Given a dish with three oranges. Suppose that you take two oranges from the dish. How many oranges do you have?
Question 2
Compare the numbers 0.99999... (infinitely many 9s) and 1. Which of the following sentences is true?
Question 4
Our earth orbits around the sun. How long does one complete orbit of the earth around the sun take?
Question 5
The earth not only orbits around the sun, but also spins round her axis. How long does one complete turn of the earth round her axis take?
Question 6
In our western calendar there are years of 365 days and leap years of 366 days. How often is it a leap year in our calendar?
Question 7
The calendar that we use has a name. What is the name of our western calendar?
Question 8
The year is divided into four seasons: spring, summer, autumn and winter. On the northern hemisphere it is summer when it is winter on the southern hemisphere, and the other way around. Which of the following sentences is true?
Question 9
Given the mathematical set N of natural numbers (0, 1, 2, 3, 4, 5, ...) and the set Z of integer numbers (..., -3, -2, -1, 0, 1, 2, 3, 4, ...). Which of the following sentences is true?
Question 10
As you know, the world population is growing very fast. The main cause is of course that a lot of babies are born. How many babies are born every minute worldwide (approximately)?
Question 1
Given a dish with three oranges. Suppose that you take two oranges from the dish. How many oranges do you have?
The Solution: 2
An Explanation
You take two oranges from the dish, so then you have two oranges.
Question 2
Compare the numbers 0.99999... (infinitely many 9s) and 1.
Which of the following sentences is true?
The Solution: 0.99999... is equal to 1
An Explanation
Let x = 0.99999...
Then:
10x = 9.99999...
x = 0.99999... -
------------------
9x = 9.00000...
So 9x = 9, from which follows that x = 1.
Because also holds that x = 0.99999..., we can deduce that: 0.99999... = 1.
For those who still don't believe us, here is another explanation:
1/3 + 2/3 = 1, right?
1/3 = 0.33333...
2/3 = 0.66666...
Now substitude the decimals for the fractions and you get: 0.33333... + 0.66666... = 1
Or, simplified: 0.99999... = 1.
Question 3
A certain farmer has 100 hens, numbered from 1 up to and including 100. Only the hens with the numbers 13 up to and including 48 each lay one egg. How many of the hens haven't laid an egg?
The Solution: 64
An Explanation
(48 - 13) + 1 = 36 hens have laid an egg.
100 - 36 = 64 hens haven't laid an egg.
Question 4
Our earth orbits around the sun. How long does one complete orbit of the earth around the sun take?
The Solution: less than 365� days
An Explanation
The earth makes one orbit around the sun in 365.2422 days.
Question 5
The earth not only orbits around the sun, but also spins round her axis. How long does one complete turn of the earth round her axis take?
The Solution: less than 24 hours
An Explanation
A year equals 365.2422 days. If the earth wouldn't move around the sun, then the earth would make 365.2422 turns round her axis in one year. But because the earth also makes exactly one orbit around the sun in that year, the earth makes 365.2422 + 1 = 366.2422 turns round her axis in one year. One turn therefore takes
365.2422 � 24 hours / 366.2422 = 23 hours, 56 minutes and 4 seconds.
Question 6
In our western calendar there are years of 365 days and leap years of 366 days. How often is it a leap year in our calendar?
The Solution: less than once in every four years
An Explanation
In our western calendar every year of which the number is divisible by 4 is a leap year, except century years not divisible by 400. For example, the years 1700, 1800 and 1900 were no leap years, but the year 2000 will be. Therefore not every fourth year is a leap year.
Question 7
The calendar that we use has a name. What is the name of our western calendar?
The Solution: Gregorian calendar
An Explanation
In 45 B.C. Julius Caesar replaced the Roman calendar by the Julian calendar. In 1582 A.D. pope Gregory XIII replaced the Julian calendar by the Gregorian calendar, by improving the leap year rule. This Gregorian calendar is the calendar we still use today. The International calendar is one of the many proposals that have been done for the 'improvement' of the Gregorian calendar.
Question 8
The year is divided into four seasons: spring, summer, autumn and winter. On the northern hemisphere it is summer when it is winter on the southern hemisphere, and the other way around. Which of the following sentences is true?
The Solution: The summer on the northern hemisphere is longer than the summer on the southern hemisphere
An Explanation
The summer on the northern hemisphere, which lasts from the summer solstice (21 June) until the autumnal equinox (23 September), has an approximate length of 93.6 days. The winter on the northern hemisphere (and so the summer on the southern hemisphere), which lasts from the winter solstice (21 December) until the vernal equinox (21 March), has an approximate length of 89.0 days.
Question 9
Given the mathematical set N of natural numbers (0, 1, 2, 3, 4, 5, ...) and the set Z of integer numbers (..., -3, -2, -1, 0, 1, 2, 3, 4, ...).
Which of the following sentences is true?
The Solution: N has as many numbers as Z
An Explanation
Two sets A and B have the same number of elements if and only if there exists a so-called bijective function f from A to B.
Define the bijective function f: N -> Z as follows:
f(n) = -�n for n even
= �(n + 1) for n odd
So for example, f(0) = 0, f(1) = 1, f(2) = -1, f(3) = 2, f(4) = -2, f(5) = 3 etcetera. f is a bijective function from N to Z, and therefore N and Z have the same number of elements.
Question 10
As you know, the world population is growing very fast. The main cause is of course that a lot of babies are born.
How many babies are born every minute worldwide (approximately)?
The Solution: 151-300
An Explanation
Approximately 250 babies are born every minute worldwide (1996 estimate).
