1.1 Übungen

Aus Online Mathematik Brückenkurs 1

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===Exercise 1.1:1===
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===Übung 1.1:1===
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Work out (without the help of a calculator)
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Berechne folgendes (ohne Taschenrechner)
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|| <math>3-(7-(4+6))-5</math>
|| <math>3-(7-(4+6))-5</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.1:1|Solution a|Solution 1.1:1a|Solution b|Solution 1.1:1b|Solution c|Solution 1.1:1c|Solution d|Solution 1.1:1d}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:1|Lösung a|Solution 1.1:1a|Lösung b|Solution 1.1:1b|Lösung c|Solution 1.1:1c|Lösung d|Solution 1.1:1d}}
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===Exercise 1.1:2===
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===Übung 1.1:2===
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Simplify
Simplify
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|| <math>3\cdot(-7)-(4+6)/(-5)</math>
|| <math>3\cdot(-7)-(4+6)/(-5)</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.1:2|Solution a|Solution 1.1:2a|Solution b|Solution 1.1:2b|Solution c|Solution 1.1:2c|Solution d|Solution 1.1:2d}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:2|Lösung a|Solution 1.1:2a|Lösung b|Solution 1.1:2b|Lösung c|Solution 1.1:2c|Lösung d|Solution 1.1:2d}}
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===Exercise 1.1:3===
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===Übung 1.1:3===
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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|| <math>(-8)\cdot(-4)</math>
|| <math>(-8)\cdot(-4)</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.1:3|Solution a|Solution 1.1:3a|Solution b|Solution 1.1:3b|Solution c|Solution 1.1:3c|Solution d|Solution 1.1:3d|Solution e|Solution 1.1:3e|Solution f|Solution 1.1:3f}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:3|Lösung a|Solution 1.1:3a|Lösung b|Solution 1.1:3b|Lösung c|Solution 1.1:3c|Lösung d|Solution 1.1:3d|Lösung e|Solution 1.1:3e|Lösung f|Solution 1.1:3f}}
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===Exercise 1.1:4===
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===Übung 1.1:4===
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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|| <math>\pi+1</math>
|| <math>\pi+1</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.1:4|Solution a|Solution 1.1:4a|Solution b|Solution 1.1:4b|Solution c|Solution 1.1:4c|Solution d|Solution 1.1:4d|Solution e|Solution 1.1:4e|Solution f|Solution 1.1:4f}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:4|Lösung a|Solution 1.1:4a|Lösung b|Solution 1.1:4b|Lösung c|Solution 1.1:4c|Lösung d|Solution 1.1:4d|Lösung e|Solution 1.1:4e|Lösung f|Solution 1.1:4f}}
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===Exercise 1.1:5===
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===Übung 1.1:5===
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Arrange the following numbers in ascending order
Arrange the following numbers in ascending order
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|width="100%"| <math>\tfrac{1}{2}</math>, <math>\tfrac{2}{3}</math>, <math>\tfrac{3}{5}</math>, <math>\tfrac{5}{8}</math> och <math>\tfrac{21}{34}</math>
|width="100%"| <math>\tfrac{1}{2}</math>, <math>\tfrac{2}{3}</math>, <math>\tfrac{3}{5}</math>, <math>\tfrac{5}{8}</math> och <math>\tfrac{21}{34}</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.1:5|Solution a|Solution 1.1:5a|Solution b|Solution 1.1:5b|Solution c|Solution 1.1:5c}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:5|Lösung a|Solution 1.1:5a|Lösung b|Solution 1.1:5b|Lösung c|Solution 1.1:5c}}
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===Exercise 1.1:6===
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===Übung 1.1:6===
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Give the decimal expansion of the following to three decimal places.
Give the decimal expansion of the following to three decimal places.
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|width="25%"| <math>\sqrt{2}</math>
|width="25%"| <math>\sqrt{2}</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.1:6|Solution a|Solution 1.1:6a|Solution b|Solution 1.1:6b|Solution c|Solution 1.1:6c|Solution d|Solution 1.1:6d}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:6|Lösung a|Solution 1.1:6a|Lösung b|Solution 1.1:6b|Lösung c|Solution 1.1:6c|Lösung d|Solution 1.1:6d}}
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===Exercise 1.1:7===
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===Übung 1.1:7===
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Which of the following numbers are rational? Give them as a fraction of two integers.
Which of the following numbers are rational? Give them as a fraction of two integers.
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|width="100%" valign="top"| <math>0\textrm{.}10\,100\,1000\,10000\,1\ldots\,</math> (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)
|width="100%" valign="top"| <math>0\textrm{.}10\,100\,1000\,10000\,1\ldots\,</math> (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)
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</div>{{#NAVCONTENT:Answer|Answer 1.1:7|Solution a|Solution 1.1:7a|Solution b|Solution 1.1:7b|Solution c|Solution 1.1:7c|Solution d|Solution 1.1:7d}}
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</div>{{#NAVCONTENT:Answer|Antwort 1.1:7|Lösung a|Solution 1.1:7a|Lösung b|Solution 1.1:7b|Lösung c|Solution 1.1:7c|Lösung d|Solution 1.1:7d}}

