50/1
Mathematics
Paper 1
July
2009
1¼ 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 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.
8
A list of formulae is provided.
This question paper consists 20 printed pages.
55
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1.
a m  a n  a m n
2.
a m  a n  a mn
3.
(a m )n  a mn
4.
Distance =
5.
Midpoint
( x2  x1 )2  ( y2  y1 )2
y  y2 
 x  x2
, 1
( x, y) =  1

2 
 2
distance travelled
time taken
6.
Average speed =
7.
Mean =
8.
Pythagoras Theorem
c 2  a 2  b2
sum of data
number of data
SHAPE AND SPACE
1.
Area of rectangle = length  width
2.
Area of triangle =
3.
Area of parallelogram = base  height
4.
Area of trapezium =
1
 base  height
2
1
 sum of parallel sides  height
2
56
5.
Circumference of circle =  d  2 r
6.
Area of circle =  r 2
7.
Curved surface area of cylinder = 2 rh
8.
Surface area of sphere = 4 r 2
9.
Volume of right prism = cross sectional area  length
10.
Volume of cuboid = length  width  height
11.
Volume of cylinder =  r 2 h
12.
Volume of cone =
13.
Volume of sphere =
14.
Volume of right pyramid =
15.
Sum of interior angles of a polygon = (n  2)  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 =
19.
Area of image = k 2  area of object
1 2
r h
3
4 3
r
3
1
 base area  height
3
PA
PA
57
Answer all questions.
1.
2.
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
Which of the following fractions has value greater than
A
B
C
D
3.
4.
3
?
4
7
8
2
3
1
2
5
7
Express 33
168
as a decimal
100000
A
33.168
B
33.0168
C
33.00168
D
33.000168
Table 4 shows the temperature for four towns on a particular day.
Town
E
F
G
H
Temperature (°C)
-2
3
9
-8
Table 4
Which town was the coldest on that day?
A E
B F
C G
D H
58
5.
Diagram 5 shows a sequence of prime numbers.
17,
19,
m,
n,
31
Diagram 5
Find the value of m + n.
A 44
B 48
C 52
D 56
6.
Diagram 6 shows some factors of 54.
1
9
6
54
27
Diagram 6
Identify three other factors of 54.
A 2, 3, 18
B 2, 18, 29
C 3, 4, 8
D 3, 4, 18
7.
Tharma’s 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, a
distance 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
59
9.
In Diagram 9, ABC is a straight line.
D
A
125º
xº
B
55o
Diagram 9
C
Calculate the value of x.
A 55
B 60
C 70
D 75
10. In Diagram 10 , PQRST is a pentagon and STU is a straight line
Q
q
P
U
p
40
T
R
r

s
S
Diagram 10
Find the value of p + q + r + s.
A 220
B 400
C 500
D 540
60
11. Diagram 11 shows a polygon.
B
A
2x
3x
F
3x
75
122
C
115
D
E
Diagram 11
Find the value of x.
A 41
B 51
C 55
D 61
12. Diagram 12 shows two regular polygons.
X
m
Q
W
T
V
U
S
R
Diagram 12
Find the value of m.
A 120
B 132
C 144
D 228
61
13. In Diagram 13, PQR is a right-angled triangle, RVU is an equilateral triangle and QRVW is
a square.
P
5 cm
Q
W
12 cm
R
V
U
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.
X
15 cm
W
6 cm
Y
4 cm
V
10 cm
Z
Diagram 14
Find the area in cm², of the shaded region.
A
105
B
75
C
35
D
30
62
15. Diagram 15 shows the plan of an orchard.
4m
6m
4m
10 m
15 m
Diagram 15
2
Find the area, in m , 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
17. In Diagram 17, the volume of the cylinder is equal to the volume of the cone..
h
21
cm
4 cm
cm
44 cm
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 area
of the base is 36 cm2.
T
P
S
Q
R
Diagram 18
Find the total surface area, in cm2, of the solid.
A
144
B
96
C
51
D
48
64
19. Diagram 19 shows a prism with a right angled triangle as its uniform cross section.
P
5 cm
R
Q
3 cm
12 cm
Diagram 19
Calculate the total surface area of the prism.
A
120 cm²
B
156 cm²
C
160 cm²
D
180 cm²
20. Diagram 20 shows a rectangle PQRS and some construction lines made by a student.
P
S
Q
Diagram 20
R
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
65
21. In Diagram 21, O is the centre of the circle.
O
130⁰
x⁰
Diagram 21
Find the value of x.
