Thread: IB Maths Tutor - Sydney

1. Re: IB Maths Tutor - Sydney

heay man, I trials next week, how much do you charge.

PM, to let me know, keep in mind that I have financial problems,

can you help me!

2. Re: IB Maths Tutor - Sydney

bump for a great tutor

bump :P

4. Re: IB Maths Tutor - Sydney

Oh thanks for the bump, hsclover.

5. Bump .

6. Re: IB Maths Tutor - Sydney

IB Maths (Higher Level)
Paper 3 - Series & Differential Equations
May 2008

Q5(b): Determine whether the series is convergent or divergent:

$\sum ^{\infty}_{n=0} (\root \3 \of {n^3+1}- n)$

Solution (using difference of 2 cubes)

$0 < \root \3 \of {n^3+1} - n = \frac { {(\root \3 \of {n^3 + 1} - n) }[(n^3 + 1)^{\frac {2}{3}} + n \root \3 \of {n^3 + 1} + n^2]} {[(n^3 + 1)^{\frac{2}{3}} + n \root \3 \of {n^3 + 1} + n^2]} \\ \\$
$\\ = \frac {(n^3 +1) - n^3}{ \cdots} = \frac {1}{\cdots} < \frac {1}{n^2} and \sum ^{\infty}_{n=0} \frac {1}{n^2} converges (p-series)$

Therefore, by the Comparison Test, the given infinite series converges.

7. Re: IB Maths Tutor - Sydney

Originally Posted by Drongoski
IB Maths (Higher Level)
Paper 3 - Series & Differential Equations
May 2008

Q5(b): Determine whether the series is convergent or divergent:

$\sum ^{\infty}_{n=0} (\root \3 \of {n^3+1}- n)$

Solution (using difference of 2 cubes)

$0 < \root \3 \of {n^3+1} - n = \frac {(\root \3 \of {n^3 + 1} - n)[(n^3 + 1)^{\frac {2}{3}} + n \root \3 \of {n^3 + 1} + n^2]}{[(n^3 + 1)^{\frac{2}{3}} + n \root \3 \of {n^3 + 1} + n^2]} \\ \\ \\ = \frac {(n^3 +1) - n^3}{ \cdots} = \frac {1}{\cdots} < \frac {1}{n^2} and \sum ^{\infty}_{n=0} \frac {1}{n^2} converges$

Therefore, by the Comparison Test, the given infinite series converges.

what do you think would be the major difference between IB and HSC for maths?

8. Re: IB Maths Tutor - Sydney

The IB (Higher Level) has a Options part: You choose 1. Students do the one the school opts for. The Options is essentially a 1st Year Uni Topic. Quite impressive & demanding. Questions asked are designed to really test your understanding.

9. Re: IB Maths Tutor - Sydney

Thanks Drongoski for the paper clip trick, although I was pretty stupid and didn't recognise the circle geometry proof...sigh.

10. Re: IB Maths Tutor - Sydney

Originally Posted by Drongoski
Ah! I hope you at least drew the 2 circles & get some marks.

Proving collinearity is often tricky. You must first assume QT and TP are not parts of the same straight line.
Nup, I was pretty stupid, I went to prove similar triangles. I should at least be able to get an E4 though.

11. Re: IB Maths Tutor - Sydney

IB Maths(HL) November 2011 Exam Paper 2

Q12 (b)

$a_1, a_2, a_3 \cdots are terms of a geometric sequence with common ratio r \neq 1 .\\ \\ show that: \\ \\ (a_1 - a_2)^2 + (a_2 - a_3)^2 + (a_3 - a_4)^2 + \cdots + (a_n - a_{n+1})^2 = \frac {a_1^2 (1-r)(1-r^{2n})}{1+r}$

Will post solution later.

12. Re: IB Maths Tutor - Sydney

Proof:

$a_i = a_1r^{i-1}\\ \\ (a_i - a_{i+1})^2 = (a_1 r^{i-1} - a_1 r^i)^2 = a_1 ^2 (r^{i-1} )^2 (1-r)^2 \\ \\ \therefore \sum _{i=1} ^n (a_i - a_{i+1})^2 = \sum _{i=1} ^n a_1 ^2 (r^2)^{i-1} (1-r)^2 = a_1 ^2 (1-r)^2 \sum _{i=1} ^n (r^2)^{i-1} \\ \\ = a_1 ^2 (1-r) ^2 \times \left [ \frac {1((r^2)^n - 1)}{r^2 - 1} \right ] (a geometric sum) \\ \\ = \frac {a_1 ^2 (1-r)(1-r)(r^{2n} - 1)}{(r-1)(r+1)} = \frac {a_1 ^2 (1-r)(1 - r^{2n})}{1+r}$

QED

13. Re: IB Maths Tutor - Sydney

Bump! To what extent do IB examiners ask when it comes to series [divergence/convergence] (What is considered a tough question?)

14. Re: IB Maths Tutor - Sydney

I think it is about the standard of UNSW Maths 1231/1241.

15. Re: IB Maths Tutor - Sydney

BUMP. this guy knows his content.

16. Re: IB Maths Tutor - Sydney

Originally Posted by obliviousninja
BUMP. this guy knows his content.

Are you sure?

BAMP!!!!!!!!

18. Re: IB Maths Tutor - Sydney

Ha thanks $\sqrt$

8==D

((&))

...........

22. IB Maths Tutor - Sydney

He knows his stuff. Highly recommended

23. Re: IB Maths Tutor - Sydney

Thank you nerdo. Very much appreciated.

24. Re: IB Maths Tutor - Sydney

My IB Maths HL student got a 7 for the subject last year. This is a matter of great satisfaction for me, of course.

Temptation is to take credit for it. Fact is 90% of the success is due to her own ability and effort.

25. Re: IB Maths Tutor - Sydney

If your son or daughter needs help, please don't leave it too late.

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