kertas soalan ramalan 2009 pmr math

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www.mathgayapos.blogspot.com

FORECAST PAPER PMR 2009

_________________________________

FORECAST PAPER PENILAIAN MENENGAH RENDAH (PMR)

2009

NO.KAD PENGENALAN/I.C NUMBER - -

ANGKA GILIRAN/INDEX NUMBER

Nama Calon : Tingkatan :

MATHEMATICS

Paper 1 1 hours 15 minutes

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam bahasa Inggeris.

2. Kertas soalan ini mengandungi 40 soalan.

3. Jawab semua soalan.

4. 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. Jika anda hendak menukar 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 3.

8. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

3472/1 Forecast Paper Mathematics PMR Paper 1 September 2009 1 hour 15 minutes

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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) = ⎜⎝⎛ +

221 xx , ⎟

⎠⎞+

221 yy

6 Average speed = distance travelledtime taken

7 sum of dataMean = 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 = 213

r hπ

13 Volume of sphere = 343

rπ

14 Volume of right pyramid = 13× base area × height

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

16 arc length angle subtended at centrecircumference of circle 360

=o

17 area of sector angle subtended at centrearea of circle 360

=o

18 Scale factor, k = PAPA′

19 Area of image = 2 area of objectk ×

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Answer all questions.

1. Diagram 1 shows a sequences of numbers. -18, -17, -15, t , -8, -3, 3 Diagram 1 The value of t is A -13 B -12 C -11 D -10

2. A pair of numbers that has 80 as its lowest common multiple (LCM) is

A 14 and 20 B 16 and 40 C 18 and 60 D 20 and 80

3. The sum of all prime factors of 260 is

A 16 B 18 C 20 D 24

4. Lela bought a Nokia hand phone for RM 1 600. After a certain time, she sold the

hand phone for RM 1 200. Calculate the loss percentage. A 25 % B 30 % C 35 % D 40 %

5. Diagram 2 shows some of the factors of 220.

Diagram 2 Find the value of q . A 21 B 40 C 50 D 55

220 10

22 q 110 2

4

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6. Which of the following has the smallest value?

A 2524

B 2011

C 97

D 52

7.

Cikgu Nurul has 6 rolls of ribbon. Each roll has 212 metres of ribbon. She used 3

rolls of the ribbon and 140 cm from another roll. How much ribbon is left ? A 5.0 m B 5.4 m C 6.0 m D 6.1 m

8. In an experiment, the initial temperature of a substance is 30 0 C. The substance is

cooled at a rate of 3 0 C per minute for 15 minutes. Later, it is heated at a rate of 4 0 C per minute for 12 minutes. The final temperature of the substance, in 0 C, is A -15 B -9 C 33 D 43

9. At 1440 hours on Saturday, Siti departed from Kuala Terengganu to Kuala

Lumpur. The journey took 8 hours. Siti stayed at Kuala Lumpur for 7 hours. Then

she took 217 hours to return to Kuala Terengganu. At what time, in the 24-hour

system, did Siti reached at Kuala Terengganu? A 0920 B 1310 C 1620 D 2020

10. In the diagram 3, STU is a straight line.

Diagram 3

T U 38 0

x

S

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Find the value of x . A 11 0 B 19 0 C 22 0 D 28 0

11. In the diagram 4, LMNO is a rectangle. P and Q are midpoint of LM and MN.

Diagram 4 Find the perimeter, in cm, of the shaded region. A 42.22 B 43.63 C 63.40 D 66.34

12. Diagram 5 shows a regular pentagon ABCDE.

Diagram 5 EBS and DCT are straight lines. Which of the following is false? A EAB is an isosceles triangle B 0180=+ yx C EBC is an equilateral triangle D EBS and DCT are parallel

13. Given that q : r = 5 : 9, if q + r = 56, then q – r =

A -16 B -6 C 6 D 16

M

O N

P

Q

14 cm

6 cm

L

A

B

C D

E

0y

0x S

T

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14. In the diagram 6, PQRS is trapezium and TUVS is a parallelogram. Diagram 6 Given that TU = 10 cm and SR = 22 cm, calculate the area of the shaded region A 200 cm 2 B 205 cm 2 C 210 cm 2 D 215 cm 2

15. Diagram 7 shows two points K and L, on a Cartesian plane.

Diagram 7 Calculate the distance between the point K and the point L. A 32 units B 65 units C 84 units D 102 units

16. Diagram 8 below shows a cuboid.

Diagram 8

15 cm

20 cm P Q

R V S

10 cm

U T

x

y

2

4

6

O 2 4 6 8

K

L

4 cm

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Which of the following is a net for the cuboid. A

B

C

D

17.

