4U Maths Question Thread

[RuiAce]

Question 24 is insane

Nor is it useful to do and not worth the time and effort.

A small remark on part b) though - the radius will approach infinity, and the locus ends up being a straight line. Uncoincidentally, that straight line is the perpendicular bisector of the interval joining \(z_1\) and \(z_2\).

If you're interested in the basic ideas behind the geometric method, refer to the Wikipedia page linked.

[clovvy]

Nor is it useful to do and not worth the time and effort.

A small remark on part b) though - the radius will approach infinity, and the locus ends up being a straight line. Uncoincidentally, that straight line is the perpendicular bisector of the interval joining \(z_1\) and \(z_2\).

If you're interested in the basic ideas behind the geometric method, refer to the Wikipedia page linked.

Is this question beyond the course?

[RuiAce]

Is this question beyond the course?

No.

On the other hand, it takes far too long to do and would essentially be an 8-mark question in the HSC, and thus virtually pointless.

[aadharmg]

I'm really struggling with this, but how can I express 2cis(5pi/12) - 2cis(3pi/4) in mod-arg form? I don't know how to simplify this further. Please help.

[RuiAce]

I'm really struggling with this, but how can I express 2cis(5pi/12) - 2cis(3pi/4) in mod-arg form? I don't know how to simplify this further. Please help.

It's easily doable once we decide to use compound angles but I'm very sceptic about how you had a \( \frac{5\pi}{12} \) in there. Was this the entire question? (If not, send the previous parts.)

[aadharmg]

It's easily doable once we decide to use compound angles but I'm very sceptic about how you had a \( \frac{5\pi}{12} \) in there. Was this the entire question? (If not, send the previous parts.)

This is the entire question. I was able to cruise through the first two parts. For the third part I tried to simplify cis5pi/12 to normal x + iy form and do the same for the other complex number, then add them and work backwards to get the total mod-arg form but that led me down an extremely complicated path. Must have done something wrong on the way.

[RuiAce]

This is the entire question. I was able to cruise through the first two parts. For the third part I tried to simplify cis5pi/12 to normal x + iy form and do the same for the other complex number, then add them and work backwards to get the total mod-arg form but that led me down an extremely complicated path. Must have done something wrong on the way.

Carefully note the negative. This is because we're doing a clockwise rotation. If the rotation were anticlockwise, then we'd still use \( +\frac\pi3 \).
\begin{align*}z_2 - z_1 &= z_2 \left( \cos \frac\pi3 + i \sin \frac\pi3 \right)\\ &= 2\left( \cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12} \right)\left( \cos \left(-\frac\pi3\right) + i\sin \left(-\frac\pi3\right) \right)\\ &= 2 \left( \cos \frac\pi{12} + i\sin \frac\pi{12} \right)\end{align*}
Note that there is a slight subtlety in that \(z_2-z_1\) actually points from \(z_1\) to \(z_2\). This contributes to why the rotation is clockwise.

[aadharmg]

Carefully note the negative. This is because we're doing a clockwise rotation. If the rotation were anticlockwise, then we'd still use \( +\frac\pi3 \).
\begin{align*}z_2 - z_1 &= z_2 \left( \cos \frac\pi3 + i \sin \frac\pi3 \right)\\ &= 2\left( \cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12} \right)\left( \cos \left(-\frac\pi3\right) + i\sin \left(-\frac\pi3\right) \right)\\ &= 2 \left( \cos \frac\pi{12} + i\sin \frac\pi{12} \right)\end{align*}
Note that there is a slight subtlety in that \(z_2-z_1\) actually points from \(z_1\) to \(z_2\). This contributes to why the rotation is clockwise.

OHHHH. Okay that makes a lot more sense. I just

Carefully note the negative. This is because we're doing a clockwise rotation. If the rotation were anticlockwise, then we'd still use \( +\frac\pi3 \).
\begin{align*}z_2 - z_1 &= z_2 \left( \cos \frac\pi3 + i \sin \frac\pi3 \right)\\ &= 2\left( \cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12} \right)\left( \cos \left(-\frac\pi3\right) + i\sin \left(-\frac\pi3\right) \right)\\ &= 2 \left( \cos \frac\pi{12} + i\sin \frac\pi{12} \right)\end{align*}
Note that there is a slight subtlety in that \(z_2-z_1\) actually points from \(z_1\) to \(z_2\). This contributes to why the rotation is clockwise.

Ohhhhh. Okay that makes a lot more sense. I guess I never saw it in terms of the rotations but kept thinking about the expression algebraically. Thank you so much!

[mxrylyn]

This is not so much a maths Q as it is an advice Q.

I have been studying mx2 for an exam on wednesday. The last 4 days i have spent 8 hours a day on time set aside to study the four topics i get tested on (complex #'s, polynomials, conic and graphs).

Nothing is clicking and i cant do even the esiest of questions (apart from in complex #'s) . I dont want to drop the subject but i know im going to fail, and i hate failing.

Does anyone have any tips on a new way to apprach study for this subject? (My test is on tuesday so i only have one more day to study for it, its also worth 30% of my grade)

[jakesilove]

This is not so much a maths Q as it is an advice Q.

I have been studying mx2 for an exam on wednesday. The last 4 days i have spent 8 hours a day on time set aside to study the four topics i get tested on (complex #'s, polynomials, conic and graphs).

Nothing is clicking and i cant do even the esiest of questions (apart from in complex #'s) . I dont want to drop the subject but i know im going to fail, and i hate failing.

Does anyone have any tips on a new way to apprach study for this subject? (My test is on tuesday so i only have one more day to study for it, its also worth 30% of my grade)

Hey!

If you're doing 4U maths, that means you're good at maths. If you get the complex numbers section, then that's a really good start to understanding the rest of the 4U maths curriculum.

