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jakesilove

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4U Maths Question Thread
« on: January 28, 2016, 07:04:05 pm »
+12
HSC 4U MATHS Q&A THREAD

To go straight to posts from 2018, click here.

What is this thread for?
If you have general questions about the HSC 4U Maths course or how to improve in certain areas, this is the place to ask! 👌


Who can/will answer questions?
Everyone is welcome to contribute; even if you're unsure of yourself, providing different perspectives is incredibly valuable.

Please don't be dissuaded by the fact that you haven't finished Year 12, or didn't score as highly as others, or your advice contradicts something else you've seen on this thread, or whatever; none of this disqualifies you from helping others. And if you're worried you do have some sort of misconception, put it out there and someone else can clarify and modify your understanding! 

There'll be a whole bunch of other high-scoring students with their own wealths of wisdom to share with you. So you may even get multiple answers from different people offering their insights - very cool.


To ask a question or make a post, you will first need an ATAR Notes account. You probably already have one, but if you don't, it takes about four seconds to sign up - and completely free!

OTHER 4U MATHS RESOURCES

Original post.
Before you can ask a question, you'll have to make an ATAR Notes account here. Once you've done that, a little 'reply' button will come up when you're viewing threads, and you'll be able to post whatever you want! :)

Hey everyone!

A lot of you will have met me at the HSC Head Start lectures, where I lectured in 2U and 3U Maths, Physics and Chemistry.
My role on these forums is to help you. The HSC syllabus is tricky, nuanced and pretty damn huge. To help you out, I thought it would be a great idea to have a forum where you can just post questions, and myself or other forum members can post answers!

This is a community, so we want you to feel like you can post any type of 4U Mathematics question, no matter how "basic" you might think it is. Remember, IF YOU'RE HAVING TROUBLE WITH A TOPIC, THERE ARE THOUSANDS OF OTHERS HAVING THE SAME ISSUE. The best way to learn Maths is by looking through practice questions, and their associated answers. I honestly think a forum like this, and a place where I could always go to have difficult questions answered would have helped me in my HSC year.

Remember that Extension II Maths is a bloody difficult course. There will be lots of answers to the same questions, and I'll try give you the best or easiest to remember ones.

I got an ATAR of 99.80, and a mark of 93 in the 4U Mathematics course. There are similar forums for a bunch of other subjects, so make sure to take a look at them as well!
« Last Edit: April 24, 2018, 12:45:14 pm by Joseph41 »
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #1 on: February 05, 2016, 08:24:25 pm »
0
Hey Jake:

Hope you are impressed by this first ever 4 unit question of the year. I have little idea how to sketch this graph would you mind giving me a hand on this question? Thank you fam! :)

Essentially the question is asking me to sketch y = ln (1-|x|)
Thank you so much Jake!



Best Regards
Happy Physics Land
Mathematics: 96
Maths Extension 2: 93
Maths Extension 1: 97
English Advanced: 92
Physics: 95
Chemistry: 92
Engineering Studies: 90
Studies of Religion I: 98

2017 ATAR: 99.70
University of Sydney Civil Engineering and Commerce
University of Sydney Faculty of Civil Engineering Scholar
Student Representatives Council Student Housing Officer
City of Sydney Council Sydney Ambassador
University of Sydney Business School Student Mentor
Entrepreneur, Company of Year Junior Achievements Australia

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #2 on: February 05, 2016, 09:04:59 pm »
+3
Hey Jake:

Hope you are impressed by this first ever 4 unit question of the year. I have little idea how to sketch this graph would you mind giving me a hand on this question? Thank you fam! :)

Essentially the question is asking me to sketch y = ln (1-|x|)
Thank you so much Jake!

(Image removed from quote.)

Best Regards
Happy Physics Land

Hey HPL!

Glad I got a question from the Extension Two course! I really enjoyed this course, but seriously struggled with it, so would encourage anyone who needs help to post up some difficult questions (like the one you have asked!)

I'm sorry that the graphing is sort of dodgy, the software that I usually used has magically disappeared but I'll try find it again soon! Hope the answer helps!




I'm thinking of making a "Graph Sketching" Extension Two resource, but that's probably still a while off.

Jake :)
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #3 on: February 05, 2016, 09:25:12 pm »
0
Hey HPL!

Glad I got a question from the Extension Two course! I really enjoyed this course, but seriously struggled with it, so would encourage anyone who needs help to post up some difficult questions (like the one you have asked!)

I'm sorry that the graphing is sort of dodgy, the software that I usually used has magically disappeared but I'll try find it again soon! Hope the answer helps!

(Image removed from quote.)
(Image removed from quote.)

