Mst Mid-year Mathematics Form 3 (pmr)
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SULIT
M S T –
ANGKA GILIRAN
–
NO. KAD PENGENALAN MATH
– –
&SCIENCE MATHEMATICS AND SCIENCE TUTORIAL
Tutorial PENILAIAN MENENGAH RENDAH 2009 PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN 3
50/2 mKertas
mMATHEMATICS 2 Jun 1 m
3 jam 4
Satu jam empat puluh lima minit
Examiner’s code
m
Question JANGAN BUKA KERTAS SOALAN SEHINGGA DIBERITAHU 1. This question paper consists of 20 questions. 2. Answer all questions. 3. Answers must be written clearly in the answer space provided. 4. Show your working. It may help you to get marks. 5. If you wish to change your answer, neatly cross out the answer. 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 or parts of a question are shown in brackets. 8. A list of formulae is provided on pages 2 and 3.
1 2 3
For Examiner’s Use Full Marks 2 2
4
3 3
5 6
2 2
7 8 9 10 11 12 13 14 15 16 17 18 19 20
3 2 3 2 5 3 2 4 5 5 4 4 2 2
Marks Obtained
9. Use of non-programmable scientific calculator Total is not allowed for this paper. 60 _______________________________________________________________________ _ Kertas soalan ini mengandungi 16 halaman bercetak [Lihat sebelah
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial m SULIT 2 m MATHEMATICAL FORMULAE
SULIT 50/2
The following formulae may be helpful in answering the questions. The symbols given are commonly used. RELATIONS 1
a m × a n = a m+ n
2
a m ÷ a n = a m−n
3
(a )
4
Distance =
5
Midpoint
m n
= a mn ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2
x1 + x 2 y1 + y 2 , (x, y) = 2 2 distance travelled time taken
6
Average speed =
7
Mean =
8
Pythagoras Theorem
sum of data number of data
c2 = a2 + b2
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 3 m SHAPES AND SPACE 1
Area of rectangle = length × width
2
Area of triangle =
3
Area of parallelogram = base × height
4
Area of trapezium =
5
Circumference of circle = πd = 2 πr
6
Area of circle = πr2
7
Curve surface area of cylinder = 2 πrh
8
Surface area of sphere = 4 πr2
9
Volume of right prism = cross sectional area × length
10
Volume of cuboid = length × width × height
11
Volume of cylinder = πr2h
12
Volume of cone =
13
Volume of speher =
14
Volume of right pyramid =
15
Sum of interior angles of a polygon = ( n − 2 ) × 180°
16
Arc length Angle subtended at centre = Circumference 360°
17
Area of sector Angle subtended at centre = Area of circle 360°
18
Scale factor, k =
19
Area of image = k2 × area of object
SULIT 50/2
1 × base × height 2
1 × sum of parallel sides × height 2
1 2 πr h 3 4 3 πr 3 1 × base area × height 3
PA' PA
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 4 m [60 marks]
SULIT 50/2
Answer all questions. 1 Calculate the value of – 43 + (86 – 6 × 12). m Answer:
[2 marks]
1 2 2
3 Calculate the value of 27 − − × 4.5 and express the answer as a decimal. 4 [2 marks] Answer:
2 2
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT m 3 (a) Find the value of 0.53.
SULIT 5
50/2
For Examiner’s use
2
(b)
1 Calculate the value of 3 − 1 . 8 [3 marks]
Answer: (a)
(b)
3 3 4
Solve each of the following linear equations: (a)
x – 3 = – 12
(b)
5x + 3 = x+6 2 [3 marks]
Answer: (a)
(b)
4 3 [Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 6 m 5 Diagram 1 shows a pentagon PQRST and R’S’ a grid of equal squares. R’S’ is the image of RS under a rotation of 90º clockwise about point O.
SULIT 50/2
On Diagram 1 in the answer space, complete the image of pentagon PQRST. [2 marks] Answer:
R'
S'
T
S P
R Q
Diagram 1
5 2
.
O
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial SULIT mm SULIT 7 50/2 m 6 Diagram 2 shows two polygons, Q and Q’, drawn on a grid of equal squares with sides of 1 unit.
