Soalan Ramalan Mathematics PMR 2009 Paper 2

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SOALAN RAMALAN PMR 2009MATHEMATICS Kertas 2 Oktober 13 4

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JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU1. 2. 3. 4. 5. Tuliskan nama dan tingkatan anda pada ruang yang disediakan Kertas soalan ini adalah dalam bahasa Inggeris Kertas soalan ini mengandungi 20 soalan. Jawab semua soalan. Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan. Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyata. Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan. Anda tidak boleh menggunakan kalkulator. Untuk Kegunaan Pemeriksa Kod Pemeriksa: Soalan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Markah Penuh 2 3 2 3 3 3 3 2 3 2 5 5 3 2 3 3 5 2 2 4 Markah Diperoleh

6. 7. 8. 9.

Nama : .. Tingkatan : 3 ...

Jumlah

Kertas soalan ini mengandungi 16 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 2 3 4

a m a n = a m+ na m a n = a mn(a m ) n = a mn Distance =( x2 x1 ) 2 + ( y2 y1 ) 2

5

y + y2 x + x2 Midpoint ( x, y ) = 1 , 1 2 2distance travelled time taken

6

Average speed =

7

Mean =

sum of data number of data

8

Pythagoras Theorem, c 2 = a 2 + b 2

SHAPE AND SPACE

1 2 3 4

Area of rectangle = length width Area of triangle = 1 base height 2

Area of parallelogram = base height Area of trapezium = 1 sum of parallel sides height 2

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5 6 7 8 9 10 11 12

Circumference of circle = d = 2 r Area of circle = r 2 Curved surface area of cylinder = 2 rh Surface area of sphere = 4 r 2 Volume of right prism = cross sectional area length Volume of cuboids = length width height Volume of cylinder = r 2 h Volume of cone = 1 2 r h 3 4 3 r 3

13

Volume of sphere =

14

Volume of right pyramid =

1 base area height 3

15 16

Sum of interior angles of a polygon = (n 2) 180o arc length angle subtended at centre = circumference of circle 360o area of sector angle subtended at centre = area of circle 360o Scale factor, k = PA PA

17

18 19

Area of image = k 2 area of object

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Answer all questions.1

Calculate the value of

3 5.48 (6) and express the answer as a decimal. 4 [2 marks]

Answer:

12

2

(a) (b)

Find the value of

3

0.343 .

Calculate the value of (3)3 + 169

(

)

2

[3 marks] Answer:

23

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5

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3

Express

d d 6 as a single fraction in its simplest form. 4e 12de [3 marks]

Answer :

33

4

In Diagram 4, in the answer space, G is drawn on a grid of equal squares. 2 On the square grids, draw the image of G under a translation 3 [2 marks] Answer :

G

4

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5

(a)(b) Answer: (a)

Expand

2 7 21e f . 7 2

Simplify 4( p 1) 2 + 2 p(1 2 p) . [3 marks]

(b)

53

6

Factorise completely (a) (b) Answer: (a) 7gh 14g2h2 3p2 27 [3 marks]

(b)63

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SULIT 7

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Solve each of the following equations: (a) 3( a + 3 ) = a 5 (b) Answer: (a) (b) d +6= 5d + 3 2 [3 marks]

73

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

8

Diagram 82

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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 10

8

6 P 4 Q 2

0 State

2

4

6 Diagram 9

8

10

x

(a) Angle and direction of rotation. (b) Coordinates of the centre of rotation. [3 marks] Answer: (a)9

(b)3

10 Given that

3m 2 = 7 . Express m in terms of k. m+k [2 marks]

Answer :102

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SULIT 11

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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) (b) 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. 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. 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]

(c)

Answer: (a)

(b) and (c)

K

P

L

S

Q

N

R Diagram 11

M115

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12

Set squares and protractors are not allowed for this question Diagram 12, shows a triangle UVW. L

5 cm 60 J 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. Hence, construct a perpendicular line to the straight line JK which passes through the point L. K

(ii) (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)

125

J

K

(b)

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SULIT 13

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Diagram13, shows a right prism.

5 unit

7 unit 4 unit Diagram 13 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:

133

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14

Given that 43h +1 = 16h . Find the value of h.

[2 marks]Answer:

1422 23 1 (3 2 6 ) 2

15

Find the value of

[3 marks]Answer:

153

16

List all the integers p that satisfy both the inequalities 3 27 4p and

2p > 2. 3 [3 marks]

Answer:

163

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SULIT 17

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

July 100 35 150 April x May

June

Diagram 17 Given the number of books sold in April is 210. (a) (b) ( c) Find the value of x. Calculate the number of books sold in June. Calculate the ratio of the books sold in May to July. [5 marks]Answer:

(a)

(b)

( c)175

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18

Diagram 18 shows a polygon. 30 m

18 m

24 m

36 m 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:

182

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SULIT 19

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

12 cm

xQ

yR S

5 cm

Diagram 19 (a) (b) Find the value of cos x. Given that tan y = 1, calculate the length in cm, of RS. [2 marks]

192

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 y

3 44

2 23

1 14

0 11

1 -8

2 1

2.5 9.5

3 22

4 61

Table 20 (a) (b) ( c) By using the scale of 2 cm to 10 unit on the y-axis, complete and label the y-axis. Based on Table 20, plot the points on the graph paper. Hence, draw the graph of the function.

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16 Graph for Question 20 (a), (b) and (c) y

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3

2

1

0

1

2

x 3 4

204

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