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SOALAN RAMALAN PMR 2009 50/1 MATHEMATICS

Kertas 1

Oktober

1 ¼ jam Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. This question paper is in English language.

Kertas soalan ini adalah dalam bahasa Inggeris.

2. This question paper consists of 40 questions.

Kertas soalan ini mengandungi 40 soalan.

3. Answer all questions

Jawab semua soalan.

4. Each question is followed by four alternative answers, A, B, C or D.

For each question, choose one answer only. Blacken your answer on the objective

answer sheet provided.

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.

5. If you wish to change your answer, erase the blackened mark that you have

made. Then blacken the new answer.

Jika anda hendak menukar jawapan, padamkan tanda yang telah dibuat.

Kemudian hitamkan jawapan yang baru.

6. The diagrams in the questions provided are not drawn to scale unless stated.

Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

7. A list of formulae is provided on page 2 to 3.

Satu senarai rumus disediakan di halaman 2 hingga 3.

8. You may use a non-programmable scientific calculator.

Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

Kertas soalan ini mengandungi 30 halaman bercetak.

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The following formulae may be helpful in answering the questions. The symbols

given are the ones commonly used.

RELATIONS

1 m n m na a a

+× =

2 m n m na a a

−÷ =

3 ( )m n mna a=

4 Distance = 2 2

2 1 2 1( ) ( )x x y y− + −

5 Midpoint, ( , )x y =

+

2

21 xx ,

+

2

21 yy

6 Average speed = distance travelled

time taken

7 sum of data

Mean = number of data

8 Pythagoras Theorem, 2 2 2c a b= +

SHAPE AND SPACE

1 Area of rectangle = length × width

2 Area of triangle = 1

base height2

× ×

3 Area of parallelogram = base height×

4 Area of trapezium = 1

sum of parallel sides height2

× ×

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5 Circumference of circle = 2d rπ π=

6 Area of circle = 2rπ

7 Curved surface area of cylinder = 2 rhπ

8 Surface area of sphere = 24 rπ

9 Volume of right prism = cross sectional area × length

10 Volume of cuboid = length × width × height

11 Volume of cylinder = 2r hπ

12 Volume of cone = 21

3r hπ

13 Volume of sphere = 34

3rπ

14 Volume of right pyramid = 1

3× base area × height

15 Sum of interior angles of a polygon = ( 2) 180n − ×o

16 arc length angle subtended at centre

circumference of circle 360=

o

17 area of sector angle subtended at centre

area of circle 360=

o

18 Scale factor, k = PA

PA

′

19 Area of image = 2 area of objectk ×

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Answer all questions.

1 51750)16184(12 ÷−+× round off to the nearest hundreds is

A 100

B 130

C 2 050

D 2 100

2 23, p, q, r, s, 43 are prime numbers arranged in increasing order.

Which of the following is the number 37?

A p

B q

C r

D s

3 3 balls rotate along a circular track. Ball A makes one full rotation in 6

seconds. Ball B makes 9 seconds and ball C makes 12 seconds.

If the three balls start rotating from the same point and at the same time now,

after how many seconds will they all be at the same point again?

A 3

B 12

C 27

D 36

4 Given that 4

1

1002.0 =+

f. The value of f is

A 5

B 25

C 50

D 250

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5 Which of the following fraction has the largest value?

A 2

1−

B 4

3−

C 8

5−

D 12

7−

6 Table 1 shows the length of string needed to tie box P and Q.

Box Length of string

P 1.05 m

Q 80 cm

Table 1

Calculate the total length, in m, of string needed to tie 6 boxes of P and 3

boxes of Q.

A 6.54

B 8.70

C 11.10

D 11.40

7 Farid left town P to town Q on Wednesday at 0800. He took 7 hours to reach

town Q. After working for 8 hours, he took a rest for 2

18 hours. His return

journey to P took him 4 hours. State the day and time (in 24-hour system) he

arrived at town P.

