MathDB

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Part of 2010 Kosovo National Mathematical Olympiad

Problems(4)

Kosovo MO 2010 Grade 9, Problem 1

Source: Kosovo MO 2010 Grade 9, Problem 1

6/7/2021
Solve the equation ∣x+1∣−∣x−1∣=2|x+1|-|x-1|=2.
algebra
Kosovo 2010 Grade 10, Problem 1

Source: Kosovo 2010 Grade 10, Problem 1

6/7/2021
Find the graph of the function y=∣2∣x∣−1∣y=|2^{|x|}-1|.
algebra
Kosovo MO 2010 Grade 11, Problem 1

Source: Kosovo MO 2010 Grade 11, Problem 1

6/7/2021
Solve the inequation 3−x−x+1>12\sqrt {3-x}-\sqrt {x+1}>\frac {1}{2}.
algebra
Kosovo MO 2010 Grade 12, Problem 1

Source: Kosovo MO 2010 Grade 12, Problem 1

6/7/2021
If the real function f(x)=cos⁡x+∑i=1ncos⁡(aix)f(x)=\cos x+\sum_{i=1}^{n}\cos(a_ix) is periodic, prove that ai,i∈{1,2,...,n}a_i,i\in\{1,2,...,n\}, are rational numbers.
functionalgebra