NCEA Level 3 Calculus 2016 | AS91578 Differentiation Full Exam Walkthrough

 In this video, I work through the 2016 NCEA Level 3 Calculus differentiation exam (AS91578 – Apply differentiation methods in solving problems) step by step.

We look at how to approach the questions, how to show the working needed for NCEA, and how the more demanding Merit and Excellence problems can be tackled. Topics appearing in this exam include: basic differentiation the chain rule product and quotient rules trigonometric differentiation exponential and logarithmic functions parametric differentiation gradients and tangents stationary points second derivatives and points of inflection interpreting derivatives related rates of change optimisation maximum and minimum problems setting up equations from unfamiliar situations mathematical proof using differentiation This video is useful if you are studying NCEA Level 3 Calculus, preparing for AS91578, revising differentiation before the external exam, or working through NZQA past papers. A good way to use the video is to attempt each question yourself first, then pause and compare your approach with the worked solution. 📚 Standard: AS91578 📈 Topic: Differentiation 🎓 Level: NCEA Level 3 Mathematics / Calculus 📝 Paper: 2016 NZQA examination ⭐ Credits: 6 External Credits For more NCEA maths, statistics, physics and chemistry tutorials, exam walkthroughs and revision resources, subscribe to Captain Calculus. More NCEA resources are also available at: Captain Calculus / NCEA Help @Captain_Calc

Year 12 and 13 Students Please Watch, the "jist" of Calculus

 Some of my old students might recognise those function machines!

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