Školjka - Web archive of math problems

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What is Školjka?

Školjka is a web archive of math problems, a tool intended for primary and high school students training for math contests. It contains thousands of problems from various math contests in recent two decades.

Why Školjka?

Školjka supports searching by categories and difficulty, allowing students to quickly find the exact problems they are interested in. Likewise, Školjka can be helpful to mentors and teachers for preparing lectures.

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Općinsko natjecanje iz matematike 2024, SŠ4 3

Neka je $(a_n)$ niz definiran s $a_1=1$ , $a_2=2$ i $a_n = a_{n - 1} + (n - 1)a_{n - 2} \quad \text{za } n \geq 3.$

Dokaži da vrijedi $a_{2024} \geq \sqrt{2024!}$ .

2 years

Općinsko natjecanje iz matematike 2024, SŠ4 6

Pravokutni trokuti $ABC$ i $ABD$ imaju zajedničku hipotenuzu $\overline{AB}$ , a katete $\overline{AD}$ i $\overline{BC}$ im se sijeku u točki $E$ . Neka je $F$ ortogonalna projekcija točke $E$ na pravac $AB$ . Dokaži da je $FE$ simetrala kuta $\sphericalangle CFD$ .

2 years

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