I'm thinking of making a "Graph Sketching" Extension Two resource, but that's probably still a while off.

Jake :)

Hey Jake!

Thank you so much for your help I'm really grateful towards this very elaborative answer. It took me a while to kind of understand the range part and I think it was a really good idea to use domain and range and to check whether the function is even or odd. My initial approach was kind of like trying to start off with the parent function of y = lnx and just translate it and reflect it about the x axis and then take the absolute value of the graph. Well my method didnt quite work out. But yeah I was just ignorant of the first principles of logarithmic functions and this is definitely an effective approach I can adopt in the future. Thank you very much Jake for always helping me in times of need! :D

Best Regards
Happy Physics Land
Mathematics: 96
Maths Extension 2: 93
Maths Extension 1: 97
English Advanced: 92
Physics: 95
Chemistry: 92
Engineering Studies: 90
Studies of Religion I: 98

2017 ATAR: 99.70
University of Sydney Civil Engineering and Commerce
University of Sydney Faculty of Civil Engineering Scholar
Student Representatives Council Student Housing Officer
City of Sydney Council Sydney Ambassador
University of Sydney Business School Student Mentor
Entrepreneur, Company of Year Junior Achievements Australia

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #4 on: February 05, 2016, 10:45:53 pm »
+2
Hey Jake!

Thank you so much for your help I'm really grateful towards this very elaborative answer. It took me a while to kind of understand the range part and I think it was a really good idea to use domain and range and to check whether the function is even or odd. My initial approach was kind of like trying to start off with the parent function of y = lnx and just translate it and reflect it about the x axis and then take the absolute value of the graph. Well my method didnt quite work out. But yeah I was just ignorant of the first principles of logarithmic functions and this is definitely an effective approach I can adopt in the future. Thank you very much Jake for always helping me in times of need! :D

Best Regards
Happy Physics Land

It was a really difficult question mate, so definitely don't kick yourself for not getting it!

My biggest recommendation, for a graph that you don't have any idea how to sketch, is always to PLOT INTELLIGENT POINTS! Here,you could have just tried x=1,x=2, x=3... x=-1, x=-2, x=-3.... etc. and eventually got a good idea of what the graph should be. Whilst this probably won't get you full marks, at least it will get you something!

Still, having a good approach is always better. Start with Domain/Range, think about Even/Odd, and examine important locations (approaching asymptotes etc.).

Would love you to post any other questions you're struggling with! Love you long time HPL:)

Jake
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #5 on: February 05, 2016, 10:52:43 pm »
+1
It was a really difficult question mate, so definitely don't kick yourself for not getting it!

My biggest recommendation, for a graph that you don't have any idea how to sketch, is always to PLOT INTELLIGENT POINTS! Here,you could have just tried x=1,x=2, x=3... x=-1, x=-2, x=-3.... etc. and eventually got a good idea of what the graph should be. Whilst this probably won't get you full marks, at least it will get you something!

Still, having a good approach is always better. Start with Domain/Range, think about Even/Odd, and examine important locations (approaching asymptotes etc.).

Would love you to post any other questions you're struggling with! Love you long time HPL:)

Jake

Be prepared for me to flood you with 4u questions the days before half yearly exams Jake ;) But thank you so much for your tips Jake I really appreciate it!
Mathematics: 96
Maths Extension 2: 93
Maths Extension 1: 97
English Advanced: 92
Physics: 95
Chemistry: 92
Engineering Studies: 90
Studies of Religion I: 98

2017 ATAR: 99.70
University of Sydney Civil Engineering and Commerce
University of Sydney Faculty of Civil Engineering Scholar
Student Representatives Council Student Housing Officer
City of Sydney Council Sydney Ambassador
University of Sydney Business School Student Mentor
Entrepreneur, Company of Year Junior Achievements Australia

Neutron

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #6 on: February 06, 2016, 10:35:18 pm »
0
Hey Jake!

I'm currently doing 3 sciences, 4u maths and 2u english and was planning on dropping to 10 units (I would drop biology) however, I'm slightly hesitant as this would mean every single one of my units would count. Right now, I'm behind on biology which is giving me the incentive to drop it so I wont have to invest time catching up. What are your thoughts? Since you did 12 units? Did you feel it was more beneficial? And also, what would you say is the best way to approach 4U maths and do you think it's doable for everyone? I get stumped on quite a few questions and I feel like I'm more a rote learner than an innovative thinker if that makes sense.. Also, what are your thoughts on dot point summaries for Physics and Chemistry? Necessary or nah? My school puts a lot of emphasis on it but I find that it's extremely time consuming and I don't exactly trust my own notes anyway, but I'm scared I'm disadvantaging myself by not writing them! Thanks Jake!

