2011 masmo contest paper - secondary

Copyright 2011 byMalaysia ASEANSchoolsMathOlympiads.All rights reserved.

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MMMMMALAYSIAMALAYSIAMALAYSIAMALAYSIA ASEANASEANASEANASEAN SCHOOLSSCHOOLSSCHOOLSSCHOOLS

MATHMATHMATHMATH OOOOLYMPIADSLYMPIADSLYMPIADSLYMPIADS2020202011111111 CONTESTCONTESTCONTESTCONTEST

FullFullFullFull NameNameNameName YearYearYearYear DaDaDaDatetetete TimeTimeTimeTime

SchoolSchoolSchoolSchool NameNameNameName SchoolSchoolSchoolSchool CodeCodeCodeCode

RulesRulesRulesRules andandandand RegulationsRegulationsRegulationsRegulations(Please(Please(Please(Please readreadreadread thesethesethesethese rulesrulesrulesrules andandandand regulationregulationregulationregulation carefully)carefully)carefully)carefully)

1. Please fill in your FULL name, school name, school code and the date and time of contestclearly in the spaces above. Those who do not fill in the required particulars will be disqualifiedautomatically.

2. Do not open the question booklet until you are told to do so. You may only use 2B2B2B2B pencil whenanswering the questions.

3. No calculators and any unauthorised electronic devices (including mobile phones) are allowedduring the contest.

4. Strict silence must be observed at all times in the examination hall and please be reminded thatyou MAYMAYMAYMAY NOTNOTNOTNOT 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 hallwithin 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 furtherexplanation will be given.

8. The time allowed for the paper is 111120202020 minutesminutesminutesminutes. You must stop writing when you are told to doso.

9. You MUSTMUSTMUSTMUST fill in your answer in the answer sheet provided in second page of the questionbooklet. 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 alltypes of questions.

ScoringScoringScoringScoring SystemSystemSystemSystem1. 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 call for a re-sit in the event of malpractice and to differentiatebetween those outstanding students.

3. Contestants who are disqualified from the contest will not be awarded any certificates and willbe forfeited any right to re-sit this year.


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11111111

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3333 How many different sums can be obtained by adding two differentintegers chosen from the set below?

4444 561 is the product of 3 different prime numbers. How many factors of561 are not prime?

5555 In rectangle ABCD, P is the midpoint ofside

BC

and Q is the midpoint of

CD

. The area ofAPQ

is whatfractional part of the area of rectangleABCD?

1111 25 digits are shown.Find the sum of the digits.

2222 How many quarters (worth 25 cents each) must be added to 12nickels (worth 5 cents each), so that the average value of a coin inthe new enlarged collection is 10 cents?

2222 2222 2222 22222222 2222 6666 22222222 6666 6666 22226666 6666 6666 2222

4444 4444 4444 44444444 4444 4444 4444 4444

{ 12, 11, 10, ..., +6, +7, +8 }

P

Q

C

DA

B


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7777 Amy picks a whole number, squares it and then subtracts 1. She givesher final number to Brian. Brian adds 3 to the number Amy gave himand then doubles that result. Brians final result is 54. With whatnumber did Amy start?

6666 Write as a single decimal:

9999 The first three terms in a sequence are: 1, 2, 3. Each term afterthat is the opposite of the sum of the three previous terms. Forexample, the 4th term is 6 ( the opposite of 1 + 2 + 3 ), and the 5th termis 1.What is the 99th term?

10101010 Find the whole number value of

1 + 3 + 5 + ... + 45 + 47 + 49

1 210

3100

41000

8888 Alex, Bruno, and Charles each add the lengths of two sides of thesame triangle correctly. They get 27 cm, 35 cm, and 32 cm,respectively. Find the perimeter of the triangle, in cm.


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415

11111111 When Isaac opens a book, the product of the page numbers onthe open pages is 420. Find the sum of the two page numbers.

11114444 The picture shows a "spiral" that begins at theorigin (0,0)(0,0)(0,0)(0,0) and passes through every latticepoint in the plane. Each small arrow is 1 unit inlength. Following the "spiral", what is the lengthof the path from the origin to the point (5,3)(5,3)(5,3)(5,3)?

15151515 How many degrees are in the angle formed bythe hands of a clock at 8:24 ?

11113333 The sum of a proper fraction in lowest terms and its reciprocalequals 2 . Finds the original proper fraction.

12121212 A squirrel buries a total of 80 acorns in NNNN holes. Find the greatestpossible value of NNNN, provided :(1) No hole is empty, and(2) No two holes contain the same number of acorns.

y

y

y

y

x

x

x

x

12121212

3333

6666

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16161616 Some students are in a line. Abby is in the center of the line.Sara is 3 places in front of her, Eli is 4 places behind Sara, andKayla is 2 places in front of Eli. Kayla is the third person in line.How many students are in the line?

17171717 Given the data: 3, 6, 6, 8, 10, 12.

Express in lowest terms:mean6

modemedian3

20202020 How many different triangles can be formed whose 3 verticesare chosen from the rectangular array of 8 points shown?

19191919 A circle with radius 5 cm intersects a circle withradius 3 cm as shown. The area of the shaded

region is 27

square cm. Find the total combined

area inside the circles, but outside the shadedregion. Leave your answer in terms of .

18181818 Find the integer that exceeds 5 by the same amount that 13exceeds 1.


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21212121 How many 2-digit numbers are there in which the ones digit isgreater than the tens digit?

22222222 A bank has two plans for checking accounts. In plan A, thecharge is $7.50 a month with no fee for each check. In plan B,the charge is $3 a month plus an additional 20 cents for eachcheck written. What is the least number of checks a customermust write each month so that plan A costs less than plan B?

23232323 Suppose the base of a triangle is increased by 20%, and itsheight is increased by 30%. By what percent is the area of thetriangle increased?

24242424 Starting with 1, Sara lists the counting numbers in order butomits all those that use the digit 9. What is the 300th number onher list?

25252525 Line segments form a path that starts at (0, 0), is drawn to (1, 0),and then to (1, 2). Each new segment forms a right angle withthe segment before it and is 1 unit longer than that segment.The path ends at (0, 0). How many segments are in the shortestpossible path?(Hint: Consider horizontal and vertical segments separately.)