For Examiner’s use
Q'
Q
Diagram 2 Q’ is the image of Q under transformation M. Describe in full transformation M. m Answer:
[2 marks]
6 2 7
Factorise completely each of the following expressions: (a)
24mn – 3m
(b)
4y2 – 4 [3 marks]
Answer: (a)
(b)
7 3 [Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT m 8 Simplify (3x – 1)2 – (7x + 4). Answer:
SULIT 8
50/2 [2 marks] m
8 2 9
(a)
(b)
1
Find the value of 64 3 × 2. Simplify
16k 5
( 2k )
−3 3
. [3 marks]
Answer: (a)
(b)
9 3
(
10 Simplify 4m 3 n −2 m Answer:
10 2
)
2
÷ 8m 4 n −5 .
[2 marks]
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial SULIT mm SULIT 9 50/2 m 11 Table 1 shows the vehicles used by 1200 students of SMK ST. Mary to go to school. Types of vehicles
Number of students
Bicycle
150
Motocycle
x
Car
200
Bus
300
For Examiner’s use
Table 1 (a)
Find the value of x.
(b)
Diagram 3 in the answer space shows an incomplete pie chart. Complete the pie chart to represent all the information in Table 1. [5 marks]
Answer: (a)
(b)
Bus 90º
11
Diagram 3
5 [Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial SULIT mm SULIT 10 50/2 m 12 Table 2 shows the results conducted by a computer company regarding the number of computers owned by 30 families.
Number of computers
0
1
2
3
4
Number of families
3
10
6
6
5
Table 2 (a)
State the mode.
(b)
Find the mean number of computers owned. [3 marks]
Answer: (a)
(b)
12 3
( )( )
13 Given that 3 2 x −1 = 3 x 3 2 , calculate the value of x. m Answer:
13 2
[2 marks]
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 11 m 14 Diagram 4 consists of two triangles, PQR, RST and a square PQTU. 18 cm
P
SULIT 50/2
For Examiner’s use
U
8 cm
Q
6 cm
R
T
5 cm S Diagram 4 Calculate the perimeter, in cm, of the shaded region. m Answer:
[4 marks]
14 4
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 12 m 15 Diagram 5 in the answer space shows two squares PQTU and QRST. W, X and Y are three moving points in diagram. (a)
SULIT 50/2
W is a moving point in the diagram such that it is always equidistant from straight line PU and RS. By using letters in the diagram, state the locus of W.
(b)
On Diagram 5, draw (i) the locus of X such that it is equidistant from from the straight lines PQ and PU, (ii) the locus of Y such that YT = QT.
(c)
Hence, mark with the symbol ⊗ the intersection of locus of X and locus of Y. [5 marks]
Answer: (a)
(b) (i), (ii) (c) P
Q
R
U
T
S
Diagram 5 15 5
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 13 m 16 Set squares and protractors are not allowed for this question. Diagram 6 shows triangle KLM.
SULIT 50/2
For Examiner’s use
L
2.5 cm 30º
M
K Diagram 6 (a)
Using only a ruler and a pair of compasses, construct triangle KLM using the measurements given, beginning from the straight line KM provided in the answer space.
(b)
Based on the diagram constructed in 16 (a), measure the distance, in cm, between point K and L. [5 marks]
Answer: (a)
K
(b)
M
KL = ……………. cm 16 5
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 14 m 17 Diagram 7 shows two triangles PQT and QRS.
SULIT 50/2
S
8 cm y cm
T 10 cm
P
6 cm
x cm Q
12 cm
R
Diagram 7 Find the value of x + y. m Answer:
17 4
[4 marks]
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 15 m 18 Table 1 shows three activities participated by a group of 50 students. Activities
Number of students
Chess
24
Hockey
y
Choir
18
SULIT 50/2
For Examiner’s use
Table 1 (a)
Find the value of y.
