5. For which value of the real number $a$ is $1+\frac{1}{2+\frac{1}{3+\frac{1}{a}}}=0$?

## You have 120 minutes to solve the problems.

Solve each problem independently on the provided paper, with each problem on a separate page. Do not sign the sheets; write only your code. Write your answers in pen, clearly and neatly. Draw graphs with a pencil. If you solve a problem in multiple ways, clearly indicate which solution the evaluator should grade. If you make a mistake, cross it out.

Each problem's solution will be graded on a scale of 0 to 6 points.

The National Competition Committee wishes you great success.

## 8th Mathematics Knowledge Competition for Students of Secondary Technical and Vocational Schools  National Competition, April 19, 2008

## Problems for 2nd Year Students