Surprising results from a competition of the 7-graders.
Level: Districts of Serbia.
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.
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).
3. 19% ???
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.