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50/1

Mathematics

Paper 1

July

2009

1 hours Set 1

JABATAN PELAJARAN PERAK

PENILAIAN MENENGAH RENDAH 2009

ANSWER TO SCORE

2009 PMR FORECAST PAPER

MATHEMATICS

Paper 1

1 hour 15 minutes

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

1. This question paper consists of40 questions.

2. Answerall questions

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

4. Blacken only onespace 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.

8 A list of formulae is provided.

This question paper consists 20 printed pages.

55


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

ones commonly used.

RELATIONS

1. m n m na a a + =

2. m n m na a a =

3. ( )m n mna a=

4. Distance = 2 22 1 2 1( ) ( )x x y y +

5. Midpoint

( , )x y = +2

21 xx,

+2

21 yy

6. Average speed =distance travelled

time taken

7.sum of data

Mean =number of data

8. Pythagoras Theorem2 2 2c a b= +

SHAPE AND SPACE

1. Area of rectangle = length width

2. Area of triangle =1

base height2

3. Area of parallelogram = base height

4. Area of trapezium =1

sum of parallel sides height2

56


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5. Circumference of circle = 2d r =

6. Area of circle = 2r

7. Curved surface area of cylinder = 2 rh

8. Surface area of sphere = 24 r

9. Volume of right prism = cross sectional area length

10. Volume of cuboid = length width height

11. Volume of cylinder = 2r h

12. Volume of cone =21

3r h

13. Volume of sphere =34

3r

14. Volume of right pyramid =1

3base area height

15. Sum of interior angles of a polygon =( 2) 180n o

16.arc length angle subtended at centre

circumference of circle 360=

o

17.area of sector angle subtended at centre

area of circle 360=

o

18. Scale factor, k=PA

PA

19. Area of image =2 area of objectk

57


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Answerallquestions.

1. The number 345 678 is written as 350 000 when it is rounded off to the

A nearest ten

B nearest hundred

C nearest thousand

D nearest ten thousand

2. Which of the following fractions has value greater than4

3?

A8

7

B3

2

C2

1

D7

5

3. Express 33100000

168as a decimal

A 33.168

B 33.0168

C 33.00168

D 33.000168

4. Table 4 shows the temperature for four towns on a particular day.

Town Temperature (C)

E -2

F 3

G 9

H -8

Table 4

Which town was the coldest on that day?

A E

B F

C G

D H

5. Diagram 5 shows a sequence of prime numbers.

17, 19, m, n, 31

58


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Diagram 5

Find the value of m + n.

A 44

B 48

C 52

D 56

6. Diagram 6 shows some factors of 54.

Diagram 6Identify three other factors of 54.

A 2, 3, 18

B 2, 18, 29

C 3, 4, 8

D 3, 4, 18

7. Tharmas Poultry Farm produces 9 000 eggs a day. If 1% of the eggs are broken, calculate

the number of broken eggs produced in a week.

A 900

B 630

C 180

D 90

8. Swaran Construction Company built a road from Kampung Menora to Kampung Gelam, a

distance of 5.54 km. It then built a road connecting Kampung Gelam to Kampung Aman, adistance of 6.78 km. Calculate the total length of the road constructed by the company

A 10 km 320 m

B 11 km 320 m

C 12 km 320 m

D 13 km 320 m

9. In Diagram 9, ABC is a straight line.

59

DD

Diagram 9

1 9 54

6 27


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Calculate the value ofx.

A 55

B 60

C 70

D 75

10

.

In Diagram 10 , PQRST is a pentagon and STU is a straight line

Diagram 10

Find the value ofp + q + r + s.

A 220

B 400

C 500

D 540

11

.

Diagram 11 shows a polygon.

60

T

p

Q

S

R

40U

P

q

r

s

F

D

C

E

122

75

3x

B

A2x

3x

115


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Diagram 11

Find the value ofx.

A 41

B 51

C 55

D 61

12

.

Diagram 12 shows two regular polygons.

Diagram 12

Find the value ofm.

A 120

B 132

C 144

D 228

13

.

In Diagram 13, PQR is a right-angled triangle,

RVU is an equilateral triangle and QRVW is a

square.

61

V

m

W

XQ

T

R

US

12 cm

5 cm Q W

V

U

R

P


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Diagram 13

Calculate the perimeter, in cm, of the whole diagram.

