1. 1 SULIT ppr maths nbk
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1449/2 NAMA : ___________________________________
Matematik
Kertas 2 TINGKATAN : _____________________________
Oktober
2007
1
2 jam
2
PPSMI ASSESSMENT
2007
MATHEMATICS
Kertas 2
Dua jam tiga puluh minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Pemeriksa
Bahagian Soalan Markah Markah
1. Tulis nama dan tingkatan anda pada
ruang yang disediakan.
Penuh Diperoleh
. 1
2. Kertas soalan ini adalah dalam 2
dwibahasa. 3
4
3. Soalan dalam bahasa Inggeris
mendahului soalan yang sepadan dalam
5
bahasa Melayu A 6
7
4. Calon dibenarkan menjawab 8
keseluruhan atau sebahagian soalan 9
sama ada dalam bahasa Inggeris atau
bahasa Melayu. 10
11
5. Calon dikehendaki membaca arahan di 12 12
halaman 2 atau halaman 3. 13 12
B 14 12
15 12
16 12
Jumlah
Kertas soalan ini mengandungi 55 halaman bercetak dan 1 halaman tidak bercetak
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2. SULIT 2 1449/2
INFORMATION FOR CANDIDATES
1. This question paper consists of two sections: Section A and Section B.
2. Answer all questions in Section A and four questions from Section B.
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 and sub-part of a question are shown in brackets.
8. A list of formulae is provided on pages 4 to 7.
9. A booklet of four-figure mathematical tables is provided.
10. You may use a non-programmable scientific calculator.
11. This question paper must be handed in at the end of the examination.
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MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are the ones
commonly used.
RELATIONS
1 am × an = am + n 12 Pythagoras Theorem
c2 = a2 + b2
2 am ÷ an = am − n 13 y2 − y1
m=
x2 − x1
3 (am )n = am n 14 y − intercept
m=−
x − intercept
4 1 ⎛ d − b⎞
A−1 = ⎜ ⎟
ad − bc ⎜ − c a ⎟
⎝ ⎠
5 n( A)
P ( A) =
n( S )
6 P ( A' ) = 1 − P( A)
7 Distance = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
8 ⎛ x + x y + y2 ⎞
Midpoint, ( x, y ) = ⎜ 1 2 , 1 ⎟
⎝ 2 2 ⎠
9 distance travelled
Average speed =
time taken
10 sum of data
Mean =
number of data
11 sum of (class marks × frequency)
Mean =
sum of frequencies
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SHAPES AND SPACE
1 1
Area of trapezium = × sum of parallel sides × height
2
2 Circumference of circle = π d = 2 π r
3 Area of circle = π r 2
4 Curved surface area of cylinder = 2 π r h
5 Surface area of sphere = 4 π r 2
6 Volume of right prism = cross sectional area × length
7 Volume of cylinder = π r 2 h
8 1
Volume of cone = π r 2 h
3
9 4
Volume of sphere = π r 3
3
10 1
Volume of right pyramid = × base area × height
3
11 Sum of interior angles of polygon = (n −2)×180°
12 arc length angle subtended at centre
=
circumference of circle 360o
13 area of sector angle subtended at centre
=
area of circle 360o
14 PA'
Scale factor, k =
PA
15 Area of image = k2 × area of object
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5. 5 SULIT ppr maths nbk
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For Section A
Examiner’s
Use [52 marks]
Answer all questions in this section.
1. The Venn diagram in the answer space shows sets P , Q and R such that the universal
set ξ = P ∪ Q ∪ R.
On the diagrams in the answer space, shade
(a) the set P ∩ Q’,
(b) the set ( Q ∪ R ) ∩ P.
[3 marks]
Answer:
(a)
P R
Q
(b)
P R
Q
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6. SULIT 6 1449/2
For
Examiner’s
2(a). Diagram 1 shows a cube with horizontal base TUVW. Use
X is the midpoint of TU.
P Q
S R 6 cm
W V
T X U
DIAGRAM 1
Identify and calculate the angle between the line QX and the base TUVW.
[4 marks]
Answer:
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For
Examiner’s
Use 2(b). Diagram 2 shows a right prism with horizontal base PQRS.
