2.1 Exercises
From Förberedande kurs i matematik 1
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Revision as of 13:49, 10 September 2008
| Theory | Exercises |
Exercise 2.1:1
Expand
| a) | | b) | | c) | |
| d) |  y1−1xy+1 | e) | f) | ||
| g) | h) |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f | Solution g | Solution h
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Exercise 2.1:2
Expand
| a) | | b) | |
| c) | | d) | |
| e) |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e
Exercise 2.1:3
Factorise and simplify as much as possible
| a) | | b) | | c) | |
| d) | | e) | f) |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 2.1:4
Determine the coefficients in front of
| a) | |
| b) | |
| c) | |
Answer | Solution a | Solution b | Solution c
Exercise 2.1:5
Simplify as much as possible
| a) | | b) | |
| c) | | d) | |
Answer | Solution a | Solution b | Solution c | Solution d
Exercise 2.1:6
Simplify as much as possible
| a) |  x−y+x2y−x y2x−y−1 | b) | |
| c) | | d) | \displaystyle \displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2} |
Answer | Solution a | Solution b | Solution c | Solution 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} |
Answer | Solution a | Solution b | Solution c
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}}} |
Answer | Solution a | Solution b | Solution c
