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4.1 Exercises

From Förberedande kurs i matematik 1

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m (Robot: Automated text replacement (-{{:4.1 - Figur - Tvättlina med kavaj på galge}} +{{:4.1 - Figure - A washing line with a jacket on a hanger}}))
 
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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
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| style="border-bottom:1px solid #000" width="5px" |  
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{{Mall:Ej vald flik|[[4.1 Vinklar och cirklar|Teori]]}}
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{{Not selected tab|[[4.1 Angles and circles|Theory]]}}
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{{Mall:Vald flik|[[4.1 Övningar|Övningar]]}}
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{{Selected tab|[[4.1 Exercises|Exercises]]}}
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===Övning 4.1:1===
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===Exercise 4.1:1===
<div class="ovning">
<div class="ovning">
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Skriv i grader och radianer
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Write in degrees and radians
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ varv} </math>
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|width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ revolution} </math>
|b)
|b)
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|width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ varv}</math>
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|width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ revolution}</math>
|-
|-
|c)
|c)
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|width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ varv}</math>
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|width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ revolution}</math>
|d)
|d)
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|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ varv} </math>
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|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ revolution} </math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:1|Lösning |Lösning 4.1:1}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:1|Solution |Solution 4.1:1}}
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===Övning 4.1:2===
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===Exrecise 4.1:2===
<div class="ovning">
<div class="ovning">
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Omvandla till radianer
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Transform to radians
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 36: Line 36:
|width="25%" | <math>270^\circ</math>
|width="25%" | <math>270^\circ</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:2|Lösning |Lösning 4.1:2}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:2|Solution |Solution 4.1:2}}
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===Övning 4.1:3===
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===Exercise 4.1:3===
<div class="ovning">
<div class="ovning">
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Bestäm längden av sidan som är markerad med <math>\,x</math>
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Determine the length of the side marked <math>\,x\,\mbox{.}</math>
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="33%" |
|width="33%" |
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{{:4.1 - Figur - Rätvinklig triangel med sidor 30, 40 och x}}
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{{:4.1 - Figure - A right-angled triangle with sides 30, 40 and x}}
|b)
|b)
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|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 12, x och 13}}
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|width="33%" | {{:4.1 - Figure - A right-angled triangle with sides 12, x and 13}}
|c)
|c)
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|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}}
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|width="33%" | {{:4.1 - Figure - A right-angled triangle with sides 8, x and 17}}
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:3|Lösning a|Lösning 4.1:3a|Lösning b|Lösning 4.1:3b|Lösning c|Lösning 4.1:3c}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:3|Solution a|Solution 4.1:3a|Solution b|Solution 4.1:3b|Solution c|Solution 4.1:3c}}
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===Övning 4.1:4===
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===Exercise 4.1:4===
<div class="ovning">
<div class="ovning">
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="100%" | Bestäm avståndet mellan punkterna (1,1) och (5,4).
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|width="100%" | Determine the distance between the points (1,1) and (5,4).
|-
|-
|b)
|b)
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|width="100%" | Bestäm avståndet mellan punkterna (-2,5) och (3,-1).
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|width="100%" | Determine the distance between the points(-2,5) and (3,-1).
|-
|-
|c)
|c)
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|width="100%" | Hitta den punkt på x-axeln som ligger lika långt från punkterna (3,3) och (5,1).
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|width="100%" | Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:4|Lösning a|Lösning 4.1:4a|Lösning b|Lösning 4.1:4b|Lösning c|Lösning 4.1:4c}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:4|Solution a|Solution 4.1:4a|Solution b|Solution 4.1:4b|Solution c|Solution 4.1:4c}}
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===Övning 4.1:5===
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===Exercise 4.1:5===
<div class="ovning">
<div class="ovning">
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="100%" | Bestäm ekvationen för en cirkel med medelpunkt i (1,2) och radie 2.
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|width="100%" | Determine the equation of a circle having its centre at (1,2) and radius 2.
|-
|-
|b)
|b)
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|width="100%" | Bestäm ekvationen för den cirkel som har medelpunkt i (2,-1) och innehåller punkten (-1,1).
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|width="100%" | Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:5|Lösning a|Lösning 4.1:5a|Lösning b|Lösning 4.1:5b}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:5|Solution a|Solution 4.1:5a|Solution b|Solution 4.1:5b}}
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===Övning 4.1:6===
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===Exercise 4.1:6===
<div class="ovning">
<div class="ovning">
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Skissera följande cirklar
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Sketch the following circles
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 89: Line 89:
|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:6|Lösning a|Lösning 4.1:6a|Lösning b|Lösning 4.1:6b|Lösning c|Lösning 4.1:6c}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:6|Solution a|Solution 4.1:6a|Solution b|Solution 4.1:6b|Solution c|Solution 4.1:6c}}
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===Övning 4.1:7===
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===Exercise 4.1:7===
<div class="ovning">
<div class="ovning">
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Skissera följande cirklar
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Sketch the following circles
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 103: Line 103:
|width="50%" | <math>x^2-2x+y^2+6y=-3</math>
|width="50%" | <math>x^2-2x+y^2+6y=-3</math>
|d)
|d)
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|width="50%" | <math>x^2-2x+y^2+6y=-3</math>
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|width="50%" | <math>x^2-2x+y^2+2y=-2</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:7|Lösning a|Lösning 4.1:7a|Lösning b|Lösning 4.1:7b|Lösning c|Lösning 4.1:7c|Lösning d|Lösning 4.1:7d}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:7|Solution a|Solution 4.1:7a|Solution b|Solution 4.1:7b|Solution c|Solution 4.1:7c|Solution d|Solution 4.1:7d}}
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===Övning 4.1:8===
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===Exercise 4.1:8===
<div class="ovning">
<div class="ovning">
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Hur många varv snurrar ett hjul med radie 50 cm när det rullar 10m?
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How many revolutions does a wheel of radius 50 cm make when it rolls 10m?
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</div>{{#NAVCONTENT:Svar|Svar 4.1:8|Lösning|Lösning 4.1:8}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:8|Solution|Solution 4.1:8}}
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===Övning 4.1:9===
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===Exercise 4.1:9===
<div class="ovning">
<div class="ovning">
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På en klocka är sekundvisaren 8 cm lång. Hur stor area sveper den över på 10 sekunder?
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On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?
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</div>{{#NAVCONTENT:Svar|Svar 4.1:9|Lösning|Lösning 4.1:9}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:9|Solution|Solution 4.1:9}}
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===Övning 4.1:10===
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===Exercise 4.1:10===
<div class="ovning">
<div class="ovning">
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En 5,4 m lång tvättlina hänger mellan två vertikala träd på 4,8 m avstånd från varandra. Linans ena ände är fäst 0,6 m högre än den andra änden, och 1,2 m från trädet där linan har sin lägre infästning hänger en kavaj på en galge. Bestäm hur mycket under den nedre infästningspunkten som galgen hänger (dvs. avståndet <math>\,x\,</math> i figuren).
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A washing line of length 5.4 m hangs between two vertical trees that are at a distance of 4.8 m from each other. One end of the line is fixed 0.6 m higher than the other, and a jacket hangs from a
 +
hanger 1.2 m from the tree where the line has its lower point of attachment. Determine how far below the
 +
lower attachement point the hanger is hanging. (That is, the distance <math>\,x\,</math> in the figure).
 +
 
