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March 29, 2024, 10:06:53 pm

Author Topic: 3U Maths Question Thread  (Read 1230638 times)  Share 

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jakesilove

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Re: 3U Maths Question Thread
« Reply #1725 on: March 27, 2017, 09:29:08 am »
0
Well, the standard trick is to express

then


Generally, this is thought to be outside of the 3U curriculum. However, the working above is absolutely correct!
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dux99.95

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Re: 3U Maths Question Thread
« Reply #1726 on: March 27, 2017, 03:16:08 pm »
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Well, the standard trick is to express

then


Thanks for the other q :)
for this ^ will the answer by 1/5 a^5x? Apparently u just bring the power down


how do you solve the attached pic?
Another q - maths test tomorrow - highly unprepared. In terms of grades wise is it better to pull an all nighter or sleep? :L





Mahan

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Re: 3U Maths Question Thread
« Reply #1727 on: March 27, 2017, 03:27:13 pm »
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Thanks for the other q :)
for this ^ will the answer by 1/5 a^5x? Apparently u just bring the power down


how do you solve the attached pic?
Another q - maths test tomorrow - highly unprepared. In terms of grades wise is it better to pull an all nighter or sleep? :L
I fixed my post so you can see the full solution. I would recommend to not stay late.
the first line says you what the roots are, where the graph cuts the y-axis.
Combining second, third and last line you can conclude x= 1 is minimum. because y' =0 but y'' > 0.
Combining second and third line you get that at x=-1 you have a horizontal inflexion point, since y' = 0 and y'' = 0.
from third line you know at x=0 you have a non-horizontal inflexion point. y'' = 0
What you are left to do is to draw them.
Be careful of concavity from -1 to 0 the graph is concave down and the rest is concave up, expect the stationary points and the inflexion points.

Good luck in your exam! :)
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dux99.95

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Re: 3U Maths Question Thread
« Reply #1728 on: March 27, 2017, 06:33:03 pm »
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I fixed my post so you can see the full solution. I would recommend to not stay late.
the first line says you what the roots are, where the graph cuts the y-axis.
Combining second, third and last line you can conclude x= 1 is minimum. because y' =0 but y'' > 0.
Combining second and third line you get that at x=-1 you have a horizontal inflexion point, since y' = 0 and y'' = 0.
from third line you know at x=0 you have a non-horizontal inflexion point. y'' = 0
What you are left to do is to draw them.
Be careful of concavity from -1 to 0 the graph is concave down and the rest is concave up, expect the stationary points and the inflexion points.

Good luck in your exam! :)


Omg thanks heaps!! that helped :)

how do you solve q like the one attached? Im concerned about part iv)

RuiAce

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Re: 3U Maths Question Thread
« Reply #1729 on: March 27, 2017, 06:34:28 pm »
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Omg thanks heaps!! that helped :)

how do you solve q like the one attached? Im concerned about part iv)
iv is pretty straightforward to me

To find g(-2) just sub into the equation you were given at the start to get 4/3
Then if you need g^-1(4/3) you use the equation that you found in part ii), whatever it was

dux99.95

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Re: 3U Maths Question Thread
« Reply #1730 on: March 27, 2017, 08:03:00 pm »
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iv is pretty straightforward to me

To find g(-2) just sub into the equation you were given at the start to get 4/3
Then if you need g^-1(4/3) you use the equation that you found in part ii), whatever it was

Ohh true!! Do you have to know how to solve it using the graphical method tho? Thanks so much!! THIS IS SO HELPFUL!

More questions lool

1) Following 8 letters: AA BB CDEF
How many different 4 letter permutations can be formed?

2) attached (9 and 10 both)

jakesilove

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Re: 3U Maths Question Thread
« Reply #1731 on: March 27, 2017, 09:56:14 pm »
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Ohh true!! Do you have to know how to solve it using the graphical method tho? Thanks so much!! THIS IS SO HELPFUL!

More questions lool

1) Following 8 letters: AA BB CDEF
How many different 4 letter permutations can be formed?

2) attached (9 and 10 both)

All letter combination questions work exactly the same. First, as a general rule, if we want to choose four letters from eight letters, we can do this in



ways. However, where some of the letters are the same, we just divide be the factorial of the number of same letters that there are. Since there are two As, and two Bs, our answer will be



For the solutions to x=10cosx, sketch the function y=10cosx to scale. Then, on top of this, sketch the function y=x. The number of intersections are the number of solutions!

