Number Theory
What is the divisibility test for 3?
Sum of digits is divisible by 3
A polygon has exterior angles of 20 degrees. How many sides does it have?
18
What is the common ratio of the geometric sequence 8, 12, 18, 27?
3/2
What you get when you add the number of reindeer pulling Santa's sleigh to the number of the day in December that Christmas is celebrated on.
34
It is Christmas tradition to exchange kisses beneath what plant?
Mistletoe
If x leaves a remainder of 4 when divided by 7, what remainder does 2x leave when divided by 7
1
What is the sine of 30 degrees?
0.5
Factorise into (x + k)(y + j) = a + jk:
xy + 2x - 3y = 17
(x - 3)(y + 2) = 17 + (2)(-3)
Assuming that Christmas of 2020 lasts 12 days as told in 'The Twelve Days of Christmas', on which weekday will the final day fall on?
In this movie, an eight-year-old boy is accidentally left behind by his family while they fly off to France for Christmas vacation.
Home Alone
The following is the divisibility test for what number: take the last digit, double it and subtract it from the rest of the number. Repeat
7
A triangle has three altitudes which intersect at a point. What is the name of this point?
Orthocenter
The first term of an arithmetic sequence is 1, and the third term is -3. What is the sixth term?
-11
Product of the number of golden rings times the number of lords-a-leaping from the song "The Twelve Days of Christmas."
50
This person invented the first electric christmas lights
How many factors does 144 have?
15
What is the size of the internal angle of a octagon?
135
What is the value of 1682 - 682
23600
Santa's workshop produces 3 presents on Dec 1, and produces double that the next day, and double again and so on. How many presents are there in total by Dec 7?
381
Norwegian scientists have hypothesised that Rudolph's red nose is due to an infection of which bodily system?
Respiratory system
Given that A281B is divisible by 72, find A and B
A=6, B=7
You go to the north pole to find that it is not a cylinder, but instead is the prism of a regular n-sided polygon. Each internal angle measures 162 degrees. What is n?
20
What is the 6th term of the geometric sequence with a=5 and r=-2?
-160
Santa is magical and clones himself and his sleigh-full of presents 96 times so he ends up with 97 sleighs. If each sleigh has 93 presents, how many presents are there in total? (mental maths)
9021
This western European country started the tradition of placing Christmas trees in the home.
Germany