[smsm42]

>> how do you solve it without know the quadratic formula or some such?

This is actually possible, if you've been taught to solve problems instead of being taught to apply magic formulas. Of course, one is rarely taught math this way now.

Let me try. Suppose you have 3x^2+5+2x=7. Now, you have no idea how to solve for x. But what you could solve? If you had something like (ax+b)^2 = c, then probably this would be easy for you to solve, right (of course, provided c is not negative, won't get into that now)? We just take square root of both parts, and then it's a simple linear equation. Now, we can notice we can also get rid of a, for simplicity, by dividing both parts by a and get something like (x+b)^2 = c. Which in our example should represent 3x^2+5+2x=7 or alternatively x^2 + 2/3x - 2/3 = 0. But how we find proper b and c?

So, is there a way to make that equation look like that with suitable values? Let's look at (x+b)^2 = x^2 + 2bx + b^2. We have 2bx = 2/3x which means b = 1/3. So we have (x+1/3)^2 on one side, and on the other side we have to get 2/3 and also additional 1/9 which is the b^2, meaning c would be 7/9. So, x + 1/3 is sqrt(7/9) with + or - sign (since square on non-zero root always has 2 options), and x would be that minus 1/3.

As you can see, we used no special magic formula - only thing we needed is how to write (x+b)^2, which is easy to see just by multiplying (x+b)*(x+b) by hand.

You can do cubic equations this way too, but it is considerably more laborious. Look up Cardano and Vieta methods. Doable but I wouldn't enjoy doing it by hand too much.

[yummyfajitas]

tl;dr; If you are really good at math, but didn't follow the math curriculum closely, you can probably rederive most of it. I'm not sure this counts as "gaming" a test. I'd describe it as "understanding the material really well and getting a high score."

Remember, the goal of an exam is to measure if you have the knowledge. Whether you got the knowledge by studying hard in a traditional classroom setting as scheduled by a syllabus is irrelevant.

[smsm42]

It doesn't really qualify as "really good" (I'm not - I know people who are and they are way beyond what I can do, I mean light years beyond). It's just a set of basic tools about how to approach problems. Like when programming you don't have to have library function for everything - you learn to write your own functions, etc. You don't have to be able to write your own OS (though some people can) but going beyond clicking buttons in Word is not a bad idea.

Of course, I do not see it as "gaming" - I see it as learning the right way. IMHO, all learning should start with that and formula should come after - as a shortcut, which you can take but you know if needed you could do it from scratch because you understand where it comes from.