q

QB D

P

60°P 30° Q

[Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 10 1449/1

21 Diagram 9 shows a pole, PR on a horizontal plane.

P

160°

R QDIAGRAM 9

Calculate the angle of depression of Q from vertex P.

A 70° B 60° C 30° D 20°

22 Given that v h , then h =

t

Avt

Bvt2

2

Cv2tv 2tD2

23 There 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.

A 26.2B 30.2C 34.2D 46.0

1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 11 1449/1

24 Given that y w

1 w, express w in terms of y.

A w

B w

y1 y

y1 y

C w 1

y y

D w 1 y

y

25 In Diagram 10, Q is the image of P under a reflection.

P K

L

N M

H

Q

DIAGRAM 10

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

A K B L C MD N

26 Expressm

1 2m

as a single fraction in its simplest form.n 3n

A3m 1

4n

B 3m 1

3n 2

Cm 1

3n

D5m 1

3n

[Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 12 1449/1

27 The solution for 1 k k 3 is2

A k ≥ 4

B k ≥ 83

C k ≥ 52

D k ≥ 53

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

A 3 < n ≤ 4B –4 < n ≤ 3C –3 < n < 4D –4 < n ≤ –3

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

Red

190°

Blue

Yellow60°

DIAGRAM 11

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

A 108B 72C 36D 33

1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 13 1449/1

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

Time (min) 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35

Frequency 4 10 12 9 5

TABLE 1

Calculate the mean of the distribution.

A 21.375B 22.875C 23.125D 25.250

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

Number ofCandidates

20

15

10

5

1 2 3 4 5 Score

DIAGRAM 12

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

A 90B 70C 60D 50

[Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP S UL I T R

S UL IT 14 1449/1

32 It 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].

A 5B 6C 7D 9

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

P Q

R

DIAGRAM 13

The shaded region represents the set

A P’ (Q R) B P (Q R)’ C P (Q R)’ D P’ (Q R)

34 Diagram 14 is an incomplete Venn diagram showing the elements in sets P, Qand R.

P Q.s

.c .y.w

.m.g .q

.k

DIAGRAM 14

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

A 8B 10C 11D 12

1449/1 © 2006 Hak Cipta Sektor SBP S UL I T S UL IT 15 1449/1

35 Find y-intercept of the straight line 2 x 5 y 3 .

3 6

A 185

B 45

C185

D45

36 The 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 – 3B – 2C 2D 3

37 Diagram 15 shows two straight lines, OR and QR, on a Cartesian plane.

y

Q

R(1, 8)

P O x

DIAGRAM 15

The distance and the x-intercept of PQ is 15 units and –9 respectively.

A –1B –4C –7D –8

[Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP S UL I T SULIT

S UL IT 16 1449/1

38 Table 2 shows the distribution of a group of students playing a game.

Form One Form Two

Girls x 12

Boys 8 6

TABLE 2

A student is chosen at random from the group to start the game. The probability

that a girl from Form One will be chosen is 2 . Find the value of x.

15A 2B 4C 6D 8

39 A box contains a number of yellow marbles and 10 red marbles. A marble is chosen at random from the box. The probability of choosing a yellow marble is3

. Then, a number of red marbles is put in the box. If a marble is now selected5

at random from the box, the probability that a red marble chosen is

many red marbles are there in the box?

1 . How

2

A 15B 20C 25D 30

40 A dice is rolled twice and the sum of the number shown is noted. Find the probability that the sum of the numbers being 7.

A 16

B 14

C 13

D 12

END OF QUESTION PAPER

1449/1 © 2006 Hak Cipta Sektor SBP ##### Soalan Matematik Kertas 2 Percubaan SPM Pulau Pinang 2011banksoalanspm.com/downloads/Trialpenang2011/soalan/Soalan...Title Soalan Matematik Kertas 2 Percubaan SPM Pulau Pinang 2011
Documents ##### Soalan Matematik Kertas 1 Percubaan SPM Pulau Pinang … · Title: Soalan Matematik Kertas 1 Percubaan SPM Pulau Pinang 2011 Subject: Soalan Matematik Kertas 1 Percubaan SPM Pulau
Documents ##### SOALAN RAMALAN UPSR 2019 MATEMATIK · MATEMATIK Kertas 1 Satu Jam JANGAN BUKA KERTAS SOALAN SEHINGGA DIBERITAHU 1. Kertas soalan ini mengandungi 40 soalan. 2. Jawab semua soalan
Documents ##### 3472/2 Matematik Tambahan Kertas 2 Ogos/September …...MATEMATIK TAMBAHAN Kertas 2 Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. Kertas soalan ini
Documents ##### ERATA KERTAS MATEMATIK (1449/2) PERCUBAAN · PDF fileERATA SKEMA PEMARKAHAN KERTAS 2 MATEMATIK NO. ... TINGKATAN 5 2011 MATEMATIK ... 2. Soalan dalam bahasa Inggeris mendahului soalan
Documents ##### Kertas Soalan Percubaan Negeri Kedah UPSR 2012 Matematik Kertas 1
Education ##### Dapatkan Skema di ...Soalan Percubaan SPM Matematik Tambahan Kertas 1 Perlis 2011 Author Soalan Percubaan SPM Matematik Tambahan Kertas 1 Perlis 2011 Subject Soalan Percubaan SPM Matematik
Documents ##### Soalan Matematik Kertas 2 Percubaan SPM Pulau … Soalan Matematik Kertas 2 Percubaan SPM Pulau Pinang 2011 Subject Soalan Matematik Kertas 2 Percubaan SPM Pulau Pinang 2011 Keywords
Documents Education