The right angled triangle MPR is the uniform cross section of the prism.
N
7 cm
M 10 cm
6 cm Q
R
P
S
DIAGRAM 2
Identify and calculate the angle between the plane MSP and the plane MPR.
[4 marks]
Answer:
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SOLID GEOMETRY For
Examiner’s
3. Use
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2 y2 − 3
For
Examiner’s
Use
4. Solve the quadratic equation = 1.
5y
[4 marks]
Answer:
5. Solve the quadratic equation (4n − 1)2 = 4n2.
[4 marks]
Answer:
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6. Calculate the value of v and of w that satisfy the following simultaneous linear For
Examiner’s
equations: Use
v − 3w = 5
3v − w = 3
[4 marks]
Answer:
7. Calculate the value of d and of e that satisfy the following simultaneous linear
equations:
3d + e = 11
1
d− e=6
4
[4 marks]
Answer:
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For CIRCLES
Examiner’s
Use 8.
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12. SULIT 12 1449/2
For
Examiner’s
9(a) Combine the two statements below to form a true statement. Use
Statement I : All even numbers are divisible by 6.
Statement II : 3 is a factor of 6.
(b) Write two implications based on the following sentence.
∠M and ∠N are vertically opposite angles if and only if ∠M = ∠N.
(c) Complete the premise in the following argument.
Premise I : If the participants finish the 7km run then they will receive a certificate.
Premise II : ________________________________________________________
Conclusion : Ali will not receive a certificate.
[5 marks]
Answer:
(a)
(b)
(c)
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13. 13 SULIT ppr maths nbk
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For STRAIGHT LINE
Examiner’s
Use 10. In Diagram XX, PQ is a straight line on a Cartesian plane.
y
P(−1,3)
Q(4,1)
O x
DIAGRAM xx
(a) Calculate the gradient of the line PQ.
(b) Find the equation of the line parallel to the line PQ and passing through the
point (−5,1).
[4 marks]
Answer:
(a)
(b)
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STRAIGHT LINE For
Examiner’s
11. Diagram xx shows KL , ML and MN are straight lines on a Cartesian plane. Use
N is on the y-axis. KL is parallel to MN, ML is parallel to the y-axis and LO = ON.
y
M
K
N
x
L O
DIAGRAM xx
The equation of MN is 3x + 4y = 20.
(a) Find the equation of LM.
(b) Find the equation of KL and state its y-intercept.
[5 marks]
Answer:
(a)
(b)
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For
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16. SULIT 16 1449/2
For Section B
Examiner’s
Use [48 marks]
Answer any four questions from this section.
Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m
12(a) The Venn diagram in the answer space shows sets P, Q and R such that the universal
set ξ = P ∪ Q ∪ R.
On the diagram in the answer space, shade
(i) the set P ∩ Q’,
(ii) the set (P ∪ Q ) ∩ R’.
[3 marks]
Answer:
(i)
Q
P R
(ii)
Q
P R
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17. 17 SULIT ppr maths nbk
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Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m For
Examiner’s’
12(b) In Diagram xx, OJKL is a parallelogram and O is the origin. Uses
y
J(3,6) K(6,h)
x
O L
DIAGRAM xx
Find
(i) the value of h,
(ii) the equation of the straight line KL,
(iii) the coordinate of point C.
[5 marks]
Answer:
(i)
(ii)
(iii)
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18. SULIT 18 1449/2
For Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m
Examiner’s
Use 12(c) Diagram xx shows a cuboid with a horizontal base PQRS.
W V
6 cm
T U
S R
8 cm
P 6 cm Q
DIAGRAM xx
Calculate the angle between the plane VPQ and base PQRS.
[4 marks]
Answer:
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Maths reasoning-6m / Circles-6m For
Examiner’s’
13(a) (i) State whether the following statement is true or false. Uses
(a) 2 and 25 are perfect squares
(b) 62 = 12 or 3 − 8 = −2
(ii) Write two implications from the following sentence
“ k2 > 49 if and only if k > 7.”
(iii) Complete the premise in the following argument
Premise 1 : If m = 3 , then 6 × m = 18.
