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March 28, 2024, 10:08:44 pm

Author Topic: 3U Maths Question Thread  (Read 1230215 times)  Share 

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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #2010 on: May 18, 2017, 12:21:16 pm »
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what are the topic tests in the ext 1 maths topic test book? and how many are there? also are they in stock i had trouble with the physics book taking like 2 extra weeks coz everyone bought them and no stock ahhaha. but i got it before exams so yassssssss


So happy you ended up with it before exams! I felt so rotten that it had taken so long for you so phew!

If they are for sale on the website they should be in stock and ready to go - They are set out much like the Physics tests! Topic tests with solutions, for all the Ext 1 topics in isolation ;D

RuiAce

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Re: 3U Maths Question Thread
« Reply #2011 on: May 18, 2017, 12:25:18 pm »
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Hi! Very rusty with locus and param, need someone to help with these

1) Find the gradients of the common tangents of the parabola y= x(x-4) and the circle (x-2)^2 + y^2 = 4 (Im not quite sure, do i diff both then simultaneous or?)


RuiAce

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Re: 3U Maths Question Thread
« Reply #2012 on: May 18, 2017, 12:35:39 pm »
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2) Find the locus of P(x,y) and state any restrictions on a, given:
a) PA + PB= 1, where A(a,0) and B (-a,0)
b) ABS PA - PB=2, where A(a,0) and B (-a,0)

Can someone please verify method for 1 or provide legit method and do 1 of the question 2s as wtf is that.

Tyvm :))
It can be annoying trying to derive the equation of the ellipse. I will suggest to use this video as an aid.

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #2013 on: May 18, 2017, 12:40:20 pm »
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Hi! Very rusty with locus and param, need someone to help with these

1) Find the gradients of the common tangents of the parabola y= x(x-4) and the circle (x-2)^2 + y^2 = 4 (Im not quite sure, do i diff both then simultaneous or?)

This one actually has me a little stumped! If we look at the diagram below it doesn't really look like there is a common tangent (meaning, a point that is tangential to both the circle and the curve). If it does exist, your method is spot on - You would find an expression for the gradient of a tangent to the curve and the circle (the circle you would need to rearrange to make y the subject), and then put those equal to each other!



Edit: Or Rui has provided an alternative, but I don't think that it ends up being tangential to both, maybe?

Quote
2) Find the locus of P(x,y) and state any restrictions on a, given:
a) PA + PB= 1, where A(a,0) and B (-a,0)
b) ABS PA - PB=2, where A(a,0) and B (-a,0)

Do this by substituting the distance formula straight into the condition you are given (this gets really messy):



I'll let you take it from here - The algebra is disgusting but a HEAP of it should cancel out. You'll end up (I'm so sorry) with 16 terms on either side, but it should reduce to something fairly kind. But it is straight from the definition, and the other one will be similar!

Here's the equation in Wolfram if you need a hand with expanding it :)

RuiAce

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Re: 3U Maths Question Thread
« Reply #2014 on: May 18, 2017, 12:42:44 pm »
+1
This one actually has me a little stumped! If we look at the diagram below it doesn't really look like there is a common tangent (meaning, a point that is tangential to both the circle and the curve). If it does exist, your method is spot on - You would find an expression for the gradient of a tangent to the curve and the circle (the circle you would need to rearrange to make y the subject), and then put those equal to each other!

(Image removed from quote.)

Edit: Or Rui has provided an alternative, but I don't think that it ends up being tangential to both, maybe?

Do this by substituting the distance formula straight into the condition you are given (this gets really messy):



I'll let you take it from here - The algebra is disgusting but a HEAP of it should cancel out. You'll end up (I'm so sorry) with 16 terms on either side, but it should reduce to something fairly kind. But it is straight from the definition, and the other one will be similar!

Here's the equation in Wolfram if you need a hand with expanding it :)
I should've graphed it. I just guessed that there'd only be 2 points of intersection instead of 4.

