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2.1 Exercises

From Förberedande kurs i matematik 1

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(Translated links into English)
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||<math> (5x^3+3x^5)^2</math>
||<math> (5x^3+3x^5)^2</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:1|Lösning a|Lösning 2.1:1a|Lösning b|Lösning 2.1:1b|Lösning c|Lösning 2.1:1c|Lösning d|Lösning 2.1:1d|Lösning e|Lösning 2.1:1e|Lösning f|Lösning 2.1:1f|Lösning g|Lösning 2.1:1g|Lösning h|Lösning 2.1:1h}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:1|Solution a|Lösning 2.1:1a|Solution b|Lösning 2.1:1b|Solution c|Lösning 2.1:1c|Solution d|Lösning 2.1:1d|Solution e|Lösning 2.1:1e|Solution f|Lösning 2.1:1f|Solution g|Lösning 2.1:1g|Solution h|Lösning 2.1:1h}}
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||<math> (a+b)^2+(a-b)^2</math>
||<math> (a+b)^2+(a-b)^2</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:2|Lösning a|Lösning 2.1:2a|Lösning b|Lösning 2.1:2b|Lösning c|Lösning 2.1:2c|Lösning d|Lösning 2.1:2d|Lösning e|Lösning 2.1:2e}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:2|Solution a|Lösning 2.1:2a|Solution b|Lösning 2.1:2b|Solution c|Lösning 2.1:2c|Solution d|Lösning 2.1:2d|Solution e|Lösning 2.1:2e}}
===Exercise 2.1:3===
===Exercise 2.1:3===
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||<math> 16x^2+8x+1</math>
||<math> 16x^2+8x+1</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:3|Lösning a|Lösning 2.1:3a|Lösning b|Lösning 2.1:3b|Lösning c|Lösning 2.1:3c|Lösning d|Lösning 2.1:3d|Lösning e|Lösning 2.1:3e|Lösning f|Lösning 2.1:3f}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:3|Solution a|Lösning 2.1:3a|Solution b|Lösning 2.1:3b|Solution c|Lösning 2.1:3c|Solution d|Lösning 2.1:3d|Solution e|Lösning 2.1:3e|Solution f|Lösning 2.1:3f}}
===Exercise 2.1:4===
===Exercise 2.1:4===
<div class="ovning">
<div class="ovning">
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Determine the coefficients in front of <math>\,x\,</math> and <math>\,x^2\</math> when the following expressiona are expanded out.
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Determine the coefficients in front of <math>\,x\,</math> and <math>\,x^2\</math> when the following expressions are expanded out.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|-
|-
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:4|Lösning a|Lösning 2.1:4a|Lösning b|Lösning 2.1:4b|Lösning c|Lösning 2.1:4c}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:4|Solution a|Lösning 2.1:4a|Solution b|Lösning 2.1:4b|Solution c|Lösning 2.1:4c}}
===Exercise 2.1:5===
===Exercise 2.1:5===
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|| <math>\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}</math>
|| <math>\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:5|Lösning a|Lösning 2.1:5a|Lösning b|Lösning 2.1:5b|Lösning c|Lösning 2.1:5c|Lösning d|Lösning 2.1:5d}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:5|Solution a|Lösning 2.1:5a|Solution b|Lösning 2.1:5b|Solution c|Lösning 2.1:5c|Solution d|Lösning 2.1:5d}}
===Exercise 2.1:6===
===Exercise 2.1:6===
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|| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</math>
|| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:6|Lösning a|Lösning 2.1:6a|Lösning b|Lösning 2.1:6b|Lösning c|Lösning 2.1:6c|Lösning d|Lösning 2.1:6d}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:6|Solution a|Lösning 2.1:6a|Solution b|Lösning 2.1:6b|Solution c|Lösning 2.1:6c|Solution d|Lösning 2.1:6d}}
===Exercise 2.1:7===
===Exercise 2.1:7===
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|width="33%" | <math>\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}</math>
|width="33%" | <math>\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:7|Lösning a|Lösning 2.1:7a|Lösning b|Lösning 2.1:7b|Lösning c|Lösning 2.1:7c}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:7|Solution a|Lösning 2.1:7a|Solution b|Lösning 2.1:7b|Solution c|Lösning 2.1:7c}}
===Exercise 2.1:8===
===Exercise 2.1:8===
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|width="33%" | <math>\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</math>
|width="33%" | <math>\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.1:8|Lösning a|Lösning 2.1:8a|Lösning b|Lösning 2.1:8b|Lösning c|Lösning 2.1:8c}}
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</div>{{#NAVCONTENT:Answer|Svar 2.1:8|Solution a|Lösning 2.1:8a|Solution b|Lösning 2.1:8b|Solution c|Lösning 2.1:8c}}

Revision as of 12:49, 18 August 2008

       Theory          Exercises      


Exercise 2.1:1

Expand

a) 3x(x1) b) (1+xx2)xy c) x2(4y2)
d) x3y2y11xy+1  e) (x7)2 f) (5+4y)2
g) (y23x3)2 h) (5x3+3x5)2


Exercise 2.1:2

Expand

a) (x4)(x5)3x(2x3) b) (15x)(1+15x)3(25x)(2+5x)
c) (3x+4)2(3x2)(3x8) d) (3x2+2)(3x22)(9x4+4)
e) (a+b)2+(ab)2

Exercise 2.1:3

Factorise and simplify as much as possible

a) x236 b) 5x220 c) x2+6x+9
d) x210x+25 e) 18x2x3 f) 16x2+8x+1

Exercise 2.1:4

Determine the coefficients in front of x and x2  when the following expressions are expanded out.

a) (x+2)(3x2x+5)
b) (1+x+x2+x3)(2x+x2+x4)
c) (xx3+x5)(1+3x+5x2)(27x2x4)

Exercise 2.1:5

Simplify as much as possible

a) 1xx2x1 b) 1y22y2y24
c) (x+1)(x+2)(3x212)(x21) d) (y2+4)(y24)(y2+4y+4)(2y4)

Exercise 2.1:6

Simplify as much as possible

a) xy+x2yx  y2xy1  b) xx2+xx+32
c) 2a+ba2ab2ab d) \displaystyle \displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}

Exercise 2.1:7

Simplify the following fractions by writing them as an expression having a common fraction sign

a) \displaystyle \displaystyle \frac{2}{x+3}-\frac{2}{x+5} b) \displaystyle x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2} c) \displaystyle \displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}

Exercise 2.1:8

Simplify the following fractions by writing them as an expression having a common fraction sign

a) \displaystyle \displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ } b) \displaystyle \displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}} c) \displaystyle \displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}