NCEA 3 Calculus Exam 2022, Integration, How I'd Answer

 While doing this paper I tried very hard to only use the formulae sheet provided, and to not do anything over the top, including changing the variable or advanced techniques. 

So as much as possible everything is in dt or dx. 

NCEA 3 Calculus Differentiation Exam 2022, How I'd Answer

 

Nice Video on Implicit Differentiation

https://www.youtube.com/watch?v=fIy5Wav4rok&t=622s 

NCEA 3 Calculus Exam 2022, Complex Numbers How I'd Answer

 Here is how I'd answer the complex section of the exam. 

I don't use complex numbers in my professional life as a mathematician. This means that every time I teach this, I have to teach myself all over again how to do complex analysis, going over my university calc notes. 

This is another good reason to keep clear and concise notes--you may need to use them yourself years later!

You will use complex analysis in a range of technical fields including engineering and electrical fields. 

I do use the closely related field of linear algebra all the time, and it is very likely that you'll need to use linear algebra if you go into a technical field. 

Anyway, if I made a mistake please let me know. 

NCEA 2, Calculus Exam 2022, How I'd Answer