DO NOT OPEN THIS QUESTION PAPER UNLESS YOU ARE TOLD TO DO SO

  SULIT 50/2

  NO. KAD PENGENALAN

  50/2 Mathematics Paper 2 July

  ANGKA GILIRAN

  2006

  3

  1 hours

4 Set

  1 JABATAN PELAJARAN PERAK

PENILAIAN MENENGAH RENDAH 2006

LEARNING TO SCORE

MATHEMATICS

  Paper 2 [SET 1] I hour 45 minutes

  Question Allocated Marks

DO NOT OPEN THIS QUESTION PAPER

  Marks Obtained

UNLESS YOU ARE TOLD TO DO SO

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  1. This question paper consists of 20

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  2 questions.

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  2

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  2 2. Answer all questions.

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  3. Write your answers clearly in the spaces

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  2 provided in the question paper.

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  4. Diagrams are not drawn to scale unless

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  3 stated.

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  3 5. The marks allocated are shown in brackets.

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  60 This question paper consists of 18 printed pages.

  Unit Kurikulum

   INFORMATION FOR CANDIDATES 1. This question paper consists of 20 questions.

  2. Answer all questions.

  3. Write your answers clearly in the spaces provided in the question paper.

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

  5. If you wish to change your answer, neatly cross out the answer that you have done.

  Then write down the new answer.

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

  7. The marks allocated for each question are shown in brackets.

  8. A list of formulae is provided on pages 3 and 4.

  9. A booklet of four-figure mathematical tables is provided.

  10. Calculators are not allowed.

  11. This question paper must be handed in at the end of the examination. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. _{m n m + n}

RELATIONS

1 a = a

   õ a _{m n} m - n

  2 a  a = a _{m n mn} 3 (a ) = a _{2 2}

  4 Distance = ( x  x )  ( y  y ) _{2 1 2 1}

  5 Midpoint

  x x y y     _{1 2 1 2}

  (x,y) = ,

   

  2

  2  

  distance travelled

  6 Average speed = time taken sum of data

  7 Mean = number of data

  8 Pythagoras Theorem _{2 2 2} c = a + b

SHAPE AND SPACE

  1 Area of rectangle = length x width

  1

  2 Area of triangle = x base x height

  2

  3 Area of parallelogram = base x height

  1

  4 Area of trapezium = x sum of parallel sides x height

  2

  5 Circumference of circle = d = 2 r ₂

  6 Area of circle = r

  7 Curved surface area of cylinder = 2rh

  Unit Kurikulum

  2

  8 Surface area of sphere = 4 r

  9 Volume of right prism = cross sectional area õ length

  10 Volume of cuboid = length x width x height ₂

  11 Volume of cylinder =  r h

  1 ₂

  12 Volume of cone =  r h

  3

  4 ₃

   r

  13 Volume of sphere =

  3

  1

  14 Volume of right pyramid = x base area x height

  3

  15 Sum of interior angles of a polygon = (n – 2) x 180 16 arc length = angle subtended at centre circumference of circle 360 17 area of sector = angle subtended at centre area of circle 360

  18 Scale factor, k = PA’

   PA ₂

  19 Area of image = k x area of object

  Unit Kurikulum

  Answer all questions.

  1

  3  

  3

  2

1 Calculate the value for   and express the answer as a fraction in its

   

  3

  4  

  lowest term.

  [ 2 marks] Answer:

  1

  2

  1

  2 Calculate the value of  1  ( . 5  . 1 ) and express the answer as

  2

  a decimal. 2 marks

   Answer :

  2

  2 Unit Kurikulum

  3 3 (a) Find the value of  .

  3 . _{3 2}  

  (b) Calculate the value of 125

  

1

  3 marks Answer: (a) (b)

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  3 5 4 In Diagram 1, ABCD is a square. Given that kos x .

  °=

  13 E

  A B

  x

  °

  y

  ° D C DIAGRAM 1

  Find the value of sin y . 2 marks

   Answer :

  4

2 Unit Kurikulum

5 Diagram 2 is drawn on a Cartesan plan. On the diagram, draw and label the image triangle KLM under a rotation about R through 90° clockwise.

