Soalan Ramalan Mathematics Pmr 2009 Paper 1

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SOALAN RAMALAN PMR 2009 MATHEMATICS Kertas 1 Oktober 1 ¼ jam

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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

a m × an = am+n

2

a m ÷ a n = a m −n

3

(a m ) n = a mn

4

Distance =

5

y + y2   x + x2 Midpoint, ( x, y ) =  1 , 1  2   2

6

Average speed =

7

Mean =

8

Pythagoras Theorem, c 2 = a 2 + b 2

( x2 − x1 ) 2 + ( y2 − y1 ) 2

distance travelled time taken

sum of data number of data

SHAPE AND SPACE

1

Area of rectangle = length × width

2

Area of triangle =

3

Area of parallelogram = base × height

4

Area of trapezium =

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1 × base × height 2

1 × sum of parallel sides × height 2

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3

5

Circumference of circle = π d = 2π r

6

Area of circle = π r 2

7

Curved surface area of cylinder = 2π rh

8

Surface area of sphere = 4π r 2

9

Volume of right prism = cross sectional area × length

10

Volume of cuboid = length × width × height

11

Volume of cylinder = π r 2 h

12

Volume of cone =

13

Volume of sphere =

14

Volume of right pyramid =

15

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

16

arc length angle subtended at centre = circumference of circle 360o

17

area of sector angle subtended at centre = area of circle 360o

18

Scale factor, k =

19

Area of image = k 2 × area of object

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1 2 πr h 3 4 3 πr 3 1 × base area × height 3

PA′ PA

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Answer all questions.

1

12 × (184 + 16) − 1750 ÷ 5 round off to the nearest hundreds is 100 A 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 B C D

3

p q r s

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 B C D

4

Given that 0.2 +

A B C D

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3 12 27 36

f 1 = . The value of f is 100 4

5 25 50 250

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5

5

Which of the following fraction has the largest value? 1 A − 2 3 B − 4 5 C − 8 7 D − 12

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

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Farid left town P to town Q on Wednesday at 0800. He took 7 hours to reach 1 town Q. After working for 8 hours, he took a rest for 8 hours. His return 2 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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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.

Glass bead

600 ml of water

Container M

Container 

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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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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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 85 D

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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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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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11

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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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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13

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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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 B C D

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RM270 RM360 RM400 RM420

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In Diagram 11, OPQR is a parallelogram, drawn on a Cartesian plane. Given that point P is (0,3) and PQ = 5 units.

Diagram 11 The coordinates of point R is A (4,−3) B (5,−3) C (−3,4) D (−4,−3)

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 B C D

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7 and 3 5 and 4 1 and 6 2 and 4

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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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17

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

120°

Diagram 13

22   Find the perimeter, in cm, of the whole diagram.  Take π =  7   1 57 A 3 1 B 73 3 1 C 87 3 1 101 D 3

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

Diagram 14 22   Find the area, in cm2, of the shaded region.  Take π =  7   A 4.5π B 5π C 7.5π 9π D

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19

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 B C D

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6 × 8 + 6 × 13 + 8 × 13 1 × 6 × 8 + 6 × 13 + 8 × 13 2 1 × 6 × 8 + 6 × 13 + 8 × 13 + 10 × 13 2 1  2 × 6 × 8  + 6 × 13 + 8 × 13 + 10 × 13 2 

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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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21

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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Diagram 18 is pie chart showing the professions of a group of people in a survey. Nurses

35°

120° Teachers

Engineers

55°

60°

Lawyers

Doctors

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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23

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?

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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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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 480 400 C 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 B C D

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Write the median as 15 and 16. 15 + 16 Calculate the median as . 2 Rearrange the data as 12, 15, 16, 18, 20, 22 and then write 16 and 18 as the median. Rearrange the data as 12, 15, 16, 18, 20, 22 and then calculate the 16 + 18 median as . 2

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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 I, III and IV D

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Diagram 22 is drawn on the square grids.

V

I

II

III

IV

Diagram 22 Which of the points are situated on the axes of symmetry of the diagram? A B C D

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I and III II and IV I, II and V II, IV and V

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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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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.

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A

60x + 35y = 70

B

6x + 35y = 700

C

12x+ 7y = 140

D

12x + 7y = 1400

1 hour to travel 38 km from Town J to Town K. She then 2 3 increased her speed by 4 km/h and drove from Town K to Town L in hour. 4 Calculate the distance from Town J to Town L, in km. A 60 B 76 C 80 D 98

Mariam took

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Which of the following represents the solution for the linear inequalities 5 < 3 − 2x ≤ 9 ?

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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Which of the following graph represents y = 3 x + 6 ? A

B

C

D

END OF QUESTION PAPER

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