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Matematik

Kertas 2

Ogos

2010

13

4jam

SULIT 1 50/2

PEPERIKSAAN PERCUBAAN PMR 2010

Kertas soalan ini mengandungi 17 halaman bercetak

[Lihat sebelah

50/2 SULIT

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 ruangyang 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 menggunakankalkulator.

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 ...

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SULIT 2 50/2

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 22 1 2 1( ) ( )x x y y +

5 Midpoint

( , )x y = +

2

21 xx,

+

2

21 yy

6 Average speed =distance travelled

time taken

7sum of data

Mean = number of data

8 Pythagoras Theorem2 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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SULIT 3 50/2

5 Circumference of circle = 2d r =

6 Area of circle = 2r

7 Curved surface area of cylinder = 2 rh

8 Surface area of sphere = 24 r

9 Volume of right prism = cross sectional area length

10 Volume of cuboid = length width height

11 Volume of cylinder = 2r h

12 Volume of cone =21

3r h

13 Volume of sphere =34

3r

14 Volume of right pyramid =1

3base area height

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

16arc length angle subtended at centre

circumference of circle 360=

o

17area of sector angle subtended at centre

area of circle 360=

o

18 Scale factor, k=PA

PA

19 Area of image =2 area of objectk

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SULIT 4 50/2

Answerall questions.

1 Calculate the value of3 3 3

116 8 4

and express the answer as a fraction in its lowest term.

[2 marks]

Answer:

2 Calculate the value of3

5.48 ( 6)4 and express the answer as a decimal.

[2 marks]

Answer:

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2

2

2

1

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SULIT 5 50/2

3 (a) Find the value of 3 0.343

(b) Calculate the value of( )2

3( 3) 169 +

[3 marks]Answer:

(a)

(b)

4 In Diagram 1,JKL andLMNare right angled triangles.

Given that3

cos5

x = .

Find (a) the length ofLM

(b) tany

[3 marks]

Answer:

(a)

(b)

[Lihat sebelah

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3

3

3

4

K

J

L M

N

25 cm

15 cmx

y

10 cm

DIAGRAM 1

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SULIT 6 50/2

5 InDiagram 2, triangleP is the image of the trianglePunder 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 ofJ 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

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SULIT 7 50/2

(b) On the diagram in the answer space, draw the image of quadrilateralABCD under a

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

[3 marks]

Answer :

(a)

(b)

7 Express

2 6

4 12

d d

e de

as a single fraction in its simplest form.

[3 marks]

[Lihat sebelah

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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

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SULIT 8 50/2

Answer :

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 Simplify2(2 3) 3(3 4 )a a +

[2 marks]

Answer :

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3

8

3

7

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SULIT 10 50/2

12 Simplify

1 3

4 22 2(4 )qp q p

.

[3 marks]

Answer :

13 Given that2

2

182

F m

T= . Express Tin terms ofF and m.

[3 marks]

Answer:

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3

12

2

11

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SULIT 11 50/2

14 Solve each of the following equations.

(a) 7 5 2u u+ =

(b)3

(4 8) 72

w w + =

[3 marks]

Answer:

(a)

(b)

15 Diagram 4 in the answer space shows a rhombus. S,Xand Yare three moving points in the

diagram.

(a) S is the point which moves such that its distance from point A and point Care the

same. By using the letters in the diagram, state the locus ofS.

(b) On the diagram, draw

(i) the locus for the pointXthat is constantly 2 cm from the lineAC,

[Lihat sebelah

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3

13

3

14

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SULIT 12 50/2

(ii) the locus for the point Ythat is constantly 4 cm from the pointA

(c) Hence, state the number of intersection points of the locus ofXand the locus ofY.

[5 marks]

Answer:

(a)

(b)

`

(c)

16 Factorise completely :

(a) 24 8m m n

(b)2(3 ) 4 2y y y +

[3 marks]

Answer:

(a)

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5

15

D

C

B

A

DIAGRAM 4

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SULIT 13 50/2

(b)

17 Diagram 5 in the answer space shows polygonABCDEFG and straight linePQ 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.

[Lihat sebelah

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3

16

2

17

P

R

Q

DIAGRAM 6

S

60

DIAGRAM 5

BA

C

D

E

F

G

P

Q

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SULIT 14 50/2

(a) Using only a ruler and a pair of compasses, construct quadrilateralPQRS as shown

in Diagram 6 using the straight linesPSand SR provided in the answer space.

