Hey guys i was wondering how to effectively study maths in the sense that i do past hsc papers and review my mistakes but i feel like it isnt necessarily improving my maths skills. Like even doing maths everyday i manage to forget small details and concepts of questions, im not sure how to explain it but an example would be like one of my maths exams i did well in, when i sat the same exam again 2 months later i manage to forget how to do some of the questions despite doing at least 30mins to 2 hours of maths everyday.
Also, when a question asks for maximum velocity e.g attached how would i do part (ii)
Thanks
Hey Deng! To address your question first, the answer is to differentiate! We seek a maxima for the velocity function, so:
Any subsequent values will be irrelevant because they will give the same answer. Test those values in the original function:
Clearly, the second is larger, and you can use typical tests to deduce that there is a maxima at t equal to pi.
Note that you could, in this case, do this conceptually. A cosine function will always range between -1 and 1, and so, a -2cost function will always range between -2 and 2. Pick the case which maximises velocity, and you get the same answer as above:
As for your study dilemma, let me ask you something. When you do those papers and forget concepts, when was the last time you had studied that
specific topic, rather than Mathematics in general? Often, if you haven't done something in a while, you'll mess things up. I do it all the time if/when I revisit old math concepts. Hell, not just math, it applies to pretty much everything (writing a bit of code in a coding language you've not used in ages, or driving a manual after a year of driving an auto, for example). Your brain
will forget things, are you consistently revising the old concepts?