2012 Mathematics Paper1 S
2012 Mathematics Paper1 S
2012 Mathematics Paper1 S
Candidate Number
34
INSTRUCTIONS
56
1. Write your Candidate Number in the space provided
on Page 1. 78
2. Stick barcode labels in the spaces provided on Pages
9
1, 3, 5, 7 and 9.
Checkers
Total
Use Only
( xy ) 2
1. Simplify and express your answer with positive indices. (3 marks)
x5 y 6
Answers written in the margins will not be marked.
3. Factorize
(a) 3m 2 mn 2n 2 ,
(b) 3m 2 mn 2n 2 m + n .
(3 marks)
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(a) Find r .
Figure 1
7. In Figure 2, O is the centre of the semicircle ABCD . If AB // OC and BAD = 38 , find BDC .
(4 marks)
38
A O D
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8. In Figure 3, the coordinates of the point A are (2 , 5) . A is rotated clockwise about the origin O
through 90 to A . A is the reflection image of A with respect to the y-axis.
O x
Figure 3
District B
District A
x
72 District C
120 30
District D
District E
(a) Find x .
(b) Is the number of traffic accidents occurred in District A greater than that in District C ? Explain
your answer.
(5 marks)
(b) If the production cost of a carpet is $ 539 , find the perimeter of the carpet. (2 marks)
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12. Figure 5 shows the graph for John driving from town A to town D ( via town B and town C ) in a
morning. The journey is divided into three parts: Part I (from A to B ), Part II (from B to C ) and Part
III (from C to D ).
D 27
Distance travelled (km)
C 18
B 4
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(a) For which part of the journey is the average speed the lowest? Explain your answer. (2 marks)
(b) If the average speed for Part II of the journey is 56 km / h , when is John at C ? (2 marks)
(c) Find the average speed for John driving from A to D in m / s . (3 marks)
O x
Figure 6
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(b) Q is a moving point in the coordinate plane such that AQ = BQ . Denote the locus of Q
by .
(i) Describe the geometric relationship between and L 2 . Explain your answer.
57
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14. The data below show the percentages of customers who bought newspaper A from a magazine stall in
city H for five days randomly selected in a certain week:
(a) Find the median and the mean of the above data. (2 marks)
(b) Let a % and b% be the percentages of customers who bought newspaper A from the stall for
the other two days in that week. The two percentages are combined with the above data to form a
set of seven data.
(i) Write down the least possible value of the median of the combined set of seven data.
(ii) It is known that the median and the mean of the combined set of seven data are the same
as that found in (a). Write down one pair of possible values of a and b .
(3 marks)
(c) The stall-keeper claims that since the median and the mean found in (a) exceed 50% ,
newspaper A has the largest market share among the newspapers in city H . Do you agree?
Explain your answer. (2 marks)
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15. The seats in a theatre are numbered in numerical order from the first row to the last row, and from left to
right, as shown in Figure 7. The first row has 12 seats. Each succeeding row has 3 more seats than
the previous one. If the theatre cannot accommodate more than 930 seats, what is the greatest number
of rows of seats in the theatre?
M
K
K
29 44
28 K 45
3rd row 14 26
13 27
2nd row 2 11
1 12
1st row
Figure 7
(4 marks)
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(a) Find the probability that only 2 of the selected teachers are from school A . (3 marks)
(b) Find the probability that the numbers of selected teachers from school A and school B are
different. (2 marks)
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Scale Formula
A M = log 4 E
B N = log8 E
It is given that M and N are the magnitudes of an explosion on Scale A and Scale B respectively
while E is the relative energy released by the explosion. If the magnitude of an explosion is 6.4 on
Scale B , find the magnitude of the explosion on Scale A . (5 marks)
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20 cm
45 30
A D B
Figure 8(a)
(b) The triangular paper card in Figure 8(a) is folded along CD such that ACD lies on the
horizontal plane as shown in Figure 8(b).
B
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A D
Figure 8(b)
(i) If the distance between A and B is 18 cm , find the angle between the plane BCD and
the horizontal plane.
(ii) Describe how the volume of the tetrahedron A BCD varies when ADB increases
from 40 to 140 . Explain your answer.
(5 marks)
63
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19. In Figure 9, the circle passes through four points A , B , C and D . PQ is the tangent to the circle at
C and is parallel to BD . AC and BD intersect at E . It is given that AB = AD .
P
C
E
Q
D A
Figure 9
(b) A rectangular coordinate system is introduced in Figure 9 so that the coordinates of A , B and D
are (14 , 4) , (8 , 12) and (4 , 4) respectively. Find the equation of the tangent PQ . (7 marks)
65
END OF PAPER
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