I’m trying to write a ratio test question, and I would like to ask it in steps where it’s fine just to put the expression for a_{n+1}/a_n in the first answer, but then ask for a simplified form in the next answer, then take the limit as n goes to infinity, then give the interval of convergence.
I’m having some trouble figuring out how to specify the simplified form. I think doing symbolicCompare with normalizeOrder gets me close, but if the answer is (n+1)(x-2)/(3n), I would ideally like to include 1/3*(n+1)/n*(x-2) or similar also. ExpandOnCompare also almost works, inasmuch as it allows the breaking up into separate fractions, but then it would also accept nx-2n+x-2 in the numerator, and I don’t want that (though the odds of a student trying that might be slim). With expandOnCompare it seems like 3^2/3^3 is accepted, but not 3^n/3^(n+1). It didn’t seem to mark correct any expression with exponents on the (x-2) term, numerical or arbitrary, which is good.
Is there a way to require the exponents have been simplified and any numbers reduced to lowest terms without caring about the order or how the fractions are broken up?
Chrissy
How close can you get with simplifyOnCompare="full" (or its shortcut a plain simplifyOnCompare)? If you don’t want an expanded numerator, then expandOnCompare is a nonstarter.
If the simplify commands don’t give you options of what you need, then it may be that you are only left with the recourse of enumerating the different cases that you want to make sure are correct. You can add multiple awards to an answer. The default behavior is that it will check all the awards and give credit to the award with maximal credit.
This the format:
<answer symbolicEquality>
<award simplifyOnCompare>expression1</award>
<award simplifyOnCompare="normalizeOrder">expression2</award>
<award simplifyOnCompare>expression3</award>
</answer>
It can get laborious if you have lots of edge cases, but it should be possible to get close to your desired combination. You can move attributes between the <answer> and the <award>s, depending on whether you want them to apply to all awards. An attribute on an award will override an attribute on the answer.
Thank you!
simplify=“full” doesn’t help with marking correct a product of multiple fractions, and it also starts marking correct things like having an extra factor of 2 in both the numerator and denominator, or having +(x-x) in either the numerator or denominator.
What I really want is to have specific factors without caring about order or if it’s written as 1 fraction or as a product of multiple fractions.
It seem my best option might be to tell students to enter a single fraction and go with normalizeOrder.
I’ve wrestled a lot with this exact thing with simplifying rational expressions and wanting to check various stages of simplification along the way instead of just the final answer. I think I currently just give a prefill with a single fraction with a note for students to write their answers as a single fraction. You can then extract the numerator and denominator of the fraction and compare them separately against whatever combination of factors you’d like to compare against. I gave up on trying to get it to work with the fraction at large.