50/2MatematikKertas 2 Ogos2006

1 jam

SULIT 1 50/2

SEKTOR SEKOLAH BERASRAMA PENUH KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAAN PMR SELARAS SBP2006

Kertas soalan ini mengandungi 17 halaman bercetak

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MATEMATIK

Kertas 2

Satu jam empat puluh lima minit

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 hendaklah ditulis pada

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

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

7. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyata.

8. Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.

9. Anda tidak boleh menggunakan kalkulator.

Guru Pemeriksa

SoalanMarkah Penuh

Markah Diperoleh

1 2

2 2

3 3

4 3

5 3

6 3

7 3

8 3

9 2

10 3

11 2

12 3

13 3

14 3

15 5

16 3

17 2

18 5

19 3

20 4

Jumlah

Nama : ……………………………..

Tingkatan : 3 ………...……………

SULIT 2 50/2

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

RELATIONS

1

2

3

4 Distance =

5 Midpoint

= ,

6 Average speed =

7

8 Pythagoras Theorem

SHAPE AND SPACE

1 Area of rectangle = length width

2 Area of triangle =

3 Area of parallelogram =

4 Area of trapezium =

50/2 SULIT

SULIT 3 50/2

5 Circumference of circle =

6 Area of circle =

7 Curved surface area of cylinder =

8 Surface area of sphere =

9 Volume of right prism = cross sectional area length

10 Volume of cuboid = length width height

11 Volume of cylinder =

12 Volume of cone =

13 Volume of sphere =

14 Volume of right pyramid = base area height

15 Sum of interior angles of a polygon =

16

17

18 Scale factor, k =

19 Area of image =

[Lihat sebelah50/2 SULIT

ForExaminer’s

Use

SULIT 4 50/2

Answer all questions.

1 Calculate the value of and express the answer as a fraction in its lowest

term. [2 marks]

Answer:

2 Calculate the value of and express the answer as a decimal.

[2 marks]

Answer:

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2

2

2

1

ForExaminer’s

Use

SULIT 5 50/2

3 (a) Find the value of

(b) Calculate the value of

[3 marks]

Answer:

(a)

(b)

4 In Diagram 1, JKL and LMN are right angled triangles.

Given that .

Find (a) the length of LM (b)

[3 marks]

Answer :

(a)

(b)

[Lihat sebelah50/2 SULIT

3

3

3

4

K

J

L M

N

25 cm

15 cmx

y10 cm

DIAGRAM 1

ForExaminer’s

Use

SULIT 6 50/25 In Diagram 2, triangle P is the image of the triangle P under a transformation V.

Describe in full the transformation V.

[3 marks]Answer:

6 (a) Diagram 3 in the answer space shows J is the image of J under a certain

translation. State the translation.

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3

5

DIAGRAM 2

0 2 4 6 8 10 12

12

10

8

6

4

2

P

P

x

y

ForExaminer’s

Use

SULIT 7 50/2

(b) On the diagram in the answer space, draw the image of quadrilateral ABCD under

a 90 anticlockwise rotation about the point (4, 3).

[3 marks]

Answer :

(a)

(b)

7 Express as a single fraction in its simplest form.

[3 marks]

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3

6

J

J

DIAGRAM 3

0 2 4 6 8 10

10

8

6

4

2

x

y

C

B

A

D

ForExaminer’s

Use

SULIT 8 50/2Answer :

8 The data below shows part of the number of goals scored by the 32 teams in the first

rounds of the World Cup 2006.

1 2 0 3 0 2 1

2 1 2 1 1 0 2

0 3 1 2 3 3 3

2 0 0 1 0 0 0

2 0 1 3 1 1 1

3 0 2 1 2 3 1

(a) Using the above data, complete the tally chart in the answer space.

(b) State the mode.

[3 marks]Answer :

(a) Score Tally Frequency

0

1

2

3

(b)

9 Simplify

[2 marks]

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3

8

3

7

ForExaminer’s

Use

SULIT 9 50/2

Answer :

10 List all the integer values of m which satisfy both the inequalities and

.

[3 marks]

Answer:

11 Given . Calculate the value of n.

[2 marks]

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2

9

3

10

ForExaminer’s

Use

SULIT 10 50/2 Answer:

12 Simplify .

[3 marks]

Answer :

13 Given that . Express T in terms of F and m.

[3 marks]

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3

12

2

11

ForExaminer’s

Use

SULIT 11 50/2

Answer:

14 Solve each of the following equations.

(a)

(b)

[3 marks]

Answer:

(a)

(b)

15 Diagram 4 in the answer space shows a rhombus. S, X and Y are three moving points in

the diagram.

[Lihat sebelah50/2 SULIT

3

13

3

14

ForExaminer’s

Use

SULIT 12 50/2(a) S is the point which moves such that its distance from point A and point C are the

same. By using the letters in the diagram, state the locus of S.

(b) On the diagram, draw

(i) the locus for the point X that is constantly 2 cm from the line AC,

(ii) the locus for the point Y that is constantly 4 cm from the point A

(c) Hence, state the number of intersection points of the locus of X and the locus of Y.

[5 marks]

Answer:

(a)

(b)

`

(c)

16 Factorise completely :

(a)

(b)

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5

15

D

C

B

A

DIAGRAM 4

ForExaminer’s

Use

SULIT 13 50/2

[3 marks]

Answer:

(a)

(b)

17 Diagram 5 in the answer space shows polygon ABCDEFG and straight line PQ drawn

on a grid of equal squares.

Starting from the line PQ, draw polygon PQRSTUV which is congruent to polygon

ABCDEFG.

[2 marks]

Answer:

18 Set squares and protractors are not allowed for this question.

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3

16

2

17

P

R

Q

DIAGRAM 6

S

60

DIAGRAM 5

BA

C

D

EF

G

P

Q

ForExaminer’s

Use

SULIT 14 50/2

(a) Using only a ruler and a pair of compasses, construct quadrilateral PQRS as shown in Diagram 6 using the straight lines PS and SR provided in the answer space.

(b) Based on the diagram constructed in (a), construct QT, angle bisector of the PQR such that point T lies on the line PS. Measure the length QT.

[5 marks]

Answer:

19 The pictograph below shows the number of cakes sold by a school canteen within a week.

Monday

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5

18

RS

P

ForExaminer’s

Use

SULIT 15 50/2

Tuesday

Wednesday

Thursday

Friday

Key : represents 10 cakes

Draw a line graph in the answer space to represent all the information in the pictograph above.

[3 marks]

Answer:

20 Use the graph paper given to answer this problem.

Table 1 shows the value of two variables, x and y of a function.

[Lihat sebelah50/2 SULIT

3

19

3

19

Day

Num

ber

of c

ake

MON TUE WED THU FRI

120

100

80

60

40

20

ForExaminer’s

Use

SULIT 16 50/2

x 4 3 2 1 0 1 2

y 5 0 3 4 3 0 5

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 unit on the y-axis, draw the graph of the function on the graph paper provided in the answer space.

[4 marks]

Answer:

(Refer to graph on page 17)

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4

20

TABLE 1