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.
P
50°
S
T
70°
x°
Q
R
Diagram 22
Find the value of x.
A 55
B 40
C 35
D 30
66
23. Diagram 23 shows a circle with centre O. PT, QU, RV and SW are diameters of the circles.
W
V
P
30°
U
Q
O
50°
T
R
S
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.
O●
Diagram 24
Using π =
22
, calculate the area in cm², of the shaded part.
7
A 38.5
B 77.0
C 115.5
D 154.0
67
25. In Diagram 25, PQRST is a trapezium, QST and QRS are right-angled triangles.
16 cm
Q
P
20 cm
R
T
S
5 cm
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.
C
3 cm B
6 cm
A
6 cm
D
E
Diagram 26
Given CD = 6 cm, calculate the length, in cm, of BE.
A 3
B 4
C 6
D 9
27. Given x  3 y  9 and 2 x  3 y  6 , calculate the value of x.
A 2
B 3
C 4
D 5
68
28.
Solve the following inequality.
3
3
y + 3 <
4
4
A y<3
B
y < -3
C y>3
D y > -3
29.
In Diagram 29, B is the midpoint of the straight line AC.
y
C (p, 8)
B (4, 5)
●
●
A (-1, 2)
●
x
0
Diagram 29
Find the value of p.
A 9
B
6
C 3
D 2
69
30.
Diagram 30 shows five points on a Cartesian plane.
y
x
Q(-3, 10) ●
●
-
P(8, 6)
-
x
R(-9, -2)●
S(-6, -8)
O
●
T(11, 5)
●
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.
22
( Use  = )
7
54
A
B 61
C 70
D 82
70
32. Table 32 shows the registration fees for an examination
Basic fee
RM150
Fee 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 RM75
B RM95
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.
1
hours. He started his
2
journey at 7.40 a.m. and arrived Ipoh 20 minutes late. What time did Daud arrive Ipoh?
Daud drove from Kluang to Ipoh. His journey was expected to take 6
A 2.40 p.m.
B 2.30 p.m.
C 2.10 p.m.
D 1.50 p.m.
71
35 Diagram 35 is a pie chart showing the number of ice cream sold at a stall on a certain day.
Chocolate
60
Vanilla
36
Strawberry
10
y
Orange
22
x
Corn
32
Diagram 35
Find the value of x + y.
A
68°
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.
72
37. Table 37 shows the number of teachers in five housing estates.
Housing estates
Number of teachers
A
10
B
13
C
p
D
7
E
5
Table 37
The mode is B.
Find the possible value of p.
A 12
B 14
C 25
D 35
38. Table 38 shows the scores in a game
Score
Frequency
0
5
1
7
2
2
3
6
4
4
5
6
Table 38
The median score is
A 1
B 2
C 3
D 4
39. Table 39 shows the values of variables x and y for the function of y = 3x2 – 2x
x
y
-2
m
-1
5
0
0
1
1
2
8
Table 39
Find the value of m.
A 16
B 8
C -8
D -16
73
40.
Which of the following graphs represents y = x + 6
A
y
(0,6 )
x
0
B
(6,0 )
y
(6,0 )
x
0
(0,-6)
C
y
(6,0 )
0
x
(0,-1 )
D
y
(0,6 )
(-6,0 )
x
0
END OF QUESTION PAPER
74
50/1
Mathematics
Paper 1
July
2009
1¼ hours
Set 2
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 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.
8.
A list of formulae is provided.
This question paper consists 21 printed pages.
75
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1.
a m  a n  a m n
2.
a m  a n  a mn
3.
(a m )n  a mn
4.
Distance =
5.
Midpoint
( x2  x1 )2  ( y2  y1 )2
y  y2 
 x  x2
, 1
( x, y) =  1

2 
 2
distance travelled
time taken
6.
Average speed =
7.
Mean =
8.
Pythagoras Theorem
c 2  a 2  b2
sum of data
number of data
SHAPE AND SPACE
1.
Area of rectangle = length  width
2.
Area of triangle =
3.
Area of parallelogram = base  height
4.
Area of trapezium =
1
 base  height
2
1
 sum of parallel sides  height
2
76
5.
Circumference of circle =  d  2 r
6.
Area of circle =  r 2
7.
