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<i>Copyright © 2015 by ASIAN Science & Math Olympiads. All rights reserved</i>

<b>Full Name</b>: <b>IC No:</b>

<b>Date</b>: <b>Time</b>：

<b>School Name</b>： <b>Class</b>：

<b>Rules and Regulations</b>

<b>(Please read these rules and regulation carefully)</b>

1. Please fill in your<b>FULL name</b> correctly, IC No, school name, class 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 <b>2B</b> 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 you

<b>MAY NOT</b>leave 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 is<b>120 minutes</b>. You must stop writing when you are told to do so.
9. You <b>MUST</b> 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. <b>Please tear off the answer sheet carefully and returned to invigilator along with contest paper.</b>
<b>Participant only can bring back the contest papers on next week.</b>

12. <b>Please be reminded that if the contestants can’t attend the contest, we don’t accept any</b>
<b>replacement contestants. If found any, the contestant will be disqualified automatically.</b>

<b>Scoring System</b>

1.Scoring system for each question are as below:
I. Questions 1-10 : 3 Marks x 10 = 30 Marks
II. Questions 11 - 20 : 4 Marks x 10 = 40 Marks
III. Questions 21 - 25 : 6 Marks x 5 = 30 Marks

IV. <b>Total</b> <b>: 100 Marks</b>

2. The organizer reserves the right to disqualified the event of malpractice to differentiate between
those outstanding students.

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<b>4 Calculate:</b>













₂₀₁₄

₎

2

₍

₂₀₁₄

₂₀₁₅

₎

2 3

₍

₂₀₁₄

₂₀₁₅

₎

3

2015

(

(3 markah)

<b>5</b> 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

(3 markah)

<b>1 If</b> (2+√ x)=3, what is the value of x?

(3 markah)

<b>3</b> 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?

(3 markah)

<b>2</b> If 20201515 2<i>p</i>3<i>q</i>5<i>r</i>, then <i>p</i><i>q</i><i>r</i> ?

(3 markah)

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<i>Copyright © 2015 by ASIAN Science & Math Olympiads. All rights reserved</i>
<b>7</b> 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 n2_{+ 290n − 2490. Determine n}

(3 markah)
<b>8</b> If
65
1
1
1
1
1
,
2015 










<i>a</i>

<i>c</i>
<i>c</i>
<i>b</i>
<i>b</i>
<i>a</i>
<i>b</i>
<i>a</i>
<i>c</i>
<i>b</i>
<i>a</i>

Solve ?






 <i>b</i> <i>c</i>

<i>a</i>
<i>a</i>
<i>c</i>
<i>b</i>
<i>b</i>
<i>a</i>
<i>c</i>
(3 markah)

<b>1. 9</b> 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 .

(4 markah)

<b>10</b> Find the remainder of when it is divided by 11.

(4 markah)

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

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<b>15 Rectangle ABCD is divided into three identical rectangles as shown. Line AE</b>

with E on BC is drawn such that the area of GBEF is twice the area of FECM.
The ratio of the area of AIH to the area of ABCD is (write in the simplest
fraction)

<b>12</b>. If M = (│x – 1 │+│x│– 1 ), find the range of M

(4 markah)

<b>11 Find the value of</b> – 2 – 4x + 1999 , given that of + 2x +4 = 0.

(4 markah)

<b>13</b>. 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)

<b>14</b> Real number a,b,c fulfill the equation below,

0
9
6
2
2
2

2 2 2

2 _ <i>_b</i> _ <i>_c</i> _ <i>_ab</i>_ <i>_bc</i>_ <i>_c</i>_ _

<i>a</i>

Find the value of

a+b+c

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<i>Copyright © 2015 by ASIAN Science & Math Olympiads. All rights reserved</i>

<b>17 In the diagram, the congruent circles are tangent to the large square and each</b>

other as shown; and their centres are the vertices of the small square. The area
of the small square is 4 units. Find the area of the large suqare.

(4 markah)

<b>18 Given that</b> ,
2

1
5


<i>x</i> Find value of ₅

3 ₁

<i>x</i>
<i>x</i>

<i>x</i>  

.

(4 markah)
16 In the rhombus one diagonal is 8 cm longer than the other diagonal. If the

area of the rhombus is 24 cm2_{then the length of the longer diagonal, in cm, is}

(4 markah)

<b>19 Solve the following equation :</b>

+

+

+

…

_{= 2014}

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<b>20</b> In△ABC , the length of the sides of the triangle a,b and c are

integers.Given that b = 4 and a≤b≤c, how many such triangle are there?

(4 markah)

<b>21</b> Given that = = , Find the value of 3xy – yz – 2xz .

(6 markah)

1.

<b>2. 22</b> 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.

(6 markah)
3.

A

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<i>Copyright © 2015 by ASIAN Science & Math Olympiads. All rights reserved</i>

<b>25 Given</b> + = 1 , evaluate θ+ θ .

(6 marks)

<b>1.</b> <b>24</b> A billiard ball is hit on a rectangular pool table , 2 m by 1 m, from a point X, it

comes to rest at Y, as shown in the diagram. X is 0.6 m from AD and 0.2 m
from DC.Y is 0.2 m from AD and 0.25 m from AB. If the ball always

rebounds at the same angle as it hits the side, thendetermine the distance

traveled by the ball from X to Y. (6 markah)

2.

1. <b>23</b> 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)
2.

(6 marks)

●

●

●

A

B

C

a b

c

X
Y

A _B

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