Neutron

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #7 on: February 06, 2016, 10:41:59 pm »
0
And also, I didn't do amazingly well in the first term, got around ranked 20th for my subjects.. What do I do? I really want to improve my ranks but have I already stuffed myself up? :(

Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #8 on: February 06, 2016, 11:44:33 pm »
+5
Hey Jake!

I'm currently doing 3 sciences, 4u maths and 2u english and was planning on dropping to 10 units (I would drop biology) however, I'm slightly hesitant as this would mean every single one of my units would count. Right now, I'm behind on biology which is giving me the incentive to drop it so I wont have to invest time catching up. What are your thoughts? Since you did 12 units? Did you feel it was more beneficial? And also, what would you say is the best way to approach 4U maths and do you think it's doable for everyone? I get stumped on quite a few questions and I feel like I'm more a rote learner than an innovative thinker if that makes sense.. Also, what are your thoughts on dot point summaries for Physics and Chemistry? Necessary or nah? My school puts a lot of emphasis on it but I find that it's extremely time consuming and I don't exactly trust my own notes anyway, but I'm scared I'm disadvantaging myself by not writing them! Thanks Jake!

Hey Neutron:

Im Jake (For sure!) Im also doing physics, chem, ext 1 and ext 2 mathematics, same as you. And to be honest, I stuffed up three assessments already in the first term so Im in the same shoe as you. But what I tell myself is that the assessment is only gonna to contribute to 5% of your RAW atar for THIS ONE SUBJECT. Perhaps you and the person that came first were 20% apart from one another, if you multiply that difference by 0.05, then really you are only losing to him by 1 atar in this subject and if you consider again this 1% might go into 0.5% after scaling and then if you consider how you have 6 subjects all together you pretty much is only 0.08% apart from that guy.... So this is what l tell myself (and it is actually true!) and this is what motivates me to try even harder for my half yearlies which would weigh 5% more.

But thats all not-so-important. I would just like to share some of my extension 2 experience with you so that I can perhaps help you out in some ways. I would list them in dot points form so that it would be easier for you to understand.

1. Do LOTS AND LOTS AND LOTS of exercises on each topic, especially for complex numbers. The outrageously strange questions they can give you in complex numbers is just frustrating, so I would have done as much past HSC questions on complex numbers as possible, you can easily find ext 2 trial papers online and do questions from there. If you just can just manage to do 10 questions everyday, imagine how prepared you will be after 239 days (THATS 2390 QUESTIONS DONE!) when HSC comes.

2. Everyone pretty much knows this first tip. But what Im going to tell you now is something people might not do: FOR ALL THE QUESTIONS THAT YOU DO NOT KNOW HOW TO SOLVE, WRITE THE ENTIRE SOLUTION DOWN AND MEMORIZE HOW TO SOLVE IT. Extension 2 is a weird sort of maths, to my perpsective. Back in the 2unit days, I would be able to solve some questions on the spot without having previously encountered it before. But when I see an unfamiliar extension 2 question, it takes me almost double or even triple the time to solve it. So through memorising questions of diverse styles, there is a higher chance you will be familiarised with the questions in your exam

3. MADE A MISTAKE? JOT IT DOWN! Collect all the mistakes you have made during both your practises and your exams, write a specific question that you have made a mistake on if you want to. Look through it at least once a week. For example, in my notes I have "cos(x) - isin(x) doesnt equal to cis(x)!" and " Simplify cis(x) answers wherever necessary"

4. The first three points are just generally how you would study for extension 2. Now let's talk about some skills for complex numbers. One of the most important thing to remember is SIN (X) is an ODD FUNCTION and COS(X) is an EVEN FUNCTION. This means that sin(-x) = -sinx and cos(-x) = cos (x). This will be very useful in complex number proofs involving de'moivre's theorem

5. Another key thing to do is to MEMORISE ALL THE COMPLEX NUMBER PROPERTIES.These are your best friends in proofs,  For example, |z| = |conjugate of z| = sqrt (x^2 + y^2), arg(conjugate of z) = -arg(z), z(conjugate of z) = |z|^2 = |conjugate of z|^2 = x^2 + y^2, z + conjugate of z = 2x, z - conjugate of z = 2iy. These are only a few of the complex properties, you can find the rest either online or in your textbooks.

