1.1 Övningar

Sommarmatte 1

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Versionen från 27 april 2007 kl. 16.38 (redigera)
Annagf (Diskussion | bidrag)
(Övning 1.1:5)
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Nuvarande version (20 mars 2008 kl. 09.57) (redigera) (ogör)
KTH.SE:u1rp004j (Diskussion | bidrag)

 
(7 mellanliggande versioner visas inte.)
Rad 4: Rad 4:
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext"> $3-7-4+6-5$</td>+<td class="ntext" width="50%">$3-7-4+6-5$</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$3-(7-4)+(6-5)$</td>+<td class="ntext" width="50%">$3-(7-4)+(6-5)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">$3-(7-(4+6)-5)$</td>+<td class="ntext" width="50%">$3-(7-(4+6)-5)$</td>
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">$3-(7-(4+6))-5$</td>+<td class="ntext" width="50%">$3-(7-(4+6))-5$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
- 
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
</table> </table>
Rad 25: Rad 22:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
- +Facit till alla delfrågor
-Facit till alla delfrågorna+
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext"> $-7$</td>+<td class="ntext" width="50%">$-7$</td>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$1$</td>+<td class="ntext" width="50%">$1$</td>
- +
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">$11$</td>+<td class="ntext" width="50%">$11$</td>
-<td class="ntext">$\textrm{d)}$</td>+<td class="ntext">d)</td>
-<td class="ntext">$1$</td>+<td class="ntext" width="50%">$1$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 48: Rad 42:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br\>[[Bild:1_1_1a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_1a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br\>[[Bild:1_1_1b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_1b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br\>[[Bild:1_1_1c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_1c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d <br\>[[Bild:1_1_1d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_1d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 80: Rad 102:
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">$(3-(7-4))(6-5)$</td>+<td class="ntext" width="50%">$(3-(7-4))(6-5)$</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$3-(((7-4)+6)-5)$</td>+<td class="ntext" width="50%">$3-(((7-4)+6)-5)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">$3\cdot(-7)-4\cdot(6-5)$</td>+<td class="ntext" width="50%">$3\cdot(-7)-4\cdot(6-5)$</td>
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">$3\cdot(-7)-(4+6)/(-5)$</td>+<td class="ntext" width="50%">$3\cdot(-7)-(4+6)/(-5)$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 99: Rad 120:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
- +Facit till alla delfrågor
-Facit till alla delfrågorna+
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$0$</td>+<td class="ntext" width="50%">$0$</td>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$-1$</td>+<td class="ntext" width="50%">$-1$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">$-25$</td>+<td class="ntext" width="50%">$-25$</td>
-<td class="ntext">$\textrm{d)}$</td>+<td class="ntext">d)</td>
-<td class="ntext">$-19$</td>+<td class="ntext" width="50%">$-19$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 121: Rad 140:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br\>[[Bild:1_1_2a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_2a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br\>[[Bild:1_1_2b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_2b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br\>[[Bild:1_1_2c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_2c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d <br\>[[Bild:1_1_2d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_2d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 153: Rad 200:
rationella talen? irrationella talen? Förenkla först! rationella talen? irrationella talen? Förenkla först!
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$8$</td>+<td class="ntext" width="33%">$8$</td>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$-4$</td>+<td class="ntext" width="33%">$-4$</td>
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">$8-4$</td>+<td class="ntext" width="33%">$8-4$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{d)}$</td>+<td class="ntext">d)</td>
-<td class="ntext">$4-8$</td>+<td class="ntext" width="33%">$4-8$</td>
-<td class="ntext">$\textrm{e)}$</td>+<td class="ntext">e)</td>
-<td class="ntext">$8(-4)$</td>+<td class="ntext" width="33%">$8(-4)$</td>
-<td class="ntext">$\textrm{f)}$</td>+<td class="ntext">f)</td>
-<td class="ntext">$(-8)(-4)$</td>+<td class="ntext" width="33%">$(-8)(-4)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{g)}$</td>+<td class="ntext">g)</td>
-<td class="ntext">$\displaystyle \frac{4}{-8}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{4}{-8}$</td>
-<td class="ntext">$\textrm{h)}$</td>+<td class="ntext">h)</td>
-<td class="ntext">$\displaystyle \frac{-8}{-4}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{-8}{-4}$</td>
-<td class="ntext">$\textrm{i)}$</td>+<td class="ntext">i)</td>
-<td class="ntext">$\displaystyle \frac{\sqrt{2}}{3}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{\sqrt{2}}{3}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{j)}$</td>+<td class="ntext">j)</td>
-<td class="ntext">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td>+<td class="ntext" width="33%">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td>
