Soalan Ramalan Mathematics Pmr 2009 Paper 2

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SOALAN RAMALAN PMR 2009

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MATHEMATICS Kertas 2 Oktober 1

3 4

jam

Satu jam empat puluh lima minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. 2. 3. 4. 5.

6. 7. 8. 9.

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.

Nama : ……………………………………………….. Tingkatan : 3 ………...………………………………

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

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

a m × a n = a m+ 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 cuboids = 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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For Examiner’s Use

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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:

1 2

2

3

−0.343 .

(a)

Find the value of

(b)

Calculate the value of (−3)3 + 169

(

)

2

[3 marks] Answer:

2 3

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5

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d d −6 − as a single fraction in its simplest form. 4e 12de 2

3

Express

[3 marks] Answer :

3 3

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 2

Diagram 4

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For Examiner’s Use

5

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2⎛ 7 ⎞ ⎜ 21e − f ⎟ . 7⎝ 2 ⎠

(a)

Expand

(b)

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

Answer: (a)

(b)

5 3

Factorise completely

6

(a)

7gh – 14g2h2

(b)

3p2 – 27 [3 marks]

Answer: (a)

(b) 6 3

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7

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

7

(b)

d +6=

5d + 3 2 [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

8

Diagram 8 2

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8

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

9

image of P under a rotation. y 10

8

6 P 4 Q 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

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

Answer : 10 2

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9

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11

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

For Examiner’s Use

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)

K

P

S

N

L

Q

R

M 11

Diagram 11 5

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12

10

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

5 cm 60º K

J Diagram 12 (a)

(b)

(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.

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

J 5

K

(b)

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11

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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:

13 3

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12

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

14

[2 marks] Answer:

14 2

Find the value of

15

2 23

1 × (3 × 2 6 ) 2

[3 marks] Answer:

15 3

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

16

2p > 2. 3 [3 marks]

Answer:

16 3

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13

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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.

For Examiner’s Use

July 100° 35° 150°

June

x°

April

May

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) 17 5

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14

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Diagram 18 shows a polygon.

18

30 m

24 m

18 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:

18 2

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

19

P

12 cm

x° Q

y° R

5 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]

19 2

Use the graph paper provided to answer this question.

20

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

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

–3

–2

–1

0

1

2

x 3

4

20 4

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