   Answer :

  2 marks

  R

  5

  2 DIAGRAM 2

   6. In Diagram 3, PQRS is a rhombus. Draw its image if it is enlarged with a scale factor of 3 with centre O. 2 marks

   Answer: O

  6 DIAGRAM 3

  2 Unit Kurikulum

7 Diagram 4 shows a cuboid.

  10 cm 3 cm 5 cm

  DIAGRAM 4 Draw on the grid in the answer space the scale net of the cuboid if the shaded region is not included. The grid has equal squares with sides of 1 unit.

  3 marks

   Answer :

  7

3 Unit Kurikulum

  Unit Kurikulum 8 Table 1 shows the frequency distribution of the heights of students in Form 2A1. Height Frequency

  (a) (b)

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  3

  8

  Answer :

  2 marks

  ) ( q p q p   

  9 Simplify ^{2 2 2}

  Answer :

  140 – 144

  3 marks

  40 TABLE 1 Find (a) the value of x . (b) the percentage of pupils who are less than 150 cm tall.

  5 Total

  12 160 – 164

  155 – 159

  x

  5 145 – 149 11 150 – 154

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 

10 (a) Solve the inequality  x

  

3

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  (b) List all the integer value of x which satisfy both the inequalities

   3 m 2 m  1 and 9  

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  2

  4 marks Answer : (a) (b)

  10

  4 ₄

  1   _n 3 n .

11 Given that  , calculate the value of

   

  3  

  . [2 marks]

  Answer:

  11

2 Unit Kurikulum

12 Simplify

  Unit Kurikulum

  [3 marks]

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  3

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  Answer:

  5   , express p in terms of s .

  ^{2 2 2 3 2 1 4} ) ) 3 ( 81 ( nt t t n

  2

  1 ) 1 (

  s p

   Answer:

  [3 marks]

    .

13 Given that

14 Solve each of the following equations:

  (a)

  m   5  2 m

  3

  3 2 ( 6 )

  (b) h    h  [3 marks]

   Answer:

  (a) (b)

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3 Unit Kurikulum

  Unit Kurikulum

  15 Diagram 5 in the answer space shows a square PQRS. M and N are two moving points in the diagram.

  By constructing suitable loci, draw points M and N within the square that are 5 cm from R and equidistant from P and R. Hence, measure the distance, in cm, between the point M and the point N.

  [5 marks]

   Answer:

  DIAGRAM 5

  xy y x

   

  1

  1 as a single fraction in its simplest term.

  S R Q P

  5

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16 Express

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17 Factorize completely the following expressions.

  ₃ m  m

  (a)

   2  

  (b)

  2 rs rt s t [3 marks] Answer:

  (a) (b)

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3 Unit Kurikulum

  18 Set squares and protectors are not allowed to be used in section (a) of this question.

  Diagram 6 in the answer space shows a straight line TU. (a) Using only a ruler and a pair of compasses, construct

  (i) STU = 60, (ii) a triangle STU such that STU = 60 and TU = 5cm,

  (iii) hence, construct the perpendicular line to the straight line ST which passes through the point U. (b) Based on the diagram constructed in (a), measure the perpendicular distance between point U and the straight line ST.

  [6 marks]

  Answer: (a) (i),(ii)

  S T Diagram 6

  (b) (i) (ii)

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  6 Unit Kurikulum

  19 Table 2 shows the number of visitors to the Taiping Zoo in a week.

  On the circle in the answer space, with o, as the centre of the circle, construct a pie chart to represent all the information given in the table.

  Day Numbers of visitors Monday 12.5%

  Tuesday 10% Wednesday 22.5%

  Thursday 10% Friday 45%

  TABLE 2 [4 marks]

  O

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3 Unit Kurikulum

• – 5 –3 – 0.5 0.5

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  [4 marks]

  By using a scale of 2 cm to 1 unit on the x

  12 TABLE 2 Table 2 shows the values of two variables, x and y, of a function.

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  2

  2

  y -8

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• –axis and 2 cm to 2 units on the y –axis, draw the graph of the function.

END OF QUESTION PAPER

  Unit Kurikulum 20 Use the graph paper provided to answer this question. x