I highly recommend writing full questions to help learn content - it opens you to thinking both what is within the realm of possibility when it comes to questions, but also activates a different part of the brain. But beware - I will critique the fuck out of this.
Note, I'm not actually proof-reading your solutions, but I can see some issues for one of the show-that questions. I'll point that one out, but it's definitely worth others doing their own check of these things. (also, if you write an exam with some wrong solutions, this is *even better* for others - so if you do this in future, including some on purpose would definitely not be a bad idea.
Spoilering so people can avoid if they haven't done the exam.
1. Not bad, fairly standard. However, normally VCAA will give you numbers that come out super nice - this is going to give you some weird ones. Also, a normal equation is worth more work than 2 marks - there should be 1 for use of the derivative, 1 for the use of m1m2=-1 and 1 for the actual normal.
2. Not too bad - a somewhat wasted opportunity to not test composition domain/range stuff, which should always be asked whenever compositions, products or sums of functions are tested.
3. Fairly standard, but that "hence antidiff a cos" is unnecessary. Those questions should always be for something that cannot be anti-diffed using methods techniques - as it is, people can still get the answer mark for this even without understand integration by recognition. Also, just a nit-pick - if you're going to restrict the domain later for sketching purposes, why not just have the original function with a restricted domain?
4. This one isn't necessarily written badly - but, normal lines were already tested, so this should've been replaced with something else.
5. Same as above, we already did compositions. Also, no domain/range stuff, again. Also also, this is only true for x>0 (most index laws break down for negative bases)
6. Three for three with a repeat of transformations stuff. I know this time it's done differently (asking to do instead of asking for what did), but methods is so big you shouldn't see the same topic more than once on any given exam 1. There's definitely repeats between exams and in exam 2, but not in exam 1 - it's SO tiny.
7. Methods students should not be asked to solve a question involving sec - it is not strictly taught in methods. Yes, a lot of people know it because diffing, but it still should not be present.
8. No real issue here. You don't need to mention that a is positive real - it has to be, anyway.
9. The question seems alright, but the marks for it might be too small again. Also, related rates is normally reserved for exam 2 stuff, but presumably if you do more after you learn probability, you'd have put a probability question here, instead.
Also, a general thing for the graphs - *don't* write "axes are not to scale". You don't scale the axes, the students do, and you should always have an approrpriate scale when drawing a graph in an exam as a student. If you do not scale your axes consistently, you will lose marks for graph-sketching. Also, the bolding is pretty unnecessary in general - it's just kinda overdone, here.
Otherwise, good work - the exam does seem to be at the right difficulty, with some good throwaway marks, and some questions that'll really eat into time. You could possibly afford to get rid of one of the easier questions and put something in that'll really test students - think question 10 from last year's exam 1 type stuff. Try to make some stuff that's not just time-consuming/a lot of work, but is actually, legitimately difficult to do.
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