(b) Based on the diagram constructed in (a), construct QT, angle bisector of the

PQR such that point Tlies on the linePS. 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

Tuesday

Wednesday

Thursday

Friday

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5

18

RS

P

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SULIT 15 50/2

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 andy of a function.

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 thex-axis and 2 cm to 2 unit on they-axis, draw

the graph of the function on the graph paper provided in the answer space.

[Lihat sebelah

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3

19

TABLE 1

3

19

Day

Numberofcake

MON TUE WED THU FRI

120

100

80

60

40

20

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SULIT 16 50/2

[4 marks]

Answer:

(Refer to graph on page 17)

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4

20

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SULIT 17 50/2

KEMENTERIAN PELAJARAN MALAYSIA

[Lihat sebelah

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SULIT 18 50/2

MARKING SCHEME

PEPERIKSAAN PERCUBAAN PMR

2009

MATEMATIK

KERTAS 1 (50/1) & 2 (50/2)

Marking Scheme of Paper 2Questions Marking Scheme Marks

1 3 5

16 8

3

10

1

1 2

2 4.11 6 +1.89

1

1 2

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SULIT 19 50/2

3(a)

70.7 or

10

(b) ( )2

27 13 +196

1

1

1 3

4 a) KL = 8, LM = 17

b) tany =8

15

1, 1

1 3

5Enlargement , scale factor

1,

3at (1, 10)

1, 1, 1 3

6

(a)4

5

(b)

ABCDdrawn correctly

Note :

PointsABCDare marked without line, 1 mark

1

2 3

Questions Marking Scheme Marks

7 2

2 2

2

3 6

3 4 12

3 6

12

3

6

d d d

d e de

d d

de

d

de

+

+

1

1

1 3

[Lihat sebelah

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10

8

6

4

2

y

0 2 4 6 8 10x

CB

A

D

C

B

A

D

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SULIT 20 50/2

8

(a)

Score Tally Frequency

0

11

1

13

2 103 8

Notes:

Marked wrongly 1 or 2 tally/frequency 1 M

Marked wrongly 3tally/frequency 0 M

(b) 1

2

1 3

9 2

2

4 12 9 9 12

4 24 @ 4 ( 6)

a a a

a a a a

+

1

1 2

10 2

2

1, 0, 1, 2

m

m

>

1

1

1 3

11 2 34 4

3

2

n

n

=

=

1

1 2

12 1 1 1 34 22 2 2 2

1 3

2 22 2

2

4 ( )

2

2

q p q p

q p

q

1

1

1

3

Questions Marking Scheme Marks

13 2 2

2 2 2

18 2

9 @ 9

3

F m T

T F m T F m

T F m

=

= =

=

1

1

1 3

14(a) 1(b) 6 12 7

1

uw w

w

= =

=

11

1 5

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SULIT 21 50/2

15 (a) Straight lineBD

Note : Line BD drawn but not stated is not accepted.

(b) (i) Locus X drawn correctly

(ii) Locus Y drawn correctly

(c) 2

1

2

1

1

5

16

2 2

(a) 4 (1 2 )

(b) 3 4 2

( 4)( 4)

m mn

y y y

y y

+

+

1

1

1 3

17

Complete diagram

Note : (1) 1 or 2 sides drawn wrongly, give 1 mark

(2) Accept image drawn on the left ofPQ

2 2

Questions Marking Scheme Marks

18 (a)

[Lihat sebelah

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D

C

B

A

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SULIT 22 50/2

Construct 60Construct 90atPComplete the quadrilateralPQRS

(b) Construct angle bisectorQT

QT= 7.8 0.1 cm

1

1

1

1

1 5

19

3 3

20 Use correct scale for x-axis andy-axis

Plot all points correctly

Smooth graph

Note :

(i) 1 or 2 points plotted wrongly, give 1 mark

(ii) No mark for smooth graph if graph does not pass

through plotted points

1

2

1 4

Number

ofcake

MON TUE WED THU FRI

120

100

80

60

40

20

Complete line graph

Note : Plot all points

correctly without line,give 2 Marks

Graph for Question 20

4 3 2 1 0 1 2 3

7

6

5

4

3

2

1

1

2

3

4

5

6

x

x

x

x

x

xx

x

y