1.1 Exercises
From Förberedande kurs i matematik 1
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===Exercise 1.1:3=== | ===Exercise 1.1:3=== | ||
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| - | + | Determine whether the following are natural numbers, integers, rational numbers or irrational numbers. | |
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===Exercise 1.1:4=== | ===Exercise 1.1:4=== | ||
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| - | + | Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px" | |
| - | {| width="100%" cellspacing="10px" | + | |
|a) | |a) | ||
|width="33%"| <math>\frac{4}{-8}</math> | |width="33%"| <math>\frac{4}{-8}</math> | ||
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===Exercise 1.1:7=== | ===Exercise 1.1:7=== | ||
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| - | Which of the following numbers are rational? | + | Which of the following numbers are rational? Express them as a fraction of two integers. |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
Current revision
| 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
Determine whether the following are natural numbers, integers, rational numbers or 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
Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px"
|a)
|width="33%"| 
2 
42
2 
+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) | |
| b) | |
| c) | |
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? 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.) |
Answer | Solution a | Solution b | Solution c | Solution d
