Spb Maths P1 Pmr 2009

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BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KLUSTER KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAAN PMR 2009

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MATEMATIK Kertas 1 Ogos 2009 1

1 4

jam

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. 2. 3. 4.

5. 6. 7. 8.

Kertas soalan ini adalah dalam bahasa Inggeris. Kertas soalan ini mengandungi 40 soalan. Jawab semua soalan. Tiap-tiap soalan diikuti oleh empat pilihan jawapan, iaitu A, B, C dan D. Bagi setiap soalan, pilih satu jawapan sahaja. Hitamkan jawapan anda pada kertas jawapan objektif yang disediakan. Jika anda hendak menukar jawapan, padamkan tanda yang telah dibuat. Kemudian hitamkan jawapan yang baru. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan. Satu senarai rumus disediakan di halaman 2 hingga 3. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

Kertas soalan ini mengandungi 24 halaman bercetak

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2

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

RELATIONS

1

a m  a n  a m n

2

a m  a n  a m n

3

(a m ) n  a mn

4

Distance =

5

Midpoint

( x2  x1 ) 2  ( y2  y1 )2

y  y2   x  x2 , 1 ( x, y ) =  1  2   2

distance travelled time taken

6

Average speed =

7

Mean =

8

Pythagoras Theorem

sum of data number of data

c2  a2  b2

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SHAPE AND SPACE

1

Area of rectangle = length  width

2

Area of triangle =

3

Area of parallelogram = base  height

4

Area of trapezium =

5

Circumference of circle =  d  2 r

6

Area of circle =  r 2

7

Curved surface area of cylinder = 2 rh

8

Surface area of sphere = 4 r 2

9

Volume of right prism = cross sectional area  length

10

Volume of cuboid = length  width  height

11

Volume of cylinder =  r 2 h

12

Volume of cone =

1  base  height 2

1  sum of parallel sides  height 2

1 2 r h 3

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4

4 3 r 3

13

Volume of sphere =

14

Volume of right pyramid =

15

Sum of interior angles of a polygon = (n  2)  180

16

arc length angle subtended at centre  circumference of circle 360

17

area of sector angle subtended at centre  area of circle 360

18

Scale factor, k =

19

Area of image = k 2  area of object

1  base area  height 3

PA PA

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Answer all questions 1

Based on the number 219.438, what is the place value of the underlined digit? A B C D

2

hundreds tens tenths hundredths

Diagram 1 shows a sequence of numbers. …, 29, 31, 37, 41, x, 47, 53, y, 61, 67, …

Diagram 1 The value of y – x is A B C D

3

12 14 16 18

Sani has RM2 100. He uses

2 of this amount for personal expenses and gives 18% 3

to his mother. How much money is left now? A B C D

4

RM448 RM378 RM322 RM302

There are 15 boys in a class. The percentage of girls in the class is 20% more than the boys. The number of students in the class is A B C D

27 30 33 36

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5

Diagram 2 is part of a number line.

J

0

–12

12

H

Diagram 2 The value of J – H is A B C D

6

–28 –24 –16 –12

Diagram 3(a) and 3(b) show all factors of 30 and 45. Factors of 30 2

Factors of 45

30

m

15

n

10

p

m

n

9 15 3

q

3

Diagram 3(a)

Diagram 3(b)

Find the sum of p and q. A B C D

51 39 10 6

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In a walking competition, Zaki walked a total of 2.75 km while Chandran walked a total of 3 km 50 m. How far behind, in m, was Zaki from Chandran? A B C D

8

6

250 300 750 975

In Diagram 4, PQV is a right-angled triangle. PST is a straight line.

Q P

20o

130o

S

T xo

V Diagram 4 Find the value of x.

