1.1 Exercises
From Förberedande kurs i matematik 1
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| - | |width="100%"| <math>3{ | + | |width="100%"| <math>3\textrm{.}1416\,1416\,1416\,\ldots</math> |
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| - | |width="100%"| <math>0{ | + | |width="100%"| <math>0\textrm{.}2\,001\,001\,001\,\ldots</math> |
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| - | |width="100%" valign="top"| <math>0{ | + | |width="100%" valign="top"| <math>0\textrm{.}10\,100\,1000\,10000\,1\ldots\,</math> (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.) |
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</div>{{#NAVCONTENT:Answer|Answer 1.1:7|Solution a|Solution 1.1:7a|Solution b|Solution 1.1:7b|Solution c|Solution 1.1:7c|Solution d|Solution 1.1:7d}} | </div>{{#NAVCONTENT:Answer|Answer 1.1:7|Solution a|Solution 1.1:7a|Solution b|Solution 1.1:7b|Solution c|Solution 1.1:7c|Solution d|Solution 1.1:7d}} | ||
Revision as of 06:59, 19 September 2008
| Theory | Exercises |
Exercise 1.1:1
Work out (without the help of a calculator)
| a) | | b) | |
| c) | | d) | |
Answer | Solution a | Solution b | Solution c | Solution d
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Exercise 1.1:2
Simplify
| a) | | b) | |
| c) |  (−7)−4(6−5) | d) | (−7)−(4+6) (−5) |
Answer | Solution a | Solution b | Solution c | Solution d
Exercise 1.1:3
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
| a) | | b) | | c) | |
| d) | | e) | (−4) | f) | (−4) |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 1.1:4
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
| a) | | b) | | c) | \displaystyle \frac{\sqrt{2}}{3} |
| d) | \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 | e) | \displaystyle -\pi | f) | \displaystyle \pi+1 |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 1.1:5
Arrange the following numbers in ascending order
| a) | \displaystyle 2, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{3} och \displaystyle \tfrac{7}{3} |
| b) | \displaystyle -\tfrac{1}{2}, \displaystyle -\tfrac{1}{5}, \displaystyle -\tfrac{3}{10} och \displaystyle -\tfrac{1}{3} |
| c) | \displaystyle \tfrac{1}{2}, \displaystyle \tfrac{2}{3}, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{8} och \displaystyle \tfrac{21}{34} |
Answer | Solution a | Solution b | Solution c
Exercise 1.1:6
Give the decimal expansion of the following to three decimal places.
| a) | \displaystyle \frac{7}{6} | b) | \displaystyle \frac{9}{4} | c) | \displaystyle \frac{2}{7} | d) | \displaystyle \sqrt{2} |
Answer | Solution a | Solution b | Solution c | Solution d
Exercise 1.1:7
Which of the following numbers are rational? Give them as a fraction of two integers.
| a) | \displaystyle 3\textrm{.}14 |
| b) | \displaystyle 3\textrm{.}1416\,1416\,1416\,\ldots |
| c) | \displaystyle 0\textrm{.}2\,001\,001\,001\,\ldots |
| d) | \displaystyle 0\textrm{.}10\,100\,1000\,10000\,1\ldots\, (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.) |
Answer | Solution a | Solution b | Solution c | Solution d