A 48

B 65

C 66

D 102

14

.

Diagram 14 shows two right-angled triangles, XYZ and VWZ.

Diagram 14

Find the area in cm, of the shaded region.

A 105

B 75

C 35

D 30

15

.

Diagram 15 shows the plan of an orchard.

62

4 m

4 m 6 m

10 m

15 m

4 m

4 m 6 m

10 m

15 m

X

Y V Z

15 cm

4 cm 10 cm

6 cm

W

X

Y V Z

15 cm

4 cm 10 cm

6 cm

W


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Diagram 15

Find the area, in m2, of the whole diagram.

A 70

B 90

C 100

D 130

16

.

Which of the following geometric solid is a cone?

A

B

C

D

63


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17

.

In Diagram 17, the volume of the cylinder is equal to the volume of the cone..

Diagram 17

Calculate the height of the cylinder

A 21 cm

B 16 cm

C 14 cm

D 7 cm

18.

Diagram 18 shows a solid pyramid with a square base PQRS and height of 4 cm. The areaof the base is 36 cm2.

Diagram 18

Find the total surface area, in cm2, of the solid.

A 144

B 96

C 51

D 48

19. Diagram 19 shows a prism with a right angled triangle as its uniform cross section.

64

4 cm4 cm4 cm

21

cm

h

4 cm4 cm4 cm

21

cm

h

P

Q R

S

T

P

Q R

S

T


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Diagram 19Calculate the total surface area of the prism.

A 120 cm

B 156 cm

C 160 cm

D 180 cm

20. Diagram 20 shows a rectanglePQRSand some construction lines made by a student.

The student is constructing the locus of X such that,

A PSX = RSX

B XP = XS

C XS = SP

D XS is equidistant from line PQ and line SR

21. In Diagram 21, O is the centre of the circle.

65

P

Q

R

5 cm

3 cm

12 cm

P

Q

R

5 cm

3 cm

12 cm

P

S R

QP

S R

Q

O

130

x

O

130

x

Diagram 20


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Diagram 21

Find the value ofx.

A 115

B 110

C 80

D 50

22

.

In Diagram 22, PTR is a diameter of the circle and STQ is a straight line.

Diagram 22Find the value ofx.

A 55

B 40

C 35

D 30

23

.

Diagram 23 shows a circle with centre O. PT, QU, RV and SW are diameters of the circles.

66

P

S

R

Q

T

x

50

70

P

S

R

Q

T

x

50

70


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Diagram 23

Which of the following minor arcs is the

longest?

A TU

B UV

C WP

D RS

24

.

In Diagram 24, O is the centre of the bigger circle with a radius of 7 cm. The smaller circle

passes through O and touches the bigger circle.

Diagram 24

Using =7

22, calculate the area in cm, of the shaded part.

A 38.5B 77.0

C 115.5

D 154.0

25

.

In Diagram 25, PQRST is a trapezium, QST and QRS are right-angled triangles.

67

30

50O

W

S

U Q

P

V

R

T

30

50O

W

S

U Q

P

V

R

T

OO

PQ

RT

16 cm

20 cm


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Diagram 25

Find the length, in cm, of QR.

A 12

B 13

C 14

D 15

26

.

In Diagram 26, ACD is the image of ABE under an enlargement with centre A.

Diagram 26

Given CD = 6 cm, calculate the length, in cm, of BE.

A 3

B 4

C 6

D 9

27

.

Given 93 =+ yx and 632 = yx , calculate the value of .x

A 2

B 3C 4

D 5

28. Solve the following inequality.

4

3y + 3 3

68

S 5 cm

6 cm

3 cm

A

ED

C B6 cm


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D y > -3

29. In Diagram 29, B is the midpoint of the straight line AC.

Diagram 29

Find the value ofp.

A 9

B 6

C 3D 2

30. Diagram 30 shows five points on a Cartesian plane.

69

y

A (-1, 2)

B (4, 5)

C (p, 8)

x

0

y

A (-1, 2)

B (4, 5)

C (p, 8)

x

0

R(-9, -2)

P(8, 6)

T(11, 5)

Q(-3, 10)

S(-6, -8)

x

y

O

- -

xx

R(-9, -2)

P(8, 6)

T(11, 5)

Q(-3, 10)

S(-6, -8)

x

y

O

- -

xx


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Diagram 30

Which of the following has the same distance as OP?

