Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads.. All rights reserved.[r]
(1)Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
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, IC no, 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
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, 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
(2)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
6
7
8
9
10
11
12
13
14
15 1
2
3
4
5
16
17
18
19
20
21
22
23
24
25
2014
(3)Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
3 In a mathematics school, the proportion of students who are good
in calculus or statistics is 0.7 The proportion of students who are good in calculus or not good in statistics, on the other hand, is 0.9 If you are asked to randomly pick a student, determine the probability
of students who are good in calculus
3)
Find A and B
4 We list one 1, two 2’s, three 3’s, and so on
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, …
It can be seen that the 10th number in the list is What is the 2014th
number in the list?
5 Find the number of triple of positive integers (x, y, z) such that
x + y + z =
1 Compute 2468135792 – 246813580 × 246813578
Expand (4a + 3b2)3
(4)
Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
10 Find the value of
7 10 people come over a home to have a dinner sitting around a
round table Count the number of arrangements that can be made
6 Ali has books, while Adam has books How many possible ways
can they exchange books with each other?
9 Given two sequences
1, 2, 2, 4, 8, 32, a … 1, 2, 8, 32, 512, b, …
If b = ka, then what is the value of k?
Find the area of the triangle
(5)
Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
15 APB =BPC = CPA
PA =10cm, PB =6cm, calculate PC
A
B C
D α
2α E
F
12 Find the simplest form of
11 An urn contains 10 balls, of which are red while the rest are blue
A second urn contains 16 red balls and an unknown number of blue balls A single ball is drawn from each urn The probability that both of the drawn balls are of the same colour is 0.44 Calculate the number of blue balls in the second urn
14 Find c + d
13 Calculate the value of the following trigonometry function
(6)Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads All rights reserved
Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
16 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?
19 Calculate the minimum value of the following function
f(x, y) =
20 In a Cartesian graph, calculate the area enclose by the following
function
18 Determine the last digit of the number
(… (((77)7)7)…7),
where the innermost is raised to the 7th power 101 times
17 Find the area of quadrilateral shown in the figure below
(7)Year 11
Division
MALAYSIA ASEAN MATH OLYMPIADS
2014 CONTEST M
24 Given the following function characteristic
What is the value of f(1)+f(2)+f(3)+…+f(10)?
23 A sequence a1, a2, a3, … is defined by
a1 = 2, a2 = 5, and an+2 = for all n
Find the value of a2014.
25 Find all possible solutions for =
21 Find all the integer solutions to (p + q)2 = p3 + q3
22 Given a function and ,
,
Calculate