Ways to Overcome Negative Signs in Math Problems | Expert Tips

[Tyrion101]

I'm getting tired of getting wrong answers and going back and doing them again and again only to find there's a negative sign in the problem I didn't see through the gigantic problem I just finished. If I were doing an actual classroom and not an online that doesn't allow shown work... I'd at least get partial credit, and it's freaking me out, because I'm beginning to wonder if I'll pass this class because of it. I've practiced and practiced and I just don't seem to see the signs when it matters, and I don't know what to do, and don't want to give up, any advice?

 

[Mentallic]

Are you making an extra effort to think before you write when you encounter a negative sign?

 

[Tyrion101]

I try, but for whatever reason I just miss signs all together especially in certain places of problems. Maybe I need to spend tome not doing the problems and just spotting signs in the original?

 

[eigenperson]

Easy solution: Since you're doing this online, do all the calculations with a computer algebra system. No one will ever know.

Harder (but ultimately better) solution: Develop the habit that every time you finish a problem (and also in the middle when you reach a stopping point), you check whether the answer you got makes sense. It's very unusual to have a problem where you can't check the answer somehow. You don't have to be 100% accurate, just good enough.

Here's an example: Someone asks you to find $\sum_{n=1}^\infty {x^n \over n}$ for $\left|x\right| < 1$. You do a bunch of work and come up with $\log(1-x)$. Instead of just typing it in right away, try plugging in a number for $x$ to see if the answer makes sense. As it turns out, if $x = 1/2$, this answer does not make sense, because it is negative, whereas all the terms in the sequence were positive. So something went wrong, and you can now go through your work to locate it.

Another example: You have to find the point where $\log(u+1) - u^2$ is maximized. After a bunch of work, you get the answer 1/2. As a sanity check, the derivative should be zero there. It isn't, so something went wrong -- who knows exactly what, but something.

 

[Tyrion101]

You know I did think of writing an algebra solver, just for fun. But it'd be too tempting to use it in the class...