The fact is that 4U is totally different to every other HSC course. Usually, you'll be walking into exams knowing close to 100% of the content you'll be assessed on. Sure, you'll need to work out how exactly to answer particular questions, but for the most part you're just regurgitating.

4U is nothing like that. When you study 4U maths, you resign yourself to never being quite sure if you'll be able to answer ANY questions, or even understand what the question is getting at. It's a hard bloody subject, no doubt about it. Everyone finds it freakin' difficult, so just know that you're not alone.

Past papers, and looking at the answers to questions and trying to establish patterns for particular classes of questions, is really the best way to study in my opinion. Once you have a basic grasp of the content itself, just do a billion past papers. It sounds like you're doing that at the moment, and it doesn't feel like it's sinking in. However, I promise you that it is helping, even if only a little bit per question.

My advice at this point is to think about the TYPES of questions you'll be getting in your exam, and writing out a brief 'structure' to answer such a question. This is possible for topics like conics and graphs. Failing that, you could even just write out a list of tips and techniques you pick up from the answers to past questions. It's like developing a 'cheat sheet', which you can use to do past papers and make your life a whole lot easier.

Everyone struggles with 4U, even those ridiculously good at Maths. It sucks to feel the way you're feeling, but honestly I'm 100% sure you're better than you think you are. Just keep slugging away, and do your best to answer every question in your exam. Seriously good luck in your study!

[clovvy]

Hey!

If you're doing 4U maths, that means you're good at maths. If you get the complex numbers section, then that's a really good start to understanding the rest of the 4U maths curriculum.

The fact is that 4U is totally different to every other HSC course. Usually, you'll be walking into exams knowing close to 100% of the content you'll be assessed on. Sure, you'll need to work out how exactly to answer particular questions, but for the most part you're just regurgitating.

4U is nothing like that. When you study 4U maths, you resign yourself to never being quite sure if you'll be able to answer ANY questions, or even understand what the question is getting at. It's a hard bloody subject, no doubt about it. Everyone finds it freakin' difficult, so just know that you're not alone.

Past papers, and looking at the answers to questions and trying to establish patterns for particular classes of questions, is really the best way to study in my opinion. Once you have a basic grasp of the content itself, just do a billion past papers. It sounds like you're doing that at the moment, and it doesn't feel like it's sinking in. However, I promise you that it is helping, even if only a little bit per question.

My advice at this point is to think about the TYPES of questions you'll be getting in your exam, and writing out a brief 'structure' to answer such a question. This is possible for topics like conics and graphs. Failing that, you could even just write out a list of tips and techniques you pick up from the answers to past questions. It's like developing a 'cheat sheet', which you can use to do past papers and make your life a whole lot easier.

Everyone struggles with 4U, even those ridiculously good at Maths. It sucks to feel the way you're feeling, but honestly I'm 100% sure you're better than you think you are. Just keep slugging away, and do your best to answer every question in your exam. Seriously good luck in your study!

I agree, 4U is totally different, even if you know the contents well they can somehow chuck in questions that are unpredictable at times....  Me personally going through past papers I have seen LOTS of unpredictable questions for the topics that I am currently doing...

Contrary to public opinion of 4U students in general, my basics are actually very very poor and not up to scratch when I start my hsc, so that also causes me to struggle more as well.. Nonetheless I did enjoy the subject

[RuiAce]

Hey!

JAKE IS ALIVE.

[mxrylyn]

Hey!

If you're doing 4U maths, that means you're good at maths. If you get the complex numbers section, then that's a really good start to understanding the rest of the 4U maths curriculum.

The fact is that 4U is totally different to every other HSC course. Usually, you'll be walking into exams knowing close to 100% of the content you'll be assessed on. Sure, you'll need to work out how exactly to answer particular questions, but for the most part you're just regurgitating.

4U is nothing like that. When you study 4U maths, you resign yourself to never being quite sure if you'll be able to answer ANY questions, or even understand what the question is getting at. It's a hard bloody subject, no doubt about it. Everyone finds it freakin' difficult, so just know that you're not alone.

Past papers, and looking at the answers to questions and trying to establish patterns for particular classes of questions, is really the best way to study in my opinion. Once you have a basic grasp of the content itself, just do a billion past papers. It sounds like you're doing that at the moment, and it doesn't feel like it's sinking in. However, I promise you that it is helping, even if only a little bit per question.

My advice at this point is to think about the TYPES of questions you'll be getting in your exam, and writing out a brief 'structure' to answer such a question. This is possible for topics like conics and graphs. Failing that, you could even just write out a list of tips and techniques you pick up from the answers to past questions. It's like developing a 'cheat sheet', which you can use to do past papers and make your life a whole lot easier.

Everyone struggles with 4U, even those ridiculously good at Maths. It sucks to feel the way you're feeling, but honestly I'm 100% sure you're better than you think you are. Just keep slugging away, and do your best to answer every question in your exam. Seriously good luck in your study!

Hey,
I'd like to thank you so so so SO much for your advice.
I'm the only student in my Mx2 class and by the time I posted this I had already texted my teacher to tell him I didn't want to do the exam (because I'm dramatic af).
I ended up taking a break for the night and focusing on consolidating what i knew before trying to learn extra stuff and i eneded up with 80%, which is not where i wanted to be, but i got 40% last term to its a definite step forward.

THANK YOU!

[radnan11]

I don't understand what part b is asking for

[RuiAce]

I don't understand what part b is asking for

Suggestions regarding what its asking: Draw the line through the point P and the focus S. Let P' be where that line meets the ellipse again.

Then PP' is a focal chord. Now show that the tangents from P and from P' intersect on the directrix.

(I haven't attempted this question myself yet - no time)