-<td class="ntext">$\textrm{k)}$</td>+<td class="ntext">k)</td>
-<td class="ntext">$-\pi$</td>+<td class="ntext" width="33%">$-\pi$</td>
-<td class="ntext">$\textrm{l)}$</td>+<td class="ntext">l)</td>
-<td class="ntext">$\pi+1$</td>+<td class="ntext" width="33%">$\pi+1$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 196: Rad 239:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
- +Facit till alla delfrågor
-Facit till alla delfrågorna+
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
-<tr align="left">+<tr align="left" valign="top">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">naturliga talen, heltalen, rationella talen </td>+<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">heltalen, rationella talen </td>+<td class="ntext" width="33%">heltalen, rationella talen</td>
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">naturliga talen, heltalen, rationella talen </td>+<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
</tr> </tr>
-<tr><td height="5px"/></tr>+<tr align="left" valign="top">
-<tr align="left">+<td class="ntext">d)</td>
-<td class="ntext">$\textrm{d)}$</td>+<td class="ntext" width="33%">heltalen, rationella talen</td>
-<td class="ntext">heltalen, rationella talen </td>+<td class="ntext">e)</td>
-<td class="ntext">$\textrm{e)}$</td>+<td class="ntext" width="33%">heltalen, rationella talen</td>
-<td class="ntext">heltalen, rationella talen </td>+<td class="ntext">f)</td>
-<td class="ntext">$\textrm{f)}$</td>+<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">naturliga talen, heltalen, rationella talen, </td>+
</tr> </tr>
-<tr><td height="5px"/></tr>+<tr align="left" valign="top">
-<tr align="left">+<td class="ntext">g)</td>
-<td class="ntext">$\textrm{g)}$</td>+<td class="ntext" width="33%">rationella talen</td>
-<td class="ntext">rationella talen</td>+<td class="ntext">h)</td>
-<td class="ntext">$\textrm{h)}$</td>+<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">naturliga talen, heltalen, rationella talen </td>+<td class="ntext">i)</td>
-<td class="ntext">$\textrm{i)}$</td>+<td class="ntext" width="33%">irrationella talen</td>
-<td class="ntext">irrationella talen</td>+
</tr> </tr>
-<tr><td height="5px"/></tr>+<tr align="left" valign="top">
-<tr align="left">+<td class="ntext">j)</td>
-<td class="ntext">$\textrm{j)}$</td>+<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">naturliga talen, heltalen, rationella talen </td>+<td class="ntext">k)</td>
-<td class="ntext">$\textrm{k)}$</td>+<td class="ntext" width="33%">irrationella talen</td>
-<td class="ntext">irrationella talen</td>+<td class="ntext">l)</td>
-<td class="ntext">$\textrm{l)}$</td>+<td class="ntext" width="33%">irrationella talen</td>
-<td class="ntext">irrationella talen</td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 241: Rad 280:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br\>[[Bild:1_1_3a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br\>[[Bild:1_1_3b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br\>[[Bild:1_1_3c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d <br\>[[Bild:1_1_3d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e <br\>[[Bild:1_1_3e.gif]]+Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f <br\>[[Bild:1_1_3f.gif]]+Lösning till delfråga f)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga g <br\>[[Bild:1_1_3g.gif]]+Lösning till delfråga g)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3g.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning h&nbsp;</div>+<div class=NavHead>L&ouml;sning h)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga h <br\>[[Bild:1_1_3h.gif]]+Lösning till delfråga h)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3h.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
 +
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning i&nbsp;</div>+<div class=NavHead>L&ouml;sning i)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga i <br\>[[Bild:1_1_3i.gif]]+Lösning till delfråga i)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3i.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning j&nbsp;</div>+<div class=NavHead>L&ouml;sning j)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga j <br\>[[Bild:1_1_3j.gif]]+Lösning till delfråga j)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3j.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning k&nbsp;</div>+<div class=NavHead>L&ouml;sning k)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga k <br\>[[Bild:1_1_3k.gif]]+Lösning till delfråga k)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3k.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning l&nbsp;</div>+<div class=NavHead>L&ouml;sning l)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga l <br\>[[Bild:1_1_3l.gif]]+Lösning till delfråga l)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_3l.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 327: Rad 451:
Ordna följande tal i storleksordning Ordna följande tal i storleksordning
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$\displaystyle 2,\ \frac{3}{5},\ \frac{5}{3}\ $ och $\ \displaystyle \frac{7}{3}$</td>+<td class="ntext" width="100%">$\displaystyle 2,\ \frac{3}{5},\ \frac{5}{3}\ $ och $\ \displaystyle \frac{7}{3}$</td>
-<td class="ntext">$\textrm{b)}$</td>+</tr>
-<td class="ntext">$\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\displaystyle -\frac{1}{3}$</td>+<tr>
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{1}{2},\ \frac{2}{3},\ \frac{3}{5},\ \frac{5}{8}$ och $\displaystyle \frac{21}{34}$</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>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 343: Rad 470:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
