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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

Answer | Solution a | Solution b | Solution c | Solution 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)

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) 8 b) −4 c) 8−4
d) 4−8 e) 8(−4) f) (−8)(−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) 4−8 b) −4−8 c) 32 
d) 422  e) − f) +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) 2, 53, 35 och 37
b) −21, −51, −310 och −31
c) 21, 32, 53, 85 och 3421

Answer | Solution a | Solution b | Solution c


Exercise 1.1:6

Give the decimal expansion of the following to three decimal places.

a) 67 b) 49 c) 72 d) 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) 314
b) 3141614161416...
c) 02001001001...
d) 0101001000100001... (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)

Answer | Solution a | Solution b | Solution c | Solution d

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