2.1 Exercises
From Förberedande kurs i matematik 1
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| - | === | + | ===Exercise 2.1:1=== |
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Expand | Expand | ||
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| - | === | + | ===Exercise 2.1:2=== |
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Expand | Expand | ||
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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}} | </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}} | ||
| - | === | + | ===Exercise 2.1:3=== |
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Factorize and simplify as much as possible | Factorize and simplify as much as possible | ||
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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}} | </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}} | ||
| - | === | + | ===Exercise 2.1:4=== |
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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. | 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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</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}} | </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}} | ||
| - | === | + | ===Exercise 2.1:5=== |
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Simplify as much as possible | Simplify as much as possible | ||
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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}} | </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}} | ||
| - | === | + | ===Exercise 2.1:6=== |
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Simplify as much as possible | Simplify as much as possible | ||
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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}} | </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}} | ||
| - | === | + | ===Exercise 2.1:7=== |
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Simplify the following fractions by writing them as an expression having a common fraction sign | Simplify the following fractions by writing them as an expression having a common fraction sign | ||
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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}} | </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}} | ||
| - | === | + | ===Exercise 2.1:8=== |
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Simplify the following fractions by writing them as an expression having a common fraction sign | Simplify the following fractions by writing them as an expression having a common fraction sign | ||
Revision as of 12:47, 3 August 2008
| Theory | Exercises |
Exercise 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 |
Svar
Loading...
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Lösning g
Lösning h
Exercise 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 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Exercise 2.1:3
Factorize 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 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Exercise 2.1:4
Determine the coefficients in front of \displaystyle \,x\, and \displaystyle \,x^2\ when the following expressiona 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) |
Exercise 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)} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
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}}} |
