DO NOT OPEN THIS QUESTION PAPER UNLESS TOLD TO DO SO

  SULIT 50/2 Set 2

  NO. KAD PENGENALAN

  50/2 Mathematics Paper 2 July

  ANGKA GILIRAN

  2006

  3 1 hours

4 JABATAN PELAJARAN PERAK

  

PENILAIAN MENENGAH RENDAH 2006

LEARNING TO SCORE

MATHEMATICS

  Paper 2 I hour 45 minutes

  Question Allocated Marks Number Marks Obtained

DO NOT OPEN THIS QUESTION PAPER

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  1. This question paper consists of 20

  5

  2 questions.

  6

  2

  7

  3 2. Answer all questions.

  8

  3

  9

  2

  3. Write your answers clearly in the spaces

  10

  4 provided in the question paper.

  11

  2

  12

  3

  4. Diagrams are not drawn to scale unless

  13

  3 stated.

  14

  3

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  5

  5. The maximum marks allocated for each

  16

  3 question are shown in brackets.

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  3

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  6

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  3

  20

  4 TOTAL

  60 This question paper consists of 17 printed pages.

  

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 in the questions provided 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 m  n n}

RELATIONS

  a

  1 a = a _{m n m  n} õ 2 a  a = a _{m mn n} 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  

  6 Average speed = distance travelled time taken

  7 Mean = sum of data 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 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  r

  11 Volume of cylinder = h

  1 ₂  r

  12 Volume of cone = 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

  Answer all questions.

  3 

  1 3 

  1 Calculate the value of 2  2  and express the answer as a  

  4

  4

  5   fraction in its lowest term. 2 marks

   Answer :

  1

  2

  1

  2 Calculate the value of 3  ( ─ 1.5 )  0.8 and express the answer as a

  2 decimal. 2 marks

   Answer :

  2

  2

  2

   1 

  4  

  3 (a) Find the value of  

   8 

  5   _{3 2}

  (b) Calculate the value of 64  3 3 marks 

  Answer : (a) (b)

  3

  3 4 In Diagram 1, ABCD is a rectangle and CDE is a straight line. Find the length of AB.

  B A 10 cm 6 cm

  E D C 15 cm

  DIAGRAM 1 2 marks

   Answer :

  4

  2

  5 y

  6

  4 N

  2 M x

• 4
• 2

  2

  6

  4

• 2
• 4

  DIAGRAM 2 In Diagram 2, N is the image of M under enlargement at centre P with a scale of k.

  (a) On the Diagram, mark and label point P. (b) Find the value of k.

  2 marks

   Answer :

  (b)

  5

  2

  1

  6 Diagram 3 shows polygon ABCDEF drawn on a grid of equal squares. Shade of the

  4 figure ABCDEF.

  2 marks

   Answer :

  A F B E D C DIAGRAM 3

  6

  2

  7 Diagram 4 shows a cuboid.

  3 unit 1 unit 4 unit

  DIAGRAM 4 Make a full scale drawing of the net for the cuboid on the grid in the answer space. The grid has equal squares with sides of 1 unit.

  3 marks

   Answer :

  7

  3

  8 Table 1 shows the T-shirt size used by 30 students in a class.

  2

  2 S XL M M M S

  9

  3

  8

  x 2 marks Answer :

  5 

  x    ²

  3 

    ²

  TABLE 1 (a) Using the data, complete the frequency table in the answer space.

  9 Simplify

  XL (b)

  S M L

  

T-shirt size Frequency

  (a)

  Answer :

  3 marks

  (b) State the mode.

  XL M M S S L M M L XL M M S S L L M M L XL XL M L M

  10 (a) Solve the inequality  5  x ≤ 3

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

  

x

  2 4 x < 10 and x  ≤ 4 +

  5 4 marks

   Answer :

  (a) (b)

  10 ₂

  4 ₃  ₁

  11 Find the value of 8  3 [2 marks]

  Answer:

  11

  2 _{3 }  _{2 6  4}

  12. Simplify 2 m n ÷ 5 m n × mn [3 marks]

    Answer:

  12

  3

  5 s 

  r r t

  13. Given that = . Express s in terms of and . [3 marks] 2 t

  Answer:

  13

  3

  14. Solve each of the following equations:

  10  p

  (a) = 3

  5

  5

  4  

  25 (b)  x = 2  x [3 marks]

   

  2

  5  

   Answer:

  (a) (b)

  14

  3

  15. Diagram 5 in the answer space shows a square, TUVW. Point O is the point of intersection of diagonals TV and UW. MON is a straight line. X and Y are two points moving inside the diagram. On the diagram, (a) construct the locus of X such that XM = XN.

  (b) (i) construct the locus Y given that OY = 2.5 cm (ii) mark with the symbol  all the intersections of the locus of X and the locus of Y.

  [5 marks]

   Answer:

  M T U O W

  V N DIAGRAM 5

  15

  5

  16. Factorise completely: ₂ (a) 9m  1 ₂

  (b) 3 p  6 q  pq  2 q [3 marks]

   Answer:

  (a) (b)

  16

  3 ₂

  m

  4 m 

  12 17. Express  as a single fraction in its simplest form. 2 n 8 mn

   [3 marks] Answer:

  17

  3

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

  Q P R 120 

  T S DIAGRAM 6 Diagram 6 shows a trapezium PRST and Q is a point on PR.

  a) Start with the line TS given in the answer space, construct (i) the trapezium PRST (ii) the perpendicular line TQ from T to the line PR, with Q being on the line PR, as shown in Diagram 6.

  b) Based on the diagram constructed, measure the length of PT.

  [6 marks]

  Answer: (a) (i),(ii)

  T S

  18 (b)

  6

  19. Table 2 shows the number of gold medals won by four sports houses in a school.

  10 Sigma Gamma

  14

  16

  18

  20

  8

  2

  4

  6

  Alpha Beta

  Sports Houses Number of Gold Medals

  19 Number of gold medals Sports Houses

  3

  (a) (b)

  Answer:

  (b) Complete the bar chart to represent all the information given in the Table 2. [3 marks]

  18 TABLE 2 (a) Based on the bar chart in the answer space below, state the value of x.

  9 Sigma

  20 Beta x Gamma

  Alpha

  12

  20. Use the graph paper provided to answer this question.

  Table 3 shows the values of two variables, x and y, of a function.

  x - 4 -3 -2 -1

  1

  2

  y

  15 4 -3 -6 -5

  9 TABLE 3 Draw the graph of the function using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 unit on the y-axis.

  [4 marks]