trường thcs hoàng xuân hãn

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Full Name： Year:

IC No: Date： Time：

School Name：

Rules and Regulations

(Please read these rules and regulation carefully)

1. Please fill in your FULL name correctly, IC No, school name and the date and time of contest
clearly in the spaces above. Those who do not fill in the required particulars will be disqualified
automatically.

2. Do not open the question booklet until you are told to do so. You may only use 2B pencil when
answering the questions.

3. No calculators and any unauthorised electronic devices (including mobile phones) are allowed
during the contest.

4. Strict silence must be observed at all times in the examination hall and please be reminded that
youMAY NOTleave your seat without permission.

5. If you have any request or enquiry, please raise your hand and wait for an invigilator.

6. Only one candidate is allowed to leave the hall at a time. You are required to return to the hall
within 10 minutes or else you will automatically be disqualified from the contest.

7. Each question in the contest have been verified by experienced trainers, thus no further
explanation will be given.

8. The time allowed for the paper is120 minutes. You must stop writing when you are told to do so.

9. You MUST fill in your answer in the answer sheet provided in second page of the question

booklet. You will not be awarded marks for any answer written in the question booklet.

10. Please be reminded that this is a contest and not an examination, do not expect to answer all
types of questions.

11. Please tear off the answer sheet carefully and returned to invigilator along with contest
paper. Participant only can bring back the contest papers on next week.

Scoring System

1.ForQuestion 1- 10, 3 markswill be awarded for each correct answer.
ForQuestion 11- 20, 4 markswill be awarded for each correct answer.
ForQuestion 21- 25, 6 markswill be awarded for each correct answer.
However, you will NOT be penalised for each incorrect answer.

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5 If 20201515 2p3q5r, then pqr ?

(3 markah)
1 Calculate:





(

20152015

)(

20142014

)

20142015

)(

20152014

(

(3 markah)

2 Calculate:









2014

)

(

2014

2015

)

2 3

(

2014

2015

)

2015

(

(3 markah)

3 If (2+√ x)=3, what is the value of x?

(3 markah)

4 The value of M is 3 and M is 30% of Q, Q is 20% of P, and N is 50% of P.
What is the value of N?

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7 Simplify

( + + ) ( + - ) ( - + ) ( + + ).

(3 markah)
6 Six numbers from a list of nine integers are 7, 8, 3, 5, 9 and 5. What is

the largest possible value of the median of the nine numbers in the
list?

(3 markah)

9 In the diagram below ABC is a right-angled triangle.

cm
AC

cm
AB

B90, 6 , 10

 . Line AB is used as a diameter to

draw a semicircle, while line BC is used as a diameter to draw

another semicircle. Calculate the area of the shaded region in term of



(3 markah)
8 Some identical cubes are glued tightly together as shown in the diagram.

The volume of the solid formed in this way is 189 cm3. The surface area
of the solid, in cm2, is

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10

=

= k

, then what is the value of k ?

(3 markah)

13 AB is a chord in a circle with center O and radius 39 cm.
The point N divides the chord AB such that AN =56 cm and
NB = 16 cm. Find the length ON in cm.

(4 markah)

14 If M = (│x – 1 │+│x│– 1 ), find the range of M.

(4 markah)
12 If
65
1
1
1
1
1
,
2015 











a
c
c
b
b
a
b
a
c
b
a

Solve ?






 b c

a
a
c

b
b
a
c
(4 markah)
11 There are 300 white boxes and n red boxes in storage. Each box

contains the same number of soccer balls. The total number of soccer
balls in all of the boxes is n 2 + 290n − 2490. Determine n

(4 markah)

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16 As shown in the diagram, line AB is parallel to line CD and line EI is
perpendicular to line EG. EF≠FG≠EH≠HI. How many complementary
angles of angle EHF.

(4 markah)

17 In the diagram below A,B,C,D,E,F and G are plotted along the circle with
centre O, and line AB is the diameter of the circle. Given that

,
15
,

20  







find



(4 markah)
15 Given that f(x) = ax³ + bx² + cx + d, If x takes the value of its opposite

number, the corresponding value of f(x) is also the opposite
number,and f(-1) = 0, then find the value of

(4 markah)

18 Real number a,b,c fulfill the equation below,

0
9
6
2
2
2
2 2 2

2  b  c  ab bc c 
a

Find the value of

a+b+c

(4 markah)
B

C D

F H

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1. 22 An order pair of rational number x and y is defined as (x,y) .
2. If xy < 0 and satisfied the equations below.

3. │x│y + x = 0 and │x│+│y│= 3

then, determine the values of order pairs of x and y .

(6 markah)
23 Find the remainder of when it is divided by 11.

(6 markah)
21 Solve the following equation :

(6 markah)

+

…

= 2014

20 A circle passes through vertices A and B and touches side DC of a square. If the
square has side length 2 units, then the radius of the circle is

(4 markah)

19 Given that ,

2
1
5


x Find value of 5

3 1

x
x
x  

(4 markah)

C D

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24 Three circles lie on the straight line and touching each other as shown
in the diagram，at which a,b and c are the radii of circle A, B and C
respectively. Find the value of c in terms of a and b.

(6 markah)

25 Given that the point P is outside the equilateral triangle ABC.But
inside the region of∠ABC. If the distance from P to BC,CA,AB are

, and respectively, and - + = 4 cm, Find the the
area of△ABC.

(6 markah)

●

a b

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