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<center> {{:4.1 - Figur - Tvättlina med kavaj på galge}} </center>
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<center> {{:4.1 - Figure - A washing line with a jacket on a hanger}} </center>
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</div>{{#NAVCONTENT:Svar|Svar 4.1:10|Lösning|Lösning 4.1:10}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:10|Solution|Solution 4.1:10}}

Current revision

       Theory          Exercises      

Exercise 4.1:1

Write in degrees and radians

a) 41 revolution b) 83 revolution
c) −32 revolution d) 1297 revolution

Answer | Solution

Exrecise 4.1:2

Transform to radians

a) 45 b) 135 c) −63 d) 270

Answer | Solution

Exercise 4.1:3

Determine the length of the side marked x.

a)

[Image]

b)

[Image]

c)

[Image]

Answer | Solution a | Solution b | Solution c

Exercise 4.1:4

a) Determine the distance between the points (1,1) and (5,4).
b) Determine the distance between the points(-2,5) and (3,-1).
c) Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).

Answer | Solution a | Solution b | Solution c

Exercise 4.1:5

a) Determine the equation of a circle having its centre at (1,2) and radius 2.
b) Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).

Answer | Solution a | Solution b

Exercise 4.1:6

Sketch the following circles

a) x2+y2=9 b) (x−1)2+(y−2)2=3
c) (3x−1)2+(3y+7)2=10

Answer | Solution a | Solution b | Solution c

Exercise 4.1:7

Sketch the following circles

a) x2+2x+y2−2y=1 b) x2+y2+4y=0
c) x2−2x+y2+6y=−3 d) x2−2x+y2+2y=−2

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

Exercise 4.1:8

How many revolutions does a wheel of radius 50 cm make when it rolls 10m?

Answer | Solution

Exercise 4.1:9

On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?

Answer | Solution


Exercise 4.1:10

A washing line of length 5.4 m hangs between two vertical trees that are at a distance of 4.8 m from each other. One end of the line is fixed 0.6 m higher than the other, and a jacket hangs from a hanger 1.2 m from the tree where the line has its lower point of attachment. Determine how far below the lower attachement point the hanger is hanging. (That is, the distance x in the figure).


[Image]

Answer | Solution

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