Methods to ensure that your answers are correct - by using CAS or otherwise

[Apink!]

Hi AN!

I was wondering if any of you could help me with confirming my answers as correct?
Especially in really long problems (like worded questions), I tend to solve it only to find out that I have made a stupid mistake along the way.

Are there other ways of checking your solutions rather than just being careful, keeping a note of your common mistakes and trying to just not make those mistakes?

For example, if I was doing Specialist, and the question asks you "Express fraction A in partial fractions"

I would do this so that I can ensure that I had gotten this question right:

1. Solve it via hand
2. Using the expand function of the CAS, put the fraction in (the CAS will spit out the partial fraction)
3. Check that both answers match - I got the right answer!

But I'm not sure how I can ensure this for the methods exam or methods questions.

Does anyone know ways like this where your CAS tells you the answer, and you just compare it with your hand-written solution to see if they are identical?

Or Does anyone have 2 ways of solving a questions, so that you can try them out both and then check that they match? (confirming that they are correct answers)

I would really appreciate  it if past methods students could give me some tips on these.

I make a lot of silly mistakes, and I would be so disappointed if I lost my marks due to my mistakes, not because of my honest inability to solve the problem.

Thank you so much!

[wunderkind52]

Hi AN!

I was wondering if any of you could help me with confirming my answers as correct?
Especially in really long problems (like worded questions), I tend to solve it only to find out that I have made a stupid mistake along the way.

Are there other ways of checking your solutions rather than just being careful, keeping a note of your common mistakes and trying to just not make those mistakes?

For example, if I was doing Specialist, and the question asks you "Express fraction A in partial fractions"

I would do this so that I can ensure that I had gotten this question right:

1. Solve it via hand
2. Using the expand function of the CAS, put the fraction in (the CAS will spit out the partial fraction)
3. Check that both answers match - I got the right answer!

But I'm not sure how I can ensure this for the methods exam or methods questions.

Does anyone know ways like this where your CAS tells you the answer, and you just compare it with your hand-written solution to see if they are identical?

Or Does anyone have 2 ways of solving a questions, so that you can try them out both and then check that they match? (confirming that they are correct answers)

I would really appreciate  it if past methods students could give me some tips on these.

I make a lot of silly mistakes, and I would be so disappointed if I lost my marks due to my mistakes, not because of my honest inability to solve the problem.

Thank you so much!

There really is no "set" way of checking questions, and that's something you'll need to learn how to do as you go through specific questions. Are there any specific questions you have that you don't know how to check?

In terms of checking, if there is only one way to do the question, then if there's time try the question again on a separate area without looking at the previous working. The chances that you'll do the same mistake if you don't look at your working are quite slim, unless you've copied the question wrong. The best method of course, is to find another method, as the chances that you'll do both methods and get the same answer and be wrong are very slim.

The most simple things would be to sub in your answers, and try the question again. If you make a mistake in the middle, like a + instead of a -, your best bet is to rub out everything below that. Because chances are, you'll fail to change something, and you'll get the answer wrong anyway. Another thing is basically just a "common sense test". For instance, if you're doing probability and you end up with a negative probability, then you know you've messed up somewhere.

In terms of checking as you go, what you can try is checking your final answer. If this is wrong, you can check somewhere in the middle. This way, you will know if you've made a mistake in the top half of your working or the bottom half (that way you don't have to check every single line)

Beware that if it's a trig question, in terms of sine and cosine, most likely your answer will not match what's on the calculator. So there's a couple of ways to check that. You can type ___=____ and look for true, or you can type solve(____=_____) if that doesn't work. Or finally, you can go to your graph screen and type ___youranswer___-___calcanswer___, then press CtrlT to bring up a table. And if it's true, then you should get constant entries down your page.

[Apink!]

Beware that if it's a trig question, in terms of sine and cosine, most likely your answer will not match what's on the calculator. So there's a couple of ways to check that. You can type ___=____ and look for true, or you can type solve(____=_____) if that doesn't work. Or finally, you can go to your graph screen and type ___youranswer___-___calcanswer___, then press CtrlT to bring up a table. And if it's true, then you should get constant entries down your page

That will go under my notes (: Thank you so much, I didn't know there was even a function on the CAS that allows you to bring up a table. That's cool!