Curved surface area of cylinder = 2 rh
8.
Surface area of sphere = 4 r 2
9.
Volume of right prism = cross sectional area  length
10.
Volume of cuboid = length  width  height
11.
Volume of cylinder =  r 2 h
12.
Volume of cone =
13.
Volume of sphere =
14.
Volume of right pyramid =
15.
Sum of interior angles of a polygon = (n  2)  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 =
19.
Area of image = k 2  area of object
1 2
r h
3
4 3
r
3
1
 base area  height
3
PA
PA
77
Answer all questions.
1.
2.
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
Table 2 shows the types of item that Sarah bought from a sundry shop.
Types of item
Item A
Item B
Item C
Price per kg
RM30
RM19
RM18
Quantity
4.5 kg
2 kg 500 g
500 g
Table 2
Sarah has RM250.00
How much money is left after she has paid for all the items?
3.
A
RM61.75
B
RM5.85
C
RM105.50
D
RM58.50
5
of the durians . Later he gave 20 of the
6
remaining durians to his friends. Calculate the percentage of the durians that he has left.
Ali had 300 durians. He managed to sell
A
50
B
16.67
C
10
D
6.67
78
4.
Diagram 4 is part of a number line.
P
-12
0
Q
Diagram 4
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 is
11
of its
12
1
of her savings to buy the T-shirt. What was her
2
savings before she bought the T-shirt?
original price. Swee Lan uses
A RM22.00
B 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.
1
m long. He used 1.69 m of the rope from each roll.
2
Find the length of the remaining rope.
Ali has 5 rolls of rope. Each roll is 3
A 9.15 m
B 9.05 m
C 9.00 m
D 8.05 m
79
8.
A bus started its journey from Kuala Lumpur and arrived at Johor Bahru at 4.45 a.m. on the
1
next day. If the journey took 5 hours, the bus left Kuala Lumpur at
4
1000
hours
A
B 2200 hours
C 2230 hours
D 2330 hours
9.
In Diagram 9, ABC is a triangle
B
x°
35°
x°
62°
A
147°
C
Diagram 9
Find the value of x.
A 15
B 18
C 20
D 25
80
10. In Diagram 10, pentagon P’Q’R’S’T is the image of pentagon PQRST under an enlargement
Q’
P’
P
T’
Q
T
R
S
R’
S’
Diagram 10
Find the scale factor of this enlargement.
A 1
B 2
C 3
D 4
11. Diagram 11 shows a regular hexagon.
y
Diagram 11
Find the value of y
A 30
B 35
C 40
D 45
81
12. In Diagram 12, PQRT are five vertices of a regular polygon.
T
S
P
3x
x
Q
U
R
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 cm².
A
14cm
B
15cm
C
h cm
Diagram 14
D
Find its height, h in cm.
A 11
B 14
C 20
D 24
82
15. In Diagram 15, DEGH is a parallelogram and FGH ia a straight line.
D
E
F
H
G
Diagram 15
Given DE = 12 cm and HF = 15 cm. If the area of triangle EFG is 6 cm², 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
B
C
D
Right prism
cuboid
pyramid
cone
83
17. Diagram 17 shows two containers in the shape of a cuboid and right prism.
11 cm
6 cm
21 cm
Diagram 17
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
B
C
D
13
21
88
66
3
1
1
years old. Bala is 9
years older than Aminah. Chee Meng’s age is 2
4
12
2
times the sum of the ages of Aminah and Bala. What is Chee Meng’s age?
18. Aminah is 4
A
B
C
D
7
8
5
13
6
1
16
3
11
46
24
11
84
19. In Diagram 19, JOL is a diameter of the circle JKLM with centre O. MLN is a straight line.
K
70°
J
●
O
x°
130°
M
N
L
Diagram 19
Find the value of x.
A
B
C
D
20
25
30
70
20. In Diagram 20, DEFG is a cyclic quadrilateral.
E
D
30°
x
F
100°
G
H
Diagram 11
Find the value x.
A
B
C
D
50°
60°
80°
100°
85
21. In Diagram 21, PQR and STU are two circles with a common centre, O. PSOUR is a straight
line.
P
S
T
O
U
R
Q
Diagram 21
Given that PS = SO = 4 cm, calculate the area, in cm², of the shaded region.
A
B
C
D
8π
16π
32π
64π
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.
Q
8 cm
10 cm
●
P
O
R
Diagram 22
Find the area, in cm², of the coloured region.
