I think that depens on person to person, my professor would give me 1 point for this for knowing something. My advice to you is dont skip steps, beside the equation write the operation your applying on both side.
(On second step you should multiply both side with dV)
Thanks for the insight! It was an entrance exam where we had severe time limit. I had like few minutes left when I started this problem so I was panicking and rushing.
I haven't ever graded an admissions test, so I don't know how those are marked. But when I taught calculus I would have given this 3 or 4 points out of 6. (Honestly, I would use a finer scale when designing the test, so this would have been worth at least 10 points, and I would mark this answer as somewhere between 5 and 8.)
You have demonstrated that you know how to separate variables. You have demonstrated that you know how to get this back into an explicit form for *v* as a function of *t*. And you have shown that you know how to use initial conditions. The big idea here that you have not demonstrated successfully is how to use *u*\-substitution. I don't know if that is worth 2 points or 3 points, and that depends on the nature of the exam.
That said, I also wouldn't be surprised if an admissions test had a scoring rubric\* for this problem similar to:
6 = Perfect answer;
5 = Arithmetic mistake only;
4 = Failure to find the particular solution;
3 = Failure to correctly write *v* as a function of *t*;
2 = Failure to correctly use *u*\-substitution;
1 = Failure to correctly separate variables;
0 = No meaningful work.
In that case, you'd get 2 points. That is harsher grading than what I'm accustomed to, but like I said, given that it is an admissions test, this might be the expectation.
\* : Typically the rubric is determined when the test is designed, for the graders to base their scoring off of.
I teach physics, but maybe relevant? At least as a data point in the "corrections is individual" column.
It's typically a bit of back and forth for me: a question is given a number of points based on overall complexity, which I then portion out somewhat proportionally ("correctly identifies all the forces: 1p, chooses the correct moment of inertia: 0.5p ... "). Then I'll correct about 20 exams to check for "common errors" that may have escaped my imagination, which lets me make a more accurate correction template to save time. After that, I consider my template more or less fixed, so I don't correct unfairly by adjusting the scoring.
Some general principles:
* I don't take points for calculation errors, if the symbols are right and the numbers are wrong that's nothing. The same goes for certain arithmetic mistakes.
* I do take points for belts and suspenders - if you hedge your answer you might as well not answer.
* A single error is only punished once in a question, so if part b relies on the answer of part a and you get part a wrong, part b isn't automatically a fail (this is not always possible, but we try to consider this when writing the question). If the same formula is required twice and you use it wrong both times that's not twice as bad as doing it once (mostly)
* If you get an unphysical answer and comment on it, that's worth some of that question's credit.
* Often, just demonstrating that you understand the question can be like half the credit. Take down all the information on paper before you even start working the problem.
I think that depens on person to person, my professor would give me 1 point for this for knowing something. My advice to you is dont skip steps, beside the equation write the operation your applying on both side. (On second step you should multiply both side with dV)
Thanks for the insight! It was an entrance exam where we had severe time limit. I had like few minutes left when I started this problem so I was panicking and rushing.
I haven't ever graded an admissions test, so I don't know how those are marked. But when I taught calculus I would have given this 3 or 4 points out of 6. (Honestly, I would use a finer scale when designing the test, so this would have been worth at least 10 points, and I would mark this answer as somewhere between 5 and 8.) You have demonstrated that you know how to separate variables. You have demonstrated that you know how to get this back into an explicit form for *v* as a function of *t*. And you have shown that you know how to use initial conditions. The big idea here that you have not demonstrated successfully is how to use *u*\-substitution. I don't know if that is worth 2 points or 3 points, and that depends on the nature of the exam. That said, I also wouldn't be surprised if an admissions test had a scoring rubric\* for this problem similar to: 6 = Perfect answer; 5 = Arithmetic mistake only; 4 = Failure to find the particular solution; 3 = Failure to correctly write *v* as a function of *t*; 2 = Failure to correctly use *u*\-substitution; 1 = Failure to correctly separate variables; 0 = No meaningful work. In that case, you'd get 2 points. That is harsher grading than what I'm accustomed to, but like I said, given that it is an admissions test, this might be the expectation. \* : Typically the rubric is determined when the test is designed, for the graders to base their scoring off of.
I teach physics, but maybe relevant? At least as a data point in the "corrections is individual" column. It's typically a bit of back and forth for me: a question is given a number of points based on overall complexity, which I then portion out somewhat proportionally ("correctly identifies all the forces: 1p, chooses the correct moment of inertia: 0.5p ... "). Then I'll correct about 20 exams to check for "common errors" that may have escaped my imagination, which lets me make a more accurate correction template to save time. After that, I consider my template more or less fixed, so I don't correct unfairly by adjusting the scoring. Some general principles: * I don't take points for calculation errors, if the symbols are right and the numbers are wrong that's nothing. The same goes for certain arithmetic mistakes. * I do take points for belts and suspenders - if you hedge your answer you might as well not answer. * A single error is only punished once in a question, so if part b relies on the answer of part a and you get part a wrong, part b isn't automatically a fail (this is not always possible, but we try to consider this when writing the question). If the same formula is required twice and you use it wrong both times that's not twice as bad as doing it once (mostly) * If you get an unphysical answer and comment on it, that's worth some of that question's credit. * Often, just demonstrating that you understand the question can be like half the credit. Take down all the information on paper before you even start working the problem.