Working with numbers:
In math, you can waste a lot of time if you don't know the tricks of the trade.
Here are a few things you should know, or at least know how to get there quickly:
1. Division by 3.
If a number is divisible by 3, then the sum of its digits is also divisible by 3. For example:
483 is divisible by 3, since 4+8+3 = 15, and 15 is divisible by 3. However 482 1nd 481 are not divisible by 3.
2. You should become familiar with perfect squares.
Let's assume you know the squares up to 10.
11 * 11 = 121
12 * 12 = 144
13 * 13 = 169
15 * 15 = 225
25 * 25 = 625
Maybe you don't know 16 * 16 but you know 15 * 15.
15* 15 = 225, so 16 * 15 = 225 + 15, and 16 * 16 = 16 * 15 + 16 = 225 + 15 + 16 = 225 + 31 = 256
In general if you know x squared then (x+1) squared = x squared + x + (x + 1)
so 26 * 26 = 25* 25 + 25 + 26 = 676
3. Multiplying by 5, 15, 25 etc.
To multiply quickly by 15, multiply by 10 then add on 1/2 more.
Example: 125 * 15 = 125 * 10 = 1250 , now add 1250/2 = 625 to get 1875
To multiply by 5, multiply by 10 and divide by 2: 125 * 5 = 1250/2 = 625
To multiply by 25, multiply by 10, double it and add half of the multiple. 125*25 = 1250*2 + 625 = 3125.
You can do similar things with 35, 45,...etc.
