Sammanställning övningar

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Versionen från 21 juni 2007 kl. 13.58 (redigera)
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(→Övning 1.1:4)
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Rad 1: Rad 1:
__NOTOC__ __NOTOC__
-==Övning 1.1:1==+[[övn 1|1 Numerisk räkning]]
-<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">+[[övn 2|2 Algebra]]
-<table width="100%" cellspacing="10px">+[[övn 3|3 Rötter och algoritmer]]
-<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>+[[övn 4|4 Trigonometri]]
- +
-==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=NavFrame style="CLEAR: both">+
-<div class=NavHead>Facit&nbsp;</div>+
-<div class=NavContent>+
-Facit till alla delfrågor+
-<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>+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning a)&nbsp;</div>+
-<div class=NavContent>+
-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 class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning b)&nbsp;</div>+
-<div class=NavContent>+
-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 class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning c)&nbsp;</div>+
-<div class=NavContent>+
-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 class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning d)&nbsp;</div>+
-<div class=NavContent>+
-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>+
- +
-==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=NavFrame style="CLEAR: both">+
-<div class=NavHead>Facit&nbsp;</div>+
-<div class=NavContent>+
-Facit till alla delfrågor+
-<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>+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning a)&nbsp;</div>+
-<div class=NavContent>+
-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 class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning b)&nbsp;</div>+
-<div class=NavContent>+
-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 class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning c)&nbsp;</div>+
-<div class=NavContent>+
-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 class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning d)&nbsp;</div>+
-<div class=NavContent>+
-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>+

Nuvarande version


1 Numerisk räkning

2 Algebra

3 Rötter och algoritmer

4 Trigonometri

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