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SOALAN RAMALAN PMR 2009 50/2 MATHEMATICS Kertas 2 Oktober

1 43 jam Satu jam empat puluh lima minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Kertas soalan ini mengandungi 16 halaman bercetak

1. Tuliskan nama dan tingkatan anda pada ruang yang disediakan

Untuk Kegunaan Pemeriksa

Kod Pemeriksa:

Soalan Markah Penuh

Markah Diperoleh

1 2 2

2. Kertas soalan ini adalah dalam bahasa Inggeris

3. Kertas soalan ini mengandungi 20 soalan. 4. Jawab semua soalan. 5. Jawapan hendaklah ditulis pada ruang yang

disediakan dalam kertas soalan. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan.

3 3 2 4 3

6. Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah.

5 3 6 3 7 3 7. Rajah yang mengiringi soalan tidak

dilukiskan mengikut skala kecuali dinyata. 8 2 8. Markah yang diperuntukkan bagi setiap

soalan ditunjukkan dalam kurungan. 9 3 10 2

9. Anda tidak boleh menggunakan kalkulator. 11 5 12 5

13 3 14 2 Nama : ……………………………………………….. 15 3

Tingkatan : 3 ………...……………………………… 16 3 17 5 18 2 19 2 20 4

Jumlah

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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 ma a a +× = n

n 2 m n ma 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⎟⎠⎞+

221 yy

6 Average speed = distance travelledtime taken

7 sum of dataMean = number of data

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

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 cuboids = length × width × height 11 Volume of cylinder = 2r hπ

12 Volume of cone = 213

r hπ

13 Volume of sphere = 343

r π

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 Answer all questions.

1 Calculate the value of 3 5.48 ( 6)4

− × − − and express the answer as a decimal.

[2 marks]

Answer:

1

2

2 (a) Find the value of 3 0.343− .

(b) Calculate the value of ( )23( 3) 169− +

[3 marks] Answer:

2

3

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For Examiner’s

Use 3 Express 2 62 e4 1

d de d

−− as a single fraction in its simplest form.

[3 marks] Answer :

3

3

4 In Diagram 4, in the answer space, G is drawn on a grid of equal squares.

On the square grids, draw the image of G under a translation ⎟⎟⎠

⎞⎜⎜⎝

⎛− 32

[2 marks]

Answer :

2

4

G

Diagram 4

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For Examiner’s

Use

5 (a) Expand ⎟⎠⎞

⎜⎝⎛ − fe

2721

72 .

(b) Simplify (4 . )21(2)1 2 ppp −+−

[3 marks] Answer:

(a)

(b)

5

3

6 Factorise completely

(a) 7gh – 14g2h2

(b) 3p2 – 27 [3 marks]

Answer: (a)

(b) 6

3

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For Examiner’s

Use 7 Solve each of the following equations: (a) 3( a + 3 ) = a – 5

(b) 2

356 +=+

dd

[3 marks] Answer:

(a)

(b) 7

3

8 Diagram 8 in the answer space shows two triangles J and J’, drawn on a grid squares. J’ is the image of J’ under a reflection. On the diagram in the answer space, draw the axis of reflection.

[2 marks]

Answer :

J’

J

Diagram 8

8

2

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For Examiner’s

Use 9 Diagram 3 shows two trapeziums P and Q, which are drawn on a Cartesian plane. Q is the

image of P under a rotation.

y

Q

P

10

8

6

4

2

0 2 4 6 8 10

x

Diagram 9 State

(a) Angle and direction of rotation.

(b) Coordinates of the centre of rotation.

[3 marks] Answer:

(a)

9

(b) 3

10 Given that 723=

+−

kmm . Express m in terms of k.

[2 marks]

Answer : 10

2

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For Examiner’s

Use 11 Diagram 11, in the answer space shows a square KLMN drawn on a grid of equal squares with side of 1 unit.

X, Y and Z are three moving points in the diagram. (a) X moves such that it is equidistance from the straight lines KN and LM. By using the letters in the diagram, state the locus of X. (b) On the diagram, draw,

i) the locus of point Y, such that its distance from point M is always 7 units. ii) the locus of point Z, such that it is equidistant from the straight line KL

and LM. (c) Hence, mark all the possible positions of the intersection of the loci of the locus

of Y and the locus of Z with symbol ⊗. [5 marks]

Answer: (a)

(b) and (c)

L K P

S Q

M N R 11

5

Diagram 11

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For Examiner’s

Use 12 Set squares and protractors are not allowed for this question

Diagram 12, shows a triangle UVW.

L

5 cm

J

60º

K

Diagram 12

(a) (i) Using only a ruler and a pair of compasses, construct triangle JKL using the

measurements given, beginning from the straight line JK provided in the answer space.

(ii) Hence, construct a perpendicular line to the straight line JK which passes

through the point L. (b) Based on the diagram constructed in (a) (ii), measure the perpendicular distance

between point L and the straight line JK.

[5 marks] Answer: (a) 12

5

J K

(b)

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For Examiner’s

Use 13 Diagram13, shows a right prism.

Diagram 13 4 unit

7 unit

5 unit

Draw a full scale the net of the right prism on the grid in the answer space. The grid has

equal squares with sides of 1 unit.

[3 marks]

Answer:

13

3

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For Examiner’s

Use 14 Given that h . Find the value of h. h 164 13 =+

[2 marks]

Answer:

14

2

15 Find the value of 261

32

)23(2 ××

[3 marks]

Answer:

15

3

16 List all the integers p that satisfy both the inequalities 3 ≤ 27 – 4p and 23

2>

p .

[3 marks]

Answer:

16

3

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For Examiner’s

Use 17 Diagram 17 is a pie chart which shows the number of books sold by a book shop in four months in a particular year.

150°35°

100°

x°

April

June

May

July

Diagram 17 Given the number of books sold in April is 210. (a) Find the value of x. (b) Calculate the number of books sold in June. (c) Calculate the ratio of the books sold in May to July.

[5 marks]

Answer:

(a)

(b)

(c)

17

5

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For Examiner’s

Use 18 Diagram 18 shows a polygon.

Diagram 18

On the grid in the answer space, redraw the polygon using the scale 1 : 600. The grid has equal squares with side of 1 cm.

[2 marks]

Answer:

36 m

30 m

18 m

18

2

24 m

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For Examiner’s

Use 19 Diagram 19 shows a right angled triangle PQR and QRS is straight line.

P

5 cm R

x° y°

Q

12 cm

S

Diagram 19

(a) Find the value of cos x°.

(b) Given that tan y° = 1, calculate the length in cm, of RS.

[2 marks]

2

19

20 Use the graph paper provided to answer this question. Table 20 shows the values of two variables, x and y of a function.

x – 3 –2 –1 0 1 2 2.5 3 4

y –44 –23 –14 –11 -8 1 9.5 22 61

Table 20

(a) By using the scale of 2 cm to 10 unit on the y-axis, complete and label the y-axis.

(b) Based on Table 20, plot the points on the graph paper.

(c) Hence, draw the graph of the function.

[4 marks]

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For Examiner’s

Use Graph for Question 20 (a), (b) and (c)

– 3 – 2 – 1 0

y

x 1 2 3 4

END OF QUESTION PAPER

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