A Thursday 1130 hours

B Thursday 2330 hours

C Friday 1130 hours

D Friday 2330 hours

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8 Table 2 shows the price of three items after adjustment. Mei Ling bought a

book, a bag and a pair of shoes.

Items Original Price Percentage

decrease

Percentage

increase

Book RM 25 10% -

Bag RM 40 - 15%

Shoes RM 38 - -

Table 2

How much did Mei Ling pay for the three items?

A 50

B 94

C 106

D 107

9 Diagram 1 shows the arrangement of apparatus for an experiment. If a glass

bead is dropped into container M, 2 ml of water will flow into container N.

Container M Container �

waterof

600 ml

Glass bead

Diagram 1

Find the number of glass beads that are required to be dropped into container

M so that 25% of the water will flow into container N.

A 45

B 75

C 105

D 135

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10 In Diagram 2, JKL is a right - angle triangle. JML is a straight line.

Diagram 2

Calculate the value of x.

A 50

B 60

C 70

D 80

11 In Diagram 3, ABCD is a parallelogram. BFE is a straight line.

Diagram 3

Calculate the value of k.

A 30

B 40

C 50

D 65

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12 In Diagram 4, FGHIKL is an irregular polygon. EFG and HIJ are straight

lines.

Diagram 4

Calculate the value of x.

A 50

B 60

C 65

D 85

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13 In Diagram 5, PQRSUV is a regular hexagon. PUT and RST are straight lines.

Diagram 5

Calculate the value of x + y.

A 170

B 180

C 190

D 200

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14 In Diagram 6, PQRS is a trapezium and PST is a right angled triangle.

Diagram 6

Calculate, the area, in cm2, of the shaded region.

A 30

B 96

C 126

D 156

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15 In Diagram 7, ABFG is a square and CDEF is a rhombus. ABC and BFE are

straight lines.

Diagram 7

If the area of the square, ABFG is 16 cm2, the perimeter of the whole diagram

in cm is

A 24

B 26

C 28

D 30

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16 Diagram 8 shows a circle with the centre, O. PQR is a straight line.

Diagram 8

Calculate the value of a + b.

A 34

B 56

C 92

D 96

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17 In Diagram 9, JK is the diameter of the circle and LMN is a straight line.

Diagram 9

Find the value of x.

A 82

B 102

C 108

D 112

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18 In Diagram 10, X and Y are the centres of two semicircles.

Diagram 10

Which of the points, A, B, C or D is 8 cm from the straight line PS and 12 cm

from point Y.

19 The total cost of three badminton rackets, P, Q and R, is RM900. The cost of

the badminton rackets Q and R are in the ratio 3:4. If the badminton racket P

costs RM270, The cost of the badminton racket R is

A RM270

B RM360

C RM400

D RM420

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20 In Diagram 11, OPQR is a parallelogram, drawn on a Cartesian plane. Given

that point P is )3,0( and PQ = 5 units.

Diagram 11

The coordinates of point R is

A )3,4( −

B )3,5( −

C )4,3(−

D )3,4( −−

21 Given K is the midpoint of the straight line JL, the coordinates of J, K and L

are (p, -2), (4, q) and (6, 10) respectively.

Find the values of p and q.

A 7 and 3

B 5 and 4

C 1 and 6

D 2 and 4

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22 In Diagram 12, O is the centre of the circle and AB is the chord.

Diagram 12

Given the radius is 13 cm, and PQ = 8 cm, find the length, in cm, of AB.

A 5

B 10

C 12

D 24

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23 In Diagram 13, LMNO is a rhombus and LPN is an arc of a circle with its

centre, O.

°120

Diagram 13

Find the perimeter, in cm, of the whole diagram.

=

7

22 πTake

A 3

157

B 3

173

C 3

187

D 3

1101

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24 In Diagram 14, O is the centre of the sector and OPQ is an equilateral triangle.

Diagram 14

Find the area, in cm2, of the shaded region.

=

7

22 πTake

A 4.5π

B 5π

C 7.5π

D 9π

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25 Diagram 15 shows a right prism with a right-angled triangle, JKL, as a

uniform cross section.

