2.2 Exercises
From Förberedande kurs i matematik 1
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| - | {{Ej vald flik|[[2.2 Linjära uttryck| | + | {{Ej vald flik|[[2.2 Linjära uttryck|Theory]]}} |
| - | {{Vald flik|[[2.2 Övningar| | + | {{Vald flik|[[2.2 Övningar|Exercises]]}} |
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| - | === | + | ===Exercise 2.2:1=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equations | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 2.2:1|Lösning a|Lösning 2.2:1a|Lösning b|Lösning 2.2:1b|Lösning c|Lösning 2.2:1c|Lösning d|Lösning 2.2:1d}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:1|Lösning a|Lösning 2.2:1a|Lösning b|Lösning 2.2:1b|Lösning c|Lösning 2.2:1c|Lösning d|Lösning 2.2:1d}} | ||
| - | === | + | ===Exercise 2.2:2=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equations | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 2.2:2|Lösning a|Lösning 2.2:2a|Lösning b|Lösning 2.2:2b|Lösning c|Lösning 2.2:2c|Lösning d|Lösning 2.2:2d}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:2|Lösning a|Lösning 2.2:2a|Lösning b|Lösning 2.2:2b|Lösning c|Lösning 2.2:2c|Lösning d|Lösning 2.2:2d}} | ||
| - | === | + | ===Exercise 2.2:3=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equations | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 2.2:3|Lösning a|Lösning 2.2:3a|Lösning b|Lösning 2.2:3b|Lösning c|Lösning 2.2:3c|Lösning d|Lösning 2.2:3d}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:3|Lösning a|Lösning 2.2:3a|Lösning b|Lösning 2.2:3b|Lösning c|Lösning 2.2:3c|Lösning d|Lösning 2.2:3d}} | ||
| - | === | + | ===Exercise 2.2:4=== |
<div class="ovning"> | <div class="ovning"> | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="100%" | | + | |width="100%" | Write the equation for the line <math>\,y=2x+3\,</math> in the form <math>\,ax+by=c\,</math> |
|- | |- | ||
|b) | |b) | ||
| - | || | + | || Write the equation for the line <math> 3x+4y-5=0</math> in the form <math>\,y=kx+m\,</math> |
|} | |} | ||
</div>{{#NAVCONTENT:Svar|Svar 2.2:4|Lösning a|Lösning 2.2:4a|Lösning b|Lösning 2.2:4b}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:4|Lösning a|Lösning 2.2:4a|Lösning b|Lösning 2.2:4b}} | ||
| - | === | + | ===Exercise 2.2:5=== |
<div class="ovning"> | <div class="ovning"> | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="100%" | | + | |width="100%" | Determine the equation for the straight line that goes between the points <math>\,(2,3)\,</math> and<math>\,(3,0)\,</math> |
|- | |- | ||
|b) | |b) | ||
| - | || | + | || Determine the equation for the straight line that has gradient <math>\,-3\,</math> and goes through the point <math>\,(1,-2)\,</math> |
|- | |- | ||
|c) | |c) | ||
| - | || | + | || Determine the equation for the straight line that goes through the point <math>\,(-1,2)\,</math> and is parallel to the line <math>\,y=3x+1\,</math> |
|- | |- | ||
|d) | |d) | ||
| - | || | + | ||Determine the equation for the straight line that goes through the point <math>\,(2,4)\,</math> and is perpendicular to the line <math>\,y=2x+5\,</math> |
|- | |- | ||
|e) | |e) | ||
| - | || | + | || Determine the slope, <math>\,k\,</math> for the straight line that cuts the ''x''-axis at the point <math>\,(5,0)\,</math> and ''y''-axis at the point <math>\,(0,-8)\,</math> |
|} | |} | ||
</div>{{#NAVCONTENT:Svar|Svar 2.2:5|Lösning a|Lösning 2.2:5a|Lösning b|Lösning 2.2:5b|Lösning c|Lösning 2.2:5c|Lösning d|Lösning 2.2:5d|Lösning e|Lösning 2.2:5e}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:5|Lösning a|Lösning 2.2:5a|Lösning b|Lösning 2.2:5b|Lösning c|Lösning 2.2:5c|Lösning d|Lösning 2.2:5d|Lösning e|Lösning 2.2:5e}} | ||
| - | === | + | ===Exercise 2.2:6=== |
<div class="ovning"> | <div class="ovning"> | ||
Finn skärningspunkten mellan följande linjer | Finn skärningspunkten mellan följande linjer | ||
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</div>{{#NAVCONTENT:Svar|Svar 2.2:6|Lösning a|Lösning 2.2:6a|Lösning b|Lösning 2.2:6b|Lösning c|Lösning 2.2:6c|Lösning d|Lösning 2.2:6d|Lösning e|Lösning 2.2:6e}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:6|Lösning a|Lösning 2.2:6a|Lösning b|Lösning 2.2:6b|Lösning c|Lösning 2.2:6c|Lösning d|Lösning 2.2:6d|Lösning e|Lösning 2.2:6e}} | ||
| - | === | + | ===Exercise 2.2:7=== |