9

A

20

B C D

25 30 40

Alif spends 6 hours on Sunday for his revision on Mathematics, Science and English in ratio 2 : 5 : 3 respectively. Calculate the time difference between Mathematics and Science. A B C D

1 hour 12 minutes 1 hour 48 minutes 1 hour 8 minutes 1 hour 20 minutes

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7

Diagram 5 shows a circle JKGL with the centre O. Given that KL = 10 cm and OH = 3 OM. G

K

L

H M

13 cm

O

J Diagram 5 Find the length, in cm, of MG. A B C D 11

4 5 9 12

In Diagram 6, EFG is a right-angled triangle. G xo H

E

80o

J Diagram 6

F

The value of x is A B C D

40 50 60 70

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8

Diagram 7 shows a sector of a circle with centre O and its diameter is 21 cm. R

O

80o T

Diagram 7

Given that ROT is 80o. Calculate the perimeter, in cm, of the whole diagram. (Use   A B C D 13

22 ) 7

57.33 72.33 102.67 123.67

On the map which is to scale 1 : 4 000, the distance between town V and town W is 3 cm. Find the actual distance, in km, between the two towns. A B C D

0.12 1.2 12 120

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List all the prime numbers of x which satisfy the inequality 5 < A B C D

15

9 2x < 13. 3

11, 13, 17 7, 11, 13, 17 11, 13, 17, 19 7, 11, 13, 17, 19

Given that 2k = –3 and 4h – 6k = 1. Find the value of h. A B C D

16

–2 1 – 2 2 1 2 2

In Diagram 8, PQR is an isosceles triangle and RSTU is a trapezium. P

T

8 cm

U

10 cm 6 cm S

R

Q 16 cm Diagram 8

Find the area, in cm2, of the whole diagram. A B C D

48 60 72 84

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The point (2, 4) satisfy the function of A B C D

18

10

y = 2x + 1 y = 3x – 2 y = 3 – 2x y = 4x + 5

Diagram 9 shows a right prism. EFGH is its uniform cross section. x cm

E

F

5 cm

H

G 18 cm

4 cm

Diagram 9 Given that the volume of the prism is 810 cm3. Calculate the value of x. A B C D

14 12 11 8

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11

Table 1 shows the number of goals scored by a football club in each game they had played. Number of goals

0

1

2

3

4

Number of games

2

7

5

4

2

Table 1 Calculate the mean of the score per game. A B C D 20

0.5 1.85 2.00 3.70

In Diagram 10, JKLMNOPQ is a regular octagon and RLN is a triangle. J

K

Q

L yo

P

R

M xo O

N

Diagram 10 Find the value of x + y. A B C D

180 90 67.5 22.5

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12

In Diagram 11, EFGHJ is a regular pentagon and JKL is a straight line. F

G

L yo K

E

H o

x xo J Diagram 11 Find the value of y. A B C D

72 50 45 28

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13

In Diagram 12, O is the centre of a circle QRST. PQR and ROT are straight lines. P

Q

T

150o

O

xo

R S Diagram 12 Calculate the value of x. A B C D

30 60 120 150

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14

In Diagram 13, O is the origin. M is the midpoint of OR and the distance of PN is 9 units. y

P(0, 6)

10 units

O

R

M

x

N Diagram 13

Find the distance of MN. A B C D

24

3 4 5 6

Table 2 shows the rate of a courier service. Parcel weight

Rate

For a parcel not exceeding 400g  First 100 g  Subsequent 300 g

RM4 RM2

For a parcel exceeding 400 g  First 400 g  Subsequent 100 g

RM6 RM1

Table 2 Marini sent two parcels which were 200 g and 600 g respectively. Calculate the total payment of the services. A B C D

RM11 RM12 RM13 RM14

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15

Diagram 14 shows a graph of function y = x2 – 2 . y

 (r, 23)

O

x

–2

Diagram 14

The value of r is A B C D

25 23 10 5

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16

In Diagram 15, STU, JKL and PTK are straight lines. P o

m

S

U

T no

J

mo

K

20o

L

70o

Diagram 15 Find the value of m + n. A B C D

27

420 375 355 225

Given that R(4, 8), S(x, 6) and T(6, y). T is the midpoint of RS. What is the possible values of x and y? A x = 5, y=7 B x = 7, y=8 C x = 8, y=7 D x = 10, y = 14

