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2.1 Exercises
From Förberedande kurs i matematik 1
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Revision as of 12:21, 7 August 2008
| Theory | Exercises |
Exercise 2.1:1
Expand
| a) | | b) | | c) | |
| d) |  y1−1xy+1 | e) | f) | ||
| g) | h) |
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Exercise 2.1:2
Expand
| a) | | b) | |
| c) | | d) | |
| e) |
Exercise 2.1:3
Factorise and simplify as much as possible
| a) | | b) | | c) | |
| d) | \displaystyle x^2-10x+25 | e) | \displaystyle 18x-2x^3 | f) | \displaystyle 16x^2+8x+1 |
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)} |
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} |
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}}} |
