1. ## IB Maths Marathon

$Decided to open up a thread on all questions related to the IB Diploma . The IB is a curriculum offered by most New South Wales schools and around the world as well. Thought we could get a bit more discussion up and going on a single thread.$

$Will start off with this question From SL Cambridge Page 150 Q 4$

$The sum of the first three terms of a geometric sequence is 23 \frac{3}{4} , and the sum of the first four terms is 40 \frac{5}{8}. Find the first term and the common ratio$

2. ## Re: International Baccalaureate Marathon 2016

Originally Posted by davidgoes4wce
$Decided to open up a thread on all questions related to the IB Diploma . The IB is a curriculum offered by most New South Wales schools and around the world as well. Thought we could get a bit more discussion up and going on a single thread.$

$Will start off with this question From SL Cambridge Page 150 Q 4$

$The sum of the first three terms of a geometric sequence is 23 \frac{3}{4} , and the sum of the first four terms is 40 \frac{5}{8}. Find the first term and the common ratio$

Are you sure the IB is offered by most New South Wales schools? I thought it was relatively uncommon in NSW schools.

3. ## Re: International Baccalaureate Marathon 2016

Here was my attempt:

$S_3=\frac{a(r^3-1)}{r-1}$

$\frac{95}{4}=\frac{a(r^3-1)}{r-1} \textcircled{1}$

$S_4=\frac{a(r^4-1)}{r-1}$

$\frac{325}{8}=\frac{a(r^4-1)}{r-1} \textcircled{2}$

4. ## Re: International Baccalaureate Marathon 2016

Originally Posted by InteGrand
Are you sure the IB is offered by most New South Wales schools? I thought it was relatively uncommon in NSW schools.
I should have taken the word 'most' out of it. But I do know that St.Andrews Cathedral and Newington are 2 schools that offer it.

5. ## Re: International Baccalaureate Marathon 2016

Originally Posted by InteGrand
Are you sure the IB is offered by most New South Wales schools? I thought it was relatively uncommon in NSW schools.
Most rich private schools lel

6. ## Re: International Baccalaureate Marathon 2016

$T_4=S_4-S_3$

$T_4=\frac{325}{8}-\frac{95}{4} =\frac{135}{8}$

$Equating T_4=ar^{4-1}$

$\frac{135}{8}=ar^3$

7. ## Re: International Baccalaureate Marathon 2016

Originally Posted by Nailgun
Most rich private schools lel
The thing I learnt also, especially in NSW= rich doesn't necessarily mean better.

8. ## Re: International Baccalaureate Marathon 2016

Originally Posted by davidgoes4wce
The thing I learnt also, especially in NSW= rich doesn't necessarily mean better.
words to live by

9. ## Re: International Baccalaureate Marathon 2016

I also get the feeling this question has substitution and cancelling involved, would be great if somebody can get the derived working out as I spent around 15-20 minutes on the question.

10. ## Re: International Baccalaureate Marathon 2016

Originally Posted by InteGrand
Are you sure the IB is offered by most New South Wales schools? I thought it was relatively uncommon in NSW schools.
some

11. ## Re: International Baccalaureate Marathon 2016

Originally Posted by davidgoes4wce
I should have taken the word 'most' out of it. But I do know that St.Andrews Cathedral and Newington are 2 schools that offer it.
Trinity Grammar, MLC, Ravenswood, Kambala, Queenswood, Monte Sant Angelo, S.C.E.G.G.S. Redlands, . . . .

12. ## Re: International Baccalaureate Marathon 2016

Originally Posted by davidgoes4wce
$Decided to open up a thread on all questions related to the IB Diploma . The IB is a curriculum offered by most New South Wales schools and around the world as well. Thought we could get a bit more discussion up and going on a single thread.$

$Will start off with this question From SL Cambridge Page 150 Q 4$

$The sum of the first three terms of a geometric sequence is 23 \frac{3}{4} , and the sum of the first four terms is 40 \frac{5}{8}. Find the first term and the common ratio$

ar³ = 135/8 from the difference of the series.

a(1+r+r²+r³) = 205/8

1+r⁻¹+r⁻²+r⁻³ = 41/27

which is the quotient of the above two expressions.

