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Sommarmatte 1

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Versionen från 21 juni 2007 kl. 14.11 (redigera)
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(→Övning 1.2:3)
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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="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>+
- +
- +
-==Övning 1.2:1==+
-<div class="ovning">+
-Skriv p&aring; gemensamt br&aring;kstreck +
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{7}{4}+\frac{11}{7}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{2}{7}-\frac{1}{5}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{1}{6}-\frac{2}{5}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}$</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="33%">$\displaystyle \frac{93}{28}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{3}{35}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle -\frac{7}{30}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{47}{60}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{47}{84}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==Övning 1.2:2==+
-<div class="ovning">+
-Bestäm minsta gemensamma nämnare+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{1}{6}+\frac{1}{10}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{1}{4}-\frac{1}{8}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">c)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{1}{12}-\frac{1}{14}$</td>+
-<td class="ntext">d)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{2}{45}+\frac{1}{75}$</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%">$\displaystyle {30}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="50%">$\displaystyle {8}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">c)</td>+
-<td class="ntext" width="50%">$\displaystyle {84}$</td>+
-<td class="ntext">d)</td>+
-<td class="ntext" width="50%">$\displaystyle {225}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==Övning 1.2:3==+
-<div class="ovning">+
-Beräkna följande uttryck genom att använda minsta gemensamma nämnare:+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{3}{20}+\frac{7}{50}-\frac{1}{10}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{1}{24}+\frac{1}{40}-\frac{1}{16}$</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">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{19}{100}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="50%">$\displaystyle \frac{1}{240}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==Övning 1.2:4==+
-<div class="ovning">+
-F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}$</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="33%">$\displaystyle \frac{6}{7}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{16}{21}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{1}{6}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==&Ouml;vning 1.2:5==+
-<div class="ovning">+
-F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}$</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><td height="5px"/></tr>+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{105}{4}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$-5$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{8}{55}$</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>+
-<td align="center">+
-[[Bild:1_2_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>+
-<td align="center">+
-[[Bild:1_2_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>+
-<td align="center">+
-[[Bild:1_2_5c-1(2).gif]]+
-</td>+
-</tr>+
-<tr>+
-<td>+
-[[Bild:1_2_5c-2(2).gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+
- +
-==Övning 1.2:6==+
- +
-<div class="ovning">+
-F&ouml;renkla $\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}$+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>Facit&nbsp;</div>+
-<div class=NavContent>+
-<table align="center" width="100%"><tr><td class="ntext" align="center">$\displaystyle \frac{152}{35}$</td></tr></table> +
-</div>+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning &nbsp;</div>+
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-<table width="100%" cellspacing="10px">+
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-<td align="center">+
-[[Bild:1_2_6-1(2).gif]]+
-</td>+
-</tr>+
-<tr>+
-<td align="center">+
-[[Bild:1_2_6-2(2).gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+

Nuvarande version


1 Numerisk räkning

2 Algebra

3 Rötter och algoritmer

4 Trigonometri

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