A 25π - 24
B 25π - 30
C 25π - 48
D 100π - 48
86
23. In Diagram 23, PQRS is a cyclic quadrilateral.
NPQ is a straight line and O is the centre of the circle.
Q
P
120°
O
R
x
N
S
Diagram 23
Find the value of x.
A 50°
B 60°
C 70°
D 120°
24. Diagram 24 shows a triangular pattern on a wall.
15 m
17 m
Diagram 24
A tin of paint is required to paint an area of 5 m².
How many tins of paint if needed to paint the surface of the triangle?
A 12
B 24
C 25
D 32
87
25. Which of the following diagram shows line XY non-parallel to line PQ ?
P
X
A.
70O
70O
Q
Y
P
X
B.
70O
70O
Q
Y
C.
P
X
O
70
70O
Q
Y
D.
P
X
110O
110O
Y
Q
88
26. It is given that 2 x  3 y  17 and x  4 . Calculate the value of y.
A 3
B 4
C 5
D 6
27. Diagram 27 represent two simultaneous linear inequalities on a number line.
–4
–3
–2
–1
0
1
2
Diagram 27
Which of the following inequalities is the solution for both of the inequalities on the number
line ?
28.
A
–3 ≤ x ≤ 2
B
–3 < x < 2
C
–3 ≤ x < 2
D
–3 < x ≤ 2
In Diagram 28, CE are points on a Cartesian plane.
y
C (-7, 8) ●
0
●
x
E (5, -2)
Diagram 28
D is the midpoint of CE. The coordinates of D are
A (1, 3)
B
(2, 3)
C (-1, 3)
D (-2, 3)
89
29.
Diagram 29 shows points J, K, L and M marked on a grid of equal squares with sides of
1 unit.
K
●
●
J
●
●
O
M
●
L
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.
A
12 cm
B
150º
9 cm
C
Diagram 30
D
Calculate the perimeter of the whole diagram.
A 60.29 cm
B
72.59 cm
C 75.29 cm
D 75.59 cm
90
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
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
3 mangoesteens for RM 15
5 mangoesteen for RM 20
X
2 mangoesteens for RM 8
5 mangoesteens for RM 15
Y
3 mangoesteens for RM 21
6 mangoesteens for RM 42
Z
5 mangoesteens for RM 25
8 mangoesteens for RM 48
Table 32
Which stall sells mangoesteens at a price that is proportional to the number of
mangoesteens?
A W
B X
C Y
D Z
33. Table 33 shows the number of computers sold by a company from January to April
Month
Number of computer sold
January
1450
February
1800
March
1650
April
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
91
June
May
April
March
February
January
Number of books
34. Diagram 34 is a bar chart which shows the number of books sold by a bookshop in six
months
Month
Diagram 34
If the number of books sold in March is 20 000, find the number of books sold in February
A 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.
Durian
2y
Rambutan
Guava
60˚
160˚
5y
Mangosteen
Diagram 21
There are 252 rambutans.
How many mangosteens are in the trolley?
A 98
B 70
C 42
D 28
92
36. The line graph in Diagram 36 shows the income of a hawker in 4 months.
Income of a hawker in 4 months
Income (RM)
2000
1500
1800
1700
1400
1350
1000
500
0
Jan
Feb
Mac
Apr
Month
Diagram 36
Calculate the total income in 4 months.
A RM 6505
B RM 6500
C RM 6250
D RM 6600
37. Table 37 shows the numbers of book read by Zulkifli in 5 months.
Month
Number of books
Jan
5
Feb
3
Mac
2
Apr
6
May
4
Table 37
Calculate the mean number of books read by Zulkifli in 5 months.
A 3
B 4
C 5
D 6
93
38. Diagram 38 shows a graph of a function on a Cartesian plane.
2
-4
0
-2
2
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 of y = -2x2 + 1
x
y
-2
-7
-1
s
0
1
1
-1
2
t
Table 39
Calculate the value of s + t
A -1
B -6
C -7
D -8
94
40. In Diagram 40 ABCDEFGH is a regular octagon with sides 3 cm.
B
C
A
D
H
E
G
F
Diagram 40
X is the locus of a point which moves such that it is always equidistant from point B and D.
Y is the locus of a point which moves such that its distance from point H is always 3 cm.
