CONTENTSSASMO 2017 INFORMATION PACKMESSAGE................................................................................................3ABOUT SASMO.......................................................................................4FORMAT OF THE CONTEST.....................................................................4AWARDS.................................................................................................5REGISTRATION.......................................................................................5FREE SASMO BOOKLET...........................................................................6IMPORTANT DATES.................................................................................6SASMO ADVISORY COUNCIL (SAC).........................................................7SAMPLE QUESTIONS...............................................................................9BEFORE THE CONTEST.........................................................................14CONTEST DAY......................................................................................14AFTER THE CONTEST............................................................................15

SINGAPORE INTERNATIONAL MATH CONTESTS CENTRE

Singapore International Math Contests Centre (SIMCC, https://simcc.org/ ) is one of the largest math contests organizers in Singapore and Asia. We are committed to popularizing mathematics education through thinking games and competitions, and allowing students to interact, cooperate and build lasting bonds of friendship that transcend borders.

SIMCC is supported by Singapore Scholastic Trust Limited. SST is a not for profit foundation that organizes international academic and cultural competitions worldwide. SST supports teachers and students with book prizes and scholarships.

We would like to invite you to join SASMO 2017. You can find out more details about these contests on the following pages of the booklet.

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SASMO 2017INFORMATION PACK

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MESSAGE

Dear Principal and Maths HOD, 15 December 2016

I am the Chairman of the Advisory Council for SASMO (Singapore and Asian Schools Math Olympiad) and I am writing to invite your students to participate in the SASMO 2017 Contest, which will be held on 5 April 2017 in the afternoon.

Unlike most Math Olympiads which cater to the top 0.1% of the student population and many participants might feel discouraged by the high standards, SASMO Contests seek to stretch the top 40% of the student population by making the standards just high enough for them (see attached sample questions).

Unlike some Math Olympiads where each school can only send in a small team and there are only a few winners, schools can send in any number of students from each level (Grade 2 to Grade 10) to take part in the SASMO Contests, which seek to encourage the students by giving awards (Gold, Silver, Bronze) to the top 40% of the participants at each level.

In order to stretch the participants, they should be trained. All participants will get a free SASMO 2016 Contest Book to help them prepare for the contest. The teacher-in-charge can also conduct training for the students. Alternatively, our SASMO coaches can conduct training for your students in your school.

For any further queries, please email to admin@simcc.org .Thank you.

 Yours sincerely,

Dr Joseph Yeo B. W. 

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Chairman, SASMO Advisory Council

ABOUT SASMO

SASMO is organised by SIMCC and supported by non-profit foundations Singapore Scholastic Trust and SASMO Advisory Council (SAC). Created in 2006, SASMO is one of largest math contests in Asia. It has expanded from 155 local participants in 2006 to more than 20 000 participants from 19 countries in SASMO 2016. More than 100 schools from Singapore took part in SASMO 2016.

The SASMO Team with the support of Advisory Council spend countless hours carefully developing contest papers which will touch on both school and Olympiad maths. This combined effort allow participants to do better compared to pure-Olympiad papers, since they are familiar with some questions and are able to put on their thinking caps for others, bringing out the inner mathematician in them.

With realistic and high standards, SASMO contests aim to stretch the untapped thinking potential of the student population, their participation in SASMO will help them improve in school mathematics as well as higher order thinking skills.

FORMAT OF THE CONTEST

SASMO is open to all Grades 2 to 10 students. Each grade has a differentiated paper and contains 25 questions within 2 sections:

Section A: 15 Multiple Choice Questions (2 points for each correct answer; 0 point for each unanswered question; deduct 1 point for each wrong answer)

Section B: 10 Non-routine Questions (4 points for each correct answer; no penalty for wrong answers)

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Total: 85 points (to avoid negative scores, each student will begin with 15 points)

AWARDS

PERFECT SCORE AWARD GOLD AWARD SILVER AWARD BRONZE AWARD

All the participants will receive a Certificate.

The top 40% of the participants will receive an award certificate and a medal (Gold for top 8%, Silver for next 12% and Bronze for next 20%).

Perfect scorers will receive a Perfect Score Award and $100 cash each, up to a maximum of $5000 for all the perfect scorers. In the rare event when there are more than 50 perfect scorers, the $5000 will be divided among all the perfect scorers.

REGISTRATION

HOW TO REGISTER

Please contact us if you would like to join.

REGISTRATION FEE

The contest fee is $xx per student. We will handle the fee collection process through Telegraphic Transfer.

REGISTRATION DETAILS

Students from each school will register as a group. Every participating school must have a total of at least 10 students. The school will

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appoint a teacher-in-charge who will be responsible to liaise with SIMCC, including submitting the attached entry form, conducting of the contest and general administration.

FREE SASMO BOOKLET

Students can also purchase more past years contest papers from https://store.simcc.org .

