Level: Districts of Serbia.
Age: 13.

1. a^2 + b^2 - 2a +6b + 10 = 0. Calculate a^2009 - 2009b.

2. If AD = 9 cm, BD = 16 cm, find area and perimeter of the right angled triangle ABC (AB is hypotenuse, D is foot of the altitude from C).
Remark: Euclid's theorem and similarity is not allowed, only P.T.

3. Is it number 2009*2011-48 composite. Explain.

4. Geometry.

5. Find for digits number . Conditions are:
a+b+c+d = a*b = . ( One solution is number 2714, 2+7+1+4=2*7=14).

Results:

1. 50%
2. 75%
3. 19% ???

5. 60%

3. Formula (a-b)(a+b) = a^2-b^2 is very well known for all student at this age, but it wasn't help. Problem is in application of this formula.

Source: https://matematicar.com/rezultati/OKRUZNO%202011-GANE1.xls

2009*2011 - 48 = 2010^2 - 49 = 2003*2017

I had a look at the xls file. Serbian is very much like Russian.

Thankyou for the problems and statistics