2.1 Exercises
From Förberedande kurs i matematik 1
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- | {{ | + | {{Not selected tab|[[2.1 Algebraic expressions|Theory]]}} |
- | {{ | + | {{Selected tab|[[2.1 Exercises|Exercises]]}} |
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||<math> (5x^3+3x^5)^2</math> | ||<math> (5x^3+3x^5)^2</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 2.1:1|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:1|Solution a|Solution 2.1:1a|Solution b|Solution 2.1:1b|Solution c|Solution 2.1:1c|Solution d|Solution 2.1:1d|Solution e|Solution 2.1:1e|Solution f|Solution 2.1:1f|Solution g|Solution 2.1:1g|Solution h|Solution 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:Answer|Answer 2.1:2|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:2|Solution a|Solution 2.1:2a|Solution b|Solution 2.1:2b|Solution c|Solution 2.1:2c|Solution d|Solution 2.1:2d|Solution e|Solution 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> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 2.1:3|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:3|Solution a|Solution 2.1:3a|Solution b|Solution 2.1:3b|Solution c|Solution 2.1:3c|Solution d|Solution 2.1:3d|Solution e|Solution 2.1:3e|Solution f|Solution 2.1:3f}} |
===Exercise 2.1:4=== | ===Exercise 2.1:4=== | ||
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- | </div>{{#NAVCONTENT:Answer|Answer 2.1:4|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:4|Solution a|Solution 2.1:4a|Solution b|Solution 2.1:4b|Solution c|Solution 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> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 2.1:5|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:5|Solution a|Solution 2.1:5a|Solution b|Solution 2.1:5b|Solution c|Solution 2.1:5c|Solution d|Solution 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> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 2.1:6|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:6|Solution a|Solution 2.1:6a|Solution b|Solution 2.1:6b|Solution c|Solution 2.1:6c|Solution d|Solution 2.1:6d}} |
===Exercise 2.1:7=== | ===Exercise 2.1:7=== | ||
<div class="ovning"> | <div class="ovning"> | ||
- | Simplify the following | + | Simplify the following by writing them as a single ordinary fraction |
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|a) | |a) | ||
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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:Answer|Answer 2.1:7|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:7|Solution a|Solution 2.1:7a|Solution b|Solution 2.1:7b|Solution c|Solution 2.1:7c}} |
===Exercise 2.1:8=== | ===Exercise 2.1:8=== | ||
<div class="ovning"> | <div class="ovning"> | ||
- | Simplify the following fractions by writing them as | + | Simplify the following fractions by writing them as a single ordinary |
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|a) | |a) | ||
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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> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 2.1:8|Solution a| | + | </div>{{#NAVCONTENT:Answer|Answer 2.1:8|Solution a|Solution 2.1:8a|Solution b|Solution 2.1:8b|Solution c|Solution 2.1:8c}} |
Current revision
Theory | Exercises |
Exercise 2.1:1
Expand
a) | | b) | | c) | |
d) | ![]() ![]() | e) | f) | ||
g) | h) |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f | Solution g | Solution h
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) | ![]() ![]() ![]() ![]() | 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 by writing them as a single ordinary fraction
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 a single ordinary
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