camdaman12
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how did everyone go?
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Thoughts on 2015 CSSA MX2 Trials? (1 Viewer)
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Drsoccerball
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Re: 4u trials CSSA
Wanna see the paper
Wanna see the paper
leehuan
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Re: 4u trials CSSA
I lost one mark for...
- I wrote 2 dt/(1+t^2) in the integral but I threw the 2 out somewhere
- I don't know how to do volumes by washers anymore perpendicular to y-axis
- 3 marks on the last question because I was just stuck
- Unable to read an Argand diagram to find minimum value of arg(z-1)
- I wasn't taught any strategy for 4u perms and combs, the teacher threw it at me, so that's 1 MC mark and 3 long response marks put to risk
- ??? marks because I didn't check my answers
I lost one mark for...
- I wrote 2 dt/(1+t^2) in the integral but I threw the 2 out somewhere
- I don't know how to do volumes by washers anymore perpendicular to y-axis
- 3 marks on the last question because I was just stuck
- Unable to read an Argand diagram to find minimum value of arg(z-1)
- I wasn't taught any strategy for 4u perms and combs, the teacher threw it at me, so that's 1 MC mark and 3 long response marks put to risk
- ??? marks because I didn't check my answers
Carrotsticks
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Re: 4u trials CSSA
What was the last question about?
What was the last question about?
WhoStanLeee
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Re: 4u trials CSSA
Uhhhh did it 8 hours and suddenly forgets everything...
Question 16:
~ Induction - Strong Induction/Recursion
~ General solution of cos2x + cos3x +cos4x = 0, we were given the sums to products formula
~ Final part worth 5 marks:
(z+1)^n+(z-1)^n = 0
1) RTP: mod(z-1) = mod(z+1), and therefore prove that all roots of the equation can be expressed as i(alpha, k) where (alpha, k is a real number)
2) Sum of (roots squared) from n = 1 to k equals n(n-1)
FROM MEMORY
Uhhhh did it 8 hours and suddenly forgets everything...
Question 16:
~ Induction - Strong Induction/Recursion
~ General solution of cos2x + cos3x +cos4x = 0, we were given the sums to products formula
~ Final part worth 5 marks:
(z+1)^n+(z-1)^n = 0
1) RTP: mod(z-1) = mod(z+1), and therefore prove that all roots of the equation can be expressed as i(alpha, k) where (alpha, k is a real number)
2) Sum of (roots squared) from n = 1 to k equals n(n-1)
FROM MEMORY
RealiseNothing
what is that?It is Cowpea
Re: 4u trials CSSA
That last question seems pretty easy?Uhhhh did it 8 hours and suddenly forgets everything...
Question 16:
~ Induction - Strong Induction/Recursion
~ General solution of cos2x + cos3x +cos4x = 0, we were given the sums to products formula
~ Final part worth 5 marks:
(z+1)^n+(z-1)^n = 0
1) RTP: mod(z-1) = mod(z+1), and therefore prove that all roots of the equation can be expressed as i(alpha, k) where (alpha, k is a real number)
2) Sum of (roots squared) from n = 1 to k equals n(n-1)
FROM MEMORY
Carrotsticks
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Re: 4u trials CSSA
Seems like a very straightforward paper if that's their Q16. Surely they can do better than a general solution and strong Induction in Q16.
Seems like a very straightforward paper if that's their Q16. Surely they can do better than a general solution and strong Induction in Q16.
Ekman
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Re: 4u trials CSSA
What is being asked here? I don't know what they mean by i(alpha, k).Uhhhh did it 8 hours and suddenly forgets everything...
Question 16:
~ Induction - Strong Induction/Recursion
~ General solution of cos2x + cos3x +cos4x = 0, we were given the sums to products formula
~ Final part worth 5 marks:
(z+1)^n+(z-1)^n = 0
1) RTP: mod(z-1) = mod(z+1), and therefore prove that all roots of the equation can be expressed as i(alpha, k) where (alpha, k is a real number)
2) Sum of (roots squared) from n = 1 to k equals n(n-1)
FROM MEMORY
Ekman
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Re: 4u trials CSSA
So it is asking to prove that all the roots a imaginary then, because that would make sense.
Ekman
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Re: 4u trials CSSA
Shouldn't that be -n(n-1)?Uhhhh did it 8 hours and suddenly forgets everything...
Question 16:
~ Induction - Strong Induction/Recursion
~ General solution of cos2x + cos3x +cos4x = 0, we were given the sums to products formula
~ Final part worth 5 marks:
(z+1)^n+(z-1)^n = 0
1) RTP: mod(z-1) = mod(z+1), and therefore prove that all roots of the equation can be expressed as i(alpha, k) where (alpha, k is a real number)
2) Sum of (roots squared) from n = 1 to k equals n(n-1)
FROM MEMORY
leehuan
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Re: 4u trials CSSA
(Assuming ''Sum of (roots squared)'' referred to^2)
.)
How can the sum of squares of imaginary numbers (assuming the roots are purely imaginary) be positive?
(Assuming ''Sum of (roots squared)'' referred to
Ekman
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Re: 4u trials CSSA
^n\binom{n}{n} = 0 )
^2 = \left(\sum _{k=1} ^n i\alpha _k \right)^2 - 2\left(\sum _{k=1} ^n i\alpha _k \cdot i\alpha_{k-1}\right) )
^2 = 0 - 2\binom{n}{2} = -n(n-1) )
Edit: I noticed something fishy about roots being purely imaginary and that the double sum of roots being equal to a positive number, that could explain the reason why it would need to be positive n(n-1)?
This is exactly what I was thinking. I also did it by expanding the equation through binomial theorem:How can the sum of squares of imaginary numbers (assuming the roots are purely imaginary) be positive?
(Assuming ''Sum of (roots squared)'' referred to
Edit: I noticed something fishy about roots being purely imaginary and that the double sum of roots being equal to a positive number, that could explain the reason why it would need to be positive n(n-1)?
Last edited:
porcupinetree
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Re: 4u trials CSSA
Uh I'm (kinda) jealous of you guys who actually did a half-decent, interesting paper, the ones my school always do are super duper easy and the biggest waste of 3hrs. Literally, the last question in the exam today was a banked track question where you had to find the velocity to eliminate sideways frictional force
Uh I'm (kinda) jealous of you guys who actually did a half-decent, interesting paper, the ones my school always do are super duper easy and the biggest waste of 3hrs. Literally, the last question in the exam today was a banked track question where you had to find the velocity to eliminate sideways frictional force
integral95
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Re: 4u trials CSSA
CSSA math seems to be getting worse lol
CSSA math seems to be getting worse lol