Premise 2 : _____________________
Conclusion : m ≠ 3.
[6 marks]
Answer:
(i)(a)
(b)
(ii)
(iii)
Premise 2:
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20. SULIT 20 1449/2
For Maths reasoning-6m / Circles-6m
Examiner’s
Use 13(b) In Diagram xx, O is the centre of a circle with diameter KON.
KO is the diameter of the circle KJOH .
L
M
J
30°
K N
O
H
DIAGRAM xx
KON = 14 cm and ∠ MON = 30°.
22
Using π = ,calculate
7
(i) the perimeter, in cm, of the whole diagram,
(ii) the area, in cm2, of the shaded region.
[6 marks]
Answer:
(i)
(ii)
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21. 21 SULIT ppr maths nbk
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Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m For
Examiner’s’
9 7 Uses
14(a) Solve the quadratic equation x 2 − = 3 − x .
2 2
[4 marks]
Answer:
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For Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m
Examiner’s
Use 14(b) Calculate the value of x and of y that satisfy the following simultaneous linear
equations:
1
x + y = 17
4
1
x− y =3
3
[4 marks]
Answer:
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23. 23 SULIT ppr maths nbk
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Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m For
Examiner’s
14(c) Diagram xx shows a solid right pyramid with a square base. Use
A cuboid with a square base is taken out from the pyramid.
DIAGRAM xx
Calculate the volume , in cm3 , of the remaining solid.
[4 marks]
Answer:
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24. SULIT 24 1449/2
For Statistics-12m
Examiner’s
Use 15. The data in Diagram xx shows the time taken by 60 pupils to go school on a
particular day.
38 25 16 22 30 27 18 33 20 24 23 26
23 12 15 29 12 21 18 13 11 13 17 19
11 17 28 5 24 26 23 15 13 9 18 28
28 21 29 25 19 11 34 11 13 21 13 23
31 20 19 32 24 27 18 25 15 15 22 30
DIAGRAM xx
(a) Based on the data in Diagram xx and using a class interval of 5 minutes,
complete Table xx in the answer space.
[4 marks]
(b) For this part of the question, use the graph paper provided on page xx.
By using a scale of 2 cm to 5 minutes on the x-axis and 2 cm to 5 pupils on the
y-axis, draw an ogive for the data.
[6 marks]
(c) From your ogive in (b),
(i) find the median,
(ii) hence, using the time taken, in minutes, and the number of pupils,
explain briefly the meaning of the median.
[2 marks]
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Answer: For
Examiner’s
(a) Use
Time(minutes) Frequency Cumulative Frequency
5−9
10−14
TABLE xx
(b) Refer graph on page xx.
(c)(i)
(ii)
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Graph for Question 15
For
Examiner’s
Use
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27. 27 SULIT ppr maths nbk
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Statistics-12m For
Examiner’s
16. The data in Diagram xx show the height, in cm, of a group of 40 pupils. Use
152 167 168 177 178 174 172 173
176 154 162 173 163 155 167 164
160 175 171 178 159 174 168 176
171 169 156 166 172 153 179 174
160 158 169 151 154 167 164 154
DIAGRAM xx
(a) Based on the data in Diagram xx and by using a class interval of 5 cm,
complete Table xx in the answer space.
[3 marks]
(b) Based on the Table xx in (a), calculate the estimated mean height.
[3 marks]
(c) For this part of the question, use the graph paper provided on page xx.
By using a scale of 2 cm to 5 cm on the horizontal x-axis and 2 cm to 1 pupil
on the vertical axis, draw a histogram for the data.
[5 marks]
(d) Based on the histogram in (c), state one information relating height with
number of pupils.
[1 mark]
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28. SULIT 28 1449/2
For Answer:
Examiner’s
Use (a)
Height(cm) Lower Upper Frequency
Boundary Boundary
145 − 149
150 − 154
TABLE xx
(b)
(c) Refer graph on page xx.
(d)
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29. 29 SULIT ppr maths nbk
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Graph for Question 16
For
Examiner’s
Use
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30. SULIT 30 1449/2
END OF QUESTION PAPER
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