# bad test questions

21 posts

 1073 posts I am a bit late at asking this but I just remembered about it today and I wanted to ask you about it. How do you feel about unfair test questions at school. My particular example was "what are the numbers 1 through 3000 added together? That was an Algebra 2 star test question. I feel that must people had no way of knowing the correct answer and were not expected to know the answer. I happened to know the answer because I watched Vihart youtube videos and ONLY because I did. I am sure other people have encountered this because there was an article about ambiguous answers on new York’s standardized English test. What do you think about this? 9937 posts If the formula hasn’t been taught before I’d complain about it. That’s what I always did when I thought that something was unfair in school. 1294 posts You say that you feel that you were not expected to know the answer, so I assume that formula was not in the syllabus. Was this perhaps your teacher’s way of finding out whether anyone had taken enough interest in maths to do a bit of independent further reading? 1 post Easy to derive. 1+2 = 3 1+2+3 = 6 = (3+1) + 2 = 4 + 2 1+2+3+4 = 10 = (4+1) + (3+2) = 5 + 5 1+2+3+4+5 = 15 = (5+1) + (4+2) + 3 = 6 + 6 + 3 1+2+…+n = (n+1) + (n-1+2) + (n-2+3)+ … = (n+1)*n/2 since there are n/2 summation terms. It’s not unfair. You learned a concept and couldn’t apply it. Boo hoo. 83 posts This post has been removed by an administrator or moderator 3809 posts I personally feel that is an appropriate algebra 2 question. A question though: was this question on a New York State standardized math test? It could just be an area overlooked by your teacher. Originally posted by EPR89:If the formula hasn’t been taught before I’d complain about it. That’s what I always did when I thought that something was unfair in school. I disagree with this. Math should be taught so they can ask you questions you’ve never seen before where you have to use formulas you’ve never learned before (to some extent). Any math course that involves much memorizing is a horrible math course. 60 posts Star? Are you from Texas? I know they just started doing that here, but I’m not sure if they have it in other places. Anyways, if you had a calculator, it’s a fairly easy question, as I’m pretty sure there’s a thing you can just plug the number into, I know that sounds stupid, but I don’t know how to describe it. 18892 posts You learned a concept I like how you assume they did. How do you feel about unfair test questions at school. I only care if it means I didn’t succeed in the test. I couldn’t care enough to make a problem out of it if I did succeed, since that’s more trouble than it’s worth. 6660 posts Originally posted by XxFoYrAxX:Star? Are you from Texas? I know they just started doing that here, but I’m not sure if they have it in other places. Anyways, if you had a calculator, it’s a fairly easy question, as I’m pretty sure there’s a thing you can just plug the number into, I know that sounds stupid, but I don’t know how to describe it. They have it in CA too. Algebra 2? You should have been taught sums of series by then… it may be an issue with your teacher, rather than the test. Those tests are pretty friggin easy. 2906 posts “what are the numbers 1 through 3000 added together?” 3000 numbers × an average of 1500.5 per number. easy enough. 2345 posts Originally posted by LemonadeStandt:Easy to derive. 1+2 = 3 1+2+3 = 6 = (3+1) + 2 = 4 + 2 1+2+3+4 = 10 = (4+1) + (3+2) = 5 + 5 1+2+3+4+5 = 15 = (5+1) + (4+2) + 3 = 6 + 6 + 3 1+2+…+n = (n+1) + (n-1+2) + (n-2+3)+ … = (n+1)*n/2 since there are n/2 summation terms. It’s not unfair. You learned a concept and couldn’t apply it. Boo hoo. I would derive the formula personally. Really, I think the problem doesn’t really lie in applying a formula, but having the mental perspicacity to create a formula to apply. I mean really, this kind of pattern is extremely simple. Although you weren’t directly taught this at school, you were still prepared to succeed. An athlete isn’t expected to participate in things he hasn’t attempted before, but he would still be expected to do well even on new trials. 627 posts I could answer it. It would just take an hour and a half. ^^ I haven’t been taught this yet. I’m taking Algebra 2 soon, though. 2345 posts Originally posted by WwarMmachine:I could answer it. It would just take an hour and a half. ^^ I haven’t been taught this yet. I’m taking Algebra 2 soon, though. 90 minutes? I was doing a math competition back in middle school with a time limit of an hour (see: CEMC ) and this kind of problem was fairly commonplace. It was easily doable. I think you’re exaggerating here. Besides, the teachers aren’t supposed to give you the answers exactly, but they’re present to prepare you to answer those things yourself 2906 posts dude: 3000 numbers × an average of 1500.5 per number. easy enough. so that’s 3000000+1500000+1500=4501500 that should take 15 seconds at most. 2345 posts Originally posted by OmegaDoom:dude: 3000 numbers × an average of 1500.5 per number. easy enough. so that’s 3000000+1500000+1500=4501500 that should take 15 seconds at most. That’s when you already have the applicable formula(s) on you (in this case, [(x+y)(n/2)] or [(n(n+1))/2]- former works for all arithmetic progressions where x and y are the bounds of lowest and highest values irrespectively). Deriving it should take roughly… a minute or 2. So, you would expect to be able to achieve a solution in about 3 min. max. 2906 posts i have no idea what you’re talking about. it really shouldn’t take