 
Summary: What you need to know for the mathematics
section of the Science Foundation Module
1 Calendars
The Muslim calendar is a lunar calendar. The year consists of 12 lunar
months. The average length of a month is 29.53 days, so the year is about
354 days long. Since the solar year is about 365.25 days long, the lunar year
is about 11 days too short, so the Muslim holidays will move backwards by
about 11 days each year. They can occur at any time of the year.
The Chinese calendar is a lunisolar calendar. The year consists of 12 or
13 lunar months. A normal year is about 11 days too short, while a leap
year is about 19 days too long. Chinese New Year will move backwards 11
(or 10 or 12) days in a normal year, and jump forward 19 (or 18 or 20) days
in a leap year. Chinese New Year will always fall between January 21 and
February 21.
2 Probability
In the "car and goat" game, your chances of winning jump from 1/3 to 2/3
if you switch.
Benford's Law states that for numbers that occur naturally, the proba
bility that the first digit is d is log10(1 + 1/d).
In a group of 23 or more people, it is likely that two people will have the