- +Facit till alla delfrågor
-Facit till alla delfrågorna+
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td>+<td class="ntext" width="100%">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td>
</tr> </tr>
<tr> <tr>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td>+<td class="ntext" width="100%">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td>
</tr> </tr>
<tr> <tr>
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$</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>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 365: Rad 490:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br\>[[Bild:1_1_4a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_4a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br\>[[Bild:1_1_4b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_4b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br\>[[Bild:1_1_4c-1(2).gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_4c-1(2).gif]]
 +</td>
 +</tr>
 +<tr align="left">
 +<td width="100%" align="center">
[[Bild:1_1_4c-2(2).gif]] [[Bild:1_1_4c-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 390: Rad 540:
Ange decimalutvecklingen med tre korrekta decimaler till Ange decimalutvecklingen med tre korrekta decimaler till
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{7}{6}$</td>+<td class="ntext" width="25%">$\displaystyle \frac{7}{6}$</td>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{9}{4}$</td>+<td class="ntext" width="25%">$\displaystyle \frac{9}{4}$</td>
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{2}{7}$</td>+<td class="ntext" width="25%">$\displaystyle \frac{2}{7}$</td>
-<td class="ntext">$\textrm{d)}$</td>+<td class="ntext">d)</td>
-<td class="ntext">$\sqrt{2}$</td>+<td class="ntext" width="25%">$\sqrt{2}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 408: Rad 557:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
- +Facit till alla delfrågor
-Facit till alla delfrågorna+
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$1,167$</td>+<td class="ntext" width="25%">$1{,}167$</td>
-<td class="ntext">$\textrm{b)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$2,250$</td>+<td class="ntext" width="25%">$2{,}250$</td>
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">c)</td>
-<td class="ntext">$0,286$</td>+<td class="ntext" width="25%">$0{,}286$</td>
-<td class="ntext">$\textrm{d)}$</td>+<td class="ntext">d)</td>
-<td class="ntext">$1,414$</td>+<td class="ntext" width="25%">$1{,}414$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 428: Rad 575:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br\>[[Bild:1_1_5a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_5a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br\>[[Bild:1_1_5b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_5b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br\>[[Bild:1_1_5c.gif]]+Lösning till delfråga c)
- +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_5c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d <br\>[[Bild:1_1_5d.gif]]+Lösning till delfråga d)
- +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_5d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 459: Rad 632:
==Övning 1.1:6== ==Övning 1.1:6==
<div class="ovning"> <div class="ovning">
-Ange decimalutvecklingen med tre korrekta decimaler till+Vilka av följande tal är rationella? Ange dem som en kvot mellan heltal.
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{7}{6}$</td>+<td class="ntext" width="100%">$3,14$</td>
-<td class="ntext">$\textrm{b)}$</td>+</tr>
-<td class="ntext">$\displaystyle \frac{9}{4}$</td>+<tr align="left">
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{2}{7}$</td>+<td class="ntext" width="100%">$3{,}1416\,1416\,1416\,\dots$</td>
-<td class="ntext">$\textrm{d)}$</td>+</tr>
-<td class="ntext">$\sqrt{2}$</td>+<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>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 479: Rad 657:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
- +Facit till alla delfrågor
-Facit till alla delfrågorna+
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a)}$</td>+<td class="ntext">a)</td>
-<td class="ntext">$1,167$</td>+<td class="ntext" width="100%">Talet är rationellt och lika med $\,314/100 = 157/50\,$.</td>
-<td class="ntext">$\textrm{b)}$</td>+</tr>
-<td class="ntext">$2,250$</td>+<tr align="left">
-<td class="ntext">$\textrm{c)}$</td>+<td class="ntext">b)</td>
-<td class="ntext">$0,286$</td>+<td class="ntext" width="100%">Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.</td>
-<td class="ntext">$\textrm{d)}$</td>+</tr>
-<td class="ntext">$1,414$</td>+<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>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 499: Rad 681:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br\>[[Bild:1_1_5a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_6a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br\>[[Bild:1_1_5b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_6b-1(2).gif]]
 +</td>
 +</tr>
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_6b-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br\>[[Bild:1_1_5c.gif]]+Lösning till delfråga c)
- +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_6c-1(2).gif]]
 +</td>
 +</tr>
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_6c-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d <br\>[[Bild:1_1_5d.gif]]+Lösning till delfråga d)
- +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td width="100%" align="center">
 +[[Bild:1_1_6d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>