you “a minute or two” to figure out that 3000 numbers with an average of 1500.5 (which seems obvious, i mean we all know 5.5 is an average score in the range from 1 to 10 right? so there), summed up is the same as 1500.5×3000. i mean seriously…it’s not rocket science. and i have no idea what you wrote down formula-wise. i never use formulae and so long as i live i will continue to claim that formulae are for people that suck at math. 2345 posts Originally posted by OmegaDoom:i have no idea what you’re talking about. it really shouldn’t take you “a minute or two” to figure out that 3000 numbers with an average of 1500.5 (which seems obvious, i mean we all know 5.5 is an average score in the range from 1 to 10 right? so there), summed up is the same as 1500.5×3000. i mean seriously…it’s not rocket science. Average is pretty obvious: (n+1)/2 out of the original formula. However, you can’t get the average just by adding little intervals of them together. For example, to get the average of 1+2+…+20, you don’t simply add 5.5 + 5.5 to get 11. etc. Not really sure what you meant by the 1-10 range average as to significance in correlation. and i have no idea what you wrote down formula-wise. i never use formulae and so long as i live i will continue to claim that formulae are for people that suck at math. I think people who use formulae created by other people without understanding are stupid. On the other hand, if you know how a formula works (or even better, how it was derived), then I wouldn’t classify you as stupid even if you do rely on old principles. 2906 posts I think people who use formulae created by other people without understanding are stupid. On the other hand, if you know how a formula works (or even better, how it was derived), then I wouldn’t classify you as stupid even if you do rely on old principles. well that’s true. just so long as it’s based on understanding the math, rather than on memorising. and formulae have a tendency to be shared as a memorisible trick that circumvents understanding. you can’t get the average just by adding little intervals of them together. For example, to get the average of 1+2+…+20, you don’t simply add 5.5 + 5.5 to get 11. etc. that has me boggled. you just said “Average is pretty obvious: (n+1)/2 out of the original formula”, so what’s this about not getting the average when you’ve already got it? although of course, i prefere to derive it from understanding rather than a memorised formula. Not really sure what you meant by the 1-10 range average as to significance in correlation. depending on what country you live in, school grades are returned within the range from 1 to 10, with 5.5 being the median of possible scores, and the minimum to pass. 2345 posts Originally posted by OmegaDoom:you can’t get the average just by adding little intervals of them together. For example, to get the average of 1+2+…+20, you don’t simply add 5.5 + 5.5 to get 11. etc. that has me boggled. you just said “Average is pretty obvious: (n+1)/2 out of the original formula”, so what’s this about not getting the average when you’ve already got it? I thought you were suggesting factorization multiplication as to amplifying the value of the given average by the guidlines of the original ratio between the two identities in which you invest equal rates. In this case, I thought you meant something like: “There are 300 10s in 3000 and the average for 10 is 5.5, so we just have to multiply 5.5 by 300.” However, that is obviously wrong. It seems that I was confused by the ambiguity of your expression 2906 posts I thought you were suggesting factorization multiplication as to amplifying the value of the given average by the guidlines of the original ratio between the two identities in which you invest equal rates. lol. although more of a soft rule, this would count as a style error in writing. such a long stretch of text with no comma in it is really hard to read. also the “as to” conjunction isn’t a good one. In this case, I thought you meant something like: “There are 300 10s in 3000 and the average for 10 is 5.5, so we just have to multiply 5.5 by 300.” However, that is obviously wrong. It seems that I was confused by the ambiguity of your expression uhm…yeah, if you’re gonna read things into it that aren’t there at all, you’re forcing it to be ambiguous to you. 87 posts I think it is unrealistic to think that people can derive formulas (no matter how ‘trivial’ you think they are!) in a high-stress test environment. It’s amazing how some of the formulas we have today that seem incredibly simple and easy, weren’t actually derived until quite recently by extremely intelligent people. Take for example Euler’s formula: v – e + f = 2. This is a relatively simple formula and one could easily look at it and think it obvious and trivial – that is, after already knowing it. I think maths should teach you everything you need to know, and then ask you questions that force you to use these concepts in areas that may not be immediately obvious. Students should be given all the tools they might possibly need, and it is up to them to use them in the right way to generate the answer. Or if one wishes to test students with a new theorem they hadn’t been introduced to in class, the question should start with some situation in which the formula logically follows from the situation and in which it is reasonable the student may derive said formula, and then further parts of the question ask the student to apply this new theorem. From my university calculus classes, these were always the most fun and interesting types of questions.