2012 DSE 數學科模擬試題
香港青年協會
dse.27771112.hk
2012-DSE
MATH
Please stick the barcode label here
PAPER 1
Dick Hui Mathemagic Power
Candidate Number
MINI MOCK EXAMINATION 2012
MATHEMATICS
Compulsory Part
PAPER 1
Question-Answer Book
(1 1/2 hours)
Question No.
1
2
3
1.
Write your Candidate Number in the spaces provided on
this Page 1.
2.
5
Stick barcode labels in the spaces provide on Pages 1, 3, 5,
6
7, 9and 11.
3.
4.
This paper consists of THREE sections, A(1), A(2) and B.
7
Each section carries 35 marks.
8
Attempt ALL questions in this paper. Write your answers
in the spaces provided in this Question-Answer Book. Do
5.
4
9
not write in the margins. Answer written in the margins
10
will not be marked.
11
Graph paper and supplementary answer sheets will be
12
supplied on request. Write your Candidate Number and
stick a barcode label on each sheet, and fasten them with
string INSIDE this book.
6.
Unless otherwise specified, all working must be clearly
shown.
7.
Unless otherwise specified, numerical answers should be
either exact or correct to 3 significant figures.
8.
The diagrams in this paper are not necessarily drawn to
scale.
2012-DSE-MATH-CP 1-E1
 By Dick Hui
Total
Marker’s
Use Only
Examiner’s
Use Only
Marker No.
Examiner No.
Marks
Marks
SECTION A(1)
1.
2.
3.
(24 marks)
Factorize  x 2  3x   14  x 2  3x   40 .
2
(3 marks)
c2 x
(a) If b  p 
, express x in terms of a, b, c and p.
ax
a
(b) If p  12 , b  6 and c  9 , find the value of
.
x
2
2
(4 marks)
A piece of rod 48 cm long is cut into two parts. Each part is bent by superman
Dick Hui into a square. The total area of the two squares is 74 cm 2 . Find the
sides of the two squares.
(4 marks)
4.
Figure 1 shows a light tower L is due east of a pier P. A ship S is travelling in the
direction S 30W to P. At 4:30 p.m., the distance between the ship and the light
tower is the shortest which is 210 3 km . The ship arrives to the pier at 7:00
p.m..
(a) Find the distance between the light tower and the pier.
(b) Find the speed of the ship.
(5 marks)
North
S
P
L
Figure 1
2012-DSE-MATH-CP 1-E2
 By Dick Hui
East
5.
Given two lines L1 : 3x  y  12  0 and L2 : ax  3 y  7  0 . Find the value of a if
(a) They do not intersect;
(b) They are perpendicular to each other.
6.
(4 marks)
The figure shows the cumulative frequency polygon of the marks obtained by 40
students taking a History test.
Mark of 40 students in a History test
Find the median mark.
If 65% of the students pass the test, what is the passing mark?
(4 marks)
2012-DSE-MATH-CP 1-E3
 By Dick Hui
SECTION A(2) (24 marks)
7.
x partly varies as y2 and partly varies as z. When y  2 and z  2 , x  14 .
When y  5 and z  6 , x  68 .
(a) Express x in terms of y and z.
(3 marks)
(b) Hence find x when y  6 and z  2 .
(1 mark)
(c) If z  1  4 y , find the minimum value of x and the corresponding value of y
and z?
8.
(3 marks)
 
In the figure, AC intersects OB at K. If AB : CB = 1 : 2
(a) Prove that AOB  KAB .
(3 marks)
(b) Hence, prove that ABK is an isosceles triangle. (3 marks)
(c) If AOB  40 , find OBC
(2 marks)
9.
Figure 2.2
Figure 2.1
Figure 2.3
(a) Figure 2.1 shows a right circular cylindrical water tank of base radius 4 cm
and height 10 cm. it is placed on a horizontal table. The tank is filled with
water to a depth of 6 cm. Express the volume of water in the tank in terms
of  .
.
(3 marks)
(b) Figure 2.2 shows a solid metal right circular cone. V is the vertex and VH is
the height of the cone. K is a point on VH and A is point on the curved
surface of the cone such that VKA  90 , KA=2 cm and KH=4 cm. If
the radius of the base is r cm, show that the volume of the cone is
4 x3
cm3 .
3( x  2)
(4 marks)
(c) Now the cone is immersed in the water tank. If x = 4 cm, find the height of
water level after immersion.
(2 marks)
2012-DSE-MATH-CP 1-E4
 By Dick Hui
SECTION B (22 marks)
10. Given M  K  log a , where M, a and K represent magnitude, maximum
amplitude and a constant. If the magnitude of the first and second earthquake is
7.7 and 6.0 respectively, how many times is the maximum amplitude of the first
earthquake larger than the earthquake of the second time? (Correct to the nearest
integer).
(5 marks)
11. Dick Hui has x $50 banknotes, 4 $20 banknotes and y $10 banknotes in the total
amount of $210 in his wallet. If a banknote is selected at random from the wallet,
the probability of getting a $10 banknote is
1
.
3
(a) Find the values of x and y.
(2 marks)
(b) Dick Hui is paying a bill of $60 at a restaurant. If he randomly selects two
banknotes from his wallet, find the probability that the amount of the two
banknotes selected is enough for the bill.
(3 marks)
(c) It is known that Dick Hui uses a $50 banknote and a $10 banknote to pay
the bill in part (b) before going to the supermarket. If he randomly selects
three banknotes from his wallet for his $50 purchase at the supermarket,
find the probability that the amount of the three banknotes is not enough for
the purchase.
(3 marks)
12. From 200 to 300 inclusive, find the sum of all multiples of 3 or 4.
2012-DSE-MATH-CP 1-E5
 By Dick Hui
(9 marks)