A OQ

B OR

C OS

D OT

31

.

Diagram 31 shows a rectangle PQRS. PTU is an arc with centre Q and UVW is an arc with

centre R.

Diagram 31

Find the perimeter in cm, of the shaded region.

( Use =7

22)

A 54

B 61

C 70

D 82

32

.

Table 32 shows the registration fees for an examination

Basic fee RM150Fee per written paper RM35

Fee per oral assessment RM40

Fee per practical assessment RM38

Table 32

Mimi registers for 8 written papers, 3 oral assessments and 3 parctical assessments whereas

Roger registers for 7 written papers, 2 oral assessments and 3 practical assessments

The difference in the total registration fee paid by Mimi and Roger is

A RM75B RM95

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C RM120

D RM150

33

.

The scores obtained by Amani and Bee Leng in a game are in the ratio of 7 : 4 , while the

ratio of scores obtained by Bee Leng and Celine is 6 : 5. Find the ratio of scores obtained by

Amani, Bee Leng and Celine.

A 7 : 12 : 5

B 7 : 12 : 10

C 21 : 12 : 10

D 21 : 12 : 15

34

.Daud drove from Kluang to Ipoh. His journey was expected to take 6

2

1hours. He started

his journey at 7.40 a.m. and arrived Ipoh 20 minutes late. What time did Daud arrive Ipoh?

A 2.40 p.m.

B 2.30 p.m.

C 2.10 p.m.

D 1.50 p.m.

35 Diagram 35 is a pie chart showing the number of ice cream sold at a stall on a certain day.

Diagram 35

Find the value ofx +y.A 68

71

Chocolate60

Corn

32Orange

22

Vanilla

36

Strawberry

10

xy

Chocolate60

Corn

32Orange

22

Vanilla

36

Strawberry

10

xy


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B 135

C 153

D 163

36.

In Diagram 36, the bar chart below shows the number of students in three classes.

Diagram 36

Which of the following statement is true?

A The total number of students in three classes is 125

B The total number of girls in Class A and Class B is the same.

C The number of boys in this school is greater than the number of girls.

D The number of girls in class C is greater than the number of girls in class B.

37

.

Table 37 shows the number of teachers in five housing estates.

Housing estates A B C D E

Number of teachers 10 13 p 7 5

Table 37

The mode is B.Find the possible value of p.

A 12

B 14

C 25

D 35

72


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38

.

Table 38 shows the scores in a game

Score 0 1 2 3 4 5

Frequenc

y

5 7 2 6 4 6

Table 38

The median score isA 1

B 2

C 3

D 4

39

.

Table 39 shows the values of variables x and y for the function ofy = 3x2 2x

x -2 -1 0 1 2y m 5 0 1 8

Table 39

Find the value ofm.

A 16

B 8

C -8

D -16

40

.

Which of the following graphs representsy = x + 6

A

73

(6,0 )

(0,6 )

x

y

0 (6,0 )

(0,6 )

x

y

0

(6,0 )

(0,-6)

x

y

0

(6,0 )

(0,-6)

x

y

0


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B

C

D

END OF QUESTION PAPER

50/1

Mathematics

Paper 1

July

2009

1 hoursSet 2

74

(6,0 )

(0,-1 )

x

y

0

(6,0 )

(0,-1 )

x

y

0

(-6,0 )

(0,6 )

x

y

0

(-6,0 )

(0,6 )

x

y

0


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ANSWER TO SCORE


MATHEMATICS

Paper 1

1 hour 15 minutes

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


2. Answerall questions

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

4. Blacken only onespace 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.

8. A list of formulae is provided.


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

ones commonly used.

RELATIONS

1. m n m na a a + =

2. m n m na a a =

75


22/77

3. ( )m n mna a=

4. Distance = 2 22 1 2 1( ) ( )x x y y +

5. Midpoint

( , )x y = +2

21 xx,

+

2

21 yy

6. Average speed =distance travelled

time taken

7.

sum of data

Mean = number of data


SHAPE AND SPACE



base height2









76


23/77




3

r h


3r


3base area height

15. Sum of interior angles of a polygon = ( 2) 180n o

16. arc length angle subtended at centrecircumference of circle 360

=o


area of circle 360=

o


PA


77


24/77

Answerallquestions.