Given that R : S = 511 :

53 and S : T = 3 : 5, find R : S : T

A 2 : 3 : 5 B 3 : 2 : 5 C 5 : 3 : 6 D 6 : 3 : 5

6 cm

4 cm

4 cm

6 cm

4 cm

6 cm

4 cm

6 cm

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18. In diagram 9, W is the midpoint of the straight line VY. Diagram 9 Find the value of q A -4 B -1 C 4 D 6

19. Diagram 10 shows three congruent circles of radius 3.5 cm each and their centres

at E, F and G. Diagram 10 Which of the point A, B, C or D is at a distance of 3.5 cm from G and more than 3.5 cm from F?

20. In the diagram 11, GHIJ is a rectangle. PQR is an arc of a circle with centre S.

Diagram 11

x

y

V(10,0)

W( q , -5)

Y(-2,-10)

C A

B

D

E F G

16 cm

9 cm G H

I

Q

J P S R

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Given that JP = PS = SR = RI, find the perimeter of the whole diagram.

(722

=π )

A 50.504 B 52.584 C 54.571 D 56.554

21. Solve the inequalities 107 ≤− x

A 3−≤x B 3−≥x C 3≤x D 3≥x

22. Table 1 shows the weight of a group of pupils in a class.

Weight (kg) 30 35 40 45 50 55 Frequency 2 3 4 5 2 1

Table 1 Find the median weight, in kg, of the pupils in the class A 40 kg B 42.5 kg C 45 kg D 50 kg

23.

52

913m

m × =

A 33 −m B 3

31 m

C 33

1m

D 33

1−m

24. In Diagram 12 PQRS is a circle with centre O. POQ and STR are straight lines.

Diagram 12

P

S T R Q

O

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Given that PQ=20cm and SR=16cm. Calculate the length, in cm of OT A 6 cm B 8 cm C 12 cm D 15 cm

25. Mr. Wong bought 5 boxes of oranges which contained x oranges in each box. He

also bought 4 boxes of apples which contained y apples in each box. He sold each orange and each apple for RM0.60 and RM0.50 respectively. Which algebraic expression represents the amount of money Mr. Wong would get if he sold all the fruits? A 2x + 3y B 3x + 2y C 4x + 5y D 5x + 4y

26. Diagram 13 is a line graph showing monthly test marks of Saleha from January to

June. Diagram 13 Find the modal score A 40 B 50 C 60 D 75

27. Which of the following points lie on the graph of 52 2 += xy

A ( 0,7 ) B ( 3,1− ) C ( 3,2 −− ) D ( 23,3− )

Jan Feb Mar Apr

20

40

60

80

May Month

Marks

Jun

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28. Mr. Harris drives to his office at the average speed of 70km per hour. The distance between his house and his office is 14km. If he leaves his house at 7.50am, what is the time when he reach his office? A 8.00 am B 8.01 am C 8.02 am D 8.03 am

29. Diagram 14 shows a solid cylinder rod made of iron. The length of the cylinder is

15cm and the diameter is 4.2cm. At one end of the cylinder, a hemisphere with the same diameter is cut out. Diagram 14 Calculate the mass of the remaining cylinder if the mass of 1 3cm of iron is 144g. (

use 722

=π )

A 1.309g B 1.885g C 4.697g D 5.518g

30. In Diagram 15, PQRS is a circle with centre O. POR and QOS are straight lines.

Diagram 15

15 cm

Q

P

S

R

35O

y

O

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Find the value of y A 35o

B 70o C 110o D 162.5o

31. Diagram 16 shows the graph of function 42 −= xy

Diagram 16 Find the value of y when x = −1 A −6 B −2 C 0 D 2

32. In Diagram 17, PQRS is a quadrilateral

Diagram 17 Find the value of x

65O

Q

P

S R

110O

152O

2X

42 −= xy

x 0 - 2 - 4

- 2

2

y

2 4

- 4

6

4

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A 16.5O

B 28O C 33.5O D 35O

33. In Diagram 18 JKL is a straight line and LMN is a right-angled triangle.

Diagram 18 Find the value of x. A 25o

B 30o C 55o D 63o

34. In Diagram 19, JKLMN is a pentagon and LMP is a straight line.

Diagram 19 Find the value of yx + A 116o

B 206o C 254o D 296o

65O

K J

M

L 55O

x

115O

N

N

M L

K

J

P 66O

130O

x

y

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35. Diagram 20 shows a right cone with height 24cm. Diagram 20

Calculate the volume of the cone. ( use 722

=π )

A 200.0cm3

B 300.0cm3 C 628.6cm3 D 1283.3cm3

36. Diagram 21 shows a pie chart represents the monthly expenditure of Janice.

Diagram 21 If Janice spends RM30 for clothes, how much does she spend on books? A RM 35.00 B RM 37.00 C RM 42.50 D RM 47.50

25cm

60O 50O

165O Others

Transport Clothes

Books

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37.