Now, we have



We know that P(x) is divisible by 2. Thus,







From here, you can just sub in the multiple choice answers and see which one works!
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teapancakes08

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Re: 3U Maths Question Thread
« Reply #1732 on: March 27, 2017, 10:18:23 pm »
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I sorta stuffed the working out for (b) and (c). The answers' should be b) 12π/5 and c) 2π/35 and got neither. (Did get the correct denominator for b) though, if that means anything)

(On that note, if the attachments don't work...again...tell me to write the questions up)
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bsdfjnlkasn

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Re: 3U Maths Question Thread
« Reply #1733 on: March 29, 2017, 07:43:01 pm »
0
Hey there,

Can I please get some help with the following questions? Thank you!
« Last Edit: March 29, 2017, 07:44:45 pm by bsdfjn;lkasn »

bsdfjnlkasn

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3U Maths Question Thread
« Reply #1734 on: March 29, 2017, 08:22:59 pm »
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I sorta stuffed the working out for (b) and (c). The answers' should be b) 12π/5 and c) 2π/35 and got neither. (Did get the correct denominator for b) though, if that means anything)

(On that note, if the attachments don't work...again...tell me to write the questions up)

Hey here is the answer for part b) - I did a quick sketch off to the side and deduced which graph was on top/on the bottom. These should be graphs that we know but if you want to double check, go onto a graphing software online and it'll be really clear :)

Let me know if there's something that you would like me to clarify further :)


« Last Edit: March 29, 2017, 08:25:29 pm by bsdfjn;lkasn »

kiwiberry

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Re: 3U Maths Question Thread
« Reply #1735 on: March 29, 2017, 09:00:31 pm »
+4
Hey there,

Can I please get some help with the following questions? Thank you!

For the second one, part i):

For part ii), integrate both sides of the result from i). Hint: you'll have to use the fact that \(\tan ^{-1} a + \tan ^{-1} b= \tan ^{-1} \left(\frac{a+b}{1-ab}\right)\) somewhere :)
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #1736 on: March 29, 2017, 10:17:46 pm »
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The chain of questions and answers above makes me happy to my core ;D

I sorta stuffed the working out for (b) and (c). The answers' should be b) 12π/5 and c) 2π/35 and got neither. (Did get the correct denominator for b) though, if that means anything)

(On that note, if the attachments don't work...again...tell me to write the questions up)

Based on what I think Part C is asking (part of it is obscured for me), it wants the volume between \(y=x^3\) and \(y=x^2\). This is a volume between 0 and 1 (because those are the POI), and the \(x^2\) curve is on top, so:



That must have been the question :) does that working make sense? Happy to explain it further ;D

bsdfjnlkasn

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Re: 3U Maths Question Thread
« Reply #1737 on: March 30, 2017, 05:04:41 pm »
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Hey there,

I was wondering if I could please get some help with the attached questions?

Thank you!!

kiwiberry

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Re: 3U Maths Question Thread
« Reply #1738 on: March 30, 2017, 06:27:07 pm »
+1
Hey there,

I was wondering if I could please get some help with the attached questions?

Thank you!!

For Q8, if you construct OB, triangle OAB will be isosceles (radii are equal). So \(\angle OBA=20^o\). Triangle OBC will also be isosceles because of equal radii, so \(\angle OBC=52^o\). Therefore \(20^o + \angle ABC = 52^o \), and \(\angle ABC=32^o\) :)

For Q6, the formula for the volume between two curves is \(\pi \int_a^b{[y_1^2 - y_2^2]} dx \) where y1 is the upper curve and y2 is the lower. So in this case, the upper y1 is y=1 and the lower y2 is y=sinx, so it's D!

For the last one, you have to use the fact that \(\tan ^{-1} a - \tan ^{-1} b= \tan ^{-1} \left(\frac{a-b}{1+ab}\right)\)
« Last Edit: March 30, 2017, 06:38:48 pm by kiwiberry »
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jakesilove

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Re: 3U Maths Question Thread
« Reply #1739 on: March 30, 2017, 10:01:21 pm »
+2
I just want to say a massive thank you to all the users answering questions. Most of you are current Year 12s yourself, so the fact that you're taking the time to help others is just phenomenal. Plus, it's an insanely good way to study; if you can teach, then you understand. You keep ATAR Notes running :)
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