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Sommarmatte 1

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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="svar">+
-<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>+
- +
-==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="svar">+
-<table align="center" width="100%"><tr><td class="ntext" align="center">$\displaystyle \frac{152}{35}$</td></tr></table> +
-</div>+
- +
- +
-==&Ouml;vning 1.3:1==+
- +
-<div class="ovning">+
-Ber&auml;kna +
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="25%">$2^3\cdot3^2$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="25%">$3^5\cdot9^{-2}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="25%">$(-5)^3$</td>+
-<td class="ntext">d)</td>+
-<td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</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="25%">$72$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="25%">$3$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="25%">$-125$</td>+
-<td class="ntext">d)</td>+
-<td class="ntext" width="25%">$\displaystyle \frac{27}{8}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==&Ouml;vning 1.3:2==+
- +
-<div class="ovning">+
-Skriv som en potens av 2+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$2\cdot4\cdot8$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$0{,}25$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$1$</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%">$2^6$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$2^{-2}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$2^0$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==&Ouml;vning 1.3:3==+
- +
-<div class="ovning">+
-Skriv som en potens av 3+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="20%">$\displaystyle \frac{1}{3}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="20%">$243$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="20%">$9^2$</td>+
-<td class="ntext">d)</td>+
-<td class="ntext" width="20%">$\displaystyle \frac{1}{27}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="20%">$\displaystyle \frac{3}{9^2}$</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="20%">$3^{-1}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="20%">$3^5$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="20%">$3^4$</td>+
-<td class="ntext">d)</td>+
-<td class="ntext" width="20%">$3^{-3}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="20%">$3^{-3}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
-==&Ouml;vning 1.3:4==+
- +
-<div class="ovning">+
-Ber&auml;kna+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$2^{9}\cdot2^{-7}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$3^{13}\cdot9^{-3}\cdot27^{\,-2}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</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="33%">$4$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$3$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$625$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$16$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{1}{3750}$</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_3_4a.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_3_4b.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_3_4c.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>+
-<td align="center">+
-[[Bild:1_3_4d.gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning e)&nbsp;</div>+
-<div class=NavContent>+
-Lösning till delfråga e)+
-<table width="100%" cellspacing="10px">+
-<tr>+
-<td align="center">+
-[[Bild:1_3_4e.gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+
- +
-==&Ouml;vning 1.3:5==+
- +
-<div class="ovning">+
-Ber&auml;kna+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$4^{1/2}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$4^{-1/2}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$9^{3/2}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$\left(47^{2/3} \right) ^{3}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$3^{1{,}4}\cdot3^{0{,}6}$</td>+
-<td class="ntext">f)</td>+
-<td class="ntext" width="33%">$\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$</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="33%">$2$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$27$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$2209$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$9$</td>+
-<td class="ntext">f)</td>+
-<td class="ntext" width="33%">$\displaystyle \frac{25}{3}$</td>+
-</tr>+
-<tr><td height="5px"/></tr>+
-</table>+
-</div>+
- +
- +
-==&Ouml;vning 1.3:6==+
-<div class="ovning">+
-Avg&ouml;r vilket tal som &auml;r st&ouml;rst av +
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$256^{1/3}\ $ och $\ 200^{1/3}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$0{,}5^{-3}\ $ och $\ 0{,}4^{-3}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$0{,}2^5\ $ och $\ 0{,}2^{7}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$400^{1/3}\ $ och $\ \bigl(5^{1/3}\bigr)^{4}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$125^{1/2}\ $ och $\ 625^{1/3}$</td>+
-<td class="ntext">f)</td>+
-<td class="ntext" width="33%">$2^{56}\ $ och $\ 3^{40}$</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<br \>+
-<table width="100%" cellspacing="10px">+
-<tr align="left">+
-<td class="ntext">a)</td>+
-<td class="ntext" width="33%">$256^{1/3}>200^{1/3}$</td>+
-<td class="ntext">b)</td>+
-<td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td>+
-<td class="ntext">c)</td>+
-<td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td>+
-</tr>+
-<tr align="left">+
-<td class="ntext">d)</td>+
-<td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td>+
-<td class="ntext">e)</td>+
-<td class="ntext" width="33%">$125^{1/2}>625^{1/3}$</td>+
-<td class="ntext">f)</td>+
-<td class="ntext" width="33%">$3^{40}>2^{56}$</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_3_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>+
-<td align="center">+
-[[Bild:1_3_6b.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_3_6c.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>+
-<td align="center">+
-[[Bild:1_3_6d.gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning e)&nbsp;</div>+
-<div class=NavContent>+
-Lösning till delfråga e)+
-<table width="100%" cellspacing="10px">+
-<tr>+
-<td align="center">+
-[[Bild:1_3_6e.gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+
- +
-<div class=NavFrame style="CLEAR: both">+
-<div class=NavHead>L&ouml;sning f)&nbsp;</div>+
-<div class=NavContent>+
-Lösning till delfråga f)+
-<table width="100%" cellspacing="10px">+
-<tr>+
-<td align="center">+
-[[Bild:1_3_6f.gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</div>+

Nuvarande version


1 Numerisk räkning

2 Algebra

3 Rötter och algoritmer

4 Trigonometri

Den här artikeln är hämtad från http://wiki.math.se/wikis/sf0600_0701/index.php/Sammanst%C3%A4llning_%C3%B6vningar
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