Addition of Ordinates/Sums and Products of Functions

[TigerMum]

I'm currently going through the exercises for 3/4 Methods for next year and I've come across the exercises on sums and products of functions and addition of ordinates. (1D in Cambridge.) I understand how it works and I don't have too much trouble with the concept, I just find addition of ordinates to be really tedious, often inaccurate and annoying to do. I'm just wondering, are sums of functions ever featured on VCAA exams? If so, is there a more effective way of doing these? (I am aware of good methods using calculus to find asymptotes, stationary points etc., wondering if there are any better algebraic methods.)

[Tau]

I'm currently going through the exercises for 3/4 Methods for next year and I've come across the exercises on sums and products of functions and addition of ordinates. (1D in Cambridge.) I understand how it works and I don't have too much trouble with the concept, I just find addition of ordinates to be really tedious, often inaccurate and annoying to do. I'm just wondering, are sums of functions ever featured on VCAA exams? If so, is there a more effective way of doing these? (I am aware of good methods using calculus to find asymptotes, stationary points etc., wondering if there are any better algebraic methods.)

I don’t remember ever seeing a product of functions being required to sketch by hand, but certainly addition of ordinates. The 2018 exam had such a question.

Unfortunately, doing it by hand is exactly as you say - tedious and error prone. However, I would imagine VCAA is looking for a sufficiently good enough graph showing an understanding of asymptotic behaviour, endpoints etc. - but not necessarily perfect.

So I wouldn’t stress too much - just give it your best shot and take your time!