From here, it can be solved for r⁻¹ and then a can be found.

13. ## Re: International Baccalaureate Marathon 2016

ar³ = 135/8 from the difference of the series.

a(1+r+r²+r³) = 205/8

1+r⁻¹+r⁻²+r⁻³ = 41/27

which is the quotient of the above two expressions.

From here, it can be solved for r⁻¹ and then a can be found.
You did everything right except for that last line

1+r^-1+r^-2+r^-3=65/27

It's been a long day, and you had to do the division, which correctly pointed out. This is the kind of question they put to a Year 11, I think after today I will just stick to the Haeese textbooks (which are considerably easier).

14. ## Re: International Baccalaureate Marathon 2016

$S_4= \frac{325}{8}$

$a+ar^2+ar^3+ar^4=\frac{325}{8}$

$Dividing both LHS and RHS by ar^3=\frac{135}{8}$

$\frac{a+ar+ar^2+ar^3}{ar^3}=\frac{325}{8} \div \frac{135}{8}$

$r^{-3}+r^{-2}+r^{-1}+1=\frac{325}{135}$

$r^{-3}+r^{-2}+r^{-1}+1=\frac{65}{27}$

From there you have to use Trial and Error to solve for r or a graphics calculating facility (where they have Equation Solver )

15. ## Re: International Baccalaureate Marathon 2016

This is a Band 6 Question in IB maths..........................In IB they have 7 bands

16. ## Re: International Baccalaureate Marathon 2016

Originally Posted by davidgoes4wce
This is a Band 6 Question in IB maths..........................In IB they have 7 bands
what fun.

what fun.
Just Saying

18. ## Re: International Baccalaureate Marathon 2016

What do you reckon is harder, NSW maths or IB maths?

19. ## Re: International Baccalaureate Marathon 2016

Originally Posted by Rathin
What do you reckon is harder, NSW maths or IB maths?
Does this really have to be asked

20. ## Re: International Baccalaureate Marathon 2016

Originally Posted by leehuan
Does this really have to be asked
Do you mean the answer is obvious, or the question isn't of interest?

21. ## Re: International Baccalaureate Marathon 2016

im just curious lol

22. ## Re: International Baccalaureate Marathon 2016

My legal teacher full roasts us on how dumb we are and how much 'better' the IB kids are and whatnot...

23. ## Re: International Baccalaureate Marathon 2016

Originally Posted by InteGrand
Do you mean the answer is obvious, or the question isn't of interest?
The former haha

24. ## Re: International Baccalaureate Marathon 2016

The IB is a more rigorous and demanding programme than the NSW HSC.

You can't just pick a group of any subjects that you fancy from a menu of 100 items. If you choose the IB Maths (HL), and opted for the "Calculus" [previously called the 'Series & Differential Equations'], as most schools here do, you have to do: Sequences & Series [and their convergence/divergence, Squeeze Thm, L'Hopital's, etc ], Improper Integrals, Power Series, Maclaurin & Taylor series, Error Term, Radius and Interval of Covergence etc, Differential Equations etc.

The core course includes: vectors, dot and cross product, and Equations (vector, parametric, Cartesian) of a line, a plane , their intersection, solution sets to a set of linear equations in x, y, z.

25. ## Re: International Baccalaureate Marathon 2016

I think I'll be honest, if you read the Haeese Maths textbooks (which are published in Adelaide), you would say the NSW curriculum is harder.

Let's not kid ourselves, doing an international recognised curriculum you would generally expect the standards to be alot higher.

IB Maths November 2014
Maths Studies Candidates 2455
Maths SL Candidates 4093
Maths HL candidates 1333

IB Maths May 2014
Maths Studies 29,235
Maths SL 38,926
Maths HL 11,484

From what I gather there are two testing seasons one in May and one in November. From what I gather , is that the students in Australia prepare for the November exam. Whereas the Northern Hemisphere counterparts have to prepare for the May.

Australia has the largest intake participation in November according to the IB website with 1916/11125=17.22% candidates participating.

United States of America has the largest intake participation in May according to the IB Website with 73,028/137,330=53.17% candidates participating.

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