IB Maths Marathon (1 Viewer)

davidgoes4wce

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Re: International Baccalaureate Maths Marathon

I wasn't sure if I got the wording of this question right:



My initial thinking was to set the first derivative equal to 0 and then from that determine the intervals where it was decreasing. Reflecting back on it I see that they have set the 2nd derivative to less than zero, then determined the x-values of the decreasing gradient. (I could understand had they worded it 'concave down') . What are your guys thoughts on this question?

Q10. This was the solution:






 
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davidgoes4wce

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Re: International Baccalaureate Maths Marathon

Another point to make out to IBers for 2017, there was a mistake in the Oxford SL book by Laurie Buchanan, Jim Fensom, Ed Kemp, Paul La Rondie and Jill Stevens.



The image is a bit small but the question was



in the following line , they then wrote:

 

seanieg89

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Re: International Baccalaureate Maths Marathon

I wasn't sure if I got the wording of this question right:



My initial thinking was to set the first derivative equal to 0 and then from that determine the intervals where it was decreasing. Reflecting back on it I see that they have set the 2nd derivative to less than zero, then determined the x-values of the decreasing gradient. (I could understand had they worded it 'concave down') . What are your guys thoughts on this question?

Q10. This was the solution:






the question asked you to find where the function's gradient is decreasing, not where the function itself is decreasing.
 

davidgoes4wce

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Re: International Baccalaureate Maths Marathon

Just my opinion but comparing the IB Cambridge v HSC Cambridge (Yr 11/12 ) Extension books, the IB Cambridge is a far superior book. The book which is co-authored by 4 Cambridge University graduates, is written in a reader friendly way. I get comments from students that read the HSC Cambridge book and say it is too 'theoretical' and 'hard to understand' and I totally understand where they are coming from. You would think that be the opposite, with Cambridge Uni being a higher rank and the overall general consensus is a book written by Cambridge grads would be of higher mathematical literature.

I decided to do a bit of a comparison of the books:

WORKED EXAMPLES-
IB Cambridge- every step is explained in detail. With their graphs, they utilize different colours to break down key components. They keep things short and brief with their explanations.
HSC Cambridge- every example is black and yellow. Their explanations can be like essays sometimes.

EXPLANATION OF CONCEPTS:
IB Cambridge-Despite being 670 pages worth of content their explanations are brief and directly to the point. It's the kind of book where if you read a particular exercise it won't take you more longer than 5-15 minutes to understand what is going on, by just reading theory alone. They also include different colouring to emphasize their key points as well as bolded font to highlight some important formula. They give things like 'Exam Hints' and when linking it up to some history they keep it simple. They also provide an End of Chapter Review which goes through Key formula.
HSC Cambridge- It's a 637 page book but sometimes I feel its 6370 pages. Some exercises can go up to as much as 8 key points per exercise. I read chapter 8 of the Year 12 Cambridge and it seemed to me more of an English essay, personally feel they need to be more direct to the point and feel the need to make it more 'fun ' for the students to read. No end of chapter review summary is provided.

EXERCISES:
IB Cambridge- drill questions provide practice of new methods, they colour-code their questions to a certain IB Grade (i.e Band 4,5,6,7), questions predominantly exam-style
HSC Cambridge-breakdown is Basic, Development and Extension. Development questions are most similar to Exam style questions. Some of the exercises which have graphs, they use are hard-to-read background for the graphs.

AUTHORS:
IB Cambridge- Fannon, Kadelburg, Wooley, Stephen Ward are all Cambridge University graduates and teach both the IB and A Level Mathematics in the UK.
HSC Cambridge- Pender studied at Sydney University, Macquarie University & Bonn University. David Sadler - studied at Sydney Uni and UNSW. Julia Shea studied at University of Tasmania. David Ward studied at UNSW.

No offence to the universities in New South Wales or Australian universities but the Cambridge University maths school is better than any of the Australian University mathematics schools and the rankings prove this.
 

Drongoski

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Re: International Baccalaureate Maths Marathon

It goes without saying that Cambridge University has been the pre-eminent university in mathematics in the UK (since the days of Isaac Newton) just as Princeton is, in the U.S..
 
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davidgoes4wce

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Re: International Baccalaureate Maths Marathon

I came across a Maths SL question today. Wasn't sure if this answer was correct from this certain Maths SL textbook.



I always thought that dominate powers held true. The back of the back has the answer as "D.N.E (increases without bound)"
 

InteGrand

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Re: International Baccalaureate Maths Marathon

I came across a Maths SL question today. Wasn't sure if this answer was correct from this certain Maths SL textbook.



I always thought that dominate powers held true. The back of the back has the answer as "D.N.E (increases without bound)"
They are basically saying the limit is infinity (the numerator has higher degree than denominator).
 

davidgoes4wce

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Re: International Baccalaureate Maths Marathon




The interval notation seems a bit different to what I have read in the past. (This is from an IB source as well)

Would it be right for the 2nd row to write it along the lines of:



I noticed them using the brackets ][

 

InteGrand

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InteGrand

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Re: International Baccalaureate Maths Marathon

If I do that the derivative becomes

They mean the derivative is non-negative for all (real) x. We can thus use discriminants to obtain the desired inequality.
 

davidgoes4wce

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Re: International Baccalaureate Maths Marathon

They mean the derivative is non-negative for all (real) x. We can thus use discriminants to obtain the desired inequality.










This is the opposite direction of the inequality required in the proof. There has been a type in the whole question.
 

davidgoes4wce

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Re: International Baccalaureate Maths Marathon

By the way this is a question from Newington, seems like the staff don't know how to teach the subject properly there.

By setting the discriminant to less than equal to zero, we are trying to prove that there are no solutions for the real values of x, using the quadratics roots formula. Right?
 

InteGrand

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Re: International Baccalaureate Maths Marathon

By the way this is a question from Newington, seems like the staff don't know how to teach the subject properly there.

By setting the discriminant to less than equal to zero, we are trying to prove that there are no solutions for the real values of x, using the quadratics roots formula. Right?
Why do you think they don't know how to teach the subject properly there? Is it something their worked answers said?

The reason we can set the discriminant to be less than or equal to 0 is that we are told the quadratic is non-negative for all real x ("non-negative definite"). This implies (since it's a quadratic with real coefficients) that its discriminant is non-positive.
 
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davidgoes4wce

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Re: International Baccalaureate Maths Marathon

I'll take your word for it Integrand, I am still confused as to what non-negative means in this case.

I thought the discriminant for sure was reading the question first up.
 

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