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

  JABATAN PELAJARAN NEGERI PERAK _______________________ PENILAIAN MENENGAH RENDAH 2006 LEARNING TO SCORE MATHEMATICS

  Paper 1 1 hour 15 minutes DO NOT OPEN THIS QUESTION PAPER UNLESS YOU ARE TOLD TO DO SO 1. This question paper consists of 40 questions.

  2. Answer all questions.

  3. Answer each question by blackening the correct space on the answer sheet.

  4. Blacken only one space for each question.

  5. If you wish to change your answer, erase the blackened mark that you have made. Then blacken the space for your new answer.

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

  7. You may use a non-programmable scientific calculator.

  This question paper consists 20 printed pages.

  Set

  1 50/1 Mathematics Paper 1 July 2006 1 1/4 hours 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 = a _{m m m  n} 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  

  distance

  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  width

  1  base  height

  2. Area of triangle =

  2

  3. Area of parallelogram = base  height

  1  sum of parallel sides  height

  4. Area of trapezium =

  2 d  r

  5. Circumference of circle =  ₂ 2 

  

  6. Area of circle = r

  7. Curved surface area of cylinder = ₂ 2  rh

  

  8. Surface area of sphere = 4 r

  9. Volume of right prism = cross sectional area  length

  10. Volume of cuboid = length  width  height ₂

  11. Volume of cylinder =  r h

  1 ²

  r h

  12. Volume of cone = 

  3

  4 ³

  r

  13. Volume of sphere = 

  3

  1  base area  height

  14. Volume of right pyramid =

  3 

  15. Sum of interior angles of polygon =  n  2   180

  arc length angle subtended at centre

  16. 

  



circumfere nce of circle 360 area of sector angle subtended at centre 

  17.

   area of circle _' 360

  PA k 

  18. Scale factor,

  PA

  2

  19. Area of image = k x area of object

  Answer all questions.

  1 (24 + 35 ÷ 7) – 6 × 2 + 7 = A 10 B 19 C 24 D 29

  2 ( 12 – 7.56 ) × 2.4 ÷ 0.12 – 11.6 =  150.

  8 A

  B  62.

  8 C 13.58

  D 77.2 3  31   9   17 =

      

  57 A

  B 

  39 C 

  23 D 23

  10 

  5 3  1  1  

  4  

  14

  28

  7  

  2 A

  2

  7

  1

  1 B

  5

  49

  1 C 105

  31

  1 D

  49

  5 Which of the following is the highest common factor (HCF) of 20, 40 and 120? A 20 B 40 C 120 D 240

6 In the sequence of numbers x , 970 , 951 , 932 , y , 894 find the value of x – y .

  A 

  76 B 

  19 C 19

  D 76

  1

  7 Nadia has donated a sum of her money to charity. of the amount is donated to an

  5

  orphanage while 35% is donated to the Spastic Centre. The balance of RM2250 is donated to the National Warriors Fund. Find the total sum of money donated by Nadia.

  A RM1237.50 B RM2750 C RM3487.50 D RM5000

  8 Table 1 shows the number of share units owned by Ahmad in four companies and the percentage of dividend for each share unit given by the companies. Each unit of share is worth RM10.

  Percentage of Number of

  Company dividend for share units each share unit

  Murni

  40

  7 Sentosa

  80

  4 Mewah

  60

  6 Permai 150

  2 TABLE 1 The highest dividend received by Ahmad is from A Murni Company B Sentosa Company C Mewah Company D Permai Company

  9 Nalini travelled from Kuala Lumpur to Alor Setar. Her journey took 6 hours 20 minutes. If she reached Alor Setar at 3.00 p.m., at what time did she leave Kuala Lumpur? A 0320 hours B 0820 hours C 0840 hours D 1520 hours 10 In Diagram 1, both scale show the mass of eight cylinders and ten cubes are equals.

  5kg 5kg

  DIAGRAM 1 Find the difference of mass, in gram, between a cylinder and a cube.

