Download [PDF] Secondary 3 SASMO 2013 Problems Singapore and Asian Schools Math Olympiad

File Information

Filename:	[PDF] Secondary 3 SASMO 2013 Problems Singapore and Asian Schools Math Olympiad.pdf
Filesize:	827.82 KB
Uploaded:	24/08/2021 16:48:21
Keywords:	secondary 3 sasmo 2013 problems singapore and asian schools math olympiad pdf
Description:	Download file or read online SASMO past exam paper Secondary 3 2013 Problems - Singapore and Asian Schools Mathematics Olympiad.
Downloads:	15

File Preview

Download Urls

Short Page Link

https://www.edufilestorage.com/8QT

Full Page Link

https://www.edufilestorage.com/8QT/PDF_Secondary_3_SASMO_2013_Problems_Singapore_and_Asian_Schools_Math_Olympiad.pdf

HTML Code

<a href="https://www.edufilestorage.com/8QT/PDF_Secondary_3_SASMO_2013_Problems_Singapore_and_Asian_Schools_Math_Olympiad.pdf" target="_blank" title="Download from eduFileStorage.com"><img src="https://www.edufilestorage.com/cache/plugins/filepreviewer/4031/pdf/150x190_middle_46f4e7862b1eb5bd4935adbbba5d79e8.jpg"/></a>

Forum Code

[url=https://www.edufilestorage.com/8QT/PDF_Secondary_3_SASMO_2013_Problems_Singapore_and_Asian_Schools_Math_Olympiad.pdf][img]https://www.edufilestorage.com/cache/plugins/filepreviewer/4031/pdf/150x190_middle_46f4e7862b1eb5bd4935adbbba5d79e8.jpg[/img][/url]

[PDF] Secondary 3 SASMO 2013 Problems Singapore and Asian Schools Math Olympiad.pdf | Plain Text

Division S 3 Mathematical Olympiads 2013 Name: _________________________________ (as in Birth Cert) NRIC: ______________ Index Number: ________ Class: ______________ School: __________________________________ INSTRUCTIONS 1. Please DO NOT OPEN the contest booklet until the Proctor has given permission to start. 2. TIME : 1 hour 30 minutes 3. Attempt all 25 questions. Show your working clearly. 4. Write your answers neatly in the answers sheet in the booklet. 5. PROCTORING : No one may help any student in any way during the contest. 6. Only 2B pencil may be used. No other materials, including calculators, are allowed. 7. All students must fill in your Name, NRIC no, Index Number, Class and School. 8. MINIMUM TIME: Students must stay in the exam hall at least 1h 15 min.

SASMO 2013, Secondary 3 Contest 1 9. No exam papers and written notes can be taken out by any contestant. 10. All correct answers score 1 point each and are no marks deducted for incorrect answers. EACH QUESTION Scores 1 point each 1. Tom must travel from A to B and he plans to go at a certain speed. He would like to arrive earlier than planned and notes that traveling at a speed 5 km/h faster tha n planned, he will arrive 5 hours earlier and traveling at a speed 10 km/h faster than planned, he will arrive 8 hours earlier. What is his planned speed? ______________________________________________________________________________ 2. On the island of nobles and liars, 50 people are standing in a queue. Everyone, except the first person in the queue, said, that the person before him in the queue is a liar. The first man in the queue, said, that all people, standing after him are liars. How many liars are in the queue? (Nobles always speak the truth, and liars always tell lies.) ______________________________________________________________________________

SASMO 2013, Secondary 3 Contest 2 3. In a football league with 6 teams (A, B, C, D, E, F), each team plays each other team exactly once. So far, A has played one match, B has played 2 matches, C has played 3 matches, D has played 4 matches, and E has played 5 matches. How many matches has F played so far? 4. For how many integers does there exists a convex -gon, whose angles are in ratio ? ______________________________________________________________________________ 5. A sequence of numbers has 6 as its first term, and every term after the first is defined as follows: If a term, A, is even, the next term in the sequence is . If a term, B, is odd, the next term is . Thus, the first four terms in the sequence are 6, 3, 1 0, 5. What is the 200 th term of the sequence? ______________________________________________________________________________

SASMO 2013, Secondary 3 Contest 3 6. Tom rolls a 6 -sided die. Jerry rolls a second 6 -sided die. Tom wins if the values shown differ by 1. What is the probability that Tom wins? (Express your answer in fractions) 7. For how many integers , such that is a perfect square? _________________________________________ _____________________________________ 8. How many positive integers not exceeding 2013 are multiples of 3 and 4 but not 5? ______________________________________________________________________________ 9. How many right -angled triangles can be formed by joining three vertices of a given regular 14 -gon?

SASMO 2013, Secondary 3 Contest 4 10. The first element of the sequence , and if then . Find the value of if . ______________________________________________________________________________ 11. How many 10 -digit numbers only composed of 1, 2, and 3 exist, in which any two neighbouring digits differ by 1?

SASMO 2013, Secondary 3 Contest 5 ______________________________________________________________________________ 12. Four different numbers , , , and are chosen from the list and What is the largest possible value for the expression 13. Evaluate the following sum ______________________________________________________________________________ , find .

SASMO 2013, Secondary 3 Contest 6 ______________________________________________________________________________ 15. Let be the least number with the following property: is a perfect square and is a perfect cube. How many positive factors does the number have? 16. Two circles have their centers on the same diagonal of a square. They touch each other and the sides of the squares as shown. The square has a side of length 1 cm. What is the sum of the lengths of the radii of the circles? ______________________________________________________________________________ 17. What is the last digit of

SASMO 2013, Secondary 3 Contest 7 ______________________________________________________________________________ 18. How many 7 -digit numbers contain at least one 7? 19. Evaluate (in the simplest form) ______________________________________________________________________________ 20. How many zeros does the following product end with?

SASMO 2013, Secondary 3 Contest 8 ______________________________________________________________________________ 21. In isosceles trapezoid ( is parallel to ), is the midpoint of side and angle . Find the perimeter of the trapezoid. 22. A palindrome is a positive integer that is the same when read forwards or backwards. For example, three palindromes are 8; 343 and 5578755. Determine the number of palindromes less than 10 000?

SASMO 2013, Secondary 3 Contest 9 ______________________________________________________________________________ 23. The vertices of triangle are , , and . Points and are on so that . Find the value of . 24. Find positive solutions of the following equation .

SASMO 2013, Secondary 3 Contest 10 ______________________________________________________________________________ 25. A sequence of numbers satisfies 1. 2. Find the value of . End of Paper Name: _________________________ Class: _________________

SASMO 2013, Secondary 3 Contest 11 1. 14. 2. 15. 3. 16. 4. 17. 5. 18. 6. 19. 7. 20. 8. 21. 9. 22. 10. 23. 11. 24. 12. 25. 13. Rough Working SASMO 2013, Secondary 3 Answers

SASMO 2013, Secondary 3 Contest 12 1. 15 km/h 2. 25 3. 3 matches 4. 2 5. 2 6. 7. 103 8. 134 9. 84 10. 4027 11. 64 12. 13. 14. 15. 4x6x3=72 16. 17. 1 18. 19. 61 20. 249 21. 6 22. 198 √ √ √ √

SASMO 2013, Secondary 3 Contest 13 23. 65 24. 25. √ √