Pmr Mat K2 Set 2
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Set 2
SULIT 50/2 NO. KAD PENGENALAN
50/2 Mathematics Paper 2 July 2006 1
ANGKA GILIRAN
3 hours 4
JABATAN PELAJARAN PERAK
PENILAIAN MENENGAH RENDAH 2006 LEARNING TO SCORE MATHEMATICS Paper 2 I hour 45 minutes
DO NOT OPEN THIS QUESTION PAPER UNLESS TOLD TO DO SO
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. Diagrams are not drawn to scale unless stated. 5. The maximum marks allocated for each question are shown in brackets.
Question Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL
Allocated Marks 2 2 3 2 2 2 3 3 2 4 2 3 3 3 5 3 3 6 3 4 60
This question paper consists of 17 printed pages.
Marks Obtained
2 Learning To Score 2006 : SET 2 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.
Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
3 Learning To Score 2006 : SET 2 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
RELATIONS 1
n a m õ a = a mn
2
am an
3
a
m n
= a mn
= a mn
4
Distance =
5
Midpoint
( x 2 x1 ) 2 ( y 2 y1 ) 2
x1 x2 y1 y 2 , 2 2
(x,y) = 6
Average speed
=
distance travelled time taken
7
Mean
=
sum of data
number of data
8
Pythagoras Theorem c2 = a 2 + b2
SHAPE AND SPACE 1
Area of rectangle = length x width
2
Area of triangle =
3
Area of parallelogram = base x height
4
Area of trapezium =
Unit Kurikulum Jabatan Pelajaran Perak
1 x base x height 2
1 x sum of parallel sides x height 2
Lihat sebelah
4 Learning To Score 2006 : SET 2 5
Circumference of circle = d = 2 r
6
Area of circle
7
Curved surface area of cylinder = 2 rh
8
Surface area of sphere = 4 r2
9
Volume of right prism = cross sectional area õ length
10
Volume of cuboid = length x width x height
11
Volume of cylinder = r2 h
12
Volume of cone =
13
Volume of sphere =
14
Volume of right pyramid =
15
Sum of interior angles of a polygon = (n – 2) x 180
16
=
r2
1 r2 h 3 4 3 r 3
arc length
1 x base area x height 3
=
angle subtended at centre
circumference of circle
17
area of sector
=
angle subtended at centre
area of circle
18
Scale factor,
360
360
k =
PA’ PA
19
Area of image = k2 x area of object
Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
5 Learning To Score 2006 : SET 2 Answer all questions.
1
Calculate the value of 2
3 1 3 2 and express the answer as a 4 4 5
fraction in its lowest term.
2 marks
Answer :
1 2 2
Calculate the value of 3 decimal.
1 ( ─ 1.5 ) 0.8 and express the answer as a 2
2 marks
Answer :
2 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
6 Learning To Score 2006 : SET 2
3
1 4 8 5
(a) Find the value of
(b) Calculate the value of
3
2
64
32
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.
A
B
10 cm
E
6 cm
D
C 15 cm
DIAGRAM 1
Answer :
2 marks
4 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
7 Learning To Score 2006 : SET 2 5 y
6 4 N
2
M
0
2
x
-4
-2
4
6
-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 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
8 Learning To Score 2006 : SET 2 6
Diagram 3 shows polygon ABCDEF drawn on a grid of equal squares. Shade figure ABCDEF.
1 of the 4
2 marks
Answer :
A F B
E
D C DIAGRAM 3
6 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
9 Learning To Score 2006 : SET 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 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
10 Learning To Score 2006 : SET 2 8
Table 1 shows the T-shirt size used by 30 students in a class. S
XL
M
M
M
S
XL
M
M
S
S
L
M
M
L
XL
M
M
S
S
L
L
M
M
L
XL
XL
M
L
M
TABLE 1
(a) Using the data, complete the frequency table in the answer space. (b) State the mode.
3 marks
Answer :
(a) T-shirt size
Frequency
S M L XL
8
(b)
3 9
Simplify
3 x 2 2
x 5
2
2 marks
Answer :
9 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
11 Learning To Score 2006 : SET 2 10
5 x ≤ 3
(a) Solve the inequality
(b) List all the integer values of x which satisfy the inequalities
2 4 x < 10
and
x ≤ 4 +
x 5
4 marks
Answer : (a)
(b)
10
4 2
11
Find the value of 8 3 3
1
[2 marks]
Answer:
11
2
12.