  A 125 B 500 C 625 D 1125

  11 In Diagram 2, PRT and QRS are straight lines.

  P S

  

o

o 38 124 o

  R

  x

  Q T DIAGRAM 2 Find the value of x

  A 38 B 62 C 86 D 142

  12 In Diagram 3, P , Q , R , S , T and U are six vertices of a regular polygon. O is the centre of the polygon. POS, QOT and ROU are straight lines.

  o

60 DIAGRAM 3

  The number of sides of the polygon is A 3 B 6 C 10 D 12

  13 In Diagram 4, PQRSU is an irregular pentagon. RST is a straight line.

  P

  o

  Q

  40 o

  99 o y

  U

  o 130

  R S T DIAGRAM 4 Find the value of y A 99 B 261 C 279 D 351 14 In Diagram 5, PQRS is a rectangle, PSUT is a trapezium and QVR is a triangle.

  14cm Q P

  6cm

  V T 8cm

  5cm S U R

  6cm DIAGRAM 5

2 Calculate the area, in cm , of the shaded region.

  A 64 B 49 C 40 D 34

  15 Diagram 6 shows a right prism with PQRS as its uniform cross section.

  T W 22cm U

  

V

P S 8cm 32cm 8cm

  Q 10cm R

  DIAGRAM 6 ₂ Find the total surface area, in cm , of the prism.

  A 1376 B 1696 C 1840 D 1920

  16 Diagram 7 shows a scale drawing of the floor plan of a medium cost apartment. The shape of each area is a rectangle. The scale of the plan is 1 : 200.

  3.5cm 2cm 1cm

  m o ro

  Bedroom 1 Bedroom 2 Kitchen

  th a B

  6cm Dining & Living Bedroom 3

  3cm 2.5cm

  7cm DIAGRAM 7

2 The area, in m , of Bedroom 2 is

  A 24 B 30 C 36 D 42

  17 In Diagram 8, PQRS is a square of sides 3cm and JLN is a quadrant of a circle with centre R and radius 2cm.

  N S R M O L J K P Q

  DIAGRAM 8 X is the locus of points that are at a constant distance of 2cm from R. Y is the locus of points that are equidistant from two fixed points from points P and R. The intersections of the two loci are A M and L B M and K C L and O D L and K 18 In Diagram 9, PQRS is a circle with centre O. TSR, PQV and SOQU are straight lines.

  U 40 Q

  V P a O b

  85 T R S

  DIAGRAM 9 Find the value of a + b.

  A 45 B 50 C 95 D 135

  19 In Diagram 10, RST is an isosceles triangle and XYZ is a semicircle with centre O. SYO and RXOZT are straight lines. Given that OR = OS = 12cm.

  Y

  DIAGRAM 10

2 Calculate the area, in cm , of the shaded region.

  22 

  ( Use  )

  7 A 67 B 72 C 82 D 144

  6   

  3 20 ) is the image of R under the translation .

  If R’(3,

     3  

  What are the coordinates of R ? A (3, 0)

  

3 B ( , 0)

  C (9, 

  6 ) 

6 D (3, )

  21 In Diagram 11, ST is a straight line. y

  S

  4

  3

  2

  1 3 x

• 2 -1

  1

  2

  4

• 1
• 2

  P . T

  DIAGRAM 11 Which of the following coordinates is the image of the point P under a reflection in the line ST? A (1 , 

  1 ) 

1 B ( , 1)

  C (3 , 1) D ( 1 , 3)

  22 In Diagram 12, O is the centre of the circle.

  S P

  x

  30º O

  y

  50º Q R DIAGRAM 12

  SOQ is the diameter of the circle. The value of x + y , in degree, is A 90 B 70 C 50 D 30 23 Diagram 13 represents two simultaneous linear inequalities on a number line.

  5

• 5 -4 -3 -2 -1 1 2 3

  4 DIAGRAM 13 Which of the following is represented by the above number line ?

  

  3 A  x and x > 4 

  3 B < x < 4

  C 

  3  x < 4 

  3 D < x and x 

  4

  24 Fatiah bought a bag of apples for RM75. He sold x kg of the apples at RM4 per kg on the first day. On the second day, he sold y kg of the apples at RM3 per kg.