Nuvarande version

Innehåll

[redigera] Övning 1.1:1

Beräkna (utan hjälp av räknedosa)

a) $3-7-4+6-5$ b) $3-(7-4)+(6-5)$
c) $3-(7-(4+6)-5)$ d) $3-(7-(4+6))-5$

[redigera] Övning 1.1:2

Beräkna (utan hjälp av räknedosa)

a) $(3-(7-4))(6-5)$ b) $3-(((7-4)+6)-5)$
c) $3\cdot(-7)-4\cdot(6-5)$ d) $3\cdot(-7)-(4+6)/(-5)$

[redigera] Övning 1.1:3

Vilka av följande tal tillhör de naturliga talen? heltalen? rationella talen? irrationella talen? Förenkla först!

a) $8$ b) $-4$ c) $8-4$
d) $4-8$ e) $8(-4)$ f) $(-8)(-4)$
g) $\displaystyle \frac{4}{-8}$ h) $\displaystyle \frac{-8}{-4}$ i) $\displaystyle \frac{\sqrt{2}}{3}$
j) $\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$ k) $-\pi$ l) $\pi+1$

[redigera] Övning 1.1:4

Ordna följande tal i storleksordning

a) $\displaystyle 2,\ \frac{3}{5},\ \frac{5}{3}\ $ och $\ \displaystyle \frac{7}{3}$
b) $\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\ \displaystyle -\frac{1}{3}$
c) $\displaystyle \frac{1}{2},\ \frac{2}{3},\ \frac{3}{5},\ \frac{5}{8}\ $ och $\ \displaystyle \frac{21}{34}$

[redigera] Övning 1.1:5

Ange decimalutvecklingen med tre korrekta decimaler till

a) $\displaystyle \frac{7}{6}$ b) $\displaystyle \frac{9}{4}$ c) $\displaystyle \frac{2}{7}$ d) $\sqrt{2}$

[redigera] Övning 1.1:6

Vilka av följande tal är rationella? Ange dem som en kvot mellan heltal.

a) $3,14$
b) $3{,}1416\,1416\,1416\,\dots$
c) $0{,}2\,001\,001\,001\,\dots\,$ (därefter är var tredje decimal en 1:a och övriga 0)
d) $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.)
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