1.1 Exercises
From Förberedande kurs i matematik 1
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Work out (without the help of a calculator) | Work out (without the help of a calculator) | ||
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Simplify | Simplify | ||
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers? | Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers? | ||
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers? | Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers? | ||
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Arrange the following numbers in ascending order | Arrange the following numbers in ascending order | ||
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Give the decimal expansion of the following to three decimal places. | Give the decimal expansion of the following to three decimal places. | ||
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Which of the following numbers are rational? Give them as a fraction of two integers. | Which of the following numbers are rational? Give them as a fraction of two integers. | ||
Revision as of 11:04, 3 August 2008
| Teori | Övningar |
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 |
Svar
Loading...
Lösning a
Lösning b
Lösning c
Lösning d
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) |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 1.1:3
Which of the following belong to the natural numbers? integers? rational numbers? 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) |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Exercise 1.1:4
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
| a) | \displaystyle \frac{4}{-8} | b) | \displaystyle \frac{-8}{-4} | c) | \displaystyle \frac{\sqrt{2}}{3} |
| d) | \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 | e) | \displaystyle -\pi | f) | \displaystyle \pi+1 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning 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} |
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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 1.1:7
Which of the following numbers are rational? Give them as a fraction of two integers.
| a) | \displaystyle 3{,}14 |
| b) | \displaystyle 3{,}1416\,1416\,1416\,\ldots |
| c) | \displaystyle 0{,}2\,001\,001\,001\,\ldots |
| d) | \displaystyle 0{,}10\,100\,1000\,10000\,1\ldots\, (en 1:a, en 0:a, en 1:a, två 0:or, en 1:a, tre 0:or osv.) |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