  Given that he made a profit of RM25, the equation in x and y is A 4x + 3y = 100 B 4x + 3y = 75 C 4x + 3y = 25 D x + y = 100

  5  8 t s 

  25 Given that , then t 

   t

  3 

  A

  5

  5 B  s 

  8

3 C

  5

  5 D 8  s

  26 Diagram 14 shows a rectangle PQRS. The parallelogram ABCD is removed.

  P Q A B 20 cm

  8 cm D C 22 cm

  R S 30 cm

  DIAGRAM 14 The area, in cm², of the remaining portion is A 442 B 440 C 434 D 424

  27 Sarah bought 56 pens of Papermates RM1.20 each and Stabilo RM0.90 each. The total cost was RM56.70.

  How many Stabilo pens did she buy ? A 21 B 28 C 35 D 42

  28 Atan bought 500g of rambutans. Joshua bought half the mass of rambutans that Kim bought. They bought 3.5 kg of rambutans altogether.

  How many grammes of rambutans did Joshua bought ? A 4000 B 3000 C 2000 D 1000

  29 A laser printer can print 12 960 pages per day. One day, the printer was stopped for 75 minutes to be serviced.

  How many pages the printer can print on that day ? A 12285 B 12885 C 12825 D 18225 30 Table 2 shows the members of Mathematics Society in three forms.

MEMBERS OF MATHEMATICS SOCIETY

  FORM MALE FEMALE 1 150 180 2 140 160 3 180 204

  TABLE 2 Which of the following statement is true ? A The percentage of male students from Form 2 dan Form 3 are the same.

  B 46.7% of members from Form 1 are male students. C 53.3% of members from Form 2 are female students. D 45.5% of members from Form 3 are female students.

  31 A box of oranges is divided into 3 packets in the ratio 3 : 5 : 8. The difference between the number of oranges in the first packet and the third packet is 15.

  Calculate the number of oranges in the second packet.

  A 9 B 11 C 15 D 24

  32 V is the midpoint of the line joining U and W. The coordinates of U, V and W are (6, q), (p, 1) and ( 

  8 ,  3 ) respectively. The value of p and q are likely to be  1 

  5 A p = , q = 

  1 B p = 5, q = 

  5 C p = 1, q = 

1 D p = , q = 5

  33 Given that the distance of the point W(8, r) from the origin is 17 units, the value of r is A 9 B 12 C 15 D 25

  34 In Diagram 15, the points S, T and U are corners of a rhombus STUV. y

  10

  8 T

  6

  4

  2 U S x - 6 - 4 - 2

  2

  4

  6

  8 - 2 - 4 DIAGRAM 15

  The coordinate of point V are

  

  4 A (1, )

  B (4, 

  3 ) 

  4 C (4, ) 

  4 D (3, )

  35 Table 3 shows the numbers of questions that are answered correctly by four groups, Pintar, Bestari, Cerdik and Bijak in a Mathematics quiz. The group that succeeds in getting 65 marks and above qualifies to enter the next quiz.

  GROUP TALLY Pintar llll lll Bestari llll l Cerdik llll llll Bijak llll ll

  TABLE 3 If the total number of questions presented is 12, which groups qualify to participate in the next quiz ? A Pintar and Cerdik B Pintar and Bestari C Bestari and Cerdik D Bestari and Bijak

  36 The mean mass of 40 members of Dynamic Club is 65 kg. A member whose mass is 72kg join the club.

  Find the new mean mass, in kg, of the members.

  A 68.5 B 65.2 C 56.0 D 52.5 37 Table 4 shows the number of games each team has won.

  Diagram 16 shows a pie chart based on Table 4.

  TEAM NUMBER OF GAMES WON Q R Yellow

  7 Blue

  12 72º

  Green

  5 P Red

  6 S TABLE 4 DIAGRAM 16 Which team does P represent ? A Yellow Team B Blue Team C Green team D Red Team

  38 Diagram 17 shows a composite solid of a cylinder and a hemisphere.

  x cm

  DIAGRAM 17

  

  If the diameter and the volume of the solid are 12 cm and 864 respectively, calculate the length x, in cm, of the solid.

  A 20 cm B 24 cm C 26 cm D 30 cm 39 In Diagram 18, O is the centre of the circle.

  L M K 120º

  120º O

  x

  H N J DIAGRAM 18 Given that JOM and HJN are straight lines, the value of x is A 130º B 70º C 50º D 30º

  40 The diagrams below show 4 different brands of butter with labels showing prices and quantities.

  Which one is considered the best buy ? A

  BUTTER RM7.60 500g

  B

  BUTTER RM5.70 300g

  C

  BUTTER RM2.30 200g

  D

  BUTTER RM1.20 100g

  END OF QUESTION PAPER