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1.1 Exercises

From Förberedande kurs i matematik 1

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Current revision (23:47, 11 November 2008) (edit) (undo)
 
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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
| style="border-bottom:1px solid #000" width="5px" |  
| style="border-bottom:1px solid #000" width="5px" |  
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{{Ej vald flik|[[1.1 Olika typer av tal|Teori]]}}
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{{Not selected tab|[[1.1 Different types of numbers|Theory]]}}
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{{Vald flik|[[1.1 Övningar|Övningar]]}}
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{{Selected tab|[[1.1 Exercises|Exercises]]}}
| style="border-bottom:1px solid #000" width="100%"|  
| style="border-bottom:1px solid #000" width="100%"|  
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|| <math>3-(7-(4+6))-5</math>
|| <math>3-(7-(4+6))-5</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.1:1|Lösning a|Lösning 1.1:1a|Lösning b|Lösning 1.1:1b|Lösning c|Lösning 1.1:1c|Lösning d|Lösning 1.1:1d}}
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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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|| <math>3\cdot(-7)-(4+6)/(-5)</math>
|| <math>3\cdot(-7)-(4+6)/(-5)</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.1:2|Lösning a|Lösning 1.1:2a|Lösning b|Lösning 1.1:2b|Lösning c|Lösning 1.1:2c|Lösning d|Lösning 1.1:2d}}
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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}}
===Exercise 1.1:3===
===Exercise 1.1:3===
<div class="ovning">
<div class="ovning">
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|| <math>(-8)\cdot(-4)</math>
|| <math>(-8)\cdot(-4)</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.1:3|Lösning a|Lösning 1.1:3a|Lösning b|Lösning 1.1:3b|Lösning c|Lösning 1.1:3c|Lösning d|Lösning 1.1:3d|Lösning e|Lösning 1.1:3e|Lösning f|Lösning 1.1:3f}}
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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}}
===Exercise 1.1:4===
===Exercise 1.1:4===
<div class="ovning">
<div class="ovning">
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px"
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{| width="100%" cellspacing="10px"
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|a)
|a)
|width="33%"| <math>\frac{4}{-8}</math>
|width="33%"| <math>\frac{4}{-8}</math>
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|| <math>\pi+1</math>
|| <math>\pi+1</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.1:4|Lösning a|Lösning 1.1:4a|Lösning b|Lösning 1.1:4b|Lösning c|Lösning 1.1:4c|Lösning d|Lösning 1.1:4d|Lösning e|Lösning 1.1:4e|Lösning f|Lösning 1.1:4f}}
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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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|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:Svar|Svar 1.1:5|Lösning a|Lösning 1.1:5a|Lösning b|Lösning 1.1:5b|Lösning c|Lösning 1.1:5c}}
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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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|width="25%"| <math>\sqrt{2}</math>
|width="25%"| <math>\sqrt{2}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.1:6|Lösning a|Lösning 1.1:6a|Lösning b|Lösning 1.1:6b|Lösning c|Lösning 1.1:6c|Lösning d|Lösning 1.1:6d}}
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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}}
===Exercise 1.1:7===
===Exercise 1.1:7===
<div class="ovning">
<div class="ovning">
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Which of the following numbers are rational? Give them as a fraction of two integers.
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Which of the following numbers are rational? Express them as a fraction of two integers.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="100%"| <math>3{,}14</math>
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|width="100%"| <math>3\textrm{.}14</math>
|-
|-
|b)
|b)
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|width="100%"| <math>3{,}1416\,1416\,1416\,\ldots</math>
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|width="100%"| <math>3\textrm{.}1416\,1416\,1416\,\ldots</math>
|-
|-
|c)
|c)
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|width="100%"| <math>0{,}2\,001\,001\,001\,\ldots</math>
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|width="100%"| <math>0\textrm{.}2\,001\,001\,001\,\ldots</math>
|-
|-
|valign="top"|d)
|valign="top"|d)
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|width="100%" valign="top"| <math>0{,}10\,100\,1000\,10000\,1\ldots\,</math> (en 1:a, en 0:a, en 1:a, två 0:or, en 1:a, tre 0:or osv.)
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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.)
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.1:7|Lösning a|Lösning 1.1:7a|Lösning b|Lösning 1.1:7b|Lösning c|Lösning 1.1:7c|Lösning d|Lösning 1.1:7d}}
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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}}

Current revision

       Theory          Exercises      


Exercise 1.1:1

Work out (without the help of a calculator)

a) 3−7−4+6−5 b) 3−(7−4)+(6−5)
c) 3−(7−(4+6)−5) d) 3−(7−(4+6))−5

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.1:2

Simplify

a) (3−(7−4))(6−5) b) 3−(((7−4)+6)−5)
c) 3(−7)−4(6−5) d) 3(−7)−(4+6)(−5)

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.1:3

Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.

a) 8 b) −4 c) 8−4
d) 4−8 e) 8(−4) f) (−8)(−4)

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f


Exercise 1.1:4

Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px" |a) |width="33%"| 4−8 |b) |width="33%"| −4−8 |c) |width="33%"| \displaystyle \frac{\sqrt{2}}{3} |- |d) || \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 |e) || \displaystyle -\pi |f) || \displaystyle \pi+1 |}

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f


Exercise 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 | Solution a | Solution b | Solution c


Exercise 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 | Solution a | Solution b | Solution c | Solution d


Exercise 1.1:7

Which of the following numbers are rational? Express 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 | Solution a | Solution b | Solution c | Solution d

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