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> | ||
