Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads.. All rights reserved.[r]
(1)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
Full Name： Year: IC No: Date： Time：
School Name： School Code：
Rules and Regulations (Please read these rules and regulation carefully)
1 Please fill in your FULL name correctly, school name, school code and the date and time of contest clearly in the spaces above Those who not fill in the required particulars will be disqualified automatically
2 Do not open the question booklet until you are told to 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 you MAY NOT 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 120 minutes You must stop writing when you are told to so 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, 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 The correct answer to each problem will be awarded one (1) point However, you will NOT be penalised for each incorrect answer
2 The organizer reserves the right to disqualified the event of malpractice to differentiate between those outstanding students
(2)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
6
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11
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15 1
2
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16
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20
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25 2014
(3)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
3 Given that 6a = 8b = 125,
calculate the value of
3)
Find A and B
4 Let H(n) denote the sum of the odd digit of n For example,
H(35224) = + = Find the value of H(1) + H(2) + … + H(100)
5 What is the minimum value for the following function f(x)
1 If x + y = and xy = 7, then find the value of x2 + y2
2 What is the last digit of 20132014?
(4)
Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
10 How many positive integer solutions are there to
Error! Reference source not found.
7 Find the remainder when 333444 + 444333 is divided by
6 Find the last digit for the sum of
3 + 33 + 333 + 3333 + … +
2014 digits
9 Some positive integers add up to the sum of 25 What is the
maximum possible product of those integers?
8 What is the value of
(5)
Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
A
B C
D
α
2α E
F
12 Find the value of
1 +
11 Y is the largest integer with the properties that:
a) Y is a multiple of 8; and
b)No two digits of Y are the same
What are the last three digits of Y?
14 Calculate the value of:
sin(10)cos(20)sin(30)cos(40)sin(50)cos(60)sin(70)cos(80)
15 In the diagram below, a circle is inscribed in a square and another
square is inscribed in the circle If a side of the larger square is 10, what is the area of the smaller square?
13 6 teams are playing in a basketball tournament In the first round,
the teams are randomly assigned to games 1, 2, and In how many ways can the teams be assigned to the games?
(6)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
20 If a triangle ABC with each of its corresponding side a, b, c has the
following characteristic
Calculate the value of B
16 Find c + d
19 Find all possible solutions to the equation
=
18 Simplify
+ … +
17 A sequence is given as
a1 = , a2 = , a3 = , …
Write an in the form of mn
(7)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 10
M MATH OLYMPIADS
2014 CONTEST
24 I toss a twenty-cent coin and a fifty-cent coin in the air If one of
them lands heads up, what is the probability that the fifty-cent coin will land heads up?
23 Given that function f(x) has characteristic of f(3 + x) = f(3 - x) If
f(x) = has 10 real solution , what is the sum of all the rational roots
25 Find the area of quadrilateral shown in the figure below (NOTE:
figure is not drawn to exact scale)
21 A student prepares for an exam by studying a list of five
problems She can solve four of them For the exam, the teacher randomly selects problems from the five on the list given to the students What is the probability that the student can solve all three problems in the exam?
22 Five identical bowls are labeled as 1, 2, 3, 4, and Bowl i contains i
white and – i black balls, with i = 1, 2, … , A bowl is randomly
selected and two balls are randomly selected (without replacement) from the contents of the bowl What is the probability that both balls selected are white?