Simplify
2 m3n
2
÷ 5 m 6 n 4
× mn
[3 marks]
Answer:
12
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
12 Learning To Score 2006 : SET 2 13. Given that r =
5 s . Express s in terms of r and t . 2t
[3 marks]
Answer:
13
3 14. Solve each of the following equations: (a)
10 p = 3 5
(b)
5 4 25 x = 2 x 2 5
[3 marks]
Answer: (a)
(b)
14
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
13 Learning To Score 2006 : SET 2 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
N
V
DIAGRAM 5
15
5 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
14 Learning To Score 2006 : SET 2 16. Factorise completely: (a)
9m 2 1
(b)
3 p 6q pq 2q 2
[3 marks]
Answer: (a)
(b)
16
3
17. Express
m 4m 2 12 2n 8mn
as a single fraction in its simplest form. [3 marks]
Answer:
17
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
15 Learning To Score 2006 : SET 2 18. Set squares and protractors are not allowed for this question.
P
Q
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)
Unit Kurikulum Jabatan Pelajaran Perak
6
Lihat sebelah
16 Learning To Score 2006 : SET 2 19. Table 2 shows the number of gold medals won by four sports houses in a school.
Sports Houses Alpha Beta Gamma Sigma
Number of Gold Medals 20 x 9 18 TABLE 2
(a) Based on the bar chart in the answer space below, state the value of x. (b) Complete the bar chart to represent all the information given in the Table 2. [3 marks]
Answer: (a)
(b) Number of gold medals
20 18 16 14 12 10 8 6 4 2 Sports Houses
19
Alpha
Beta Gamma Sigma
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
17 Learning To Score 2006 : SET 2 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 y
-4 15
-3 4
-2 -3
-1 -6
0 -5
1 0
2 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]
END OF QUESTION PAPER
Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
SULIT 50/2 NO. KAD PENGENALAN
50/2 Mathematics Paper 2 July 2006 1
ANGKA GILIRAN
3 hours 4
JABATAN PELAJARAN PERAK
PENILAIAN MENENGAH RENDAH 2006 LEARNING TO SCORE MATHEMATICS Paper 2 I hour 45 minutes
DO NOT OPEN THIS QUESTION PAPER UNLESS TOLD TO DO SO
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. Diagrams are not drawn to scale unless stated. 5. The maximum marks allocated for each question are shown in brackets.
Question Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL
Allocated Marks 2 2 3 2 2 2 3 3 2 4 2 3 3 3 5 3 3 6 3 4 60
This question paper consists of 17 printed pages.
Marks Obtained
2 Learning To Score 2006 : SET 2 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.
Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
3 Learning To Score 2006 : SET 2 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
RELATIONS 1
n a m õ a = a mn
2
am an
3
a
m n
= a mn
= a mn
4
Distance =
5
Midpoint
( x 2 x1 ) 2 ( y 2 y1 ) 2
x1 x2 y1 y 2 , 2 2
(x,y) = 6
Average speed
=
distance travelled time taken
7
Mean
=
sum of data
number of data
8
Pythagoras Theorem c2 = a 2 + b2
SHAPE AND SPACE 1
Area of rectangle = length x width
2
Area of triangle =
3
Area of parallelogram = base x height
4
Area of trapezium =
Unit Kurikulum Jabatan Pelajaran Perak
1 x base x height 2
1 x sum of parallel sides x height 2
Lihat sebelah
4 Learning To Score 2006 : SET 2 5
Circumference of circle = d = 2 r
6
Area of circle
7
Curved surface area of cylinder = 2 rh
8
Surface area of sphere = 4 r2
9
Volume of right prism = cross sectional area õ length
10
Volume of cuboid = length x width x height
11
Volume of cylinder = r2 h
12
Volume of cone =
13
Volume of sphere =
14
Volume of right pyramid =
15
Sum of interior angles of a polygon = (n – 2) x 180
16
=
r2
1 r2 h 3 4 3 r 3
arc length
1 x base area x height 3
=
angle subtended at centre
circumference of circle
17
area of sector
=
angle subtended at centre
area of circle
18
Scale factor,
360
360
k =
PA’ PA
19
Area of image = k2 x area of object
Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
5 Learning To Score 2006 : SET 2 Answer all questions.
1
Calculate the value of 2
3 1 3 2 and express the answer as a 4 4 5
fraction in its lowest term.
