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

NCEA 2024 Calculus, Differentiation, How I'd Answer

 Pretty meh exam this one. Nothing too shocking or easy or hard. 

Not a lot of rates of change or parametric stuff this year. 

Again I've tried to limit myself to what a Casio calculator can do, and to techniques taught at year 13. As is the case with most things in calculus, there's often many ways to get the right answer

2024 NCEA Calculus, Complex Numbers How I'd Answer

 As always I limited myself to a trusty Casio calculator and used only techniques taught at year 13. 

Some of these questions could have been answered differently using more advanced techniques. 

I'm not a big fan of complex number analysis, I don't use them in my professional life as a mathematician. 

2024 NCEA Calculus Integration

 How I'd answer. 

This was a really long part (14 pages) for something supposed to take 60 minutes. Some of the question were quite tasty, so you'd be in trouble if you chose the wrong option when answering. 

As always I've used a trusty Casio calculator and limited myself to methods taught at year 13, so no use of integration by parts etc

NCEA 3 Calculus Exam 2023, Differentiation: How I'd Answer

 I've used the tables and formula given whenever possible. 

All in all a pretty fair introduction to differential calculus exam. Could possibly place students with only 1 hour to answer under a bit of time pressure, especially with the last question, but pretty good.