B3. Let the expression be $A=|x+3|+|x-5|$.

a) Calculate the value of the expression for $x=\sqrt{2}$.

b) Find all possible values of $x$ for which $A=4$.

19th Knowledge Competition

in Mathematics for Students of Secondary Technical and Vocational Schools

National Competition, April 13, 2019
Attach the sticker with the code

## Tasks for 2nd Year

Time for solving: 120 minutes. In section A, we will award three points for each correct answer, and deduct one point for each incorrect answer. Write the answers for section A in the left table, leave the right table blank.

![](https://cdn.mathpix.com/cropped/2024_06_07_9fbd0ae098c18b73b6bfg-06.jpg?height=163&width=319&top_left_y=661&top_left_x=640)

| B1 | B2 | B3 |
| :--- | :--- | :--- |
|  |  |  |
B3.

a) For $\mathrm{Za} x$ we substitute $\sqrt{2}$ and calculate the value of the expression $A=|\sqrt{2}+3|+|\sqrt{2}-5|=\sqrt{2}+3-\sqrt{2}+5=8$.

b) For $x$ National Competition, April 13, 2019

## Solutions to problems and scoring

(April 5, 2019, $10:30$ )

A contestant who arrives at the solution by any correct method (even if the scoring guide does not provide for it) receives all possible points.

A correct method is considered any procedure that:

- sensibly takes into account the wording of the problem,
- leads to the solution of the problem,
- is mathematically correct and complete.

If an intermediate or final result can be recognized, guessed, read from a diagram, or calculated mentally, the contestant generally receives all the points provided. However, if the solution is guessed (and cannot be arrived at without calculation), it is scored with 0 points.

A contestant who has only partially solved the problem, from otherwise correct solving procedures but without a visible path to the final solution of the problem, cannot receive more than half of the possible points.

The asterisk '*' next to the points means that the contestant can receive the point or points for a correct procedure, even if the calculation is incorrect.

## Second Year

![](https://cdn.mathpix.com/cropped/2024_06_07_9fbd0ae098c18b73b6bfg-21.jpg?height=137&width=220&top_left_y=357&top_left_x=929)