PPT SBP 2007 - Mathematics Paper 2

8/4/2019 PPT SBP 2007 - Mathematics Paper 2

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Matematik

Kertas 2

Mei

2007

13

4jam

SULIT 1 50/2

SEKTOR SEKOLAH BERASRAMA PENUHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERTENGAHAN TAHUN SELARAS SBP

TINGKATAN 3

2007

Kertas soalan ini mengandungi 16 halaman bercetak

[Lihat sebelah

50/2 2007 Hak Cipta Sektor SBP SULIT

MATEMATIK

Kertas 2

Satu jam empat puluh lima minit

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1. Tuliskan nama dan tingkatan anda padaruang yang disediakan

2. Kertas soalan ini adalah dalam bahasa

Inggeris

3. Kertas soalan ini mengandungi 20soalan.

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 kecualidinyata.

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 2

5 2

6 3

7 2

8 2

9 3

10 6

11 3

12 3

13 3

14 5

15 4

16 3

17 2

18 3

19 3

20 4

Jumlah

Nama : ..

Tingkatan : 3 ...


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

commonly used.

RELATIONS

1m n m n

a 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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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 cuboids = 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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ForExaminers

Use

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3 (a) Find the value of 364

27

(b) Calculate the value of 32 )2(163 +

[3 marks]

Answer:

(a)

(b)

4 Calculate the value of )5(38.42

1

[2 marks]

Answer:

5 In Diagram 1, in the answer space,Fis drawn on a grid of equal squares.

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3

3

2

4


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On the square grids, draw the image ofFunder a translation

2

3

[2 marks]

Answer:

6 Simplify 14223 4)6( pkpkpk .

[3 marks]

Answer:

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2

5

3

6

F

DIAGRAM 1


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7 Diagram 2 in the answer space shows two trianglesR and S, drawn on a grid squares.

Sis the image ofR under a reflection.

On the diagram in the answer space, draw the axis of reflection.

[2 marks]

8 Simplify )21(2)1(4 2 ppp + .

[2 marks]

Answer:

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2

8

2

7

DIAGRAM 2


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9 Diagram 3 shows two trapeziumsPand Q, which are drawn on a Cartesian plane. Q is the

image ofPunder a rotation.

State

a) Angle and direction of rotation.

b) Coordinates of the centre of rotation.

[3 marks]

Answer :

a)

b)

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4

9

y

DIAGRAM 3

0 2 4 6 8 10

2

4

6

8

10

x

P

Q


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

Diagram 4, shows a triangle UVW.

[6 marks]

a. (i) Using only a ruler and a pair of compasses, construct triangle UVWusing

the measurements given, beginning from the straight line UVprovided

in the answer space.

(ii) Hence, construct a perpendicular line to the straight line UVwhich passesthrough the point W.

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

between point Wand the straight line UV.

Answer:

a)

b)

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6

10

U V

W

6 cm

60

U V

DIAGRAM 4


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11 Diagram 5, shows a right prism.

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:

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3 unit

4 unit

6 unit

3

11

DIAGRAM 5


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12. Solve each of the following equations:

(a) 63=

n

(b) 237)12(5 +=+ ww

[3 marks]

Answer:

(a)

(b)

13 Find the value of 261

3

2

)23(2

[3 marks]

Answer:

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3

12

3

13


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14 Diagram 6 in the answer space shows a square KLMN drawn on a grid of equal

squares with side of 1 unit.

X, YandZare three moving points in the diagram.

a. Xmoves such that it is equidistance from the straight linesKL and MN.

By using the letters in the diagram, state the locus ofX.

b. On the diagram, draw,

. the locus of point Y, such that its distance from pointR is always 4 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 ofY

and the locus ofZwith symbol .[5 marks]

Answer:a)

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5

14

L

N M

Q

R

K P

S5

14

DIAGRAM 6


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15 Diagram 7 is a pie chart that shows the types of fruit trees planted in Pak Dins orchard.

Given the number of rambutan trees are 72, calculate the number of langsat and durian

trees.

[4 marks]

Answer:

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6

15

110

Rambutan

Langsat

Durian

DIAGRAM 7


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16 Given that hh 164 13 =+ . Find the value ofh.

[3 marks]

Answer:

17 75% of the 120 students of a school failed to achieve straight As in SPM result.

Calculate the number of students who achieved straight As.

[2 marks]

Answer:

18 Expresscd

c

d

c

8

32

4

52 +

as a single fraction in its simplest form.

[3 marks]

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3

16

2

17


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Answer:

19 Factorise completely:

(a)4

1

2

1+e

(b) 44 2 r

[3 marks]

Answer:

(a)

(b)

20 Table 1 shows the number of blood donors in a general hospital in five days.

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3

19

3

18


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Day Number Of blood donors

Monday 3

Tuesday 6

Wednesday 10

Thursday 7

Friday 7

On Diagram 8 in the answer space provided, draw a line graph to represent all the

information in Table 1.

[4 marks]

Answer:

END OF QUESTION PAPER

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TABLE 1

4

20

Monday Tuesday Wednesday Thursday Friday

Days

Numberofb

loodd

onors

Diagram 8

PPT SBP 2007 - Mathematics Paper 2

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