HSC Stuff > HSC Mathematics Advanced
Mathematics Question Thread
jakesilove:
--- Quote from: Loki98 on February 23, 2016, 08:56:39 pm ---Could someone please help with question 10a of the 2003 2u mathematics hsc paper :)
--- End quote ---
Hey Loki!
This is one of the more difficult Finance question I've seen. Once you learn the general method, however, you will have no problem! Below is my solution :)
Jake
Phillorsm:
Hey Jake, I just got my results back for my first 2u exam for year 12. It was on sequence and series, applications of calculus, integration and logs and exponentials. I got a 55/78 because I didn't finish the last section (logs and expos) of the exam. My teacher did say I smashed the first three parts though.
Firstly I wasn't super strong on logs and exponentials from the beginning, and secondly I spent way too long trying to work out a question earlier in the exam that i was sure I could get. It was a question where you had to find the equation of a parabola given its vertex and x intercepts.
Based on all this, how do you think I should move on. What can I learn from this experience, and just because I got a 70% on this exam, does that mean i'm doomed to around a 70 for the rest of my 2u math career? Like, this is the real thing now, is it still possible to recover?
Happy Physics Land:
--- Quote from: Phillorsm on February 26, 2016, 09:23:55 pm ---Hey Jake, I just got my results back for my first 2u exam for year 12. It was on sequence and series, applications of calculus, integration and logs and exponentials. I got a 55/78 because I didn't finish the last section (logs and expos) of the exam. My teacher did say I smashed the first three parts though.
Firstly I wasn't super strong on logs and exponentials from the beginning, and secondly I spent way too long trying to work out a question earlier in the exam that i was sure I could get. It was a question where you had to find the equation of a parabola given its vertex and x intercepts.
Based on all this, how do you think I should move on. What can I learn from this experience, and just because I got a 70% on this exam, does that mean i'm doomed to around a 70 for the rest of my 2u math career? Like, this is the real thing now, is it still possible to recover?
--- End quote ---
Hey Phillorsm:
Im clearly not Jake (obviously) but I just wanna to be here to tell you that getting around a 70 for your first 2u assessment is really nothing to worry about. Im not just saying this to boost you with blind confidence, Im saying this because it's too early a stage to give up. If you've ever been to one of Jake's lectures, he told us his experience not being able to finish TWO PAGES of his trial exam for maths ext 1 upon his return from the international science forum. Yet he still got a remarkable 98. So there is absolutely nothing for you to worry about.
Another real life example from me: one of my classmates for accelerated maths only got 60 percent in his first exam, and throughout the entire course his mark fluctuated around 70 percent. Yet in the end he scored a mark of 85 for his 2u mathematics. So if you look at yourself now, you are in a much better situation. You know majority of your stuff in the first three sections and you are in a better starting point than my friend! As a person who's gone through 2u hsc mathematics before, I can tell you that in the end, after the tonnes of practise papers you have done, you will begin to realise how much you have improved and how surprisingly better you will be end up doing in your hsc exam. So dont get defeated by this one exam, because to be honest, I have failed 2 of my first assessments this year as well and I found out that in the end, they only contribute to 5% (sometimes not even) of your final mark.
Ok hmmm regarding exam techniques, I think you might have been stuck on a question for too long and that may have caused your inefficiency in time management. Of course you will hear people saying to you "skip the question if its taking too long", but I do empathise with you because sometimes we are fairly certain we have seen the particular question before and it shouldnt take us much time to complete it. Unfortunately sometimes we can make a mistake that we wouldnt realise because its too trivial or the teacher could have added something extra in the question to make the question one step harder. As a general rule of thumb for me, if there is a time-consuming question that you know you definitely can solve in a multiple choice section, SKIP IT AND COME BACK LATER. Surely, if we solve the question it boosts our ego, but its not worth spending 5 minutes on a question that merely awards you with 1 mark. If a question is in the free-response section and you have looked at it for 3 minutes not knowing where you should be starting, then I would also suggest to skip it and come back later.
