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.) |
