In my view, paradoxically you have to be slower in order to be faster. To be fast at maths you have to be less focused on getting the job in front of you right now done, and more focused during the learning stage on learning deeper insights into what you're doing. When you attain a high level of MASTERY, problems are faster to solve.
I'm slow at learning maths because I need deep insights in order to remember things, and I'm never satisfied until I know something inside out.
Taking a really simple example, to calculate $5 \times (10+4)$ you might say that's $5\times14=70$ and be done with it and move on.
But if you're focused on learning deeper insights you might think about it in multiple different ways:
Multiplication distributes over addition so I can multiply before I add, or after:
$(5\times10) + (5\times 4)=5\times(10+4)=70$
You might think about how multiplying is equivalent to adding the exponents of the prime factors:
$10+4$ has the prime factors $\{2^1,7^1\}$ and $5$ has the prime factor $\{5^1\}$ so the product is $2^{1+0}\times5^{1+0}\times7^{0+1}=70$
Since we write numbers in base $10$ you might think about multiplying by five as multiplying by $\frac{10}2$ so $5 \times (10+4) = \frac{10}2\times14$ then cancel the twos to get $10\times7$
You might think of $14$ as $20-6$ giving you $100-30=70$
Then you might think about the fact that this last example is
$5\times (20-6)=(5\times20-5\times6)$ and ask yourself whether this means that multiplication distributes over subtraction.
Then you might deduce that this is true because subtraction is simply the addition of a negative number.
Then you might think about how addition is an operation on the monoid of non-negative integers, and how subtraction is the extension of rightward transformations on the real line to leftward transformations on the line which are their inverse transformations. And by introducing subtraction you extend the closure of your algebraic operations to include the negatives, and this makes the integers a group according to the group axioms. Multiplying a negative number scales to the left rather than scaling to the right.
A good exercise, is to pay attention to how you solved a problem. Sometimes you do it automatically, and the process is subconscious. Once you become conscious of your method, ask yourself what other methods you might have used, and solve the same problem by those methods. You will learn shortcuts this way and multiple ways of understanding the same thing.
The more insight you build, the more visualisation tools you have at hand on which to pin memories. Then when you have to apply quickly e.g. in an exam, it's not a case of finding your one way to solve a problem. You can see multiple ways and one may instantly jump out as a quick solution. And you can move on with confidence, knowing you've arrived at your answer by multiple different methods.
This of course, requires an investment of more time in the learning stage. But by building deeper insights and a higher level of mastery, you can progress faster when it comes to applying what you learnt.
