Övningar 1.1

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Rad 1: Rad 1:
__NOTOC__ __NOTOC__
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'''Övning 1.1:1''' '''Övning 1.1:1'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-Beräkna (utan hjälp av räknedosa)+Beräkna (utan hjälp av räknedosa)&nbsp;&nbsp;&nbsp;
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3-7-4+6-5$</td> <td class="ntext" width="50%">$3-7-4+6-5$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3-(7-4)+(6-5)$</td> <td class="ntext" width="50%">$3-(7-4)+(6-5)$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3-(7-(4+6)-5)$</td> <td class="ntext" width="50%">$3-(7-(4+6)-5)$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3-(7-(4+6))-5$</td> <td class="ntext" width="50%">$3-(7-(4+6))-5$</td>
</tr> </tr>
Rad 22: Rad 23:
'''Övning 1.1:2''' '''Övning 1.1:2'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-Beräkna (utan hjälp av räknedosa)+Beräkna (utan hjälp av räknedosa)&nbsp;&nbsp;&nbsp;
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$(3-(7-4))(6-5)$</td> <td class="ntext" width="50%">$(3-(7-4))(6-5)$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3-(((7-4)+6)-5)$</td> <td class="ntext" width="50%">$3-(((7-4)+6)-5)$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3\cdot(-7)-4\cdot(6-5)$</td> <td class="ntext" width="50%">$3\cdot(-7)-4\cdot(6-5)$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3\cdot(-7)-(4+6)/(-5)$</td> <td class="ntext" width="50%">$3\cdot(-7)-(4+6)/(-5)$</td>
</tr> </tr>
Rad 46: Rad 47:
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$8$</td> <td class="ntext" width="33%">$8$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$-4$</td> <td class="ntext" width="33%">$-4$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$8-4$</td> <td class="ntext" width="33%">$8-4$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$4-8$</td> <td class="ntext" width="33%">$4-8$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$8(-4)$</td> <td class="ntext" width="33%">$8(-4)$</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(-8)(-4)$</td> <td class="ntext" width="33%">$(-8)(-4)$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">g)</td>+<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{4}{-8}$</td> <td class="ntext" width="33%">$\displaystyle \frac{4}{-8}$</td>
-<td class="ntext">h)</td>+<td class="ntext">h)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{-8}{-4}$</td> <td class="ntext" width="33%">$\displaystyle \frac{-8}{-4}$</td>
-<td class="ntext">i)</td>+<td class="ntext">i)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{\sqrt{2}}{3}$</td> <td class="ntext" width="33%">$\displaystyle \frac{\sqrt{2}}{3}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">j)</td>+<td class="ntext">j)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td> <td class="ntext" width="33%">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td>
-<td class="ntext">k)</td>+<td class="ntext">k)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$-\pi$</td> <td class="ntext" width="33%">$-\pi$</td>
-<td class="ntext">l)</td>+<td class="ntext">l)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\pi+1$</td> <td class="ntext" width="33%">$\pi+1$</td>
</tr> </tr>
Rad 86: Rad 87:
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$\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>
</tr> </tr>
<tr> <tr>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\ \displaystyle -\frac{1}{3}$</td> <td class="ntext" width="100%">$\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\ \displaystyle -\frac{1}{3}$</td>
</tr> </tr>
<tr> <tr>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</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> <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>
Rad 106: Rad 107:
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$\displaystyle \frac{7}{6}$</td> <td class="ntext" width="25%">$\displaystyle \frac{7}{6}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$\displaystyle \frac{9}{4}$</td> <td class="ntext" width="25%">$\displaystyle \frac{9}{4}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$\displaystyle \frac{2}{7}$</td> <td class="ntext" width="25%">$\displaystyle \frac{2}{7}$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$\sqrt{2}$</td> <td class="ntext" width="25%">$\sqrt{2}$</td>
</tr> </tr>
Rad 118: Rad 119:
</table> </table>
</div> </div>
- +<br><br><br>
'''Övning 1.1:6''' '''Övning 1.1:6'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Rad 124: Rad 125:
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$3,14$</td> <td class="ntext" width="100%">$3,14$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$3{,}1416\,1416\,1416\,\dots$</td> <td class="ntext" width="100%">$3{,}1416\,1416\,1416\,\dots$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$0{,}2\,001\,001\,001\,\dots\,$ (därefter är var tredje decimal en 1:a och övriga 0)</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>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</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> <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>
Rad 142: Rad 143:
</table> </table>
</div> </div>
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Nuvarande version


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)    $3-(7-(4+6))-5$

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)    $3\cdot(-7)-(4+6)/(-5)$

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)    $\pi+1$

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 $\ \displaystyle \frac{21}{34}$

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)    $\sqrt{2}$




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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