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1.1 Exercises

From Förberedande kurs i matematik 1

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       Theory          Exercises      


Exercise 1.1:1

Work out (without the help of a calculator)

a) 3−7−4+6−5 b) 3−(7−4)+(6−5)
c) 3−(7−(4+6)−5) d) 3−(7−(4+6))−5

Svar | Lösning a | Lösning b | Lösning c | Lösning d


Exercise 1.1:2

Simplify

a) (3−(7−4))(6−5) b) 3−(((7−4)+6)−5)
c) 3(−7)−4(6−5) d) 3(−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) 8 b) −4 c) 8−4
d) 4−8 e) 8(−4) f) (−8)(−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) 4−8 b) −4−8 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}

Svar | Lösning a | Lösning b | Lösning 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}

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\, (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)

Svar | Lösning a | Lösning b | Lösning c | Lösning d

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