Congrats on completing the cylinder challenge! I'll do my best to give you useful feedback so that you can improve.
Starting with your cylinders around a random axis, overall you've done a good job of varying the foreshortening over the set (something which most students forget to do) there are a few points that you should review.
First I notice that you tend to double up some lines on the side of your cylinders. This suggests that while you may be applying the principles of markmaking and the ghosting method from Lesson 1 in part, you are allowing yourself to try to correct mistakes, or you're drawing marks automatically. You should not be. Each mark should employ the ghosting method (which I do see signs of), but that means that every stroke should be the result of planning and preparation, followed by a confident execution. If it's wrong, then it's wrong - but don't correct it, as this builds the impression in our minds that corrections are a valid course of action. This in turn can make us less likely to view the problem as being how we're thinking through it in the planning phase, which is where the real issue lies.
This ties into the first point but I'm also seeing that you tend to only draw through your ellipses only once while at other times you draw through them twice. The ones where you draw through them twice look very confident while the ones where you draw only one ellipse looks more wonky and unconfident. Therefore I suggest that you stick to drawing through them 2-3 times.
Finally I suggest that you review the notes on the minor axis and "folding the ellipse in half" as at times your error checking lines do not cut the ellipse in half
Continuing onto your cylinders in boxes, overall you've done pretty decently here, although there are some points to pay closer attention to. This exercise is really all about helping develop students' understanding of how to construct boxes which feature two opposite faces which are proportionally square, regardless of how the form is oriented in space. We do this not by memorizing every possible configuration, but rather by continuing to develop your subconscious understanding of space through repetition, and through analysis (by way of the line extensions).
Where the box challenge's line extensions helped to develop a stronger sense of how to achieve more consistent convergences in our lines, here we add three more lines for each ellipse: the minor axis, and the two contact point lines. In checking how far off these are from converging towards the box's own vanishing points, we can see how far off we were from having the ellipse represent a circle in 3D space, and in turn how far off we were from having the plane that encloses it from representing a square.
In being as fastidious as you have been in applying the line extensions as instructed, I can see that you've been giving yourself ample opportunity to assess where your approach could be adjusted to bring those convergences together from one page to the next. As a result, your awareness of those proportions have improved, and while there is of course still plenty of room for improvement, you should be well equipped to tackle the related issues that arise as we tackle Lesson 6.
Finally I'll end the critique with a few points on the boxed cylinders
First, the same issue with the ellipses and general linework appear here too, so that would be the area where you can improve the most. I suggest you also be more attentive when applying the error checking to the ellipses as they have the same issue of not cutting the ellipse in half as the cylinders around a random axis
Second, I notice that you put X's down on the page for lines that were diverging rapidly and while it's good that you notice your errors the "X's" don't really tell you how to fix it. All they do is highlight the error and not much more. If you still want to use the X's then use them in conjunction with words that tell you how to adjust so that you can pay more attention to that specific issue if it keeps coming up. For example you could write "more to the left/right" for a line. By telling yourself what to do / how to fix the issue you can focus on that specific issue to fix it faster.
That's about it, overall you've done a good job and have done the exercise correctly. The main thing to work on would be the confidence of your ellipses and making sure you don't double up lines.
Next Steps:
Lesson 6
Like the Staedtlers, these also come in a set of multiple weights - the ones we use are F. One useful thing in these sets however (if you can't find the pens individually) is that some of the sets come with a brush pen (the B size). These can be helpful in filling out big black areas.
Still, I'd recommend buying these in person if you can, at a proper art supply store. They'll generally let you buy them individually, and also test them out beforehand to weed out any duds.
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