(b)
Hence, represent all the data from the table by drawing a bar chart in the answer space. [4 marks]
Answer: Number of students
28 24 20 16 12 8 4
O
Activities Chess
Hockey
Choir
18 4
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT m 19 Simplify ( 2 p − q ) 2 + q (4 p − q ). m Answer:
SULIT 16
50/2 [2 marks]
19 2 2
12 2 20 Find the value 2m n ÷ 2m −1 n 3 . m Answer:
20 2
END OF QUESTION PAPER
[2 marks]
50/2 © mm
2009 Hak Cipta Mathematics and Science Tutorial
SULIT
M S T –
ANGKA GILIRAN
–
NO. KAD PENGENALAN MATH
– –
&SCIENCE MATHEMATICS AND SCIENCE TUTORIAL
Tutorial PENILAIAN MENENGAH RENDAH 2009 PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN 3
50/2 mKertas
mMATHEMATICS 2 Jun 1 m
3 jam 4
Satu jam empat puluh lima minit
Examiner’s code
m
Question JANGAN BUKA KERTAS SOALAN SEHINGGA DIBERITAHU 1. This question paper consists of 20 questions. 2. Answer all questions. 3. Answers must be written clearly in the answer space provided. 4. Show your working. It may help you to get marks. 5. If you wish to change your answer, neatly cross out the answer. 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 or parts of a question are shown in brackets. 8. A list of formulae is provided on pages 2 and 3.
1 2 3
For Examiner’s Use Full Marks 2 2
4
3 3
5 6
2 2
7 8 9 10 11 12 13 14 15 16 17 18 19 20
3 2 3 2 5 3 2 4 5 5 4 4 2 2
Marks Obtained
9. Use of non-programmable scientific calculator Total is not allowed for this paper. 60 _______________________________________________________________________ _ Kertas soalan ini mengandungi 16 halaman bercetak [Lihat sebelah
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial m SULIT 2 m MATHEMATICAL FORMULAE
SULIT 50/2
The following formulae may be helpful in answering the questions. The symbols given are commonly used. RELATIONS 1
a m × a n = a m+ n
2
a m ÷ a n = a m−n
3
(a )
4
Distance =
5
Midpoint
m n
= a mn ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2
x1 + x 2 y1 + y 2 , (x, y) = 2 2 distance travelled time taken
6
Average speed =
7
Mean =
8
Pythagoras Theorem
sum of data number of data
c2 = a2 + b2
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 3 m SHAPES AND SPACE 1
Area of rectangle = length × width
2
Area of triangle =
3
Area of parallelogram = base × height
4
Area of trapezium =
5
Circumference of circle = πd = 2 πr
6
Area of circle = πr2
7
Curve surface area of cylinder = 2 πrh
8
Surface area of sphere = 4 πr2
9
Volume of right prism = cross sectional area × length
10
Volume of cuboid = length × width × height
11
Volume of cylinder = πr2h
12
Volume of cone =
13
Volume of speher =
14
Volume of right pyramid =
15
Sum of interior angles of a polygon = ( n − 2 ) × 180°
16
Arc length Angle subtended at centre = Circumference 360°
17
Area of sector Angle subtended at centre = Area of circle 360°
18
Scale factor, k =
19
Area of image = k2 × area of object
SULIT 50/2
1 × base × height 2
1 × sum of parallel sides × height 2
1 2 πr h 3 4 3 πr 3 1 × base area × height 3
PA' PA
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 4 m [60 marks]
SULIT 50/2
Answer all questions. 1 Calculate the value of – 43 + (86 – 6 × 12). m Answer:
[2 marks]
1 2 2
3 Calculate the value of 27 − − × 4.5 and express the answer as a decimal. 4 [2 marks] Answer:
2 2
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT m 3 (a) Find the value of 0.53.
SULIT 5
50/2
For Examiner’s use
2
(b)
1 Calculate the value of 3 − 1 . 8 [3 marks]
Answer: (a)
(b)
3 3 4
Solve each of the following linear equations: (a)
x – 3 = – 12
(b)
5x + 3 = x+6 2 [3 marks]
Answer: (a)
(b)
4 3 [Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 6 m 5 Diagram 1 shows a pentagon PQRST and R’S’ a grid of equal squares. R’S’ is the image of RS under a rotation of 90º clockwise about point O.
SULIT 50/2
On Diagram 1 in the answer space, complete the image of pentagon PQRST. [2 marks] Answer:
R'
S'
T
S P
R Q
Diagram 1
5 2
.
O
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial SULIT mm SULIT 7 50/2 m 6 Diagram 2 shows two polygons, Q and Q’, drawn on a grid of equal squares with sides of 1 unit.
