International Mathematics Olympiad (IMO) 2011

It is the dream of all mathematics olympiad contestant around the world to be a winner! The 52nd International Mathematical Olympiad (IMO) will be held in the Netherlands in July 2011.

Deadlines

28 February 2011: Online confirmation of participation
28 March 2011: Receipt of problem proposals
25 April 2011:
Online registration of (deputy) leader, single rooms and observers (if applicable)
For leaders and observers A: registration of arrival day (12 or 13 July 2011)
Online registration of the number of contestants
30 May 2011:
Online registration of contestants
Full payment of the charges for single rooms and observers in cleared funds
13 June 2011: online registration of all travel details

See: https://www.imo2011.nl/

USA And International Mathematical Olympiads 2005: Examples-pictures-proofs (Problem Books)

Try IMO 2010 problems:

Bank Problems (Geometric Series)

A bank invites term deposits under the following conditions:
1. The deposit (or initial principal) may be any amount in dollars and cents, with a
minimum of $1.
2. The yearly interest, calculated at the end of each year and added to the principal, is
one cent less than 10% of the current principal, fractions of a cent being discarded.
3.The deposit with accumulated interest is returned at end of the sixth year.

Find the smallest initial deposit which would result in no fractions of cents being discarded
in any of the six years.

Hints.
Let $\displaystyle \large {\color{Yellow} x_{n}}$   be the value of the principal at the end of the nth year.
Derive a relationship between $\displaystyle \large {\color{Yellow} x_{n}}$   and $\displaystyle \large {\color{Yellow} x_{n-1}}$
Guess a relationship between $\displaystyle \large {\color{Yellow} x_{n}}$   and $\displaystyle \large {\color{Yellow} x_{0}}$   ( $\displaystyle \large {\color{Yellow} x_{0}}$   is the initial principal). This relationship should remind you of the compound interest formula.
Prove your guess by mathematical induction.
What's the sum of a geometric series?
Now think in terms of congruences.

Source: Lecture Notes on Mathematical Olympiad Courses: For Junior Section Vol 1 (Mathematical Olympiad Series)

Geometry Problem for High School

1. ABCD is a square with E insides it. If ABE is a equilateral triangle, then <BEC = ....

2.   Below is the picture of semicircle with diameter AC. AB is 3 units longer than BC. If BD= 5 units and perpendicular with AC, then BC = .... 

International Mathematics and Science Olympiad (IMSO) for Primary School 2005

1. Complete the magic triangle so that the numbers along each side give the same sum. Use each of the numbers 5,6,7,8,9 and 10 only once. (Give only one solution)

2. The height of the ground floor of a building is 4 m. The height of each of the other floors is 3m. The total height of this building is 61 m. Inclusive og the ground floor, how many floors does the building have?

3. The composition of Scotty Cake for 6 servings is :

3/4 kg rice flour
45 gr margarin
4 egg
220 gr sugar
300 ml margarin
1/2 tea spoon vanilla


How much rice flour is needed to make Scotty cake for 10 servings?

4. If a positive number B is divided by 2, 3, 4, 6 or 9, the remainder is 1. Find the smallest possible value of B.

Algebra and Number Problem (With Hint)

Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads

1. For every positive integers n ,

 divisible by 2000. Proof it.

Hint: 2000 = 125 x 16

2. If

 Find a x b x c x d

Hint: a is integer part of 57/17

Probability Problem

The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications)

1. A survey of the non-healthy habits of 80 sophomore students of a certain seminary showed the following result.
45 drink alcoholic beverages
42 stay up late
40 smoke cigarettes
25 drink alcohol and smoke
19 stay up late and smoke
22 drink alcohol and stay up late
9 practice clean healthy living by not doing any of the 3

If a seminarian sophomore is randomly picked, what is the probability that he:
a. is just an insomniac (or just stay up late)
b. smokes and/or drinks but is a sleepyhead (or smokes and/or drinks but sleeps early)
c. he should be kicked out of the seminary (by doing all the three things)


2. What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?

Geometry Problem for High School

California Geometry: Concepts, Skills, and Problem Solving


1. In circle O, <PRS= 50⁰ and
 

Find the measure of <QPR.

2. Given that HURN is a square of side x and ∆HUT is equilateral. What is the area of ∆UER in terms of x?

     From: MSA Math Competition High School

 

Math Olympiad Example Problem for Grade 6

Prentice Hall Mathematics California Grade 6 Math

Problems

1.  What are the possible dimensions of a rectangle with integer-valued side lengths in which the numerical value of the area is twice the perimeter?

2.  In celebration of her birthday, Claudine threw a big party. Every two persons shared a bowl of rice, every three persons shared a bowl of fruit salad, and every four persons shared a bowl of soup. There were 130 bowl used together. How many guests were present ?

3.  Calculate:

4.  The pages of the Math Book are numbered consecutively, starting with page 1. The book is bound in ten booklets, with equal number of pages in each booklet. If the sum of the numbers on the first page of every booklet is 4150, how many pages does each booklet have?

5.  Angela is fond of making a wish everytime her car’s odometer displays a number read the same forward and backward (palyndrome). At 10:18 am the odometer read 87978 km. Traveling continuosly the odometer displayed the next possible number that in palyndrome at 11:13 am. During this time, what was the car’s average speed in kilometers per hours ?
 

6.  Eight of the angles of an undecagon have measures whose sum is 1380˚. Of the remaining three angles, two are complementary to each other and two are supplementary to each other. Find the measure of the largest of these three angles.

7.  What is the sum of the numbers less than 200 that has exactly 3 divisors?

Math Olympiad Example Problem for K9

1.     ABC is a right triangle with <ACB= 74° and AM=MQ=QP. Find <QPB. 

math olympiad example problem

2.   How many positive integer n , if n-1 is the factor for 3n-6

3.   <A=60^o and the radius of big circle is 6. Find the radius of small circle.

math olympiad example problem

Singapore Math Olympiad (SMO) 2011

Competition Math for Middle School

One of Mathematical Olympiad competition in south east Asia. The current name Singapore Mathematical Olympiad is held for Junior, Senior and Open. For 2011, the Singapore Mathematical Olympiad schedule is:

Example problems:




Singapore National Mathematical Olympiad 2010

See also:
SMO
Art of Problem Solving

Canadian Math Olympiad

canadian math olympiad

Resource, problem and sample of solution for competitors see http://www.math.ca/Competitions/CMO/%20 .