Mathematics Challenge

admin — Fri, 22 Oct 2010 14:31:12 +0000

Problem:
1. If 2x + y = 13 and x + 2y = 11, what is the value of x + y?
2. Determine the units digit of the integer equal to 9 + 9² + 9³ + 9⁴.
(The units digit of an integer is its rightmost digit. For example, the units digit of
the integer 1234 is 4.)

Answer ?
Solution 1
Adding the two equations gives (2x + y) + (x + 2y) = 13 + 11 or 3x + 3y = 24.
Thus, x + y = 1/3(24) = 8.

Solution 2
We note that 9 + 9² + 9³+ 9⁴ = 9(1 + 9¹) + 9³(1 + 9¹) = (9 + 9³)(1 + 9) = 10(9 + 9³).
Therefore, 9 + 9² + 9³ + 9⁴ is an integer that is divisible by 10, so its units digit is 0.

Math Olympiad

admin — Fri, 24 Apr 2009 10:43:28 +0000

Many comments on this blog who want to set shoptalk mathematics olympiad for both primary schools, junior and senior high school. Willingness to meet, in the post this time, I will give a link containing a collection of shoptalk Olympic level mathematics for elementary, junior and senior high school.

Although not much, hopefully just shoptalk can be useful for you, either for study or for their children give the Olympyad selection process will follow the district-level mathematics, provincial, national or international. Of course, all for the sake of education your children.

Elementary School – Grade 5-6
Junior High school – Grade 7-9
Senior High School – Grade 10 – 12

Click here to download problem solving of mathematics olympiad for Elementary, Junior dan Senior High School
Click here to download problem solving of mathematics olympiad for Junior High School

Math Olympiad For Primary School » matematika sma

Mathematics Challenge

Math Olympiad