1. Which of the following numbers when rounded off to the nearest hundred thousand becomes

8 700 000 ?

A 8 754 321

B 8 654 321

C 8 643 210

D 8 554 321

2. Table 2 shows the types of item that Sarah bought from a sundry shop.

Types of item Price per kg Quantity

Item A RM30 4.5 kg

Item B RM19 2 kg 500 g

Item C RM18 500 g

Table 2

Sarah has RM250.00

How much money is left after she has paid for all the items?

A RM61.75

B RM5.85

C RM105.50

D RM58.50

3. Ali had 300 durians. He managed to sell

6

5of the durians . Later he gave 20 of the

remaining durians to his friends. Calculate the percentage of the durians that he has left.

A 50

B 16.67

C 10

D 6.67

4. Diagram 4 is part of a number line.

Diagram 4

78

P -12 0 Q


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What is the value of P and Q?

A P = -18 , Q = 18

B P = -14 , Q = 12

C P = -12 , Q = 9

D P = -6 , Q = 18

5. The original price of a T-shirt is RM24.00. The selling price of the T-shirt is12

11of its

original price. Swee Lan uses2

1of her savings to buy the T-shirt. What was her

savings before she bought the T-shirt?

A RM22.00B RM28.80

C RM44.00

D RM39.60

6. Which of the following is the common multiple of 3 and 5?

A 8

B 9

C 25

D 45

7. Ali has 5 rolls of rope. Each roll is2

13 m long. He used 1.69 m of the rope from each roll.

Find the length of the remaining rope.

A 9.15 m

B 9.05 m

C 9.00 m

D 8.05 m

8. A bus started its journey from Kuala Lumpur and arrived at Johor Bahru at 4.45 a.m. on the

next day. If the journey took4

15 hours, the bus left Kuala Lumpur at

A 1000 hoursB 2200 hours

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C 2230 hours

D 2330 hours

9. In Diagram 9, ABC is a triangle

Find the value ofx.

A 15

B 18

C 20

D 25

10

.

In Diagram 10, pentagon PQRST is the image of pentagon PQRST under an enlargement

80

S

T

P

R

Q

P Q

T

R

S

A

x x35

62

147

B

CA

x x35

62

147

B

C

Diagram 9


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28/77

Diagram 12

Find the number of sides of the polygon?

A 6

B 8

C 10

D 12

13

.

The cost of a metre of fencing is RM13.60. The Vision Home for the Poor wants to fence a

rectangular compound 25 m by 75 m. How much is the cost of fencing the rectangular

compound?

A RM2 520

B RM2 620

C RM2 720

D RM2 820

14

.

In Diagram 14, ACD is a right-angled triangle. The area of triangle ABD is 168 cm.

Find its height, h

in cm.

A 11

B 14

C 20

D 24

15

.

In Diagram 15, DEGH is a parallelogram and FGH ia a straight line.

82

h cm

C15cm

14cmA B

D

Diagram 14


29/77

Diagram 15

Given DE = 12 cm and HF = 15 cm. If the area

of triangle EFG is 6 cm, find the area of the

whole diagram.

A 40

B 54

C 60

D 96

16

.

Diagram 16 shows the net of a geometric solid.

Diagram 16

Name the geometric solid.

A Right prism

B cuboid

C pyramid

83

FGH

DE


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D cone

17

.

Diagram 17 shows two containers in the shape of a cuboid and right prism.

The cuboid is fully filled with water. All the water in the cuboid is then poured into the right

prism. The base area of the right prism is 66 cm2 . Calculate the height, in cm of the water

level in the right prism.

A 13

B 21

C 88

D 66

18

.

Aminah is4

34 years old. Bala is

12

19 years older than Aminah. Chee Mengs age is

2

12

times the sum of the ages of Aminah and Bala. What is Chee Mengs age?

A8

711

B6

513

C3

116

D24

1146

84

6 cm

21 cm

11 cm

Diagram 17


31/77

19

.

In Diagram 19, JOL is a diameter of the circle JKLM with centre O. MLN is a straight line.

Diagram 19

Find the value ofx.

A 20

B 25

C 30

D 70

20

.

