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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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OOOOLYMPIADSLYMPIADSLYMPIADSLYMPIADS2020202011111111
CONTESTCONTESTCONTESTCONTEST
1111
2222
3333
4444
5555
6666
7777
8888
9999
10101010
11111111
12121212
13131313
14141414
15151515
16161616
17171717
18181818
19191919
20202020
21212121
22222222
23232323
24242424
25252525
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SCHOOLSSCHOOLSSCHOOLSSCHOOLS
MATHMATHMATHMATH
OOOOLYMPIADSLYMPIADSLYMPIADSLYMPIADS2020202011111111
CONTESTCONTESTCONTESTCONTEST
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
9999
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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.)