2 marks
Answer :
1 2 2
Calculate the value of 3 decimal.
1 ( ─ 1.5 ) 0.8 and express the answer as a 2
2 marks
Answer :
2 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
6 Learning To Score 2006 : SET 2
3
1 4 8 5
(a) Find the value of
(b) Calculate the value of
3
2
64
32
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.
A
B
10 cm
E
6 cm
D
C 15 cm
DIAGRAM 1
Answer :
2 marks
4 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
7 Learning To Score 2006 : SET 2 5 y
6 4 N
2
M
0
2
x
-4
-2
4
6
-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 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
8 Learning To Score 2006 : SET 2 6
Diagram 3 shows polygon ABCDEF drawn on a grid of equal squares. Shade figure ABCDEF.
1 of the 4
2 marks
Answer :
A F B
E
D C DIAGRAM 3
6 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
9 Learning To Score 2006 : SET 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 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
10 Learning To Score 2006 : SET 2 8
Table 1 shows the T-shirt size used by 30 students in a class. S
XL
M
M
M
S
XL
M
M
S
S
L
M
M
L
XL
M
M
S
S
L
L
M
M
L
XL
XL
M
L
M
TABLE 1
(a) Using the data, complete the frequency table in the answer space. (b) State the mode.
3 marks
Answer :
(a) T-shirt size
Frequency
S M L XL
8
(b)
3 9
Simplify
3 x 2 2
x 5
2
2 marks
Answer :
9 2 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
11 Learning To Score 2006 : SET 2 10
5 x ≤ 3
(a) Solve the inequality
(b) List all the integer values of x which satisfy the inequalities
2 4 x < 10
and
x ≤ 4 +
x 5
4 marks
Answer : (a)
(b)
10
4 2
11
Find the value of 8 3 3
1
[2 marks]
Answer:
11
2
12.
Simplify
2 m3n
2
÷ 5 m 6 n 4
× mn
[3 marks]
Answer:
12
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
12 Learning To Score 2006 : SET 2 13. Given that r =
5 s . Express s in terms of r and t . 2t
[3 marks]
Answer:
13
3 14. Solve each of the following equations: (a)
10 p = 3 5
(b)
5 4 25 x = 2 x 2 5
[3 marks]
Answer: (a)
(b)
14
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
13 Learning To Score 2006 : SET 2 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
N
V
DIAGRAM 5
15
5 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
14 Learning To Score 2006 : SET 2 16. Factorise completely: (a)
9m 2 1
(b)
3 p 6q pq 2q 2
[3 marks]
Answer: (a)
(b)
16
3
17. Express
m 4m 2 12 2n 8mn
as a single fraction in its simplest form. [3 marks]
Answer:
17
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
15 Learning To Score 2006 : SET 2 18. Set squares and protractors are not allowed for this question.
P
Q
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)
Unit Kurikulum Jabatan Pelajaran Perak
6
Lihat sebelah
16 Learning To Score 2006 : SET 2 19. Table 2 shows the number of gold medals won by four sports houses in a school.
Sports Houses Alpha Beta Gamma Sigma
Number of Gold Medals 20 x 9 18 TABLE 2
(a) Based on the bar chart in the answer space below, state the value of x. (b) Complete the bar chart to represent all the information given in the Table 2. [3 marks]
Answer: (a)
(b) Number of gold medals
20 18 16 14 12 10 8 6 4 2 Sports Houses
19
Alpha
Beta Gamma Sigma
3 Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
17 Learning To Score 2006 : SET 2 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 y
-4 15
-3 4
-2 -3
-1 -6
0 -5
1 0
2 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]
END OF QUESTION PAPER
Unit Kurikulum Jabatan Pelajaran Perak
Lihat sebelah
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