IB Maths Marathon

davidgoes4wce · Jun 19, 2016

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

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

$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}. $Find the first term and the common ratio$

Answer: a=5, r =1.5

InteGrand · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

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

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

$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}. $Find the first term and the common ratio$

Answer: a=5, r =1.5

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

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

Here was my attempt:

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

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

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

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

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

InteGrand said:
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.

Nailgun · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

InteGrand said:
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

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

$T_4=S_4-S_3$

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

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

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

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

Nailgun said:
Most rich private schools lel

The thing I learnt also, especially in NSW= rich doesn't necessarily mean better.

Nailgun · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

davidgoes4wce said:
The thing I learnt also, especially in NSW= rich doesn't necessarily mean better.

words to live by

davidgoes4wce · Jun 19, 2016

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.

Drongoski · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

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

some

Drongoski · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

davidgoes4wce said:
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, . . . .

Paradoxica · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

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

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

$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}. $Find the first term and the common ratio$

Answer: a=5, r =1.5

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.

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

Paradoxica said:
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).

davidgoes4wce · Jun 19, 2016

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 )

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

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

Paradoxica · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

davidgoes4wce said:
This is a Band 6 Question in IB maths..........................In IB they have 7 bands

what fun.

davidgoes4wce · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

Paradoxica said:
what fun.

Just Saying

Green Yoda · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

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

leehuan · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

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

Does this really have to be asked

InteGrand · Jun 19, 2016

Re: International Baccalaureate Marathon 2016

leehuan said:
Does this really have to be asked

Do you mean the answer is obvious, or the question isn't of interest?

IB Maths Marathon

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