Version vom 09:58, 18. Okt. 2008

 

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Übung 1.1:1

Berechne folgendes (ohne Taschenrechner)

a) \displaystyle 3-7-4+6-5 b) \displaystyle 3-(7-4)+(6-5)
c) \displaystyle 3-(7-(4+6)-5) d) \displaystyle 3-(7-(4+6))-5
Answer
Antwort 1.1:1
Lösung a
Solution 1.1:1a
Lösung b
Solution 1.1:1b
Lösung c
Solution 1.1:1c
Lösung d
Solution 1.1:1d


Übung 1.1:2

Simplify

a) \displaystyle (3-(7-4))(6-5) b) \displaystyle 3-(((7-4)+6)-5)
c) \displaystyle 3\cdot(-7)-4\cdot(6-5) d) \displaystyle 3\cdot(-7)-(4+6)/(-5)
Answer
Antwort 1.1:2
Lösung a
Solution 1.1:2a
Lösung b
Solution 1.1:2b
Lösung c
Solution 1.1:2c
Lösung d
Solution 1.1:2d


Übung 1.1:3

Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?

a) \displaystyle 8 b) \displaystyle -4 c) \displaystyle 8-4
d) \displaystyle 4-8 e) \displaystyle 8\cdot(-4) f) \displaystyle (-8)\cdot(-4)
Answer
Antwort 1.1:3
Lösung a
Solution 1.1:3a
Lösung b
Solution 1.1:3b
Lösung c
Solution 1.1:3c
Lösung d
Solution 1.1:3d
Lösung e
Solution 1.1:3e
Lösung f
Solution 1.1:3f


Übung 1.1:4

Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?

a) \displaystyle \frac{4}{-8} b) \displaystyle \frac{-8}{-4} c) \displaystyle \frac{\sqrt{2}}{3}
d) \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 e) \displaystyle -\pi f) \displaystyle \pi+1
Answer
Antwort 1.1:4
Lösung a
Solution 1.1:4a
Lösung b
Solution 1.1:4b
Lösung c
Solution 1.1:4c
Lösung d
Solution 1.1:4d
Lösung e
Solution 1.1:4e
Lösung f
Solution 1.1:4f


Übung 1.1:5

Arrange the following numbers in ascending order

a) \displaystyle 2, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{3} och \displaystyle \tfrac{7}{3}
b) \displaystyle -\tfrac{1}{2}, \displaystyle -\tfrac{1}{5}, \displaystyle -\tfrac{3}{10} och \displaystyle -\tfrac{1}{3}
c) \displaystyle \tfrac{1}{2}, \displaystyle \tfrac{2}{3}, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{8} och \displaystyle \tfrac{21}{34}
Answer
Antwort 1.1:5
Lösung a
Solution 1.1:5a
Lösung b
Solution 1.1:5b
Lösung c
Solution 1.1:5c


Übung 1.1:6

Give the decimal expansion of the following to three decimal places.

a) \displaystyle \frac{7}{6} b) \displaystyle \frac{9}{4} c) \displaystyle \frac{2}{7} d) \displaystyle \sqrt{2}
Answer
Antwort 1.1:6
Lösung a
Solution 1.1:6a
Lösung b
Solution 1.1:6b
Lösung c
Solution 1.1:6c
Lösung d
Solution 1.1:6d


Übung 1.1:7

Which of the following numbers are rational? Give them as a fraction of two integers.

a) \displaystyle 3\textrm{.}14
b) \displaystyle 3\textrm{.}1416\,1416\,1416\,\ldots
c) \displaystyle 0\textrm{.}2\,001\,001\,001\,\ldots
d) \displaystyle 0\textrm{.}10\,100\,1000\,10000\,1\ldots\, (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)
Answer
Antwort 1.1:7
Lösung a
Solution 1.1:7a
Lösung b
Solution 1.1:7b
Lösung c
Solution 1.1:7c
Lösung d
Solution 1.1:7d
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/1.1_%C3%9Cbungen“