1.1 Exercises

From Förberedande kurs i matematik 1

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{{Mall: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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{{Mall:Vald flik|[[1.1 Övningar|Övningar]]}}
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{{Selected tab|[[1.1 Exercises|Exercises]]}}
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===Övning 1.1:1===
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===Exercise 1.1:1===
<div class="ovning">
<div class="ovning">
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Beräkna (utan hjälp av räknedosa)
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Work out (without the help of a calculator)
{| 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: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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===Övning 1.1:2===
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===Exercise 1.1:2===
<div class="ovning">
<div class="ovning">
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Beräkna
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Simplify
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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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}}
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===Övning 1.1:3===
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===Exercise 1.1:3===
<div class="ovning">
<div class="ovning">
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Vilka av följande tal tillhör de naturliga talen? heltalen? rationella talen? irrationella talen?
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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}}
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===Övning 1.1:4===
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===Exercise 1.1:4===
<div class="ovning">
<div class="ovning">
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Vilka av följande tal tillhör de naturliga talen? heltalen? rationella talen? irrationella talen?
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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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===Övning 1.1:5===
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===Exercise 1.1:5===
<div class="ovning">
<div class="ovning">
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Ordna följande tal i storleksordning.
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Arrange the following numbers in ascending order
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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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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===Övning 1.1:6===
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===Exercise 1.1:6===
<div class="ovning">
<div class="ovning">
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Ange decimalutvecklingen med tre korrekta decimaler till
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Give the decimal expansion of the following to three decimal places.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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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}}
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===Övning 1.1:7===
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===Exercise 1.1:7===
<div class="ovning">
<div class="ovning">
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Vilka av följande tal är irrationella? Skriv dessa som en kvot mellan två heltal.
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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>
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|-
|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) \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
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


Exercise 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
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

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

Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px" |a) |width="33%"| \displaystyle \frac{4}{-8} |b) |width="33%"| \displaystyle \frac{-8}{-4} |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
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


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
Answer 1.1:5
Solution a
Solution 1.1:5a
Solution b
Solution 1.1:5b
Solution c
Solution 1.1:5c


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
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

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
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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