SULIT ANGKA GILIRAN

NO. KAD PENGENALAN

PENILAIAN MENENGAH RENDAH 2009 PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 3

mMATHEMATICS 50/2 mKertas 2

Jun

1 jam Satu jam empat puluh lima minit mm

JANGAN BUKA KERTAS SOALAN SEHINGGA DIBERITAHU

1. This question paper consists of 20 questions.

2. Answer all questions.

3. Answers must be written clearly in the answer space provided.

4. Show your working. It may help you to get marks.

5. If you wish to change your answer, neatly cross out the answer. Then write down the new answer.

6. The diagrams in the questions provided are not drawn to scale unless stated.

7. The marks allocated for each question or parts of a question are shown in brackets.

8. A list of formulae is provided on pages 2 and 3.

9. Use of non-programmable scientific calculator is not allowed for this paper.

________________________________________________________________________Kertas soalan ini mengandungi 16 halaman bercetak

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MATHEMATICS AND SCIENCE TUTORIAL

M S T – –

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Examiner’s code

For Examiner’s Use

Question FullMarks

MarksObtained

60

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MATHEMATICAL FORMULAE

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

RELATIONS

1

2

3

4 Distance =

5 Midpoint

(x, y) =

6 Average speed =

7 Mean =

8 Pythagoras Theorem

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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 circle = πd = 2 πr

6 Area of circle = πr2

7 Curve surface area of cylinder = 2 πrh

8 Surface area of sphere = 4 πr2

9 Volume of right prism = cross sectional area × length

10 Volume of cuboid = length × width × height

11 Volume of cylinder = πr2h

12 Volume of cone = πr2h

13 Volume of speher = πr3

14 Volume of right pyramid =

15 Sum of interior angles of a polygon =

16

17

18 Scale factor, k =

19 Area of image = k2 × area of object

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[60 marks]

Answer all questions.

1 Calculate the value of – 43 + (86 – 6 × 12). [2 marks] m Answer:

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

[2 marks]

Answer:

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2

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2

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3 (a) Find the value of 0.53.

(b) Calculate the value of

[3 marks]

Answer:

(a)

(b)

4 Solve each of the following linear equations:

(a) x – 3 = – 12

(b)

[3 marks]

Answer:

(a)

(b)

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5 Diagram 1 shows a pentagon PQRST and R’S’ a grid of equal squares. R’S’ is the image of RS under a rotation of 90º clockwise about point O.

On Diagram 1 in the answer space, complete the image of pentagon PQRST.[2 marks]

Answer:

Diagram 1

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2

6 Diagram 2 shows two polygons, Q and Q’, drawn on a grid of equal squares with sides of 1 unit.

Diagram 2

Q’ is the image of Q under transformation M.

Describe in full transformation M. [2 marks] mAnswer:

7 Factorise completely each of the following expressions:

(a) 24mn – 3m

(b) 4y2 – 4 [3 marks]

Answer:

(a)

(b)

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3

8 Simplify (3x – 1)2 – (7x + 4). [2 marks] mAnswer:

9 (a) Find the value of

(b) Simplify

[3 marks]

Answer:

(a)

(b)

10 Simplify [2 marks] m

Answer:

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Types of vehicles Number of students

Bicycle 150

Motocycle x

Car 200

Bus 300

Table 1

(a) Find the value of x.

(b) Diagram 3 in the answer space shows an incomplete pie chart.

Complete the pie chart to represent all the information in Table 1.[5 marks]

Answer:

(a)

(b)

Diagram 3

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11

5

12 Table 2 shows the results conducted by a computer company regarding the number of computers owned by 30 families.

Number of computers 0 1 2 3 4

Number of families 3 10 6 6 5

Table 2

(a) State the mode.

(b) Find the mean number of computers owned.[3 marks]

Answer:

(a)

(b)

13 Given that , calculate the value of x. [2 marks] m Answer:

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14 Diagram 4 consists of two triangles, PQR, RST and a square PQTU.

Diagram 4

Calculate the perimeter, in cm, of the shaded region. [4 marks] m

Answer:

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15 Diagram 5 in the answer space shows two squares PQTU and QRST. W, X and Y are three moving points in diagram.

(a) W is a moving point in the diagram such that it is always equidistant from straight line PU and RS.

By using letters in the diagram, state the locus of W.

(b) On Diagram 5, draw

(i) the locus of X such that it is equidistant from from the straight lines PQ and PU,

(ii) the locus of Y such that YT = QT.

(c) Hence, mark with the symbol the intersection of locus of X and locus of Y.[5 marks]

Answer:

(a)

(b) (i), (ii)

(c)

Diagram 5

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15

5

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

Diagram 6 shows triangle KLM.

Diagram 6

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

(b) Based on the diagram constructed in 16 (a), measure the distance, in cm, between point K and L.

[5 marks]

Answer:

(a)

K M

(b) KL = ……………. cm

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K

L

M

30º

2.5 cm

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17 Diagram 7 shows two triangles PQT and QRS.

Diagram 7

Find the value of x + y. [4 marks] mAnswer:

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18 Table 1 shows three activities participated by a group of 50 students.

Activities Number of students

Chess 24

Hockey y

Choir 18

Table 1

(a) Find the value of y.

(b) Hence, represent all the data from the table by drawing a bar chart in the answer space.

[4 marks]

Answer:

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18

4

19 Simplify [2 marks] mAnswer:

20 Find the value [2 marks] m

Answer:

END OF QUESTION PAPER

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