In Diagram 20, DEFG is a cyclic quadrilateral.

Diagram 11

Find the valuex.

A 50

B 60

85

J

K

LM

O

N

x

70

130

J

K

LM

O

N

x

70

130

D

E

F

GH

x

30

100

D

E

F

GH

x

30

100


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C 80

D 100

21

.

In Diagram 21, PQR and STU are two circles with a common centre, O. PSOUR is a straight

line.

Diagram 21

Given that PS = SO = 4 cm, calculate the area, in cm, of the shaded region.

A 8

B 16

C 32

D 64

22

.

In Diagram 22, O is the centre of the circle and POR is a diameter of the circle.

PQR is a right-angled triangle.

Diagram 22

Find the area, in cm, of the coloured region.

A 25 - 24

B 25 - 30

86

OP R

Q

10 cm

8cm

OP R

Q

10 cm

8cm

R

ST

U

P

Q

O

R

ST

U

P

Q

O


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C 25 - 48

D 100 - 48

23

.

In Diagram 23, PQRS is a cyclic quadrilateral.

NPQ is a straight line and O is the centre of the circle.

Diagram 23

Find the value ofx.

A 50

B 60

C 70

D 120

24

.

Diagram 24 shows a triangular pattern on a wall.

Diagram 24

A tin of paint is required to paint an area of 5 m.

How many tins of paint if needed to paint the surface of the triangle?

A 12

B 24

C 25

D 32

87

15 m

17 m

15 m

17 m


34/77

25

.

Which of the following diagram shows line XY non-parallel to line PQ ?

A.

B.

C.

D.

88

X

Y

P

Q

70O

70O

70O

70O

X

Y

P

Q

70O

70O

X

Y

P

Q

110O

110O

X

Y

P

Q


35/77


36/77

C (-1, 3)

D (-2, 3)

29. Diagram 29 shows points J, K, L and M marked on a grid of equal squares with sides of

1 unit.

Diagram 29

Which points are equidistant from point O?

A M and J

B M and K

C K and L

D K and J

30. In Diagram 30, C is the centre of the circle and ABC is a right-angled triangle.

Calculate the perimeter of the whole diagram.

A 60.29 cm

B 72.59 cm

C 75.29 cm

D 75.59 cm

31

.

Sally, Shirley and Susan invested a sum of money in a bookstore in the ratio 7 : 5 : 6.

The total amount invested by Sally and Susan was RM624. find the total amount invested by

90

A

B

D

12 cm150

C9 cm

A

B

D

12 cm150

C9 cm

Diagram 30

J

K

LM

O

J

K

LM

O


37/77

Sally and Shirley.

A RM864

B RM576

C RM288

D RM48

32

.

Table 32 shows the price of mangoesteens sold at four stalls, W, X, Y and Z

W X

3 mangoesteens for RM 15

5 mangoesteen for RM 20



Y Z3 mangoesteens for RM 21




Table 32

Which stall sells mangoesteens at a price that is proportional to the number of

mangoesteens?

A W

B XC Y

D Z

33

.

Table 33 shows the number of computers sold by a company from January to April

Month January February March April

Number of computer sold 1450 1800 1650 1600

Table 33

Based on the data in table above, which of the following statements is not true ?

A The difference between the highest and the lowest number of computers sold in a month

is 350

B The mean number of computers sold for a month over this four month period is 1625

C The total number of computer sold after February is 3250

D The number of computers sold in April is equivalent to 30% of the total number of

computer sold over the four month period

34.

Diagram 34 is a bar chart which shows the number of books sold by a bookshop in sixmonths

91


38/77

Diagram 34

If the number of books sold in March is 20 000, find the number of books sold in FebruaryA 8 000

B 10 000

C 12 000

D 16 000

35

.

Diagram 21 is a pie chart showing the types of fruits in a trolley.

Diagram 21

There are 252 rambutans.

How many mangosteens are in the trolley?

A 98

B 70

C 42

D 28

36

.

The line graph in Diagram 36 shows the income of a hawker in 4 months.

92

January

Month

February

March

April

May

Numb

erofbooks

June

January

Month

February

March

April

May

Numb

erofbooks

June

Rambutan

160

Mangosteen

Guava

Durian

5y

2y

60

Rambutan

160

Mangosteen

Guava

Durian

5y

2y

60


39/77


40/77

38

.

