What Do I Need To Pass This Class?

I admit a bit of difficulty in identifying with people who are very worried about their grades. I stopped worrying about my grades somewhere around fifth grade, when I missed a straight-A report card by one question on one spelling test and decided the stress wasn’t worth it for changing one B+ into an A-. But it’s a question instructors get, increasingly, as the final exam approaches, and students are almost never satisfied with the correct answers, especially when circumstances require a time machine. I suppose I understand the despair in that case.

Anyway, working out the minimum grade you need to pass — or what you need to get an A, or to get a B, or whatever you like — is an easy enough problem it’s surprising when students don’t work it out on their own. Maybe they don’t realize this is what they learn algebra for. But here’s how to do it.

You need to know a couple things in order to work out what score you’ll need on the final. Let me list them, and how I’ll represent them in the equation to be worked out.

Quantity Where You Know It From Symbol Representing It
Pre-Final Course Grade You have been tracking that, right? C
Minimum Score To Pass If it’s not on the syllabus it’s probably 60 or 65 P
Any Extra Credit If you got any extra credit (or lost any) you know it EC
The Final Exam’s weight What fraction of the course grade is the final worth; it’s on the syllabus w
The Pre-Final Grade’s weight What fraction of the course grade is everything but the final worth 1 – w

And there’s then the score on the final exam, which I choose to call F. We’re be learning what range of values allow one to pass by algebra.

The symbols for all these quantities can be anything, but it’s often good form to let them be something that suggests what they mean. Thus, C for the Course grade (pre-final), P for the score to Pass, EC for the Extra Credit, w for the final’s weight. I decided to have capital letters represent scores and w represent, well, non-scores. To me it feels like there’s a sensible distinction to draw between the scores that are unique to the student and the weighting that’s attached to the entire class, but you’re not wrong if you decide that’s a distinction not worth noting in the symbols. The symbols are there to help sort out what we want to know; we don’t need them to do absolutely everything.

The weight, by the way, should be between 0 and 1, the way I’ve set this up. If the final is 25 percent of the course grade, then w is 25/100 or 1/4. If the final’s 33 percent, then w is 33/100 or, probably, it’s meant to actually be 1/3, and so on. Everything else is worth one minus that, so, 3/4 or 2/3 or some other likely number.

The extra credit, by the way, can include demerits, if you’ve lost credit for failing to attend or for using your cell phone in the middle of class or whatnot. If you’ve lost credits, the extra credit will be a negative number. If you like you could break off the demerits to a separate score, maybe called D, but I’m comfortable with positive and negative scores and so don’t worry about such things.

The course’s total score is going to be the weight of the final times the final’s score — w times F — plus the pre-final’s weight times the pre-final’s score — (1-w) times C — plus whatever the extra credit EC is. If this total is greater than or equal to the passing score, then, you’ve passed. To put this symbolically, one passes if it’s true that

w\cdot F + (1 - w)\cdot C + EC \ge P

To find what scores F make the above relationship true, well, that’s some algebra. The goal is moving everything that isn’t F over to one side of the equation. There are a couple different ways to order how we do that, but they all amount to: subtract the number EC from both sides; subtract the number (1 - w)\cdot C from both sides; and divide both sides by w. So:

w\cdot F + (1 - w)\cdot C + EC \ge P 		\\   w\cdot F + (1 - w)\cdot C  \ge P - EC		\\   w\cdot F \ge P - EC	- (1 - w)\cdot C	\\   w\cdot F \ge P - EC	+ (w - 1)\cdot C	\\   F \ge \frac1w P - \frac1w EC + \left(1 - \frac1w\right)\cdot C

And that last line, really, is all there is to it. Let me bring it out again so it’s not quite so lost at the end of an array of equations. If P is what you need to pass the course, and EC is how much extra credit you’ve gotten, and C is the course average so far, and w is what fraction of the course grade the final exam is worth, then on the final exam you need a score F which satisfies:

F \ge \frac1w P - \frac1w EC + \left(1 - \frac1w\right)\cdot C

Now, for example, if the final is worth 25 percent of the course grade — that’s w = 1/4 — and your pre-final average is 70 percent — that’s C = 70 — and you got a 5 percent bonus in extra credit — that’s EC = 5 — and passing is at 65 percent — that’s P = 65 — then, for the final exam you need to get at least:
F \ge \frac1{\frac14}65 - \frac1{\frac14} 5 + \left(1 - \frac1{\frac14} 70\right)	\\   F \ge 4\cdot 65 - 4\cdot 5 + (1 - 4)\cdot 70	\\   F \ge	260  - 20 - 3\cdot 70	\\   F \ge 240 - 210 = 30

So you might feel reasonably confident at this point. On the other hand, let’s suppose you want a B+ in the course, and that a B+ starts at 85 percent as the course average. That means we work it out again with P = 85, and then:

F \ge \frac1{\frac14}85 - \frac1{\frac14} 5 + \left(1 - \frac1{\frac14}70\right)	\\   F \ge 4\cdot 85 - 4\cdot 5 + (1 - 4)\cdot 70	\\   F \ge	340  - 20 - 3\cdot 70	\\   F \ge 320 - 210 = 110

You see the use for a time machine in this case.

Anyway, this speaks only to what score you need on the final exam. What you need to pass is to be interested in the material, to work at it, to seek extra help from the instructor and whatever tutorial services are available as soon as you realize that you’re in trouble, and to for crying out loud not go in grubbing for every single percentage point or half-percent you can squeeze out. Meetings begging for points are unpleasant for the student and stressful for the instructor and leave a lingering rotten taste in everyone’s mouth and is it really worth that for two percentage points out of a hundred on a midterm that was worth one-third of three-quarters of the class’s total score?

It’s possible that your homework and exam scores don’t reflect how well you know the material, and maybe you can convince your instructor of that. That’s a long shot, however, and your instructor is under no obligation to go along with you, and probably dislikes making such special exemptions. They can be administratively awkward, and giving special exemptions can be dangerous on principle: it makes it too easy to play favorites, or anti-favorites, or to appear to. Your best chance at getting such a special dispensation, though, is if you show you are really interested in the subject matter: if you’re reading about the course topics even from outside the requirements (from textbooks and journals, not from SparkNotes and study sheets); if you’re thinking about it, including problems that are like but not identical to what you’ve seen in class, on homework, or in exams; if you’re talking in appropriate forums about the material; if you are engaged with it. That’s what you need to pass this class, or to get an A, or whatever it is you are looking for exactly.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

14 thoughts on “What Do I Need To Pass This Class?”

  1. Reblogged this on nebusresearch and commented:

    I haven’t gone in for reblogging my own posts, but, I realized I have two that are somewhat timely. That’s my post about how to calculate the minimum grade you need on the final exam to get a desired final score, and then a set of tables that work out the minimum scores for people who aren’t confident they’re going to get the formula worked out right. I hope people will be patient with repetitions of these postings. This is the post with the complete formula, and instructions how to work it out, so, it’s to be used by those who felt they knew what was going on in pre-algebra and regular algebra.


  2. I had NOT read this before. It is really good! Truth be told, if students had a time machine, they would probably use it for something other than learning the course material better, but that is what they think they want.


    1. Thank you.

      I suppose what students would use a time machine for depends on who’s controlling the time machine. It might be in the possession of the tutoring department, after all, and they’d want to even out their workload over the whole term.


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