Övningar 1.1
Sommarmatte 1
(Skillnad mellan versioner)
| Versionen från 16 juli 2007 kl. 09.41 (redigera) KTH.SE:u1zpa8nw (Diskussion | bidrag) ← Gå till föregående ändring |
Versionen från 16 juli 2007 kl. 09.43 (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) Gå till nästa ändring → |
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| Rad 7: | Rad 7: | ||
| <td class="ntext">a) </td> | <td class="ntext">a) </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) </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) </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) </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 27: | Rad 27: | ||
| <td class="ntext">a) </td> | <td class="ntext">a) </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) </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) </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) </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 48: | Rad 48: | ||
| <td class="ntext">a) </td> | <td class="ntext">a) </td> | ||
| <td class="ntext" width="33%">8</td> | <td class="ntext" width="33%">8</td> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </td> |
| <td class="ntext" width="33%">-4</td> | <td class="ntext" width="33%">-4</td> | ||
| - | <td class="ntext">c)</td> | + | <td class="ntext">c) </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) </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) </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) </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) </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) </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) </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) </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) </td> |
| <td class="ntext" width="33%">-\pi</td> | <td class="ntext" width="33%">-\pi</td> | ||
| - | <td class="ntext">l)</td> | + | <td class="ntext">l) </td> |
| <td class="ntext" width="33%">\pi+1</td> | <td class="ntext" width="33%">\pi+1</td> | ||
| </tr> | </tr> | ||
| Rad 90: | Rad 90: | ||
| </tr> | </tr> | ||
| <tr> | <tr> | ||
| - | <td class="ntext">b)</td> | + | <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> | <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) </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 108: | Rad 108: | ||
| <td class="ntext">a) </td> | <td class="ntext">a) </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) </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) </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) </td> |
| <td class="ntext" width="25%">\sqrt{2}</td> | <td class="ntext" width="25%">\sqrt{2}</td> | ||
| </tr> | </tr> | ||
| Rad 128: | Rad 128: | ||
| </tr> | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </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) </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) </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> | ||
Versionen från 16 juli 2007 kl. 09.43
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.) |
