f4 final sbp2006 math p1

ppr maths nbk

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

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

MATEMATIK

Kertas 1

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

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SULIT 1449/1

1449/1 © 2006 Hak Cipta Sektor SBP SULIT

2

MATHEMATICAL FORMULAE

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 = ( )212

212 )( yyxx −+−

5. Midpoint

(x, y) = ⎟⎠⎞

⎜⎝⎛ ++

2,

22121 yyxx

6. Average speed = 7. Mean = 8. Pythagoras Theorem

c2 = a2 + b2

9. 12

12

xxyy

m−−

=

distance traveled time taken

sum of data number of data

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SHAPE AND SPACE

1 Area of trapezium = 21 × sum of parallel sides × height

2 Circumference of circle = πd = 2πr 3 Area of circle = πr2 4 Curved surface area of cylinder = 2πrh 5 Surface area of sphere = 4πr2 6 Volume of right prism = cross sectional area × length 7 Volume of cuboid = length × width × length 8 Volume of cylinder = πr2h

9 Volume of cone = 31πr2h

10 Volume of sphere = 34 πr3

11 Volume of right pyramid = 31 × base × height

12 Sum of interior angles of a polygon = (n – 2) × 180° 13 14

15 Scale factor, k = PAPA'

16 Area of image = k2 × area of object.

arc length angle subtended at centre

circumference of circle 360° =

area of sector angle subtended at centre

area of circle 360° =

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Answer all questions 1 Round off 0.0608 correct to two significant figures.

A 0.060 B 0.061 C 0.0610 D 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 80.0 B 79.5 C 79.50 D 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 =+50000

6050368.0

A 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.

DIAGRAM 1

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

A

P

B

Q R

S

87° 62°

y°

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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.

DIAGRAM 2 Find the value of y. A 110 B 115 C 120 D 125 8 In Diagram 3, PQRST is a pentagon. STU is a straight line.

DIAGRAM 3

Find the value of x + y. A 212 B 362 C 384 D 392

S T U

P

Q R

32°

y°

x°

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B

A

C D

E 40° 80°

y°

O

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

DIAGRAM 4

The value of m is A 24 B 32 C 48 D 50 10 Diagram 5 shows the graphs of y = sin x and y = cos x.

DIAGRAM 5 The x-coordinate of point P is A 270°

B 225° C 215° D 180°

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

A 117°

B 207°

C 243°

D 297°

P

R

S

T

U V

W

X Q

m°

y

P

360° O

1

– 1

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

DIAGRAM 6

The value of tan x is

A 41

−

B 31

−

C –3 D –4 13 Simplify p × (2p–1)3 ÷ 2p –4.

A 3p B 3p2

C 4p D 4p2

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

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?

K

J

x°

L M N 12 cm 3 cm

D

B

A

C

K

M

L

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15 Express w

wuwu −

−+ 212 as a single fraction in its simplest form.

A uw

uw−1

B uw

uw 1+

C uwuwu 12 −+

D uwu 12 −

16 32 × =× 23

21

218 = A 36 B 54 C 108 D 162

17 =×

4)5(4 42

123

A 2 B 5 C 37.5 D 50

18 8pq – (3p + q)2 =

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

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

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?

A C B D

K L

M

N

P

Q

5 cm

6 cm 8 cm

P 60°

Q 30°

Q

30°

P

60°

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Q P

Q

P

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

DIAGRAM 9 Calculate the angle of depression of Q from vertex P. A 70°

B 60° C 30° D 20°

22 Given that thv π= , then h =

A πvt

B 2πvt

C t

v2

2

π

D 2

2

πtv

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 26.2 B 30.2 C 34.2 D 46.0

R Q

P

160°

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24 Given that w

wy−

=1

, express w in terms of y.

A y

yw+

=1

B y

yw−

=1

C y

yw += 1

D y

yw −= 1

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

DIAGRAM 10

The axis of reflection is the straight line that joins H and A K B L C M D N

26 Express n

mnm

321+− as a single fraction in its simplest form.

A n

m4

13 −

B 2313

nm −

C n

m3

1−

D n

m3

15 −

H

N

K

L

M

P

Q

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27 The solution for 32

1 −≤− kk is

A k ≥ 4

B k ≥ 38

C k ≥ 25

D k ≥ 35

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

A 3 < n ≤ 4 B –4 < n ≤ 3 C –3 < n < 4 D –4 < n ≤ –3 29 Diagram 11 is a pie chart showing the colours of t-shirts chosen by a number of

students.

DIAGRAM 11 If 18 students chose yellow t-shirts, find the number of students who chose red

t-shirts. A 108 B 72

C 36 D 33

60°190°

Red

Blue

Yellow

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

TABLE 1

Calculate the mean of the distribution. A 21.375 B 22.875

C 23.125

D 25.250

31 Diagram 12 is a bar chart showing the number of candidates who obtained

scores 1 to 5 in a Mathematics test.

DIAGRAM 12

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

A 90

B 70

C 60

D 50

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

Frequency 4 10 12 9 5

Score

1 2 3 4 5

5

10

15

20

Number of Candidates

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32 It is given that the universal set ξ = {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 5

B 6

C 7 D 9 33 Diagram 13 is a Venn diagram showing the sets P, Q and R such that the

universal set ξ = 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, Q

and R.

DIAGRAM 14

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

A 8 B 10 C 11 D 12

P R Q

.c .s

.g .w

.y .m

.k .q

P Q

R

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35 Find y-intercept of the straight line 36

53

2 =− yx .

A 5

18−

B 54−

C 5

18

D 54

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 – 3

B – 2 C 2 D 3 37 Diagram 15 shows two straight lines, OR and QR, on a Cartesian plane.

DIAGRAM 15

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

Find the gradient of QR. A –1 B –4 C –7 D –8

x

y

O

R(1, 8)

Q

P

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

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 152 . Find the value of x.

A 2 B 4

C 6

D 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 is

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

at random from the box, the probability that a red marble chosen is 21 . How

many red marbles are there in the box?

A 15 B 20 C 25 D 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 61

B 41

C 31

D 21

END OF QUESTION PAPER

Form One Form Two

Girls x 12

Boys 8 6

f4 final sbp2006 math p1

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