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March 28, 2024, 07:25:27 pm

Author Topic: 3U Maths Question Thread  (Read 1230135 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #855 on: October 23, 2016, 02:05:43 pm »
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Hiya, how do you solve these 2 questions? (I'm assuming there's a more efficient way of solving Q9 than expanding it all out haha  :P)



atar27

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Re: 3U Maths Question Thread
« Reply #856 on: October 23, 2016, 03:06:52 pm »
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I can't solve for k+1
Can someone please help! Thank you!

RuiAce

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Re: 3U Maths Question Thread
« Reply #857 on: October 23, 2016, 03:13:27 pm »
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(Image removed from quote.)

I can't solve for k+1
Can someone please help! Thank you!


MysteryMarker

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Re: 3U Maths Question Thread
« Reply #858 on: October 23, 2016, 03:29:52 pm »
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Hey guys, just got a few questions which I'm not too confident with.

1. |x+1| +x = |x-1|

2. When you are finding the volume of a curve that has been rotated about lets say the x axis, and the question specifically asks to use simpsons rule. Do you just find y2, input the values into the simpsons formula and then multiply it by pi?

3. What is the value of integral of [cos-1xdx]a-a where -1<=a<=1

4. How many times must a die be rolled so that the probability of rolling at least one size is greater than 95%?
« Last Edit: October 23, 2016, 03:32:47 pm by MysteryMarker »

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #859 on: October 23, 2016, 04:06:53 pm »
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Hey guys, just got a few questions which I'm not too confident with.

1. |x+1| +x = |x-1|

2. When you are finding the volume of a curve that has been rotated about lets say the x axis, and the question specifically asks to use simpsons rule. Do you just find y2, input the values into the simpsons formula and then multiply it by pi?

3. What is the value of integral of [cos-1xdx]a-a where -1<=a<=1

4. How many times must a die be rolled so that the probability of rolling at least one size is greater than 95%?

For your first one, doing that algebraically would probably be gross. I'd take a graphical approach. If you draw the two sides of that equation on the same graph, just pick where they intersect and that's your answer! Drawing the one on the right is easy; the one on the left might be tricky; have a think! Here is what you should get :)

For your second one, yes :)

For your third one, do you mean you need to integrate \(\cos^{-1}{x}\)? Or just evaluate that anti-derivative in the brackets? Snap a pic of the original question? ;D

Your fourth one, we could use binomial theorem and other such things; but let's just think of it simply. Every time we roll a dice, our probability of rolling NOT A SIX is \(\frac{5}{6}\). But as soon as we fail to do that, we have rolled a six. So, instead of considering how many times we need to roll to have a 95% chance of getting A six, let's just consider how many times we need to roll such that the probability of throwing NO SIXES becomes less than 5%! It's a complementary event ;D

So we seek the lowest integer value of n such that:



By trial and error, the answer is 17 ;D
« Last Edit: October 23, 2016, 04:10:08 pm by jamonwindeyer »

MysteryMarker

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Re: 3U Maths Question Thread
« Reply #860 on: October 23, 2016, 04:28:00 pm »
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Oh thanks, and yeah for the third one it asks to integrate cos-1x dx and evaluate it with the bounds given. Its a multiple choice question where the options are

a) 0
b) a x (pi)/2
c) a x (pi)
d) 2 x a x (pi)

RuiAce

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Re: 3U Maths Question Thread
« Reply #861 on: October 23, 2016, 05:59:50 pm »
+1
Oh thanks, and yeah for the third one it asks to integrate cos-1x dx and evaluate it with the bounds given. Its a multiple choice question where the options are

a) 0
b) a x (pi)/2
c) a x (pi)
d) 2 x a x (pi)





MysteryMarker

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Re: 3U Maths Question Thread
« Reply #862 on: October 23, 2016, 07:01:51 pm »
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Cheers guys, I'm gonna be spamming this thread with a lot of questions :P

Is there a shorter method to finding the general solution to cos2x = cosx rather than using double angle formula and solving for the quadratic?


jakesilove

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Re: 3U Maths Question Thread
« Reply #863 on: October 23, 2016, 07:11:45 pm »
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Cheers guys, I'm gonna be spamming this thread with a lot of questions :P

Is there a shorter method to finding the general solution to cos2x = cosx rather than using double angle formula and solving for the quadratic?

Potentially, you can sketch the two graphs and see if it's obvious where the intercepts lie. However, I would always suggest using double angle formula etc. etc. for a question like that :)
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RuiAce

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Re: 3U Maths Question Thread
« Reply #864 on: October 23, 2016, 07:13:54 pm »
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Cheers guys, I'm gonna be spamming this thread with a lot of questions :P

Is there a shorter method to finding the general solution to cos2x = cosx rather than using double angle formula and solving for the quadratic?
Not really. Other methods risk losing solutions. Better off just to pull it safe with the quadratic here

Potentially, you can sketch the two graphs and see if it's obvious where the intercepts lie. However, I would always suggest using double angle formula etc. etc. for a question like that :)
But sketching is tedious pls.

Cindy2k16

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Re: 3U Maths Question Thread
« Reply #865 on: October 23, 2016, 07:29:14 pm »
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hi for Q5 a) ii) of 1997 HSC Maths ext http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2000exams/hsc00_maths/97MAT3U.PDF
how are you supposed to know that the fastest speed occurs at a=0 if the particle isnt moving in SHM?
Thanks in advance :)
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Re: 3U Maths Question Thread
« Reply #866 on: October 23, 2016, 07:34:06 pm »
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hi for Q5 a) ii) of 1997 HSC Maths ext http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2000exams/hsc00_maths/97MAT3U.PDF
how are you supposed to know that the fastest speed occurs at a=0 if the particle isnt moving in SHM?
Thanks in advance :)

Hey! Ignoring simple harmonic motion for a second, how do we usually find maximum values? By finding stationary points. These stationary points will occur when the derivative equals zero, which for velocity happens to mean that acceleration has to equal zero! So, for any turning point of velocity, acceleration will need to equal zero, regardless of the type of motion. This is because velocity REACHES A MAXIMUM VALUE, and then must slow down again. For a moment, acceleration will exactly equal zero!
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FallonXay

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Re: 3U Maths Question Thread
« Reply #867 on: October 23, 2016, 07:41:03 pm »
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Heyy, how do you solve this graph question? I always get confused with graphs  :P
Thanks!
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jakesilove

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Re: 3U Maths Question Thread
« Reply #868 on: October 23, 2016, 07:45:55 pm »
+1
Heyy, how do you solve this graph question? I always get confused with graphs  :P
Thanks!

Personally, for questions like this, I would just sub values in for t and see which one gives you zero. You'll find that only A and C do, however A would be the first intercept (as it is smaller) making C the second intercept, and our answer. Otherwise, use the general solution on your formula sheet to do this formally
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Re: 3U Maths Question Thread
« Reply #869 on: October 23, 2016, 07:47:52 pm »
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Heyy, how do you solve this graph question? I always get confused with graphs  :P
Thanks!

P is the point of intersection at the x-axis.





Therefore C is the correct answer, as 11pi/12 is the second intercept.
« Last Edit: October 23, 2016, 08:05:32 pm by Syndicate »
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