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17

In Diagram 16, PQRS is a rectangle and KLM is a sector of a circle with centre K. Q

P L 10 cm

45º

S

K

R

M Diagram 16

Given that SK = KM = MR = 7 cm Calculate the area, in cm2, of the shaded region. (Use   A B C D

29

22 ) 7

199.00 190.75 188.00 133.75

In Diagram 17, EFG is a right-angled triangle and GHJK is a square with area of 16 cm2. E

J

H

K

G

F

Diagram 17

Given that K is the midpoint of EG. EKG and FGH are straight lines. FGH =19 cm. Find the perimeter, in cm, of the whole diagram. A B C D

48 52 76 84

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18

Diagram 18 is a pictogram showing the number of learner drivers who passed a driving test on a certain day at the Seberang Jaya Road Transport Department.

Desa Driving School Mutiara Driving School Murni Driving School

Diagram 18 Given that the difference between the learner drivers who passed from Desa Driving School and Mutiara Driving School is 24. What is the number of learner drivers from Murni Driving School who passed this test? A B C D 31

32 28 16 8

The following triangles are similar except A 70o 50o

B

C

50o

60o

70o 40o

D 70

o

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60o

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19

In Diagram 19, N is the image of N under an enlargement at O.

N’

.

.C

N

.D

M

.B .A

O

Diagram 19 Which of the point A, B, C or D is the image of M under the same enlargement? 33

In Diagram 20, O is the centre of the circle EFGHJ. EKOG and FKJ are straight lines. F

E

xo

K

O 110º

yo

G 120º

J

H

Diagram 20 Given that EGH = 2EFJ Calculate the value of x + y. A B C D

140 130 110 80

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20

Diagram 21 shows a right pyramid with a square base KLMN. VO is the height of the pyramid. V

N

M O

K

L

Diagram 21 Given that the area of triangle VLM is 65 cm2 and KL = 10 cm. Calculate the length, in cm, of VO. A B C D

35

13 12 10 5

A car in a formula one race, decelerated from 144 kmh-1 for a pit stop and took 2 seconds to completely stop. Calculate the acceleration of the car, in ms-2. A B C D

–2 – 12 – 20 – 72

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21

Diagram 22 shows a combined solid of a cone and a cylinder.

13 cm

17 cm Diagram 22 Given that slant height of the cone is 13 cm. The radius of the base of the cylinder and the base of the cone is 5 cm. Calculate the volume, in cm3, of the solid. A B C D

37

170 210 425 525

Tasnim departed from Sungai Petani at 6.30 am and arrived at Ipoh at 9.15 am. If her average speed was 100 kmh-1, calculate, in km, the distance she travelled. A B C D

275 245 235 215

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22

Diagram 23 shows the apparatus of an experiment. Metal ball

240 cm³

Container K

Container M Diagram 23

Three metal balls are dropped into container K and the water will be displaced and collected in container M. Given that the volume of each metal ball is 20.5 cm3. Calculate the percentage of the water displaced in container M. A

8.5

B

25.6

C

26.3

D

61.5

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23

Diagram 24 is a line graph which shows the marks of the monthly Mathematics Test obtained by Rona.

The Monthly Mathematics Marks Obtained By Rona Marks 100 X X

80

X

60

X

X

X

X

40

20

JAN

FEB

MAR

APR

Diagram 24

MAY

JUN

JUL Month

What is the mode of the marks? A B C D

50 60 80 90

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24

Diagram 25 is a bar chart which shows the number of form 3 students in a school. Number of students

Boys

Girls

3A

3B

3C

3D

Class

Diagram 25 Given that the number of boys in 3A is 12. Calculate the total number of girls in this form. A B C D

42 48 56 64

END OF QUESTION PAPER

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