Test #1- Solutions and grading

Below, I’ll link to a scan of my own solutions for your test. They’re not super detailed, but this paper would have received full credit (but if you catch an error, uh, let me know). You can use these to compare to your own tests, which were returned to you today, and to the mystery person’s test that you’ll be grading for next week.

Rough grading guidelines:

Please email me (kpoirier@citytech.cuny.edu) the overall grade for the test you’re grading as a percent by Sunday night, March 30. (I don’t care how late, I just want all the grades by the time I wake up on Monday.)

I can add details to the posted solutions as necessary (likely as comments on this post), so let me know if you have any questions about a particular solution that you’re assigning a grade for. You can email me a photo or scan of the solution if you like, or just post a comment here.

• For 5-point questions, if you can see that the person mostly has the right idea, start at 5 points and deduct 1 point for each minor error.
• For 5-point questions, if you can’t tell what’s happening (if it looks like the person may not have the right idea) start at 0 and add 1 point for each statement that is correct and relevant. You’ll have to read these solutions carefully because sometimes a person has just answered a question correctly in an unconventional way, and really deserves full credit. Ask me if you’re unsure.
• Question 3(a) is worth 3 points. I expect everyone will get full credit, but you can deduct a point if you catch a small error.
• Question 3(b) is worth 2 points. If someone answers “yes” and gives an appropriate , then they should receive full credit. If the person answers “yes” they should receive one point but you should check to make sure the person is answering the correct question…this was something a few people had trouble with on the in-class test.
• Question 4 is worth 10 points. To have the right idea here, the answer should include the appropriate use of the chain rule, product rule, and quotient rule (all applied in the right order). It’s easy to make minor errors here, so check everything that’s written carefully). Deduct 1 point for each such error.
• For question 4, If it looks like the person has messed up using the chain rule, product rule, or the quotient rule…or if it’s not clear how they’ve put the components together…then you can start at 0 points and add 1 point for each derivative that is correct and relevant. (For example, if all the person has written is , they’d get 1 point out of 10.)
• Question 5(a) is worth 3 points. For full credit, the graph should look just like the one in the solutions, except it may be shifted up or down. For 2 points, the graph should have roughly the right shape. It’d be tough to earn 1 point for this question…perhaps if the graph has the right shape in one region.
• Question 5(b) is worth 2 points. The answer is “yes,” since if you shift the graph of up or down, you won’t change its derivative. For full credit, the solution should say something like this. Again, on the in-class test that I graded, a number of people seemed to be answering a different question. Certainly, if you start with and are asked to graph , then there’s only one answer. However this question gives you and asks you for . Assign 1 point out of 2 if the word “yes” is there with nothing else. Assign 0 if the person seems to be answering a different question, or if their answer is “no.”
• Questions 6(a) and 6(b) were probably the trickiest on the test. That’s why they’re not worth 5 points each, but only 3 and 2 respectively. The function is defined piecewise but it turns out to be both continuous and differentiable at .  You can see in the solutions that I used the squeeze theorem for (a) and (b), but this is not the only way to see continuity and differentiability. I’m interested in hearing how people answered these questions on the extra-credit assignment. To receive full credit, the argument should do a good job of convincing you. Especially if you didn’t get this question right yourself, or if you solved it in a way that’s different from the solution you’re grading…read it carefully. There may be lots of ways to assign partial credit. Let me know if you’re not sure what to do here.
• Question 7 is worth 10 points. Deduct 2 points if the graph fails the vertical line test, and deduct 1 point for each property (a) through (h) that the graph fails. There are lots and lots and lots of correct graphs, so ask if you’re unsure.
• Question 8 is worth 5 points total; 1 for each part. The answers don’t need justification, but I included some in my own solutions.
• Question 9(a) (the extra-credit question) is worth 1 point. The answer must look exactly like the one in the solutions.
• Question 9(b) (extra-credit) is worth 4 points. There are different ways to be correct here. If someone has done something that’s wildly different than what’s in the solutions and you’re unsure if it’s correct or not, let me know.

Test1Solutions