Genera nvmerorvm: introdvctio

Antequam vnitatem incipias, pvnctvm vnde proficisceris metire. Brevis est sui ipsivs probatio: non aestimatvr, et eivs exitvs in solo tvo navigatro servatvr.

1. Qvaestio 1Qvae ex his aeqvationibvs solvtionem in $\mathbb{R}$ habet, sed non in $\mathbb{Q}$?

   $x^2 = 3$

   $3x = 2$

   $x + 5 = 3$

   $x^2 = -4$

2. Qvaestio 2In constrvctione nvmerorvm integrorvm, qvod ex his paribvs nvmerorvm natvralivm evndem nvmervm integrvm repraesentat atqve par $(3, 7)$?

   $(6, 10)$

   $(7, 3)$

   $(6, 14)$

   $(4, 7)$

3. Qvaestio 3Compvtare $\frac{5}{12} - \frac{7}{18}$ et effectvm vt fractionem irredvcibilem dare.

4. Qvaestio 4Qvae ex his fractionibvs expressionem decimalem finitam habet?

   $\frac{7}{40}$

   $\frac{7}{30}$

   $\frac{4}{45}$

   $\frac{13}{48}$

5. Qvaestio 5Qvae est copia nvmerorvm realivm $x$ qvi condicioni $\abs{2x - 3} < 5$ satisfacivnt?

   $\ioo{-1}{4}$

   $\ioo{-4}{1}$

   $\icc{-1}{4}$

   $\ioo{-\infty}{4}$

6. Qvaestio 6Compvtare $8^{-\frac{2}{3}}$.

7. Qvaestio 7Qvis est effectvs, cvm denominator nvmeri $\frac{4}{\sqrt{7} - \sqrt{3}}$ rationalis redditvr?

   $\sqrt{7} + \sqrt{3}$

   $\frac{2}{5}\left(\sqrt{7} + \sqrt{3}\right)$

   $\sqrt{7} - \sqrt{3}$

   $2$

8. Qvaestio 8Pro qvo valore nvmeri $k$ systema $2x + 3y = 7$, $4x + 6y = k$ infinitas solvtiones habet?

9. Qvaestio 9Qvae svnt solvtiones in $\mathbb{C}$ aeqvationis $z^2 - 4z + 13 = 0$?

   $2 + 3i$ et $2 - 3i$

   $-2 + 3i$ et $-2 - 3i$

   $4 + 6i$ et $4 - 6i$

   $5$ et $-1$

10. Qvaestio 10Epistomivm male clavsvm gvttam qvibvsqve $2$ secvndis cadere sinit, et qvaeqve gvtta volvmen $5{,}0 \cdot 10^{-2}$ millilitrorvm habet. Qvot litra aqvae amittit in anno $365$ diervm? Effectvm notatione scientifica exprimere, ad dvos digitos significantes rotvndatvm.

    $7{,}9 \cdot 10^2$ litra

    $7{,}8 \cdot 10^2$ litra

    $7{,}9 \cdot 10^5$ litra

    $1{,}6 \cdot 10^3$ litra

11. Qvaestio 11Ex vnitatibvs prioribvsQvi svnt qvotiens $q$ et residvvm $r$ divisionis cvm residvo nvmeri $-29$ per $6$?

    $q = -5$ et $r = 1$

    $q = -4$ et $r = -5$

    $q = -4$ et $r = 5$

12. Qvaestio 12Ex vnitatibvs prioribvsMaximvm commvnem divisorem nvmerorvm $84$ et $120$ compvtare.

13. Qvaestio 13Ex vnitatibvs prioribvsSi nvmervs primvs $p$ nvmervm $n^2$ dividit, cvm $n$ natvrali, qvid affirmari potest?

    Nvmervm $p$ dividere $n$.

    Nihil, nisi $n$ primvs est.

    Nvmervm $p^2$ non dividere $n^2$.

    Solvm nvmervm $p$ dividere $n$ si $p = 2$.