Övn 1.1
Sommarmatte 1
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| Versionen från 16 juli 2007 kl. 07.35 (redigera) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Ny sida: ==Övning 1.1:1== <div class="ovning"> Beräkna (utan hjälp av räknedosa) <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="50%...) ← Gå till föregående ändring |
Nuvarande version (16 juli 2007 kl. 08.01) (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Tar bort sidans innehåll) |
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| (3 mellanliggande versioner visas inte.) | |||
| Rad 1: | Rad 1: | ||
| - | ==Övning 1.1:1== | ||
| - | <div class="ovning"> | ||
| - | Beräkna (utan hjälp av räknedosa) | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$3-7-4+6-5$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$3-(7-4)+(6-5)$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$3-(7-(4+6)-5)$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$3-(7-(4+6))-5$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | <div class="svar"> | ||
| - | |||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$-7$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$1$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$11$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$1$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | |||
| - | </div> | ||
| - | |||
| - | ==Övning 1.1:2== | ||
| - | <div class="ovning"> | ||
| - | Beräkna (utan hjälp av räknedosa) | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$(3-(7-4))(6-5)$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$3-(((7-4)+6)-5)$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$3\cdot(-7)-4\cdot(6-5)$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$3\cdot(-7)-(4+6)/(-5)$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | <div class="svar"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$0$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$-1$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$-25$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$-19$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.1:3== | ||
| - | <div class="ovning"> | ||
| - | Vilka av följande tal tillhör de naturliga talen? heltalen? | ||
| - | rationella talen? irrationella talen? Förenkla först! | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">$8$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">$-4$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">$8-4$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="33%">$4-8$</td> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="33%">$8(-4)$</td> | ||
| - | <td class="ntext">f)</td> | ||
| - | <td class="ntext" width="33%">$(-8)(-4)$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">g)</td> | ||
| - | <td class="ntext" width="33%">$\displaystyle \frac{4}{-8}$</td> | ||
| - | <td class="ntext">h)</td> | ||
| - | <td class="ntext" width="33%">$\displaystyle \frac{-8}{-4}$</td> | ||
| - | <td class="ntext">i)</td> | ||
| - | <td class="ntext" width="33%">$\displaystyle \frac{\sqrt{2}}{3}$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">j)</td> | ||
| - | <td class="ntext" width="33%">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td> | ||
| - | <td class="ntext">k)</td> | ||
| - | <td class="ntext" width="33%">$-\pi$</td> | ||
| - | <td class="ntext">l)</td> | ||
| - | <td class="ntext" width="33%">$\pi+1$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | <div class="svar"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">heltalen, rationella talen</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="33%">heltalen, rationella talen</td> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="33%">heltalen, rationella talen</td> | ||
| - | <td class="ntext">f)</td> | ||
| - | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">g)</td> | ||
| - | <td class="ntext" width="33%">rationella talen</td> | ||
| - | <td class="ntext">h)</td> | ||
| - | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | ||
| - | <td class="ntext">i)</td> | ||
| - | <td class="ntext" width="33%">irrationella talen</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">j)</td> | ||
| - | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | ||
| - | <td class="ntext">k)</td> | ||
| - | <td class="ntext" width="33%">irrationella talen</td> | ||
| - | <td class="ntext">l)</td> | ||
| - | <td class="ntext" width="33%">irrationella talen</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.1:4== | ||
| - | <div class="ovning"> | ||
| - | Ordna följande tal i storleksordning | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle 2,\ \frac{3}{5},\ \frac{5}{3}\ $ och $\ \displaystyle \frac{7}{3}$</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\ \displaystyle -\frac{1}{3}$</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle \frac{1}{2},\ \frac{2}{3},\ \frac{3}{5},\ \frac{5}{8}\ $ och $\ \displaystyle \frac{21}{34}$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | <div class="svar"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.1:5== | ||
| - | <div class="ovning"> | ||
| - | Ange decimalutvecklingen med tre korrekta decimaler till | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="25%">$\displaystyle \frac{7}{6}$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="25%">$\displaystyle \frac{9}{4}$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="25%">$\displaystyle \frac{2}{7}$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="25%">$\sqrt{2}$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | <div class="svar"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="25%">$1{,}167$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="25%">$2{,}250$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="25%">$0{,}286$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="25%">$1{,}414$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.1:6== | ||
| - | <div class="ovning"> | ||
| - | Vilka av följande tal är rationella? Ange dem som en kvot mellan heltal. | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">$3,14$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">$3{,}1416\,1416\,1416\,\dots$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">$0{,}2\,001\,001\,001\,\dots\,$ (därefter är var tredje decimal en 1:a och övriga 0)</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="100%">$0{,}10\,100\,1000\,10000\,1\dots\, $ (en 1:a, en 0:a, en 1:a, två 0:or, en 1:a, tre 0:or osv.)</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | <div class="svar"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">Talet är rationellt och lika med $\,314/100 = 157/50\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">Talet är rationellt och lika med $\,1999/9990\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="100%">Talet är irrationellt.</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