In Diagram 22, T ’ is the image of T under translation ⎟⎟⎠

⎞⎜⎜⎝

⎛ba

.

Diagram 22

Translation ⎟⎟⎠

⎞⎜⎜⎝

⎛ba

is

A ⎟⎟⎠

⎞⎜⎜⎝

⎛−54

B ⎟⎟⎠

⎞⎜⎜⎝

⎛− 54

C ⎟⎟⎠

⎞⎜⎜⎝

⎛− 45

D ⎟⎟⎠

⎞⎜⎜⎝

⎛−45

4

4 6 2

6

8

2

0

y

x 8

T’

T

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38. Diagram 23 shows a bar chart which shows the number of pupils in three classes. Diagram 23 Find the difference between the total number of boys and the total number of girls in the three classes. A 7 B 8 C 10 D 14

class

8

12

16

4 6

10

14

2

22

26

30

18

24

28

32

20

36

38

40

34

Num

ber o

f pup

ils

3A 3B 3C

girl

boy

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39. In Diagram 24, POQ and ROU are two arcs of a circle with centre O. Given that OR=5cm and ST=2cm. S is the midpoint of OP. Diagram 24

Calculate the area, in cm2 , of the shaded region. ( use 722

=π )

A 18.46 B 18.56 C 18.66 D 18.76

40. Diagram 25 shows a square ABCD within a circle. The diameter of the circle is the

diagonal of the square. Diagram 25 Calculate the area of the shaded region, in cm2. A 3612 +π B 3612 −π C 3618 +π D 3618 −π

6cm

A B

C

30o

45o

7 cm

O

S

P

T R

Q

U

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-KERTAS SOALAN TAMAT-

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2009

MATEMATICS Paper 2

1 hour 45 minutes

NO.KAD PENGENALAN/I.C NUMBER - -

ANGKA GILIRAN/INDEX NUMBER

Examiner’s Code Question Full

Marks 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Total

Nama Calon : Tingkatan :

3472/1 Forecast Paper Mathematics PMR Paper 2 September 2009 1 hour 45 minutes

JANGAN BUKA KERTAS SOALAN INI SEHINGGA

DIBERITAHU

1. Tuliskan nama dan tingkatan anda pada ruang yang

disediakan.

2. Kertas soalan ini adalah dalam bahasa Inggeris.

3. Kertas soalan ini mengandungi 20 soalan.

4. Jawab semua soalan.

5. Jawapan anda hendaklah ditulis pada ruang yang

disediakan dalam Kertas soalan ini.

6. Tunjukkan langkah-langkah penting dalam kerja mengira

anda. Ini boleh membantu untuk mendapatkan markah.

7. Jika anda hendak menukar jawapan, batalkan jawapan

yang telah dibuat. Kemudian tulis jawapan yang baru.

8. Rajah yang mengiringi soalan tidakdilukis mengikut skala

kecuali dinyatakan.

9. Markah yang diperuntukkan bagi setiap soalan ditunjukkan

dalam kurungan.

10. Penggunaan kalkulator tidak dibenarkan.

11. Serahkan kertas soalan ini kepada pengawas peperiksaan

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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 = ⎜⎝⎛ +

221 xx , ⎟

⎠⎞+

221 yy

6 Average speed = distance travelledtime taken

7 sum of dataMean = 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 = 213

r hπ

13 Volume of sphere = 343

rπ

14 Volume of right pyramid = 13× base area × height

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

16 arc length angle subtended at centrecircumference of circle 360

=o

17 area of sector angle subtended at centrearea of circle 360

=o

18 Scale factor, k = PAPA′

19 Area of image = 2 area of objectk ×

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For

examiner’s use

1. Calculate the value of 108 – 3(12 + 56 ÷ 7). Answer:

[ 2 marks ]

2. Calculate the value of 3.45 × 0.7 – (–241 ) and express the answer correct to one

decimal place . Answer:

[ 2 marks ]

3. (a) Find the value of (– 31 )3 .