Diagram 15

Which of the following shows the correct calculation of the total surface area

of the prism?

A 13813686 ×+×+×

B 138136862

1×+×+××

C 1310138136862

1×+×+×+××

D 1310138136862

12 ×+×+×+

××

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26 Diagram 16 shows the net of a right cone.

Diagram 16

Calculate the volume, in cm3, of the cone.

A 100π

B 150π

C 180π

D 210π

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27 In Diagram 17, the solid consists of a pyramid and a cuboid.

Diagram 17

Find the volume, in cm3, of the solid if the height of the pyramid is 8 cm.

A 280

B 340

C 370

D 420

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28 Diagram 18 is pie chart showing the professions of a group of people in a

survey.

Doctors

°120

°35

°55

°60Teachers

Nurses

Lawyers

Engineers

Diagram 18

If the number of doctors is 20, find the number of engineers in the group.

A 30

B 40

C 50

D 120

29 Table 3 shows the number of canned drinks consumed by a group of Form 3

boys in a week.

Number of tins 0 1 2 3 4 5

Number of boys 7 5 10 x 6 7

Table 3

The mode of canned drinks consumed is 2. Find the possible value of x.

A 9

B 10

C 11

D 12

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30 Diagram 19 is a pictogram showing the number of houses sold by a developer

in three months.

October

November

December

represents 5 houses

Diagram 19

Which of the statement below is true?

A The total number of houses sold in three months is 17 units.

B The most number of houses sold in a month is 35 units.

C The number of houses sold in March is 36 units.

D The sale in January is more than the sale in February by 3 houses.

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31 The bar chart in Diagram 20 shows the sales of cars in a car sales centre for

five months.

Diagram 20

Calculate the mean of the sales per month for the period shown in the chart.

A 600

B 480

C 400

D 380

32 Table 4 shows the marks obtained by a group of students in a History test.

18 20 15 16 22 12

Table 4

Determine the correct working to find the median of the data.

A Write the median as 15 and 16.

B Calculate the median as .2

1615 +

C Rearrange the data as 12, 15, 16, 18, 20, 22 and then write 16 and 18 as

the median.

D Rearrange the data as 12, 15, 16, 18, 20, 22 and then calculate the

median as .2

1816 +

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33 Diagram 21 shows four nets of a solid.

I II

III IV

Diagram 21

Which of the following are the nets of a pyramid?

A I and II

B II, III and IV

C I, II and IV

D I, III and IV

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34 Diagram 22 is drawn on the square grids.

I II III

IV

V

Diagram 22

Which of the points are situated on the axes of symmetry of the diagram?

A I and III

B II and IV

C I, II and V

D II, IV and V

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35 In Diagram 23, OP’Q’R’ is the image of OPQR under a certain enlargement.

Given that the area of the object is 12 cm2.

Diagram 23

Find the area of the shaded region.

A 24

B 36

C 96

D 108

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36 Table 5 shows the entrance fees for a circus show. On certain day, x adults and

y children went to the show, and the total collection was RM700.

Visitor Entrance Fee

Adult RM 6

Child RM 3.50

Table 5

Form an equation relating x and y.

A 60x + 35y = 70

B 6x + 35y = 700

C 12x+ 7y = 140

D 12x + 7y = 1400

37 Mariam took 2

1hour to travel 38 km from Town J to Town K. She then

increased her speed by 4 km/h and drove from Town K to Town L in 4

3hour.

Calculate the distance from Town J to Town L, in km.

A 60

B 76

C 80

D 98

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38 Which of the following represents the solution for the linear inequalities

9235 ≤−< x ?

A

B

C

D

39 Table 6 shows the values of x and y for the function y = 2x2 – x – 3.

x 0 1 2 3 4

y -3 m 3 n 25

Table 6

Find the value of m + n.

A 4

B 8

C 10

D 14

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40 Which of the following graph represents ?63 += xy

A

B

C

D

END OF QUESTION PAPER