Mathematics Question Thread

[K9810]

Hey!

Can you please explain how you know whether the points are included/excluded?

Thanks!

[jamonwindeyer]

Hey!

Can you please explain how you know whether the points are included/excluded?

Thanks!

Hey! It's because the inequality for that bottom line is strict: \(y>4\), not \(y\ge4\). So, points on that line aren't included in the region

[chloeemadavis]

Hi!
Would someone be able to help me with a question?
1/ Evaluate the integral between 1 and 0 of 5/square root (e^x) dx
Thankyou!!

[Bubbly_bluey]

Hi!
Would someone be able to help me with a question?
1/ Evaluate the integral between 1 and 0 of 5/square root (e^x) dx
Thankyou!!

Hey! so that question looks pretty nasty with its root, so lets change that 5th root into index.
Just for reference: sqroot (x)= x^1/2
                              So: 5throot(x) = x^1/5
Now you have an intergation of e^x/5.
Intergation e^x/5 dx = (e^x/5) / (1/5)
now you can sub in your borders. Hope it makes sense

[jamonwindeyer]

Hi!
Would someone be able to help me with a question?
1/ Evaluate the integral between 1 and 0 of 5/square root (e^x) dx
Thankyou!!

Welcome to the forums Chloe! Hopefully I've interpreted your question correctly:



Hopefully this makes sense!! Feel free to shoot any other questions our way

[Leah_Mer]

Hey there, I'm wondering about school assessment marks and how badly they impact your final mark in the hsc! For adv maths, I'm ranked second in my class with one other above me who is really great at maths and we're usually a few marks from each other and always above 90%, however, in the half yearly I absolutely bombed the exam and am expecting a mark of about 30%-40% at the MOST (it was weighted 30%). What I'm wondering is, is it possible to get a band 6 with a school assessment mark of like 75? Whats the lowest raw school mark that still allows for a band 6 in maths, if you were to smash the HSC exam?

[jamonwindeyer]

Hey there, I'm wondering about school assessment marks and how badly they impact your final mark in the hsc! For adv maths, I'm ranked second in my class with one other above me who is really great at maths and we're usually a few marks from each other and always above 90%, however, in the half yearly I absolutely bombed the exam and am expecting a mark of about 30%-40% at the MOST (it was weighted 30%). What I'm wondering is, is it possible to get a band 6 with a school assessment mark of like 75? Whats the lowest raw school mark that still allows for a band 6 in maths, if you were to smash the HSC exam?

Hey Leah! Welcome to the forums!

You should give this guide a read - It goes through the entire process of how your marks are calculated. Essentially, you could get a Band 6 with a school assessment mark of 30. The mark is irrelevant - It's the rank that matters, and even that matters far less than a strong performance in the HSC exam. The guide contains the details, but the answer to your question is - Yes, you absolutely can!

A poor half yearly result isn't the end of the world - I got one, and it does suck, but it can be the motivator that pushes you to work harder and do really well in the more important exams at the end of the year! keep your chin up, learn from your mistakes - This is just a bump in the road

[Leah_Mer]

Hey Leah! Welcome to the forums!

You should give this guide a read - It goes through the entire process of how your marks are calculated. Essentially, you could get a Band 6 with a school assessment mark of 30. The mark is irrelevant - It's the rank that matters, and even that matters far less than a strong performance in the HSC exam. The guide contains the details, but the answer to your question is - Yes, you absolutely can!

A poor half yearly result isn't the end of the world - I got one, and it does suck, but it can be the motivator that pushes you to work harder and do really well in the more important exams at the end of the year! keep your chin up, learn from your mistakes - This is just a bump in the road

Thank you so much! Very good reassurance to hear that and will definitely be more motivated for maths study after this! Also thanks for getting back to me so quickly

[laurenf58]

Could I have some help with these questions please?

Thanks!

[jamonwindeyer]

Could I have some help with these questions please?

Thanks!

Hey! So even functions are symmetrical about the y-axis, so draw a mirrored copy of the curve on the other side of the axis! Just like, say, the parabola \(y=x^2\) is the same on both sides of the y-axis because it is even

Odd functions have rotational symmetry, meaning you spin the curve 180 degrees around the origin to get the other side of the curve! To picture this, think the graph of \(y=x^3\) (see here) see how you can get the bottom left by spinning the top right around to the opposite corner? That's what you'll do for your curve

Hope that helps!

[cxmplete]

Hi,
Can someone please explain how to do exponential growth and decay questions (from ACPW)?

[jakesilove]

Hi,
Can someone please explain how to do exponential growth and decay questions (from ACPW)?

Could you give us an example of a question we can help you with?

[cxmplete]

question 15 from this paper https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/exams/2015-hsc-maths.pdf

[jakesilove]

question 15 from this paper https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/exams/2015-hsc-maths.pdf

Cool! So, the first part is pretty straight forward; we just sub the value of C that they gave us into the differential equation.



as required. Now, we are given that the initial quantity of caffeine is 130 mg. So, we sub in t=0 to find the value of A.






Then, to find the amount of caffeine in the body after 7 hours, we just sub in t=7



Finally, we want to find the time taken for the amount of caffeine in Lee's body to half. Thus, we want C to equal 130/2=65mg. So,

[jakesilove]

Hello, I am new to this forum and am not sure if this has been posted or not.

This is from one of my schools past HSC trial paper. I need help with the whole question except for c)  (I can do it myself after i find all the other answers)

(Image removed from quote.)

Thank you cuties!

Hey! So, the equation we have been given is



and we want to rewrite it in standard form. First, we need to complete the square, as the final answer is in the form (x-h)^2. So,



And that's our answer! We got



Great! Now, we want to calculate the roots of the function. The easiest way of doing this is the quadratic equation.



Easy as Now, with all of the above information (and subbing in x=0, y=0 etc.) you can easily sketch the graph!

For the last part, we essentially want to know where f(x) is ABOVE the x-axis. We know the function is a positive parabola, so this will occur to either side of the roots (ie. to the left of the first x intercept, and to the right of the second x intercept). This will become super obvious once you draw the sketch