For Examiner’s use
Q'
Q
Diagram 2 Q’ is the image of Q under transformation M. Describe in full transformation M. m Answer:
[2 marks]
6 2 7
Factorise completely each of the following expressions: (a)
24mn – 3m
(b)
4y2 – 4 [3 marks]
Answer: (a)
(b)
7 3 [Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT m 8 Simplify (3x – 1)2 – (7x + 4). Answer:
SULIT 8
50/2 [2 marks] m
8 2 9
(a)
(b)
1
Find the value of 64 3 × 2. Simplify
16k 5
( 2k )
−3 3
. [3 marks]
Answer: (a)
(b)
9 3
(
10 Simplify 4m 3 n −2 m Answer:
10 2
)
2
÷ 8m 4 n −5 .
[2 marks]
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial SULIT mm SULIT 9 50/2 m 11 Table 1 shows the vehicles used by 1200 students of SMK ST. Mary to go to school. Types of vehicles
Number of students
Bicycle
150
Motocycle
x
Car
200
Bus
300
For Examiner’s use
Table 1 (a)
Find the value of x.
(b)
Diagram 3 in the answer space shows an incomplete pie chart. Complete the pie chart to represent all the information in Table 1. [5 marks]
Answer: (a)
(b)
Bus 90º
11
Diagram 3
5 [Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial SULIT mm SULIT 10 50/2 m 12 Table 2 shows the results conducted by a computer company regarding the number of computers owned by 30 families.
Number of computers
0
1
2
3
4
Number of families
3
10
6
6
5
Table 2 (a)
State the mode.
(b)
Find the mean number of computers owned. [3 marks]
Answer: (a)
(b)
12 3
( )( )
13 Given that 3 2 x −1 = 3 x 3 2 , calculate the value of x. m Answer:
13 2
[2 marks]
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 11 m 14 Diagram 4 consists of two triangles, PQR, RST and a square PQTU. 18 cm
P
SULIT 50/2
For Examiner’s use
U
8 cm
Q
6 cm
R
T
5 cm S Diagram 4 Calculate the perimeter, in cm, of the shaded region. m Answer:
[4 marks]
14 4
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 12 m 15 Diagram 5 in the answer space shows two squares PQTU and QRST. W, X and Y are three moving points in diagram. (a)
SULIT 50/2
W is a moving point in the diagram such that it is always equidistant from straight line PU and RS. By using letters in the diagram, state the locus of W.
(b)
On Diagram 5, draw (i) the locus of X such that it is equidistant from from the straight lines PQ and PU, (ii) the locus of Y such that YT = QT.
(c)
Hence, mark with the symbol ⊗ the intersection of locus of X and locus of Y. [5 marks]
Answer: (a)
(b) (i), (ii) (c) P
Q
R
U
T
S
Diagram 5 15 5
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 13 m 16 Set squares and protractors are not allowed for this question. Diagram 6 shows triangle KLM.
SULIT 50/2
For Examiner’s use
L
2.5 cm 30º
M
K Diagram 6 (a)
Using only a ruler and a pair of compasses, construct triangle KLM using the measurements given, beginning from the straight line KM provided in the answer space.
(b)
Based on the diagram constructed in 16 (a), measure the distance, in cm, between point K and L. [5 marks]
Answer: (a)
K
(b)
M
KL = ……………. cm 16 5
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 14 m 17 Diagram 7 shows two triangles PQT and QRS.
SULIT 50/2
S
8 cm y cm
T 10 cm
P
6 cm
x cm Q
12 cm
R
Diagram 7 Find the value of x + y. m Answer:
17 4
[4 marks]
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT 15 m 18 Table 1 shows three activities participated by a group of 50 students. Activities
Number of students
Chess
24
Hockey
y
Choir
18
SULIT 50/2
For Examiner’s use
Table 1 (a)
Find the value of y.
(b)
Hence, represent all the data from the table by drawing a bar chart in the answer space. [4 marks]
Answer: Number of students
28 24 20 16 12 8 4
O
Activities Chess
Hockey
Choir
18 4
[Lihat sebelah
For Examiner’s use
50/2 © 2009 Hak Cipta Mathematics and Science Tutorial mm SULIT m 19 Simplify ( 2 p − q ) 2 + q (4 p − q ). m Answer:
SULIT 16
50/2 [2 marks]
19 2 2
12 2 20 Find the value 2m n ÷ 2m −1 n 3 . m Answer:
20 2
END OF QUESTION PAPER
[2 marks]
50/2 © mm
2009 Hak Cipta Mathematics and Science Tutorial
SULIT
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