22 Given that car park of Jazz Supermarket has 15 cars, the cars start to move in and out start from 6am (The first car moves out from the car park at 6am sharp).. After every 6 minutes,[r]
(1)Year 7
M MALAYSIA ASEAN
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 yourFULL 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 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 so. YouMUSTfill 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.
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(3)Year 7
M MALAYSIA ASEAN
MATH OLYMPIADS
2014 CONTEST
3Calculate the value of
2009
2009 2010
2011 2012
2013 2014
2
2 2
2 2
2
2
4
Find the last digit of the sum of the above numbers given
5 If given that 2014x2– 2013x + = a(x – 2)2+ b(x – 2) + c, what is the
value of a – b + c?
1 Consider the sequence , , , , , , 10 … of all positive integers for which they are all not perfect square
Determine 2014thterm of this sequence.
2 Given that 1099– 99 equals to X The sum of each digit in X is Y.
(4)10 “1stJanuary 2014 is Wednesday.”
Calculate what day it would be on 3rdMay 1976.
7 For X is a positive integer, find X if
32x + 1– 10 (3x) + = 0
6
Find the number of triangles that can be drawn, having three of these points as vertices
9 A1234567B is a nine-digit number which is divisible by 45.
What is the value for A + B?
8 Find A given that
(5)Year 7
M MALAYSIA ASEAN
MATH OLYMPIADS
2014 CONTEST
12 In Grade 2, there are 110 students who are compulsory to take at least one course of Science, Mathematics and English 52 students are in Science whereby 16 of them took one course only 61
students are in English, but 15 of them took English only There are 63 students took Mathematics in which 21 of them did not join any other courses Find the number of students who took all three courses
11 X and Y are both three-digit numbers, and their sum is 999
We insert a decimal mark between X and Y (i.e 123.456).Given that X Y = 6(Y X)
Calculate the difference between X and Y
14 The sum of the first 105 numbers
15 If the product of 45and 513is written as integer, how many digits
are there in this integer?
13 Let x1, x2are the real root of X2– 2(k + 1) + k2+ = 0, where
(x1+ 1)(x2+ 1) = 8, then k is?
In Pascal’s Triangle is Y Evaluate
5
4 1
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numbers, what is the value of x
19 In how many ways can five students A, B, C, D and E line up in one row if students B, C and D must stay together?
18
Given X : Y = 10 : 33, evaluate the difference between X and Y
(7)Year 7
M MALAYSIA ASEAN
MATH OLYMPIADS
2014 CONTEST
22 Given that car park of Jazz Supermarket has 15 cars, the cars start to move in and out start from 6am (The first car moves out from the car park at 6am sharp) After every minutes, another car from the car park will move out At the same time, a car move into the car park after minutes when the first car move out from car park After every minutes, another car will moves into the car park This process repeat and repeat until there is no car in the car park for the first time What is the time for there is no car in the car park for the first time?
24 A paper of square shape consists of four vertexes ABCD Side AB is folded along line PQ to location AB’ Extending AB’ connect to line DC at point x
Given that AX = 5cm, BY = 2cm, calculate value of DX
23 As shown in the following diagram, a point X is within triangle ABC Perpendicular line is draw to each of the sides of the triangle, intersect each of the edge of PQR The following information is available:
PX = 1cm RX = cm Find the value of CS – QX
25 Given that real number a, b, c where abc= -1 , a + b + c =
21 The diameter (centimeter) of the circles shown is 6, 4, 4, and If V is the shaded area region inside the biggest circle and W is the total shaded area of the remaining circles, then what is the relationship between V and W?