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M Year 11

MALAYSIA ASEAN MATH OLYMPIADS 2014 CONTEST

Full Name：

Year:

IC No:

Date：

School Name：

School Code：

Time：

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 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 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 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. 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.

3.

Contestants or a team who are disqualified from the contest will be forfeited any right to re-sit this year.

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.

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MALAYSIA ASEAN 2014 MATH OLYMPIADS

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ANSWER SHEET 2014 CONTEST

Year 11

1

6

11

16

21

2

7

12

17

22

3

8

13

18

23

4

9

14

19

24

5

10

15

20

25

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.

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MALAYSIA ASEAN MATH OLYMPIADS 2014 CONTEST

Year 11

1 Compute 2468135792 – 246813580 × 246813578

2 Expand (4a + 3b2)3.

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.

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 4. What is the 2014th number in the list? 3) 5

Find the number of triple of positive integers (x, y, z) such that Find A and B

x + y + z = 7.

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.

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MALAYSIA ASEAN MATH OLYMPIADS

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2014 CONTEST

Year 11

6

Ali has 6 books, while Adam has 7 books. How many possible ways can they exchange 4 books with each other?

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.

8 Find the area of the triangle.

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?

10

Find the value of

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.

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MALAYSIA ASEAN MATH OLYMPIADS

M

2014 CONTEST

Year 11

11

An urn contains 10 balls, 4 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.

12

Find the simplest form of

A

D α F

B

13

14

15

2α E

Calculate the value of the following trigonometry function

. Find c + d.

APB =BPC = CPA PA =10cm, PB =6cm, calculate PC.

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.

C

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MALAYSIA ASEAN MATH OLYMPIADS 2014 CONTEST

Year 11

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?

17

Find the area of quadrilateral shown in the figure below.

18

Determine the last digit of the number (… (((77)7)7)…7), where the innermost 7 is raised to the 7th power 101 times.

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

.

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.

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MALAYSIA ASEAN MATH OLYMPIADS

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2014 CONTEST

Year 11

21

Find all the integer solutions to (p + q)2 = p3 + q3.

22

Given a function

and

,

, Calculate

23

.

A sequence a1, a2, a3, … is defined by a1 = 2, a2 = 5, and an+2 =

for all n

1.

Find the value of a2014.

24

Given the following function characteristic

What is the value of f(1)+f(2)+f(3)+…+f(10)?

25

Find all possible solutions for

= 1.

Copyright © 2014 by Malaysia ASEAN Science & Math Olympiads. All rights reserved.