2.1 Übungen
Aus Online Mathematik Brückenkurs 1
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||<math> (5x^3+3x^5)^2</math> | ||<math> (5x^3+3x^5)^2</math> | ||
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| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:1| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:1|Lösung a|Lösung 2.1:1a|Lösung b|Lösung 2.1:1b|Lösung c|Lösung 2.1:1c|Lösung d|Lösung 2.1:1d|Lösung e|Lösung 2.1:1e|Lösung f|Lösung 2.1:1f|Lösung g|Lösung 2.1:1g|Lösung h|Lösung 2.1:1h}} |
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||<math> (a+b)^2+(a-b)^2</math> | ||<math> (a+b)^2+(a-b)^2</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:2| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:2|Lösung a|Lösung 2.1:2a|Lösung b|Lösung 2.1:2b|Lösung c|Lösung 2.1:2c|Lösung d|Lösung 2.1:2d|Lösung e|Lösung 2.1:2e}} |
===Übung 2.1:3=== | ===Übung 2.1:3=== | ||
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||<math> 16x^2+8x+1</math> | ||<math> 16x^2+8x+1</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:3| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:3|Lösung a|Lösung 2.1:3a|Lösung b|Lösung 2.1:3b|Lösung c|Lösung 2.1:3c|Lösung d|Lösung 2.1:3d|Lösung e|Lösung 2.1:3e|Lösung f|Lösung 2.1:3f}} |
===Übung 2.1:4=== | ===Übung 2.1:4=== | ||
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|- | |- | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:4| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:4|Lösung a|Lösung 2.1:4a|Lösung b|Lösung 2.1:4b|Lösung c|Lösung 2.1:4c}} |
===Übung 2.1:5=== | ===Übung 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:5| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:5|Lösung a|Lösung 2.1:5a|Lösung b|Lösung 2.1:5b|Lösung c|Lösung 2.1:5c|Lösung d|Lösung 2.1:5d}} |
===Übung 2.1:6=== | ===Übung 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:6| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:6|Lösung a|Lösung 2.1:6a|Lösung b|Lösung 2.1:6b|Lösung c|Lösung 2.1:6c|Lösung d|Lösung 2.1:6d}} |
===Übung 2.1:7=== | ===Übung 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:7| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:7|Lösung a|Lösung 2.1:7a|Lösung b|Lösung 2.1:7b|Lösung c|Lösung 2.1:7c}} |
===Übung 2.1:8=== | ===Übung 2.1:8=== | ||
| Zeile 145: | Zeile 145: | ||
|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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:8| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.1:8|Lösung a|Lösung 2.1:8a|Lösung b|Lösung 2.1:8b|Lösung c|Lösung 2.1:8c}} |
Version vom 09:29, 22. Okt. 2008
Übung 2.1:1
Expand
| a) | \displaystyle 3x(x-1) | b) | \displaystyle (1+x-x^2)xy | c) | \displaystyle -x^2(4-y^2) |
| d) | \displaystyle x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right) | e) | \displaystyle (x-7)^2 | f) | \displaystyle (5+4y)^2 |
| g) | \displaystyle (y^2-3x^3)^2 | h) | \displaystyle (5x^3+3x^5)^2 |
Antwort
Laden...
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Lösung g
Lösung h
Übung 2.1:2
Expand
| a) | \displaystyle (x-4)(x-5)-3x(2x-3) | b) | \displaystyle (1-5x)(1+15x)-3(2-5x)(2+5x) |
| c) | \displaystyle (3x+4)^2-(3x-2)(3x-8) | d) | \displaystyle (3x^2+2)(3x^2-2)(9x^4+4) |
| e) | \displaystyle (a+b)^2+(a-b)^2 |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Übung 2.1:3
Factorise and simplify as much as possible
| a) | \displaystyle x^2-36 | b) | \displaystyle 5x^2-20 | c) | \displaystyle x^2+6x+9 |
| d) | \displaystyle x^2-10x+25 | e) | \displaystyle 18x-2x^3 | f) | \displaystyle 16x^2+8x+1 |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Übung 2.1:4
Determine the coefficients in front of \displaystyle \,x\, and \displaystyle \,x^2\ when the following expressions are expanded out.
| a) | \displaystyle (x+2)(3x^2-x+5) |
| b) | \displaystyle (1+x+x^2+x^3)(2-x+x^2+x^4) |
| c) | \displaystyle (x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4) |
Übung 2.1:5
Simplify as much as possible
| a) | \displaystyle \displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x} | b) | \displaystyle \displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4} |
| c) | \displaystyle \displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)} | d) | \displaystyle \displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 2.1:6
Simplify as much as possible
| a) | \displaystyle \left(x-y+\displaystyle\frac{x^2}{y-x}\right) \displaystyle \left(\displaystyle\frac{y}{2x-y}-1\right) | b) | \displaystyle \displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2 |
| c) | \displaystyle \displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b} | d) | \displaystyle \displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 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} |
Übung 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}}} |
