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Sammanställning övningar

Sommarmatte 1

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Versionen från 21 juni 2007 kl. 14.10 (redigera)
KTH.SE:u1xsetv1 (Diskussion | bidrag)
(→Övning 1.2:2)
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KTH.SE:u1zpa8nw (Diskussion | bidrag)

 
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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=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="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>+
-</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_3a.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_3b.gif]]+
-</td>+
-</tr>+
-</table>+
-</div>+
-</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>+
-<div class=NavContent>+
-<table width="100%" cellspacing="10px">+
-<tr>+
-<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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