Diagram 38 shows a graph of a function on a Cartesian plane.

Diagram 38

The equation that represents the function is

A y = x - 2

B y = - x

C y = x + 2

D y = - x + 2

39

.

Table 39 shows the values of variables x and y for the function ofy = -2x2 + 1

x -2 -1 0 1 2

y -7 s 1 -1 t

Table 39Calculate the value ofs + t

A -1

B -6

C -7

D -8

94

2

-2 0 2-4


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40

.

In Diagram 40ABCDEFGHis a regular octagon with sides 3 cm.

Diagram 40

Xis the locus of a point which moves such that it is always equidistant from pointB andD.

Yis the locus of a point which moves such that its distance from pointHis always 3 cm.

Which of the following points is the intersection of locusXand locus Y

A C

B G

C A

D E

END OF QUESTION PAPER

95

B C

A D

E

FG

H


42/77

50/1

Mathematics

Paper 2

July

2009

1 hoursSet 1



ANSWER TO SCORE



96

MATHEMATICS

Paper 2

1 hour 45 minutes

DO NOT OPEN THIS QUESTION PAPER

UNTIL YOU ARE TOLD TO DO SO


2. Answer allquestions. Answerallquestions

3. Write your answers clearly in the spaces

provided in the question paper.

4. Diagrams are not drawn to scale unless

stated.

5. The marks allocated are shown in brackets.

QuestionAllocated

Marks

Marks

Obtained

1 2

2 2

3 3

4 3

5 2

6 2

7 3

8 3

9 3

10 3

11 3

12 3

13 4

14 3

15 216 5

17 4

18 5

19 2

20 3

Total


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INFORMATION FOR CANDIDATES

1. This question paper consists of 20 questions.

2. Answerall 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 notallowed.

11. This question paper must be handed in at the end of the examination.

97


44/77


45/77




8. Surface area of sphere =2

4 r





3r h


3r


3base area height



circumference of circle 360

=o


area of circle 360=

o


PA


99


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1. Calculate the value of 42 6 10 =

Answer :

[ 2 marks]

2.Calculate the value of

4.0

24.06=

Answer :

[ 2 marks]

3. a) Find the value of3

216

1=

b) Calculate the value of ( )[ ]23 1693 + =

Answer :

a)

b)

[ 3 marks]

4. Solve each of the following equations :

100


47/77

a) 2 ( r 2 ) = 10 5r

b)

2

6+s= 4s

Answer :

a)

b)

[ 3 marks]

5. Diagram 5 in the answer space shows quadrilateralABCD. CD is the image ofCD under

a reflection in the straight lineLM.

On Diagram 5 in the answer space, complete the image of quadrilateralABCD.

Answer:

Diagram 5

[ 2 marks]

6. Diagram 6 shows two quadrilaterals, KLMN and KLMN, drawn on a grid of equal

101

L

M

A B

C

D

C

D

L

M

A B

C

D

C

D


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squares with sides of 1 unit.

Diagram 6

KLMN is the image ofKLMNunder transformationP.Describe in full transformationP.

Answer:

[2 marks]

7. Factorise completely each of the following expressions :

102

K L

M

N

K L

M

N

K L

M

N

K L

M

N


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a) x8 xy4

b) k6 183 + k Answer :

a)

b)

[ 2 marks]

8. Simplify each of the following

a) ( )342 +x b) ( ) ( )443 xx Answer :

a)

b)

[ 3 marks ]

9.Express

mn

n

m

2

5

3as a single fraction in its simplest form.

Answer :

[ 3 marks]

10. a) Solve the inequality 8 + x < 14

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

103


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2 - 3x < 11 and 8 -3

1x 7

Answer :

a)

b)

[ 3 marks]

11.Given that k

m=

+

4

52, express m in terms ofk

Answer :

[ 3 marks]

12. (a) Simplify (p4

q2

) 21

(p2

q1

)2

104


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(b) Find the value of 3 23

3 21

Answer :

a)

b)

[ 3 marks]

13. The frequency table in table 13 shows the number of car owners in a housing park.

105


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Table 13

Represent all the data by drawing a horizontal dual bar chart in the answer space.

