How to Get an A* in A-Level Maths

I'd usually argue that if you're learning how to answer A-level questions by rote (memorization rather than understanding), then you're getting yourself into trouble.

Here's an example of where learning by rote can be useful. Get a stopwatch ready.

1) Time yourself: Write down the seven times table in decimal (7,14,21,...) up to seven times thirteen
2) Time yourself: Write down the seven times table in binary (111,1110,10101,...) up to seven times thirteen

You might argue that (2) will take longer because there's more digits to write. OK then...

3) Time yourself: Write down the seven times table in base 11 (7,13,1a,...) up to seven times thirteen

Please let me know your results!

A little mathematical help

In decimal (base 10) we use 10 symbols (digits) to write numbers: 0,1,2,3,4,5,6,7,8,9.
In binary (base 2) we just use 2 symbols: 0 and 1, to produce the same effect. Instead of Units, Tens, Hundreds and Thousands we have Units, Twos, Fours and Eights.
Computers frequently use base 2 as it's easy to represent this as on and off states.

The only real reason we use base 10 is because we have 10 fingers and that's what's been selected as the standard way - there's no reason not to any other number of symbols - like in base 11 we'll use 0-9 and then 'a' to represent ten. Historically not everyone has used base 10

(Although whatever base you choose should be called "base 10" I suppose!)