Logarithmic function and exponentials definitely can be hard, perhaps one of the hardest concepts in 2u. I would recommend, ofc, to do past trial papers (you can find links in atarnotes to access trial papers) and practise those questions on the topic. Also practise some past HSC questions.
Tips I would give on logarithmic functions:
- (This is especially common with difficult integration questions involving logs). KNOW YOUR YEAR 8 GEOMETRY WELL! If you look up question 16b) on 2015 paper you will realise that you have to draw a rectangle and use integration about y-axis to figure out the area encompassed by the y-axis, the scope of the rectangle and the curve first, then use your area of rectangle to subtract that area to find the area you were asked to find. This is a VERY USEFUL TECHNIQUE.
- I often struggled with the idea of changing the bases, simply because its not frequently tested. But if the teacher wants to make a hard question, you would need to change the base as a technique to approach your final answer, so be familiar with the process
- I remember in one of my earlier exams, I was asked to find the area under a log curve and I accidentally wrote 1/x as an integral of ln x. Sometimes when the exam pressure kicks in, you really can be making those sorts of mistakes. So just remember that at your level, you definitely wouldnt be required to integrate ln x, and if you did end up having to integrate ln x, you know there must be an easier way.
- There is also that kind of typical question that's involved in both integration and the integration of logarithmic functions that involve several parts. The first part would most likely ask you to differentiate and then in the second step ask you to integrate. Keep in mind if you see this sort of question in integration/integration of logs and exponentials, you know that you can use part I in part II. You can somehow manipulate what you are required to integrate in part II into the outcome of differentiation in part I and then just integrate it saying "using part I, we know that _____ is a primitive function to _____, hence the integral is ______"
I will say this much for now, but yes definitely do not give up. The game has just started and sometimes its good to be on a lower end of a ladder because it avoids arrogance and it allows you to put in more effort to do better in the next exams.
Good luck!
Best Regards
Happy Physics Land
jakesilove:
--- Quote from: Phillorsm on February 26, 2016, 09:23:55 pm ---Hey Jake, I just got my results back for my first 2u exam for year 12. It was on sequence and series, applications of calculus, integration and logs and exponentials. I got a 55/78 because I didn't finish the last section (logs and expos) of the exam. My teacher did say I smashed the first three parts though.
Firstly I wasn't super strong on logs and exponentials from the beginning, and secondly I spent way too long trying to work out a question earlier in the exam that i was sure I could get. It was a question where you had to find the equation of a parabola given its vertex and x intercepts.
Based on all this, how do you think I should move on. What can I learn from this experience, and just because I got a 70% on this exam, does that mean i'm doomed to around a 70 for the rest of my 2u math career? Like, this is the real thing now, is it still possible to recover?
--- End quote ---
Hi Phillorsm!
Firstly, I just wanted to congratulate you on your fantastic 2u result! 71% is nothing to be worried about: in fact, I would say that the fact that you were able to do so well in the sections you completed puts you in good stead for the HSC (more on that later).
Next, I want to echo the words of HPL. I absolutely agree with his advice, and won't repeat anything he has said. Specifically, the idea of skipping questions and coming back and knowing specific techniques to answer difficult questions.
The only point that I would add, when discussing ways to speed up exam completion, is DO PAST PAPERS! Do them again, and again, and again. This is the best way to speed up answering questions. The reason is that, if you can spend one minute less per question figuring out what you actually need to do (ie. by recognizing that an answer should be identical to a practice response you did the day before), you will gain so much extra time. This is extremely valuable in finishing assessment tasks!
So, my main tip for you is to just do hundreds of past papers, in timed conditions, again and again. There are never too many papers you can complete!
The fact that you know your stuff is a really good indicator of how you are going in the year. Timing can always be improved, and the more past papers you do the faster you will get in completing individual questions. Knowing the content in-depth, however, is a far more difficult task. So, congratulations for where you are at! Just keep doing past papers, and keep in mind the comments made by HPL.
Jake :)
amandali:
cos(2x+pie/6)=1/root2 -pie<=x<=pie
how do i find the angles in a simple way without getting the angles confused?
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