1.1 Exercises
From Förberedande kurs i matematik 1
| Theory | Exercises |
Exercise 1.1:1
Work out (without the help of a calculator)
| a) | \displaystyle 3-7-4+6-5 | b) | \displaystyle 3-(7-4)+(6-5) |
| c) | \displaystyle 3-(7-(4+6)-5) | d) | \displaystyle 3-(7-(4+6))-5 |
Loading...
Exercise 1.1:2
Simplify
| a) | \displaystyle (3-(7-4))(6-5) | b) | \displaystyle 3-(((7-4)+6)-5) |
| c) | \displaystyle 3\cdot(-7)-4\cdot(6-5) | d) | \displaystyle 3\cdot(-7)-(4+6)/(-5) |
Exercise 1.1:3
Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.
| a) | \displaystyle 8 | b) | \displaystyle -4 | c) | \displaystyle 8-4 |
| d) | \displaystyle 4-8 | e) | \displaystyle 8\cdot(-4) | f) | \displaystyle (-8)\cdot(-4) |
Exercise 1.1:4
Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px" |a) |width="33%"| \displaystyle \frac{4}{-8} |b) |width="33%"| \displaystyle \frac{-8}{-4} |c) |width="33%"| \displaystyle \frac{\sqrt{2}}{3} |- |d) || \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 |e) || \displaystyle -\pi |f) || \displaystyle \pi+1 |}
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} |
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} |
Exercise 1.1:7
Which of the following numbers are rational? Express 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.) |
