Soalan P2 Mid Year

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NAMA: ____________________________

TING:3_________

Matematik Kertas 2 Mei 2009 1

3 jam 4

UNIT PENGURUSAN AKADEMIK PEJABAT PELAJARAN DAERAH JOHOR BAHRU PEPERIKSAAN PERTENGAHAN TAHUN SETARA 2009

MATEMATIK TINGKATAN 3 Kertas 2 Satu jam empat puluh lima minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam Bahasa Inggeris sahaja. 2. Calon dikehendaki membaca maklumat di halaman 2.

Soala n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Markah Markah Penuh Diperoleh

Jumlah

___________________________________________________________________________ Kertas soalan ini mengandungi 16 halaman bercetak

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INFORMATION FOR CANDIDATES 1. This question paper consists of 20 questions. 2. Answer all questions. 3. Write your answers in the spaces provided in the question paper. 4. Show your working. It may help you to get the marks. 5. If you wish to change any answer, neatly cancel the answer that had been done. Then write your new answer. 6. The diagrams in the questions provided are not drawn to scale unless stated. 7. Mark allocated for each questions are shown in brackets. 8. A list of formulae is provided on the pages 3 to 4. 9. All types of calculator are not allowed. 10. Hand it all your answer sheets at the end of the examination.

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MATHEMATICAL FORMULAE The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATION 1

a m × a n = a m+ n

2

a m ÷ a n = a m−n

3

(a )

4

Distance =

5

 x1 + x 2 y1 + y 2  ,  Midpoint, ( x, y ) =  2   2

m n

= a mn

( x1 − x 2 ) 2 + ( y1 − y 2 ) 2

6

Average speed = distance travelled time taken

7

Mean =

8

Pythagoras Theorem, c 2 = a 2 + b 2

sum of data number of data

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SHAPES AND SPACE 1

Area of rectangle = length × width

2

Area of triangle =

3

Area of parallelogram = base × height

4

Area of trapezium =

5

Circumference of cirle = πd = 2πr

6

Area of cirle = πr 2

7

Curved suurface area of cylinder = 2πrh

8

Surface area of sphere = 4πr 2

9

Volume of right prism = cross sectional area × length

10

Volume of cuboid = length × width × height

11

Volume of cylinder = πr 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 ) × 180°

1 × base × height 2

1 × sum of parallel sides × height 2

1 2 πr h 3 4 3 πr 3 1 × base area × height 3

16

arc length = angle subtended at centre circumference of cirle 360º

17

area of sector area of circle

18

Scale factor, k, =

19

Area of image = k 2 × area of object

=

angle subtended at centre 360º

PA ' PA

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Answer all questions 1.

Calculate the value of ( −5.6 ) × 0.4 + (− 3.15) and write the answer to the nearest whole number.

[ 2 marks]

Answer :

2.

1 ÷ 3 fraction in its lowest term. Calculate the value of 2

7 1  −  and express the answer as a  9 3

[2 marks]

Answer :

3.

[ 3 marks]

Calculate the values of: a) 0.0025 b) 23 × 3 −

1 64

Answer : a)

b)

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[ 3 marks]

Solve each of the following equations: a) x – 8 = -10 b) 3x + 1 = 5 2x - 4 Answer : a)

b)

5.

Diagram 1 shows a hexagon. Find the value of x o.

[3 marks]

60o 80o

125o

2x o

xo 95o Diagram 1

Answer :

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6.

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Diagram 2 in the answer space shows square grids with side 1 unit. On the diagram, draw and label K’L’M’N’, image of quadrilateral  − 3 KLMN, under a translation   . 5 

[ 2 marks]

Answer :

L

K

M N Diagram 2

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7.

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In diagram 3 below, a) .Draw the image of A under a reflection in x = -1, as A’ b). Determine the axis of reflection of object (A) and the image (B)

[ 2 marks]

Answer :

A

y5

B 5

x

0

Diagram 3 8.

[ 3 marks]

Factorise completely : a) 16pq – 4q² b) x² - 6(x + 1) – (8 – x) Answer : a)

b)

9.

[ 2 marks]

Simplify (3x – 1 )² - ( 8x + 3) Answer :

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Express

[ 3 marks]

1 _ n + 2 as a single fraction in its simplest form. 2n 6n²

Answer :

11. Set squares and protractors are not allowed for part (a) and (b) of this question.

[ 5 marks]

Diagram 4 shows a parallelogram PQRS. S A

R

5 cm

60o P

120o Q

8 cm Diagram 4

(a) Using only a ruler and a pair of compasses, construct Diagram 4 using the measurements given, beginning from the straight line PQ provided in the answer space.

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(b) Based on the diagram constructed in (a), construct a perpendicular line from S to PQ. (c) Measure the length of the line drawn in (b).

Answer : a), b)

Q

P

c)

12 .

Simplify k3 x k k-2

[ 2 marks]

Answer :

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1

13 .

1

If x 2 + 2y 2 = 24, and y = 81, find the value of x.

[ 3 marks]

Answer :

14 .

Given that 2(p – 4 ) = 5 , express p in terms of k

[ 3 marks]

K

Answer :

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Table 1 below shows the number of notebooks sold by three shops within one year. Shop

[ 4 marks]

Number of notebooks sold

x

P Q R

90 135

Table 1 It is given that the total number of notebooks by the three shops is 300 units. The information for shop Q is shown completely in the pictograph in the answer space. (a) Find the value of x. (b) Complete the pictograph provided in the answer space to represent all the information . Answer : (a) (b) Number of Notebook

P

Q

R

represent _______ notebook 50/2©2009 Pejabat Pelajaran Daerah Johor Bahru

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[3

Table 2 shows the scores collected by a group of students in class

marks]

3B. Score Frequency

1 3

2 8

3 15

4 7

5 8

Table 2 a) State the mode of the data b) Find the median of the data

Answer : a) b)

17 .

Diagram 5 shows a square PQRS. W, X and Y are three moving points in the diagram. (a) W is a point which moves such that it is equidistant from PQ and PS. By using the letters in the diagram, state the locus of W.

[ 5 marks]

(b) On the diagram, construct (i) the locus of point X such that XP=3 cm. (ii) the locus of point Y is such that QY=YR (c) Hence, mark with

the intersection of locus X and LocusY

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Answer : (a) (b) (c)

P

S

Q

R Diagram 5

For Examiner’s Use

18

Diagram 6 shows a solid cube. On the square grid provided below,

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draw the net of the cube.

2 units

Diagram 6 Answer :

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Given area of the circle is 154 cm2. Find its radius.

[3 marks]

Answer :

20 .

Table 3 shows the favourite food of form 3 Beta students from a school. Favourite Food Fried noodles Fried rice Chicken rice Curry noodles Table 3

[4 marks]

Number of students 12 10 8 14

Based on Table 3, construct a bar chart on the square grids given in the answer space. Answer :

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END OF THE QUESTIONS

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