Mathematics Question Thread

[jakesilove]

HSC MATHEMATICS 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 Mathematics 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 MATHEMATICS RESOURCES

CLICK ME!

* Free Mathematics notes
* How to Get a Band 6 in HSC Mathematics
* Mathematics Question Thread
* Compilation of solutions to HARD past HSC papers (2U)
* Mathematics MEGA THREAD
* Mathematics Challenge Marathon
* 5 Methods for Studying Mathematics
* Basic Arithmetic and Algebra in 2U: How It Can Come Back to Bite You
* Sequences and Series: Tackling the Financial Math Questions
* A Geometry Guide: Tackling Proofs in the HSC
* Plane Geometry in 2 Unit and Extension One
* Trigonometry: Part 1 (2 Unit)
* HSC Dysfunction: The Functions You'll See in 2/3 Unit
* Differentiation in HSC Mathematics: What You Need to Know!
* Integration in the HSC: What You Should Know!
* A Guide on Probability in the HSC You Probably (Definitely) Should Read
* Common Mistakes in Mathematics
* HSC Revision Videos: Mathematics
* 12 Avoidable Mistakes Students Make in Math Exams
* LaTeX Guide
* Verbs and Maths

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 2U 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.

I got an ATAR of 99.80, and a mark of 96 in the Mathematics course. There are similar forums for a bunch of other subjects, so make sure to take a look at them as well!

[liiz]

Hey Jake - I'm struggling with this question from my maths textbook: "A rectangular box is to have a square base and no top. If it's volume is 500cm³, find the least area of sheet metal of which it can be made." I'm not understanding how all this maximum and minimum stuff is applied to these kind of questions, I thought it just had to do with graphs? Thanks!!

[Happy Physics Land]

Hey Jake - I'm struggling with this question from my maths textbook: "A rectangular box is to have a square base and no top. If it's volume is 500cm³, find the least area of sheet metal of which it can be made." I'm not understanding how all this maximum and minimum stuff is applied to these kind of questions, I thought it just had to do with graphs? Thanks!!

Hey Liiz:

HEY Im jake (obviously not haha). Im a year 12 student who completed my 2u HSC mathematics course in year 11 and lm just happy to help out here. Now, this type of question is amongst one of the most difficult ones in geometrical applications of calculus, and unfortunately in HSC exams there WILL be harder ones. But don't worry, once you have practised enough, you will begin to seize some tricks to approach these questions.

Before I begin answering your question, just a few generally tips to help you answer questions like these where only one number value is provided:

BEFORE YOU DO ANYTHING, DRAW A DIAGRAM WITH LABELS
1. Highlight all USEFUL INFORMATIONS (in this case, highlight rectangular box, square base, no top, 500cm^3 and least area)
2. Appoint two variables to the unknown sides (in this case, I named the side length of the square base as x, and the height of the rectangular box as L)
3. There will be at least one number quantity in every one of these questions in 2u mathematics, so the first equation you should construct, using your name variables to construct an equation that uses the numbers provided by the question
4. Draw out the relationship between the two variables through this equation that you have constructed
5. Construct another equation using your variables and the subject that is asked for in the question (In this case, for example, we constructed an Area equation which directly relates to what we are asked to find)
6. Substitute in the equivalent expression of a variable (In this case, for example, L = 500/x^2, so we substitute any L we see with 500/x^2) to reduce the total number of values down to one, so that we can construct an equation entire out of only one variable, which then allows us to perform differentiation
7. Clean up the equation after the substitution to make life easier
8. Differentiate the equation
9. Let this derivative = 0 to find any stationary points (In an Exam, YOU MUST STATE "LET dy/dx = 0 TO FIND ANY STATIONARY POINTS, OTHERWISE MARKS MAYBE DEDUCTED!!!)
10. Solve the derivative equation and find a value for your variable which will be your stationary point
11. Test both sides to show that a local minimum/maximum occurs at your stationary points
12. Substitute your minimum value back into the area equation (or maximum value if the question asks for maximum area) to find the minimum area (or the maximum area if you substitute in the maximum value)

So here is my solution:


Hope you find my solutions clear and useful! If you are confused with anything, dont hesitate to ask!!!

Best Regards
Jacky He

[jakesilove]

Hey Jake - I'm struggling with this question from my maths textbook: "A rectangular box is to have a square base and no top. If it's volume is 500cm³, find the least area of sheet metal of which it can be made." I'm not understanding how all this maximum and minimum stuff is applied to these kind of questions, I thought it just had to do with graphs? Thanks!!

Hey Liiz! I see that HPL has already posted an answer, but I'll throw mine in as well in case any of the methodology is different. Hope it helps, and thanks for the questions!