Answer :

Women

Men

[4 marks]

106

Types of Cars Number of Women Number of Man

Kancil 15 5Persona 18 22

Waja 20 28


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54/77

15. Diagram 15 shows surfaces of a right prism drawn in the square grid of 1 cm.

Diagram 15

When the right prism is constructed, what would be its volume?

Answer :

[3 marks]

108


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16. Diagram 16 below shows a circle with centre O, which is divided into four equal parts. W,

Xand Yare three moving points in the diagram.

a) Wis a moving point such that it is always equidistant from point Q and point S. By using

the letters in the diagram, state the locus ofW.

b) On the diagram draw

i) The locus of pointXsuch that it is equidistant from line OPand line OQ.

ii) The locus of point Ysuch that YR = RQ.

c) Hence, mark with the symbol the intersection of the locus ofXand the locus ofY.

Answer :

Diagram 16

[5 marks]

109

P

Q

R

S

OP

Q

R

S

O


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

Table 17 shows the values of two variables,x andy, for a function.

x -3 -2.5 -2 -1 0 1 2 3 4

y 0 -10 -15 -14 -9 0 10 21 32.5

Table 17

Thex axis and they axis are provided on the graph paper.

a) By using a scale of 2cm to 5 units, complete and label they axis.

b) Based on table 17, plot the points on the graph paper.

c) Hence, draw the graph of the function.

[4 marks]

110


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

Diagram 18 in the answer space shows two straight lines,PQ and QR.

Using only a ruler and a pair of compasses,

i) construct a rectanglePQRS.

ii) construct a perpendicular line RT from the pointR to the straight line QSwhere thepoint Tlies on the straight line QS.

Answer :

Diagram 18

[5 marks]

19. Diagram 19 in the answer space shows trianglePQR drawn on a grid of the equal squares.TrianglePQR is enlarged by the scale factor 2 from the centre O. Draw the image of

trianglePQR in the answer space.

Answer :

112

P

Q R


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Q

Diagram 19

[2 marks]

20. Diagram 20 shows two right angled triangles,PMNandPQR.MPQ is straight line.

113

P

Q R

M 6 cm N

x

12 cm

y

P

R

O


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Diagram 20

It is given that cos xo =5

3and sin yo =

5

4

a) Find the value of tan xo

b) Calculate the length ofMPQ in cm

Answer :

a)

b)

[3 marks]

50/1

Mathematics

Paper 2July

2009

1 hoursSet 2



ANSWER TO SCORE

114


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INFORMATION FOR CANDIDATES

1. This question paper consists of 20 questions.

2. Answerall 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.

115

MATHEMATICS

Paper 2

1 hour 45 minutes

DO NOT OPEN THIS QUESTION PAPER

UNTIL YOU ARE TOLD TO DO SO

1. This question paper consists of20

questions.

2. Answerallquestions. Answerallquestions

3. Write your answers clearly in the spaces

provided in the question paper.4. Diagrams are not drawn to scale unless

stated.

5. The marks allocated are shown in brackets.

QuestionAllocated

Marks

Marks

Obtained

1 2

2 3

3 2

4 2

5 2

6 2

7 4

8 2

9 3

10 411 3

12 3

13 3

14 3

15 3

16 5

17 5

18 3

19 3

20 3

Total


62/77


63/77

5. Midpoint

( , )x y = +2

21 xx,

+

2

21yy

6. Average speed = distance travelledtime taken

7.sum of data

Mean =number of data


SHAPE AND SPACE



base height2












3r h

117


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3r


3base area height



circumference of circle 360=

o


area of circle 360=

o

18. Scale factor, k=

PA

PA


1.Calculate the value of

2

3

3

2

5

7

Answer :

[2 marks]

118


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2.Calculate the value of 2.6 3.5

5

32 and express the answer as a decimal.

Answer :

[3 marks]

3. Diagram 3, in the answer space shows two triangles,PQR andPQR, drawn on a grid of

equal squares.PQR is the image ofPQR under an enlargement.

On Diagram 3 in the answer space, markTas the centre of enlargement.

Answer:

119


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Diagram 3

[2 marks]

4. Diagram 4 in the answer space shows quadrilateralsPQRSand straight line WX drawn on a

grid of equal squares.

Starting from the line WX, draw quadrilateral WXYZwhich is congruent to quadrilateral

PQRS.