IMPORTANT DATES

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SASMO 2017 Registration opensPrice is $xx

January 2, 2017

SASMO 2017 Registration closesMarch 24

SASMO 2017 Contest DayApril 5

Deadline for submission of scanned AESApril 15

Announcement of results on SASMO website. May 1-3

SASMO ADVISORY COUNCIL (SAC)

Dr Yeo Boon Wooi, Joseph SAC ChairmanSAC Chairman Mathematics professor at Singapore’s

National Institute of Education Recipient of the prestigious Nanyang

Excellence in Teaching Award in 2013 First author of the New Syllabus

Mathematics used in secondary schools marketed worldwide

Specializes in training in-service math teachers for Singapore’s Ministry of Education

Developed the viral math problem “Cheryl’s Birthday”

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Dr Yeap Ban Har

SAC Member

Principal of the Marshall Cavendish Institute Director of Curriculum and Professional

Development at Pathlight School, an autism-oriented K-10 school in Singapore

Advisory board of the SEED Institute and several schools in Singapore and Asia

Collaborates with the Curriculum Planning and Development Division of the Ministry of Education in Singapore regularly

Consultant assisting Brunei’s MOE in their new Math text books and trains Brunei government teachers

Dr Wong Khoon YoongSAC Member Retired as an Associate Professor in

mathematics education from the National Institute of Education and Nanyang Technological University

Taught mathematics in Malaysia and mathematics education courses in universities in Australia, Brunei Darussalam, and Singapore over four decades

Provided consultancy to Singapore schools and education institutes in Chile, Hong Kong, the Philippines, and the United States

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Principal investigator for Singapore in two major international studies on mathematics teacher education

Co-authored a teacher training manual on mathematical thinking for the Australian national statement

SAMPLE QUESTIONS

PRIMARY SCHOOLS

There are some easier questions (to encourage students) and some more difficult questions (which is why students need to prepare themselves or go for training). Some of the questions are related to what they have learnt in their school maths, but require a bit of higher order thinking.

1. The diagram shows some cubes of the same size stacked at a corner of a room. How many cubes are there altogether? (Note: The floor is horizontal and the two walls are vertical. There are no gaps or holes behind the visible cubes.)

2. The Southeast Asian (SEA) Games is held once every two years, except in 1963 (i.e. it was held in 1961 and 1965, but not in 1963). Singapore hosted the 28th SEA Games in 2015. When was the first SEA Games held (although it was known as South East Asian Peninsula Games at that time)?

3. A bag contains some sweets that can be divided equally among 3, 4 or 6 children with no remainder. What is the smallest possible number of sweets in the bag?

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4. The following bar graph shows the favourite colour of a class of 40 students (each student chooses exactly one colour). The tick marks on the vertical axis are equally spaced. How many students’ favourite colour is blue?

5. What is the largest number of parts that can be obtained from cutting a circle using 4 straight cuts? (Note: Do not count the parts outside the circle.)

6. A particular month has 5 Fridays. The first and the last day of the month are not Fridays. What day is the last day of the month?

7. A circle is inscribed in a square as shown in the diagram. The perimeter of the square is 32 cm. Find the area of the circle in terms of π.

A bag of candy is shared between Amy and Ben in the ratio 5 : 3. After

Amy gives 12 of her share to Ben, Ben has 18 pieces of candy more than

Amy. How many pieces of candy are there altogether?

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Favourite ColourNo. of students

Colourredgreen blueyellow

8. In a chess tournament, each player has to play one game with every other player. Five players, Albert, Ben, Charles, Dennis and Ethan, took part in the tournament. So far, Albert has played 4 games, Ben has played 3 games, Charles has played 2 games and Dennis has played 1 game. How many games has Ethan played?

9. A drawer contains 40 coloured socks: 10 black, 14 blue and 16 white. Daniel takes some socks from the drawer without looking at the colours of the socks. What is the least number of socks he must take so that he has at least 2 socks of the same colour? [Hint: Consider the worst case scenario.]

10. Find the last digit of 320. [Hint: The last digit repeats.]

11. The police arrested four suspects who know one another. The suspects know which one of them has stolen the watch, but the police could not find the watch on any one of them.

Albert: I did not steal the watch.

Bernard: Albert is lying.

Cecilia: Bernard stole the watch.

Denise: Bernard is lying.

If only one of them is telling the truth, who stole the watch?

SECONDARY SCHOOLS

There are some easier questions (to encourage students) and some more difficult questions (which is why students need to prepare themselves or go for training). Some of the questions are related to what they have learnt in their school maths, but require a bit of higher order thinking.

1. Find the least value of n such that its LCM (n, 16) = 18.

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2. A man walks for 5 metres in one direction, turns 45o to his right and walks for another 5 metres in that direction. Then he turns another 45o to his right and walks for another 5 metres in that direction. He continues walking in this pattern until he reaches his original starting point. Find the total distance that the man has walked.

3. What is the largest product that can be formed from using the digits 2, 3, 4 and 5, and one multiplication sign? You are only allowed to combine the digits to form two numbers, e.g. 2 × 345, but you are not allowed to use indices, e.g. 23 × 45 is not allowed.

