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2.2 Exercises

From Förberedande kurs i matematik 1

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===Exercise 2.2:6===
===Exercise 2.2:6===
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Finn sk&auml;rningspunkten mellan f&ouml;ljande linjer
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Find the points of intersection between the pairs of lines in the following
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===Exercise 2.2:7===
===Exercise 2.2:7===
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Skissera grafen till f&ouml;ljande funktioner
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Sketch the graph of the functions
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===Exercise 2.2:8===
===Exercise 2.2:8===
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Rita in i ett ''xy''-plan alla punkter vars koordinater <math>\,(x,y)\,</math> uppfyller
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In the ''xy''-plane, draw in all the points whose coordinates <math>\,(x,y)\,</math> satisfy
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===Exercise 2.2:9===
===Exercise 2.2:9===
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Ber&auml;kna arean av den triangel som
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Calculate the area of the triangle which
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="100%" | har h&ouml;rn i punkterna <math>\,(1,4)\,</math>, <math>\,(3,3)\,</math> och <math>\,(1,0)\,</math>.
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|width="100%" | has corners at the points <math>\,(1,4)\,</math>, <math>\,(3,3)\,</math> and <math>\,(1,0)\,</math>.
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|-
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|b)
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|| begr&auml;nsas av linjerna <math>\ x=2y\,</math>, <math>\ y=4\ </math> och <math>\ y=10-2x\,</math>.
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|| is bordered by the lines <math>\ x=2y\,</math>, <math>\ y=4\ </math> and <math>\ y=10-2x\,</math>.
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|-
|c)
|c)
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|| beskrivs av olikheterna <math>\ x+y \geq -2\,</math>, <math>\ 2x-y \leq 2\ </math> och <math>\ 2y-x \leq 2\,</math>.
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|| is described by the inequalities <math>\ x+y \geq -2\,</math>, <math>\ 2x-y \leq 2\ </math> and <math>\ 2y-x \leq 2\,</math>.
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</div>{{#NAVCONTENT:Svar|Svar 2.2:9|Lösning a|Lösning 2.2:9a|Lösning b|Lösning 2.2:9b|Lösning c|Lösning 2.2:9c}}
</div>{{#NAVCONTENT:Svar|Svar 2.2:9|Lösning a|Lösning 2.2:9a|Lösning b|Lösning 2.2:9b|Lösning c|Lösning 2.2:9c}}

Revision as of 13:15, 3 August 2008

       Theory          Exercises      

Exercise 2.2:1

Solve the equations

a) x−2=−1 b) 2x+1=13
c) 31x−1=x d) 5x+7=2x−6

Svar | Lösning a | Lösning b | Lösning c | Lösning d

Exercise 2.2:2

Solve the equations

a) 65x−9x+2=21 b) 78x+3−45x−7=2
c) (x+3)2−(x−5)2=6x+4 d) (x2+4x+1)2+3x4−2x2=(2x2+2x+3)2

Svar | Lösning a | Lösning b | Lösning c | Lösning d

Exercise 2.2:3

Solve the equations

a) x−3x+3−x−2x+5=0
b) 4x4x−7−12x−3=1
c) 1x−1−1x+1x2+21=3x−36x−1 
d) x2−314x+21−12x−322−12x+3112x−31=0 

Svar | Lösning a | Lösning b | Lösning c | Lösning d

Exercise 2.2:4

a) Write the equation for the line y=2x+3 in the form ax+by=c
b) Write the equation for the line 3x+4y−5=0 in the form y=kx+m

Svar | Lösning a | Lösning b

Exercise 2.2:5

a) Determine the equation for the straight line that goes between the points (23) and(30)
b) Determine the equation for the straight line that has gradient −3 and goes through the point (1−2)
c) Determine the equation for the straight line that goes through the point (−12) and is parallel to the line y=3x+1
d) Determine the equation for the straight line that goes through the point (24) and is perpendicular to the line y=2x+5
e) Determine the slope, k for the straight line that cuts the x-axis at the point (50) and y-axis at the point (0−8)

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e

Exercise 2.2:6

Find the points of intersection between the pairs of lines in the following

a) y=3x+5  och x-axeln b) y=−x+5  och y-axeln
c) 4x+5y+6=0  och y-axeln d) x+y+1=0  och  x=12
e) \displaystyle 2x+y-1=0\ och \displaystyle \ y-2x-2=0

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e

Exercise 2.2:7

Sketch the graph of the functions

a) \displaystyle f(x)=3x-2 b) \displaystyle f(x)=2-x c) \displaystyle f(x)=2

Svar | Lösning a | Lösning b | Lösning c

Exercise 2.2:8

In the xy-plane, draw in all the points whose coordinates \displaystyle \,(x,y)\, satisfy

a) \displaystyle y \geq x b) \displaystyle y < 3x -4 c) \displaystyle 2x+3y \leq 6

Svar | Lösning a | Lösning b | Lösning c

Exercise 2.2:9

Calculate the area of the triangle which

a) has corners at the points \displaystyle \,(1,4)\,, \displaystyle \,(3,3)\, and \displaystyle \,(1,0)\,.
b) is bordered by the lines \displaystyle \ x=2y\,, \displaystyle \ y=4\ and \displaystyle \ y=10-2x\,.
c) is described by the inequalities \displaystyle \ x+y \geq -2\,, \displaystyle \ 2x-y \leq 2\ and \displaystyle \ 2y-x \leq 2\,.

Svar | Lösning a | Lösning b | Lösning c

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