Math for Smarties! Trivia Quiz

Answer: 13

Here is the way to work it out

12 squared= 144
5 squared= 25

144+25= 169

The square root of 169= 13
So 13 is the hypotenuse.

Answer: 1949

There isn't much to explain really. But, having to add something, a prime number is a number that is only divisible by itself and one.

Answer: 28

The pattern is made by the list of 'happy numbers'.

A happy number works like this - Using 7 as an example (it is a happy number):

7 squared equals 49.
4 squared = 16, and 9 squared= 81
81+16= 97
then 9 squared + 7 squared= 130.
1 squared + 3 squared + 0 squared =1+9+0=10. 1 squared+ 0 squared= 1
(if this last number is one it's a 'happy number' and anything else is an 'unhappy number')

Another example: number 19 is happy:

1 squared + 9 squared = 82
8 squared + 2 squared = 68
6 squared + 8 squared = 100
1 squared + 0 squared + 0 squared = 1.

The happy numbers up to 100 are:
1, 7, 13, 19, 23, 28, 44, 49, 68, 79.

Answer: 2

If you visualize the books, the first thing on the left is actually the back of the first book. Next the front of the first book, and the back and front of the second book. The back of the third book is the next thing, so really the earthworm is only traveling through the second only.

Answer: 360 degrees

A polygon is any flat shape with straight sides. Exterior angles of a polygon will always add up to 360 degrees, as no matter how scrambled and weird the sides are, they will always make one rotation.
See here for an expkanation:
http://www.mathsisfun.com/geometry/exterior-angles-polygons.html

Answer: 58

The pattern started at zero and adds on the sequence of prime numbers (1 is a special number)

So, 0, (+2), 2, (+3), 5, (+5), 10, (+7), 17, (+11), 28 etc.

Answer: 5x -2y -7

Simplify means to remove the brackets.
Here are a few steps to work it out- (working left to right, try to follow. don't worry if you don't understand)

2 times x equals 2x
2 times +4 equals +8
+3 times x equals 3x
+3 times -5 equals -15
leave the -2y alone

Now you get 2x +8 +3x -15 -2y
Then, add together the ones that you can
2x +3x =5x
-2y =-2y
+8 -15 =-7

The final result will be 5x -2y -7

Answer: 6(3x -2y -5z)

Factorize means to put in brackets. Factorizing is a lot easier than simplifying if you understand it.

So, with 18x -12y -30z, you have to find the highest common factor, which in this case is 6. Starting with 18x, you multiply 6 with a number to make 18x. That number is 3x, which you put into the bracket (6(3x). You do the same with -12y (2y) and -30x (5z). The final answer is 6(3x -2y -5z).

Answer: 315

The square root of 225 is 15, and double it to get 30. 30 squared equals 900, which is the amount of degrees in a heptagon. A heptagon has seven sides, which you times by 45 to get 315.

Answer: 15

David is 15, which makes Bob 7 and Jim 12.