Which of the following points is the intersection of locus X and locus Y
A C
B G
C A
D E
END OF QUESTION PAPER
95
50/1
Mathematics
Paper 2
July
2009
1¾ hours
Set 1
JABATAN PELAJARAN PERAK
PENILAIAN MENENGAH RENDAH 2009
ANSWER TO SCORE
2009 PMR FORECAST PAPER
MATHEMATICS
Paper 2
1 hour 45 minutes
DO NOT OPEN THIS QUESTION PAPER
UNTIL YOU ARE TOLD TO DO SO
1.
2.
3.
4.
5.
This question paper consists of 20
questions.
Answer all questions. Answer all
questions
Write your answers clearly in the spaces
provided in the question paper.
Diagrams are not drawn to scale unless
stated.
The marks allocated are shown in
brackets.
Question
Allocated
Marks
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
2
16
5
17
4
18
5
19
2
20
3
Marks
Obtained
Total
This question paper consists 18 printed pages.
96
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.
97
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1.
a m  a n  a m n
2.
a m  a n  a mn
3.
(a m )n  a mn
4.
Distance =
5.
Midpoint
( x2  x1 )2  ( y2  y1 )2
y  y2 
 x  x2
, 1
( x, y) =  1

2 
 2
distance travelled
time taken
6.
Average speed =
7.
Mean =
8.
Pythagoras Theorem
c 2  a 2  b2
sum of data
number of data
SHAPE AND SPACE
1.
Area of rectangle = length  width
2.
Area of triangle =
3.
Area of parallelogram = base  height
4.
Area of trapezium =
1
 base  height
2
1
 sum of parallel sides  height
2
98
5.
Circumference of circle =  d  2 r
6.
Area of circle =  r 2
7.
Curved surface area of cylinder = 2 rh
8.
Surface area of sphere = 4 r 2
9.
Volume of right prism = cross sectional area  length
10.
Volume of cuboid = length  width  height
11.
Volume of cylinder =  r 2 h
12.
Volume of cone =
13.
Volume of sphere =
14.
Volume of right pyramid =
15.
Sum of interior angles of a polygon = (n  2)  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 =
19.
Area of image = k 2  area of object
1 2
r h
3
4 3
r
3
1
 base area  height
3
PA
PA
99
1.
Calculate the value of
– 42  6 – 10 =
Answer :
[ 2 marks]
2.
Calculate the value of
6  0.24
0.4
=
Answer :
[ 2 marks]
3.
1
216
a)
Find the value of
b)
Calculate the value of  3  169
3

=
3

2
=
Answer :
a)
b)
[ 3 marks]
100
4.
Solve each of the following equations :
a)
2 ( r – 2 ) = 10 – 5r
b)
s6
= 4s
2
Answer :
a)
b)
[ 3 marks]
5.
Diagram 5 in the answer space shows quadrilateral ABCD. C’D’ is the image of CD under
a reflection in the straight line LM.
On Diagram 5 in the answer space, complete the image of quadrilateral ABCD.
Answer:
M
D’
D
C’
C
A
B
L
Diagram 5
[ 2 marks]
101
6.
Diagram 6 shows two quadrilaterals, KLMN and K’L’M’N’, drawn on a grid of equal
squares with sides of 1 unit.
N’
K’
L’
M’
N
K
L
M
Diagram 6
K’L’M’N’ is the image of KLMN under transformation P.
Describe in full transformation P.
Answer:
[2 marks]
102
7.
Factorise completely each of the following expressions :
a)
8 x ²  4 xy
b)
6k ²  3k  18
Answer :
a)
b)
[ 2 marks]
8.
Simplify each of the following
a) 24 x  3
b)  3x  4  x  4
Answer :
a)
b)
[ 3 marks ]
9.
3 2n

 as a single fraction in its simplest form.
5m  mn 
Answer :
Express
[ 3 marks]
103
10.
a) Solve the inequality 8 + x < 14
b) List all the integer values of x which satisfy the inequalities
1
2 - 3x < 11 and 8 - x  7
3
Answer :
a)
b)
[ 3 marks]
11.
Given that
m2  5
 k , express m in terms of k
4
Answer :
[ 3 marks]
104
12.
4
2
(a) Simplify (p q )
1
2
 (p 2 q  1 ) 2
3
1
(b) Find the value of 3 2 × 3 2
Answer :
a)
b)
[ 3 marks]
105
13.
The frequency table in table 13 shows the number of car owners in a housing park.