(b) Calculate the value of ( 4.8 ÷ 3 64− )2 .

Answer: (a) (b)

[ 3 mark]

2

1

2

2

3

3

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For examiner’s

use

4. In Diagram 1, PQR is a straight line.

Diagram 1

Given tan y = 21 , find the length of PQ.

Answer:

[ 2 marks ]

5. Diagram 2, shows two triangles, PQS and QRS.

Diagram 2

Given that sin y = 178 , find the value of cos x.

Answer:

[ 2 marks ]

2

4

2

5

P Q R

S

15 cm

10 cm

S R

Q P

8 cm

y

20 cm

x

yo

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For examiner’s

use

6. Diagram 3 in the answer space shows figure S and R, which are drawn on a Cartesian plane.

On the diagram: (a) Mark the centre of enlargement as P. (b) State the coordinate of the centre of enlargement. Answer: (a)

Diagram 3

(b

[ 2 marks ]

2

6

2

4

6

8

3

5

7

1

2 1 3 4 5 6 7 8 0

S R

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For

examiner’s use

7. Diagram 4 shows pentagon P,Q and R, which are drawn on a Cartesian plane.

Diagram 4 (a) Q is the image of P under transformation M. Describe in full the transformation

M. (b) R is the image of Q under a rotation of 900. State: i) the direction of the rotation ii) the coordinate of the centre of the rotation

Answer: (a) (b) i) ii)

[ 4 marks ]

4

7

1

2 3

5

1

2

3

4

4 5

6

6

7

7 8 1

9

1

9

1

0

1

8

1-1

1-1

1-2

1-3

1-4

1-2 1-3 1-4

P

Q

R

1x

1y

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For

examiner’s use

8. Diagram 5 shows a trapezium.

Diagram 5

On the grid in the answer space, draw Diagram 5 using the scale 1 : 31 .

Answer:

[ 3 marks ]

3

8

5 unit

4 unit

2 unit

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For

examiner’s use

9. Diagram 6 in the answer space shows a regular hexagon DEFGHI. P,Q and R are three moving points in the diagram. (a) P is the point which moves such that it is equidistant from line DE and EF. By using the letter in the diagram, state the locus of P . (b) In the diagram, draw i) the locus of point Q such that equidistant from point H and point F. ii) the locus of point R such that RG = 5.5 cm (c) Hence, mark with the symbol ⊗ the intersection of the locus of Q and the locus

of R.

Answer: (a) (b) (i), (ii) (c)

Diagram 6

[ 5 marks ] 5

9

D

E F

G

H I

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For

examiner’s use

Set squares and protractor are not allowed for part (a) of this question. 10. Diagram 7, shows a parallelogram KLMN.

Diagram 7 (a) Starting from the triangle KLM in the answer space, construct i) parallelogram KLMN ii) perpendicular line NT such that point T lies on the line KM. (b) Based on the diagram constructed in (a), measure the length of NT.

Answer:

(b)

[ 5 mark ]

5

10

K L

N M

K L

M

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For

examiner’s use

11. Simplify each of the following expressions: (a) 5x – 3(x – 3) (b) (x – 2)2 – 2(x – 3)

Answer: (a) (b)

[ 3 marks ]

12. Factorise completely each of the following expressions: (a) 6mn – 8m2n (b) 3a2 – 48b2

Answer: (a) (b)

[ 3 marks ]

3

11

3

12

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For

examiner’s use

13. Express p3

2 – pq

q6

25 − as a single fractions in its simplest form.

Answer:

[ 3 marks ]

14. Given that 2

3 2m + 5 = n , express m in term of n.

Answer:

[ 3 marks ]

15. Solve each of the following equation: (a) 5n = 42 – 2n (b) 4(m – 3) – 6 = m

Answer: (a) (b)

[ 3 marks ]

3

13

3

14

3

15

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For

examiner’s use

16. Simplify (2x– 4) 2 × (x – 2) – 3 ÷ x5.

Answer:

[ 3 marks ]

17. Given that 23n – 1 = (22)(2n). Find the value of n. Answer:

[ 2 marks ]

18. Solve the inequality 5 – q < 6 – 3 q Answer:

[ 2 marks ]

3

16

2

17

2

18

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For

examiner’s use

19. Table 1 shows the number of members in basket ball club who attend the club meeting in five consecutive months.

Table 1

On the grid in the answer space, draw a bar chart to represent all the information in

Table 1.