Thanks for your post!

If anyone else wants to ask or answer questions, I would really appreciate the contribution! 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!

[Happy Physics Land]

Hey Liiz! I see that HPL has already posted an answer, but I'll throw mine in as well in case any of the methodology is different. Hope it helps, and thanks for the questions!

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

Thanks for your post!

If anyone else wants to ask or answer questions, I would really appreciate the contribution! 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!

Great work Jake, I think it was a really good idea for you to first state the equation of how to calculate the volume of the rectangular box (cant believe l forgot to include that) and to state that x does not equal to 0 which is the condition which must be met despite obvious in this case. Great combined effort and a really good question Liiz!!!

[brenden]

Great work Jake, I think it was a really good idea for you to first state the equation of how to calculate the volume of the rectangular box (cant believe l forgot to include that) and to state that x does not equal to 0 which is the condition which must be met despite obvious in this case. Great combined effort and a really good question Liiz!!!

You have the best handwriting I've ever seen.

[Happy Physics Land]

You have the best handwriting I've ever seen.

This is the best forum I have ever seen!

[liiz]

Thanks everyone for the help with the question!! It was really useful to see both solutions

[Jacqui105]

Hi,

Okay, so I've got a (possibly silly) question to ask, but I actually - GENUINELY - do not have any idea and need help:

How does one study for Maths?

I seem to have a really consistent system for each of my subjects as to approaching study in the most efficient way possible, but I can not seem to find an effective way of studying for Maths. I've tried everything I can think of. Please help.

Thank you

[jamonwindeyer]

Hi,

Okay, so I've got a (possibly silly) question to ask, but I actually - GENUINELY - do not have any idea and need help:

How does one study for Maths?

I seem to have a really consistent system for each of my subjects as to approaching study in the most efficient way possible, but I can not seem to find an effective way of studying for Maths. I've tried everything I can think of. Please help.

Thank you

Hey Jacqui105!

Firstly, absolutely not a silly question. I guarantee a large portion of the students reading this would be wanting to ask something similar.

This is a huge question that demands a huge response. We are planning a resource specifically answering this exact question for you, so stay tuned! 

In the meantime, I'll direct you to this guide I wrote a little while ago that has helped quite a few people. It contains a whole bunch of tips for everything Math related, including study tips!

Good luck 

[caninesandy]

Hello HSC Math geniuses
I have a math differentiation and integration assessment soon and was just wondering if you could help me on how to set answers out, especially with lengthy questions. Here is one question I have recently, recived the correct answers but was not sure on how to structure my answer exactly:
A magazine advertisement is to contain 50cm^2 of lettering with clear margins of 4cm each at the top and bottom and 2cm at each side. Find the overall dimensions if the total area of the advertisement is to be a minimum.
Thank you so much for your help!!!!!!
 

[jakesilove]

Hello HSC Math geniuses
I have a math differentiation and integration assessment soon and was just wondering if you could help me on how to set answers out, especially with lengthy questions. Here is one question I have recently, recived the correct answers but was not sure on how to structure my answer exactly:
A magazine advertisement is to contain 50cm^2 of lettering with clear margins of 4cm each at the top and bottom and 2cm at each side. Find the overall dimensions if the total area of the advertisement is to be a minimum.
Thank you so much for your help!!!!!!
 

Hey Caninesandy!

This was actually quite a difficult question, which required me to draw the picture in order to figure out what was going on! My general tips for these questions are

1. Figure out the equations that you have
2. Sub in the equations, so that you have a differentiatable one
3. Differentiate, and find the required minimum
4. Sub the found value into the original, to find the solution.

Here is the solution I came up with. Hope it helps! This is exactly how I would set out any question similar to this




Jake

[Happy Physics Land]

Hey Caninesandy!

This was actually quite a difficult question, which required me to draw the picture in order to figure out what was going on! My general tips for these questions are

1. Figure out the equations that you have
2. Sub in the equations, so that you have a differentiatable one
3. Differentiate, and find the required minimum
4. Sub the found value into the original, to find the solution.

Here is the solution I came up with. Hope it helps! This is exactly how I would set out any question similar to this

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

Jake

Sorry to challenger your authority jake, but did you mean h = 50/(x-4) + 8??? (Is it a transcription error?)

[jamonwindeyer]

Sorry to challenger your authority jake, but did you mean h = 50/(x-4) + 8??? (Is it a transcription error?)

Definitely a transcription error HPL 

[jakesilove]

Sorry to challenger your authority jake, but did you mean h = 50/(x-4) + 8??? (Is it a transcription error?)

Yep, definitely an error there, thanks for pointing that out! I'll fix up the proof and update the answer in a second.

Jake