Types of Cars
Number of Women
Number of Man
Kancil
15
5
Persona
18
22
Waja
20
28
Table 13
Represent all the data by drawing a horizontal dual bar chart in the answer space.
Answer :
Women
Men
[4 marks]
106
14.
The diagram 14 below shows the number of books borrowed from a school library by 14
students.
3
4
2
2
4
5
3
5
5
3
6
2
2
6
Diagram 14
a ) Using the data, complete the frequency table below.
b) State the median
.
Answer :
a)
Number
2
3
4
5
6
Frequency
b)
[3 marks]
107
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
16.
Diagram 16 below shows a circle with centre O, which is divided into four equal parts. W,
X and Y are three moving points in the diagram.
a) W is 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 of W.
b) On the diagram draw
i) The locus of point X such that it is equidistant from line OP and line OQ.
ii) The locus of point Y such that YR = RQ.
c) Hence, mark with the symbol  the intersection of the locus of X and the locus of Y.
Answer :
Q
O
P
R
S
Diagram 16
[5 marks]
109
17.
Use the graph paper provided to answer this question.
Table 17 shows the values of two variables, x and y, for a function.
x
y
-3
0
-2.5
-10
-2
-15
-1
-14
0
-9
1
0
2
10
3
21
4
32.5
Table 17
The x – axis and the y – axis are provided on the graph paper.
a) By using a scale of 2cm to 5 units, complete and label the y – axis.
b) Based on table 17, plot the points on the graph paper.
c) Hence, draw the graph of the function.
[4 marks]
110
Answer :
111
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 rectangle PQRS.
ii) construct a perpendicular line RT from the point R to the straight line QS where the
point T lies on the straight line QS.
Answer :
P
Q
R
Diagram 18
[5 marks]
19.
Diagram 19 in the answer space shows triangle PQR drawn on a grid of the equal squares.
Triangle PQR is enlarged by the scale factor 2 from the centre O. Draw the image of
triangle PQR in the answer space.
Answer :
Q
O
P
R
Diagram 19
[2 marks]
112
20.
Diagram 20 shows two right angled triangles, PMN and PQR. MPQ is straight line.
6 cm
M
N
x˚
P
y˚
Q
R
12 cm
Diagram 20
3
4
and sin yo =
5
5
a) Find the value of tan xo
b) Calculate the length of MPQ in cm
It is given that cos xo =
Answer :
a)
b)
[3 marks]
113
50/1
Mathematics
Paper 2
July
2009
1¾ hours
Set 2
JABATAN PELAJARAN PERAK
PENILAIAN MENENGAH RENDAH 2009
ANSWER TO SCORE
2009 PMR FORECAST PAPER
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 of 20
questions.
2. Answer all questions. Answer all questions
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.
Question
Allocated
Marks
1
2
2
3
3
2
4
2
5
2
6
2
7
4
8
2
9
3
10
4
11
3
12
3
13
3
14
3
15
3
16
5
17
5
18
3
19
3
20
3
Marks
Obtained
Total
This question paper consists 16 printed pages.
114
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.
115
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1.
a m  a n  a m n
2.
a m  a n  a mn
3.
(a m )n  a mn
4.
Distance =
5.
Midpoint
( x2  x1 )2  ( y2  y1 )2
y  y2 
 x  x2
, 1
( x, y) =  1

2 
 2
distance travelled
time taken
6.
Average speed =
7.
Mean =
8.
Pythagoras Theorem
c 2  a 2  b2
sum of data
number of data
SHAPE AND SPACE
1.
Area of rectangle = length  width
2.
Area of triangle =
3.
Area of parallelogram = base  height
4.
Area of trapezium =
1
 base  height
2
1
 sum of parallel sides  height
2
116
5.
Circumference of circle =  d  2 r
6.
Area of circle =  r 2
7.
Curved surface area of cylinder = 2 rh
8.
Surface area of sphere = 4 r 2
9.
Volume of right prism = cross sectional area  length
10.
Volume of cuboid = length  width  height
11.
Volume of cylinder =  r 2 h
12.
Volume of cone =
13.
Volume of sphere =
14.
Volume of right pyramid =
15.
Sum of interior angles of a polygon = (n  2)  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 =
19.
Area of image = k 2  area of object
1 2
r h
3
4 3
r
3
1
 base area  height
3
PA
PA
117
1.