Answer:

[ 4 marks ]

Month Number of students March 27 April 21 May 18 June 15 July 24

4

19

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For

examiner’s use

Use the graph paper provided to answer this question. 20. Table 2 shows the value of two variables, x and y, of a function. By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis draw

the graph of function.

x - 3 - 2 - 1 0 1 2 3 y - 25 - 6 1 2 3 10 29

Answer:

[ 4 marks ]

4

20

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-END-

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2009

MARKING SCHEME

MATHEMATICS PAPER 1 &PAPER 2

NOTE

This marking scheme serves as a guide only. Other method which are equivalent and Suitable may also be adapted and used in the awarding of marks.

THANK YOU

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MARKING SCHEME

MATHEMATICS PAPER 1

FORECAST PAPER 2009

1 B 21 B2 B 22 A3 C 23 C4 A 24 A5 D 25 B6 D 26 C7 D 27 D8 C 28 C9 B 29 A10 C 30 C11 A 31 A12 C 32 A13 A 33 B14 D 34 B15 B 35 D16 C 36 C17 B 37 A18 C 38 B19 B 39 D20 C 40 D

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MARKING SCHEME

MATHEMATICS PAPER 2

No Soalan Skima pemarkahan markah

1 108 - 3 ( 20 ) 1 markah48 1 markah

2

22.415 + 2.25 1 markah4.6654.7 1 markah

2

3 a. -271 1 markah

b. (-1.2 ) ² 1 markah

1.44 1 markah

3

4

30 - 10 1 markah20 1 markah

Nota : 30 dilihat ( dari sumber yang betul ) P 1

2

5

Cos x º = 2520 1 markah

x º = 54 1 markah

Nota : 25 dilihat ( dari sumber yang betul ) P 1

2

a. Tandaan P yang betul pada rajah 1 markah

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6

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b. ( 0 , 4 ) 1 markah

a. Penjelmaan M ialah translasi 1 markah

93

1 markah

b. i. 90 º ikut arah jam 1 markahii. ( 4 ,4 ) 1 markah

2

4

815 unit betul (pada sisi yang sepadan ) 1 markah 12 unit betul ( pada sisi yangsepadan ) 1 markah6 unit betul ( pada sisi yang sepadan ) 1 markah

3

9 Locus RLocus Q I H

pp persilanganD G

E F

a. Garis lurus EH 2 markah

NOTA: Jika EH di label pada rajah 1 markah (lukisan garis lurus EH )

b. i. locus Q 1 markahii. locus R 1 markah

c. Satu titik persilangan 1 markah

5

10

a. Pembinaan lengkuk untuk sisi KN= ML 1 markahPembinaan lengkuk untuk sisi MN = Kl 1 markahPembinaan lengkuk untuk garis serenjang dari N

1 markah

persilangan

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Garis serenjang dilukis penuh 1 markah

b. ± 3.8 cm 1 markah

a. 2x + 9 1 markah

b. x ² - 4x + 4 ATAU2x - 6 1 markah x ²- 6x + 10 1 markah

5

3

122mn ( 3 – 4m ) 1 markah

3 ( a ² - 16 b ² ) 1 markah3 ( a - 4 b ) ( a + 4b ) 1 markah

3

13pqq

64 -

pqq

625 2 1 markah

pqqq

6254 25 1 markah

pqq6

56 5 1 markah

3

14

3 m ² = 2n – 5 1 markah

m ² = 3

52 5n 1 markah

m = 3

52 5n 1 markah

3

a. n= 6 1 markah

b. 3m = 18 1 markah 3

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15 m = 6 1 markah

16 4x 88 ATAU1 markah

x 6

4 x 568 568 1 markah4 x 77 1 markah

3

17

2n = 3 1 markah

n = 23 1 markah 2

18

2 q ≤ 1 1 markah

q ≤ 21 1 markah

2

19

Menggunakan skala yang sesuai 1 markah Semua lima palang ditanda betul 2 markahGarisan palang yang dilukis lurus 1 markah

Nota : Jika 3 atau 4 bar saja yang betul P 1

4

20

Kedua-dua paksi-x dan paksi-y dilukis betul dengan skala yang seragam dan betul 1 markah

Kesemua tujuh titik ditanda betul 2 markah

Lengkung licin melalui semua (7 ) titik 1 markah

Nota : Jika 5 atau 6 titik ditanda betul 1 markah

Untuk skala lain , tolak 1 makah daripada Keseluruhan markah yang didapati

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FORECAST PAPER 2009 -END-

kertas soalan ramalan 2009 pmr math

Documents

sector angle

jawab semua

distance travelled

circle 360o

straight line

bar chart

2 b2shape

y2