If there's 4 points of intersection that's another wrong question.
___________

Yeah that second one is the derivation of the equation of an ellipse without bothering with a directrix. It's too much to work with fourth powers.

legorgo18

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Re: 3U Maths Question Thread
« Reply #2015 on: May 18, 2017, 03:59:15 pm »
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Hey rui so i tried my method for the first one and after double checking i got this: 4x^4 - 32x^3 + 81x^2 - 68x + 4=0 seems impossible to solve.... yea the answer in the back states 4 solns for this q +- 2 root 2, +- 2root 6 am i doing something wrong?

AND JAMON OMG I ACTUALLY DID THAT DISGUSTING ALGEBRA. SO SATISFIED RN :DDDDDDDDDDDD OH GOD IT WAS SO BAD IN THE SQUARING BIT.
so do i do the same thing for b? Does the abs value matter or?
« Last Edit: May 18, 2017, 04:31:52 pm by legorgo18 »
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RuiAce

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Re: 3U Maths Question Thread
« Reply #2016 on: May 18, 2017, 04:33:54 pm »
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Hey rui so i tried my method for the first one and after double checking i got this: 4x^4 - 32x^3 + 81x^2 - 68x + 4=0 seems impossible to solve.... yea the answer in the back states 4 solns for this q +- 2 root 2, +- 2root 6 am i doing something wrong?
The method I stated was invalid since the very beginning because I didn't realise how the curves intersected until I saw Jamon's diagram. So ignore it. (Although I don't quite agree with your quartic it doesn't actually matter.)

There are no common tangents because of how the curves intersect. I'm not sure what goes on but quite a few of the questions you posted up seem to be incorrect. Just look at Jamon's graph again - There are no common tangents.

I haven't had much time to reverse engineer the question to see what it should've been but I don't see any potential correction to the question either. What is the source?

legorgo18

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Re: 3U Maths Question Thread
« Reply #2017 on: May 18, 2017, 05:00:37 pm »
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Most of the source is from my yr 12 cambridge, mif (school, ik ... awful) and my dr du A(3) level hw. They expect everyone to do 4u there #exception hence sometimes the questions do go way over...  yea thank god i didnt pick 4u i just hate math so much
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RuiAce

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Re: 3U Maths Question Thread
« Reply #2018 on: May 18, 2017, 06:52:59 pm »
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Most of the source is from my yr 12 cambridge, mif (school, ik ... awful) and my dr du A(3) level hw. They expect everyone to do 4u there #exception hence sometimes the questions do go way over...  yea thank god i didnt pick 4u i just hate math so much
Hm alright, was that particular question just now out of MIF?

hanaacdr

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Re: 3U Maths Question Thread
« Reply #2019 on: May 19, 2017, 06:11:14 am »
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Hi i was wondering if i could get some help on this question part (iv)
I got the first three part and am stuck on part 4
Thank you!

ellipse

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Re: 3U Maths Question Thread
« Reply #2020 on: May 19, 2017, 07:32:36 am »
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(Image removed from quote.)

Hi i was wondering if i could get some help on this question part (iv)
I got the first three part and am stuck on part 4
Thank you!

substitute m=1 to get:
99.55
unsw engo/sci

mx2-99
mx1-98
phys-94
chem-94
eng-88 (rip me)

beau77bro

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Re: 3U Maths Question Thread
« Reply #2021 on: May 19, 2017, 04:13:19 pm »
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The photos on the site for the extension 1 topic tests won't load, what are the tests in it like what topics and how many, and that kinda jazz?

hanaacdr

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Re: 3U Maths Question Thread
« Reply #2022 on: May 19, 2017, 08:50:44 pm »
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hanaacdr

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Re: 3U Maths Question Thread
« Reply #2023 on: May 19, 2017, 09:01:19 pm »
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substitute m=1 to get:


do you know how to do part v??

kiwiberry

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Re: 3U Maths Question Thread
« Reply #2024 on: May 19, 2017, 09:24:58 pm »
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do you know how to do part v??
I think part v) got cut off your photo!
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