Showing posts with label math olympiad. Show all posts
Showing posts with label math olympiad. Show all posts

4/05/2011

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?

4/04/2011

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


 

4/03/2011

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