4. There are two circles, each of radius 8 cm, lying on a plane and tangential to each other (i.e. the two circles just touch each other at one point). Find the number of circles of radius 16 cm lying on the same plane and tangential to the first two circles.

5. The following histogram shows the average amount of money spent by students in the school canteen every day.

Which one of the following statement is true?

(a) The median is $1.

(b) The students spent more money in the canteen during the middle of the day.

(c) If the school decided to increase the price of the food in the canteen, then the heights of the columns would get higher.

(d) The mode is 200 students.

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Money SpentNo. of

students

Money(in dollars)

0

100

200

(e) None of the above

6. Alice throws a ball into the air. The path of the ball can be modelled by the equation h = t 2 + 4t + 1, where t, in seconds, is the time from the moment the ball is thrown, and h, in metres, is the height of the ball above the ground. Find the difference in height between the ball at its highest point and at the point from which it is thrown.

7. There are n balls in a bag. Three of the balls are blue and the rest are red. The balls are identical except for the colour. Sam randomly takes out two balls from the bag. The probability that the two balls taken

out are blue is 12. Find the value of n.

8. In a chess tournament, each player has to play one game with every other player. Seven players, Albert, Ben, Charles, Dennis, Ethan, Francis and George, took part in the tournament. So far, Albert has played 6 games, Ben has played 5 games, Charles has played 4 games, Dennis has played 3 games, Ethan has played 2 games and Francis has played 1 game. How many games has George played?

9. Find the last digit of 32015. [Hint: The last digit repeats.]

10. Given that n! = n (n 1) (n 2) … 3 2 1, find the remainder when

1! + 2! + 3! + … + 2015!

is divided by 8. [Hint: 4! Is divisible by 8]

11. Find the value of (80)+(81)+(82)+…+(8

8), where each (8r ) is a Binomial

coefficient.

[Hint: Let x = 1 in the Binomial expansion of (1 + x)8.]

12. The following is a conversation between Gabriel and Heather.

Gabriel: I thought of two distinct one-digit numbers. Can you guess the sum of these two numbers?

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Heather:No. Can you give me a clue?

Gabriel: The last digit of the product of the two numbers is your house number.

Heather:Now I know the sum of the two numbers.

So what is the sum of the two numbers?

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BEFORE THE CONTEST

REGISTRATION OF STUDENTS AND SCHOOLS

School candidates Only school teachers are allowed to register school candidates Competition fee: $xx Interested school teacher must fill up the Registration form

(excel file), submit the form and make the payment to SIMCC. Interested school teachers are responsible for ensuring that the submitted names of the students, name of the school are spelt correctly as these will be printed on the certificates. A charge of USD$10 per certificate will be levied for reprints and it will take at least 2-3 months to reprint the certificates.

INDEX NUMBER

Index number is unique 8-digit identification number of every SASMO participant

First 2 digits represent a country code. Next 3 digits represent a school code. Assign unique school code

for every school which is joining the contest from the range of school codes given to your region. Assign ONE school code to all the individual candidates. In other words, all individual candidates are considered to be from one school. The ranges of school codes for every region are given below in the table.

Last 3 digits represent a student code. Assign unique student code for every participant from the same school.

EXAMPLE Park Ha Na from Cheongna Dalton School, South Korea

2 7 0 1 0 0 2 3

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Country codeSouth Korea

School Codeof Cheongna Dalton School

Student codePark Ha Na

CONTEST PACKAGE

Contest package will be sent via mail one week before the contest. Contest package consists of

Contest papers Answer Entry Sheets (AES)

Check to make sure you have received the correct number of contest papers and Answer entry sheets. Store in a secure place until the contest day.

CONTEST DAY

1. At least 2 weeks before contest date, complete planning and/or bookings to ensure the following will be available:

Contest Venue - please allow 30 minutes in addition to the competition time: All levels are given 90 minutes. Ensure that there is no display of Mathematics material in the exam room.

Desks and chairs for the students A supply of spare 2B pencils, erasers and scrap paper. It is

compulsory to use a 2B PENCIL when filling in student details and answers.

2. Proctors and classrooms are assigned for contest3. Proctors to be there 30 minutes beforehand to prep for students to enter the exam room 10 minutes before start of Contest. Lay out contest papers on the desks. Proctors receive a copy of the Contest Proctoring Instructions. It is recommended that a meeting be held with Proctors to familiarise them with the running of the competition and the format of the Answer entry sheets.4. Collect back all the contest papers and the answer entry sheets.

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AFTER THE CONTEST

SCANNING THE ANSWER ENTRY SHEETS (AES)

Scanning of the AES must be done within 3-4 working days after the contest

Hard Copies of Answer Entry Sheet MUST be scanned using FEEDER type scanner

Flatbed scanner must NOT be used Scanning settings: 300 DPI, Black and White If country partner doesn’t have a feeder scanner, please outsource

the scanning of AESs

Certificates and Medals

All the certificates will be printed in Singapore and will be sent to you by the end of May. Perfect Score, Gold, Silver, Bronze and Participation cert are given.

Each certificate will contain unique Cert Number. Medals will be given to every student who wins an award.

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