6. REMEMBER THE SHAPE OF YOUR LOCUS.  This is so important. Of course, you can always work out your locus through algebraic means, but by remembering the general shape of your complex locus, you would not be required to spend as much time. Just to list a few:
- |z| = r is a circle
- |z-w| = r is the equation of a circle with the centre at w=a+ib and radius r.
- |z - z1| = |z - z2| is the equation of the perpendicular bisector of the line AB
- arg (z-z1) = x, where x is a constant, is the equation of a half-ray, starting at the fixed point z1
- arg(z-z1) - arg(z-z2) = x, 0<x<pi, is the equation of an arc of a circle on the chord AB, where A and B represent z1 and z2 respectively


7. MULTIPLYING A COMPLEX NUMBER THROUGH BY CIS(X) TURNS THE GRAPH ANTI-CLOCKWISE BY X DEGREES, and of course, multiplying a complex number through by i turns the graph by 90 degrees anti-clockwise

8. These are just some of the core tips of complex numbers, I can go into the specifics if you are willing to supply some questions? Now let's have a look at some essential tips for the topics of Graphs.
- -f(x) = reflection of graph over the x-axis
- f(-x) = reflection of graph over the y-axis
- f(x) + t = moving the graph up by t units in the y-direction
- f(x) - t = moving the graph down by t units in the y-direction
- f(x+t) = moving the graph t units to the left along x-direction
- f(x-t) = moving the graph t units to the right along x-direction
- |f(x)| = reflect everything below the y-axis over to above the y-axis
- f(|x|) = delete left hand side, reflect everything on the right over y-axis
-|y| = f(x) = delete everything on the bottom, reflect everything above x-axis over to the bottom of x-axis

And of course, if you want to sketch 1/f(x), sqrt (f(x)), [f(x)]^2 and [f(x)]^3, always draw the lines y = 1 and y = -1 and locate where f(x) = 0

In regards to the dot point summaries I would definitely recommend to do them and begin revising them 1 month before your exam and constantly revise them over time. This is something l do and I would strongly recommend you to make revision notes that would suit your own style.

Anyways I hope my tips would help you in extension 2 and best of luck!

Best Regards
Happy Physics Land
Mathematics: 96
Maths Extension 2: 93
Maths Extension 1: 97
English Advanced: 92
Physics: 95
Chemistry: 92
Engineering Studies: 90
Studies of Religion I: 98

2017 ATAR: 99.70
University of Sydney Civil Engineering and Commerce
University of Sydney Faculty of Civil Engineering Scholar
Student Representatives Council Student Housing Officer
City of Sydney Council Sydney Ambassador
University of Sydney Business School Student Mentor
Entrepreneur, Company of Year Junior Achievements Australia

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #9 on: February 07, 2016, 12:19:23 pm »
+4
Hey Jake!

I'm currently doing 3 sciences, 4u maths and 2u english and was planning on dropping to 10 units (I would drop biology) however, I'm slightly hesitant as this would mean every single one of my units would count. Right now, I'm behind on biology which is giving me the incentive to drop it so I wont have to invest time catching up. What are your thoughts? Since you did 12 units? Did you feel it was more beneficial? And also, what would you say is the best way to approach 4U maths and do you think it's doable for everyone? I get stumped on quite a few questions and I feel like I'm more a rote learner than an innovative thinker if that makes sense.. Also, what are your thoughts on dot point summaries for Physics and Chemistry? Necessary or nah? My school puts a lot of emphasis on it but I find that it's extremely time consuming and I don't exactly trust my own notes anyway, but I'm scared I'm disadvantaging myself by not writing them! Thanks Jake!

Hey Neutron!

I'll address your points one at a time.

Doing 10 units as opposed to 12

I feel like, if you do think you're quite behind on Biology, and you don't feel very confident with it, dropping it isn't the worst idea. That being said, if you feel like you can catch up (despite having to do a lot of work to get there) I would definitely recommend that. Having 12 units, rather than 10, is almost always beneficial. Between scaling, difficulty of the actual HSC etc. having a fallback is seriously a good idea. You never know what will happen throughout the year, and having only 10 units is definitely risky. However if you're 100% sure you're going to do worse in Biology that ALL of your other 10 units, dropping it may make sense.

I will say, however, that there is a direct correlation between high number of units and high marks. Usually, the highest mark students have between 12-13 units under their belt.

Approaching Extension 2 Maths

Firstly, massive thank you to HPL for writing out those tips. Seriously helpful stuff, so take note! If you've gotten through Maths so far, I think that it is definitely doable for you. Whilst it is definitely substantially more difficult than the other maths courses, once you've done practice papers enough time you can answer a paper in a "rote learner" sense rather than innovative. Really, by the HSC you'll just be spouting off answers. As to getting stumped on some questions.... If you weren't stumped of Extension 2 Maths questions, you would be some kind of savant. It is an insanely difficult course: Getting a raw mark of 60 is seriously good. I think that if you are still going, and you just spend lots of time practicing practicing practicing (taking into account HPL's tips) you will definitely get to a comfortable level of knowledge.