120

- 6 - 4 - 2 0 2 4 6 8

8

6

4

2

-2

x

y

P

Q R

Q R

P

- 6 - 4 - 2 0 2 4 6 8

8

6

4

2

-2

x

y

P

Q R

Q R

P


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Answer:

Diagram 4

[2 marks]

5. Diagram 5 in the answer space shows triangleKLMdrawn on a grid of equal squares. On

the diagram in the answer space, draw the image of the triangleKLMunder a rotation of

90 clockwise about the pointP.

Answer:

Diagram 5

[2 marks]

6. Given that, 53 =

k

pexpressp in terms ofk

Answer :

121

P

Q

R

S

W

XP

Q

R

S

W

X

P

L M

K

L M

K


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[2 marks]

7. Solve each of the following equations :

a) - 4 6x = 14

b)

m

m

4

103 = 2

Answer :

a)

b)

[4 marks]

8. Simplify :

736 + bab ( )abb 4522 +Answer :

[2 marks]

122


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9. Diagram 9 shows polygonABCDEFdrawn on a grid of equal squares.

.

Diagram 9

On the grid in the answer space, redraw the polygon using the scale of 1 : 2.

123

E

BA

C

F

D

Answer :


70/77

[3 marks]

10. The diagram 10 in the answer space shows a rectangle,PQRSwhich is drawn on a grid of

squares with sides 1 unit. O is the midpoint ofPQ.X, YandZare three moving points in the

diagram.

(a) On the diagram draw

(i) The locus of Xsuch that it is constantly 3 units from linePQ.

(ii)

(iii)

The locus ofYsuch that it is always 5 units from lineRQ.

The locus ofZsuch that pointZfrom O is always 5 units.

(b) Hence, mark with the symbol the intersection of the locus ofYand the locus ofZ.

Answer :

Diagram 10

[4 marks]

11. Expand each of the following expressions :

(a) 2 ( )3+x + 5 ( )2+x(b) ( )mn ( )mn 3Answer :

a)

124

O

S

P

R

Q


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b)

[3 marks]

12.Express

2

32 +a3

4 a as a single fraction in its simplest form.

Answer :

[3 marks]

13. In Diagram 13, trianglesJKNandJLMare similar.

Diagram 13

State

(a) The angle in triangleJLMwhich corresponds to JKN.

(b) Find the length, in cm, ofLM.

Answer :

a)

125

3 cm

2 cm

6 cm

J

N

ML

K


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b)

[3 marks]

14. List all the integer values of k which satisfy both the inequalities

2k + 2 - 4 and 4 - k > 0

Answer :

[3 marks]

15. Diagram 15 is an incomplete line graph which shows the monthly sales of chickens in a

market.

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Diagram 15

(a) In which month the number of chickens sold are the highest ?

(b) If the number of chickens sold in January is half of that in Mac, how many chickens

are sold in January?

Answer :

a)

b)

[3 marks]

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

Table 16 shows the values of two variables,x andy of a function.

x -2 -1 0 1 2 3 4

y 4 0 -2 -2 0 4 10

Table 16

127

Month


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Thex-axis and they-axis are provided on the graph paper.

(a) By using the scale of 2 cm to 2 units, complete and label they-axis.

(b) Based on table 1, plot the points on the graph paper.

(c) Hence, draw the graph of the function.

Answer :

128


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[5 marks]

17. Use of set squares and protractors are not allowed for this question.

Diagram 17 shows a quadrilateral ABCD.

129

x

-2 -1 0 1 2 3

y

x

-2 -1 0 1 2 3

y


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Diagram 17

Using only a ruler and a pair of compasses, construct diagram 17, beginning from the

line AB provided in the answer space.

Answer :

[5 marks]

18. Simplify (3hm 2 ) 4 (m 2 ) 1 h 7 m 3 .

Answer :

[3 marks]

19. Find the value of 3 21

54 21

2 23

.

130

C

BA

D

60

6 cm3 cm

A B


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Answer :

[3 marks]

20. Diagram 20 shows a right - angled trianglePQR.

Diagram 20

It is given that tan x =3

4. calculate the length, in cm, ofPR.

Answer :

P

Q

R

x

9 cm

kertasmodelpepsebenar(pmr)

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