<div class="ovning"> | <div class="ovning"> | ||
Skissera grafen till följande funktioner | Skissera grafen till följande funktioner | ||
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</div>{{#NAVCONTENT:Svar|Svar 2.2:7|Lösning a|Lösning 2.2:7a|Lösning b|Lösning 2.2:7b|Lösning c|Lösning 2.2:7c}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:7|Lösning a|Lösning 2.2:7a|Lösning b|Lösning 2.2:7b|Lösning c|Lösning 2.2:7c}} | ||
| - | === | + | ===Exercise 2.2:8=== |
<div class="ovning"> | <div class="ovning"> | ||
Rita in i ett ''xy''-plan alla punkter vars koordinater <math>\,(x,y)\,</math> uppfyller | Rita in i ett ''xy''-plan alla punkter vars koordinater <math>\,(x,y)\,</math> uppfyller | ||
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</div>{{#NAVCONTENT:Svar|Svar 2.2:8|Lösning a|Lösning 2.2:8a|Lösning b|Lösning 2.2:8b|Lösning c|Lösning 2.2:8c}} | </div>{{#NAVCONTENT:Svar|Svar 2.2:8|Lösning a|Lösning 2.2:8a|Lösning b|Lösning 2.2:8b|Lösning c|Lösning 2.2:8c}} | ||
| - | === | + | ===Exercise 2.2:9=== |
<div class="ovning"> | <div class="ovning"> | ||
Beräkna arean av den triangel som | Beräkna arean av den triangel som | ||
Revision as of 13:05, 3 August 2008
| Theory | Exercises |
Exercise 2.2:1
Solve the equations
| a) | \displaystyle x-2=-1 | b) | \displaystyle 2x+1=13 |
| c) | \displaystyle \displaystyle\frac{1}{3}x-1=x | d) | \displaystyle 5x+7=2x-6 |
Svar
Loading...
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 2.2:2
Solve the equations
| a) | \displaystyle \displaystyle\frac{5x}{6}-\displaystyle\frac{x+2}{9}=\displaystyle\frac{1}{2} | b) | \displaystyle \displaystyle\frac{8x+3}{7}-\displaystyle\frac{5x-7}{4}=2 |
| c) | \displaystyle (x+3)^2-(x-5)^2=6x+4 | d) | \displaystyle (x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 2.2:3
Solve the equations
| a) | \displaystyle \displaystyle\frac{x+3}{x-3}-\displaystyle\frac{x+5}{x-2}=0 |
| b) | \displaystyle \displaystyle\frac{4x}{4x-7}-\displaystyle\frac{1}{2x-3}=1 |
| c) | \displaystyle \left(\displaystyle\frac{1}{x-1}-\frac{1}{x+1}\right)\left(x^2+\frac{1}{2}\right)=\displaystyle\frac{6x-1}{3x-3} |
| d) | \displaystyle \left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 2.2:4
| a) | Write the equation for the line \displaystyle \,y=2x+3\, in the form \displaystyle \,ax+by=c\, |
| b) | Write the equation for the line \displaystyle 3x+4y-5=0 in the form \displaystyle \,y=kx+m\, |
Exercise 2.2:5
| a) | Determine the equation for the straight line that goes between the points \displaystyle \,(2,3)\, and\displaystyle \,(3,0)\, |
| b) | Determine the equation for the straight line that has gradient \displaystyle \,-3\, and goes through the point \displaystyle \,(1,-2)\, |
| c) | Determine the equation for the straight line that goes through the point \displaystyle \,(-1,2)\, and is parallel to the line \displaystyle \,y=3x+1\, |
| d) | Determine the equation for the straight line that goes through the point \displaystyle \,(2,4)\, and is perpendicular to the line \displaystyle \,y=2x+5\, |
| e) | Determine the slope, \displaystyle \,k\, for the straight line that cuts the x-axis at the point \displaystyle \,(5,0)\, and y-axis at the point \displaystyle \,(0,-8)\, |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Exercise 2.2:6
Finn skärningspunkten mellan följande linjer
| a) | \displaystyle y=3x+5\ och x-axeln | b) | \displaystyle y=-x+5\ och y-axeln |
| c) | \displaystyle 4x+5y+6=0\ och y-axeln | d) | \displaystyle x+y+1=0\ och \displaystyle \ 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
Skissera grafen till följande funktioner
| a) | \displaystyle f(x)=3x-2 | b) | \displaystyle f(x)=2-x | c) | \displaystyle f(x)=2 |
Exercise 2.2:8
Rita in i ett xy-plan alla punkter vars koordinater \displaystyle \,(x,y)\, uppfyller
| a) | \displaystyle y \geq x | b) | \displaystyle y < 3x -4 | c) | \displaystyle 2x+3y \leq 6 |
Exercise 2.2:9
Beräkna arean av den triangel som
| a) | har hörn i punkterna \displaystyle \,(1,4)\,, \displaystyle \,(3,3)\, och \displaystyle \,(1,0)\,. |
| b) | begränsas av linjerna \displaystyle \ x=2y\,, \displaystyle \ y=4\ och \displaystyle \ y=10-2x\,. |
| c) | beskrivs av olikheterna \displaystyle \ x+y \geq -2\,, \displaystyle \ 2x-y \leq 2\ och \displaystyle \ 2y-x \leq 2\,. |