I never FULLY understood the course in year 12, so don't expect to. You should just be able to do SOME maths and see what happens, even if you can't get an answer out.

Dotpoint notes

I think the best way to make notes is FROM ANOTHER STUDENT'S NOTES. What I mean by that is: buy a set of notes, find a set of notes, and TAKE NOTES FROM THAT in a more succinct way. I do think it is really important to make your own notes. It just means that you have to think about your notes a little bit more, go through the content a few more times. I would really recommend it: even if it is time consuming it is really really worth it.

General "HOW DO I COPE"

It doesn't matter if your rank is not 1st or 2nd at this stage. You have so much time, never mind half-yearlies and trials, to pick up your marks. That being said, you could come 20th overall and still get a fantastic ATAR. Don't worry about ranks, just do the best you can! Seriously, it sounds cliched and stupid but ignore the stupid competition side and just do as well as possible.

Use this forum if you need support! This is a community of students, built to help one another. I hope to see you on here often!

Great question, glad you asked as this will help so many students. For anyone else interested in contributing or asking question, it would seriously help build this community exponentially. Before you can ask or answer a question, you'll have to make an ATAR Notes account here. Once you've done that, a little 'reply' button will come up when you're viewing threads, and you'll be able to post whatever you want! :)

ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

Neutron

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #10 on: February 07, 2016, 02:10:11 pm »
0
Thank you both Happy Physics Land and Jake for your amazingly comprehensive responses! They were definitely helpful but I have a question on what Jake said about the summarising another student's notes. Do you mean I highlight them and study them as though they were my own or do I continue to write my own but take theirs into consideration? Sorry for my confusion!

Neutron

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #11 on: February 07, 2016, 03:34:46 pm »
+2
Thank you both Happy Physics Land and Jake for your amazingly comprehensive responses! They were definitely helpful but I have a question on what Jake said about the summarising another student's notes. Do you mean I highlight them and study them as though they were my own or do I continue to write my own but take theirs into consideration? Sorry for my confusion!

Neutron

Hey Neutron,

Totally valid question, sorry I didn't make that clear! I would be writing you own notes, using basically only another set of notes that you know are good. What I mean is going through, highlighting important information, and summarising the notes into a set of your own.
For instance, if you had a chapter of the texbook, or a paragraph of someone else's notes, I would highlight the important parts, and summarise all the information into a single dot-point. Still have the lengthier notes on hand, but having a super succinct set of notes is really really useful for last minute study.
So, basically, my answer is do all of the above! You can never have too-few notes!

Feel free to send through example notes, or just anything you'd like us to look over. Looking forward to hearing from you!

Jake
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

xXCandyDXx

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #12 on: February 10, 2016, 09:55:28 pm »
0
Hey Jake! How's it going? Hope everything is good! Anywho, I have a question from polynomials. The question asks me to solve an equation 'given that the roots form an arithmetic series'... But my teacher hasn't really gone through series ( unless it's just saying 'plus or minus k )... Here's the question! Q6!!!!!
 

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #13 on: February 10, 2016, 10:10:48 pm »
+4
Hey Jake! How's it going? Hope everything is good! Anywho, I have a question from polynomials. The question asks me to solve an equation 'given that the roots form an arithmetic series'... But my teacher hasn't really gone through series ( unless it's just saying 'plus or minus k )... Here's the question! Q6!!!!!
 (Image removed from quote.)

Hey Candy!

Great question! Plus, you've identified the most difficult part: what the "Arithmetic series" bit actually means! Once you've taken a look through this solution, you should be able to answer any similar question. Hope that this helps!



Absolutely great question! I really encourage everyone to keep posting questions on the forum, so that everyone can benefit from this community.

Jake :)
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

Happy Physics Land

  • ATAR Notes Legend
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Re: 93 in 4U Maths: Ask me Anything!
« Reply #14 on: February 11, 2016, 12:12:53 am »
+1
Damn Jake, looks like I missed out on some delicious polynomial questions :/
Mathematics: 96
Maths Extension 2: 93
Maths Extension 1: 97
English Advanced: 92
Physics: 95
Chemistry: 92
Engineering Studies: 90
Studies of Religion I: 98

2017 ATAR: 99.70
University of Sydney Civil Engineering and Commerce
University of Sydney Faculty of Civil Engineering Scholar
Student Representatives Council Student Housing Officer
City of Sydney Council Sydney Ambassador
University of Sydney Business School Student Mentor
Entrepreneur, Company of Year Junior Achievements Australia