Calculate the value of
3 7 2
×  
2 5 3
Answer :
[2 marks]
2.
Calculate the value of
3

2.6 × 3.5    2  and express the answer as a decimal.
5

Answer :
[3 marks]
118
3.
Diagram 3, in the answer space shows two triangles, PQR and P’Q’R’, drawn on a grid of
equal squares. P’Q’R’ is the image of PQR under an enlargement.
On Diagram 3 in the answer space, mark T as the centre of enlargement.
Answer:
y
P’
8
6
P
4
Q
R
2
Q’
R’
x
-6
-4
-2
0
2
4
6
8
-2
Diagram 3
[2 marks]
119
4.
Diagram 4 in the answer space shows quadrilaterals PQRS and straight line WX drawn on a
grid of equal squares.
Starting from the line WX, draw quadrilateral WXYZ which is congruent to quadrilateral
PQRS.
Answer:
S
R
P
X
Q
W
Diagram 4
[2 marks]
5.
Diagram 5 in the answer space shows triangle KLM drawn on a grid of equal squares. On
the diagram in the answer space, draw the image of the triangle KLM under a rotation of
90˚ clockwise about the point P.
Answer:
L
K
M
●P
Diagram 5
[2 marks]
120
6.
Given that,
p 3
 5 express p in terms of k
k
Answer :
[2 marks]
7.
Solve each of the following equations :
a)
- 4 – 6x = 14
b)
3m  10
=2
4m
Answer :
a)
b)
[4 marks]
8.
Simplify :
6ab  3b  7  22b  5  4ab
Answer :
[2 marks]
121
9.
Diagram 9 shows polygon ABCDEF drawn on a grid of equal squares.
.
A
B
E
F
D
C
Diagram 9
On the grid in the answer space, redraw the polygon using the scale of 1 : 2.
Answer :
[3 marks]
122
10.
The diagram 10 in the answer space shows a rectangle, PQRS which is drawn on a grid of
squares with sides 1 unit. O is the midpoint of PQ. X, Y and Z are three moving points in the
diagram.
(a) On the diagram draw
(i)
The locus of X such that it is constantly 3 units from line PQ.
(ii)
The locus of Y such that it is always 5 units from line RQ.
(iii) The locus of Z such that point Z from O is always 5 units.
(b) Hence, mark with the symbol  the intersection of the locus of Y and the locus of Z.
Answer :
S
R
P
O
Q
Diagram 10
[4 marks]
11.
Expand each of the following expressions :
(a)  2 x  3 + 5 x  2
(b) n  m n  3m
Answer :
a)
b)
[3 marks]
123
12.
Express
2a  3 a  4
as a single fraction in its simplest form.

2
3
Answer :
[3 marks]
13.
In Diagram 13, triangles JKN and JLM are similar.
J
3 cm
K
6 cm
N
2 cm
L
M
Diagram 13
State
(a) The angle in triangle JLM which corresponds to JKN.
(b) Find the length, in cm, of LM.
Answer :
a)
b)
[3 marks]
124
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.
Number of
chickens
●
400
●
350
●
300
●
250
●
200
150
100
50
JAN
FEB
MAC
APR
MAY
JUN
Month
Diagram 15
125
(a)
(b)
In which month the number of chickens sold are the highest ?
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 and y of a function.
x
y
-2
4
-1
0
0
-2
1
-2
2
0
3
4
4
10
Table 16
The x-axis and the y-axis are provided on the graph paper.
(a) By using the scale of 2 cm to 2 units, complete and label the y-axis.
(b) Based on table 1, plot the points on the graph paper.
(c) Hence, draw the graph of the function.
126
Answer :
y
x
-2
-1
0
1
2
3
[5 marks]
127
17.
Use of set squares and protractors are not allowed for this question.
Diagram 17 shows a quadrilateral ABCD.
C
D
6 cm
3 cm
60˚
A
B
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 :
A
18.
B
[5 marks]
Simplify (3hm 2 ) 4 × (m 2 ) 1  h 7 m 3 .
Answer :
[3 marks]
128
19.
1
2
1
2
Find the value of 3 × 54 × 2
3
2
.
Answer :
[3 marks]
20.
Diagram 20 shows a right - angled triangle PQR.
P
R
x○
9 cm
Q
Diagram 20
It is given that tan x○ =
4
. calculate the length, in cm, of PR.
3
Answer :
[3 marks]
129