| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
Last edited by InteGrand; 16 Feb 2017 at 6:25 AM.
Not sure what the best way to study for sequences and series, whether it be HSC or IB but should we tell the students to memorise the formulae (even though the formuale sheet is provided)?
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
This is a Band 7 IB question (equivalent to a HSC Band 6 aiming for 95%+ on paper)
With regards to (b) , would it be OK to not write the answer involving sequences? i.e doing it manually in order to get the marks
My way I did it was just using the 'common sense method':
Notice both answers do give slightly different decimal values .
Last edited by davidgoes4wce; 21 Feb 2017 at 9:37 PM.
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
0.892 and 0.655536 are wrong. By doing it manually like this you are greatly increasing the number of points at which you can mess up the calculation. And of course this won't be feasible if 9 is replaced by 1000.
The correct answer is the expression t8 (although the 2 is +2, not -2), which in decimal form is exactly 15.31564544.
Ps. alarm bells should be ringing in your head at "slightly different decimal values". The only step in which any rounding is involved is at the very end, so these answers should coincide exactly prior to rounding, which they clearly don't.
Last edited by seanieg89; 21 Feb 2017 at 3:33 PM.
OK yep I see it
should be 0.8192 metres and 0.65536 metres
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
Depends what you mean by suitable.
a) Will the answer be the same?
Yes, obviously. Summing a geometric series manually will give you the same result as applying the formula for the sum of a geometric series.
b) Will markers treat the solution as being equally valid?
I don't know the marking criteria, but I can't imagine any reason why not.
c) Do I recommend manually summing geometric/arithmetic series?
Definitely not, unless the series is only a couple of terms long. As I said in my previous post, you are greatly increasing the number of places at which you can make mistakes. The method is also slower (assuming proficiency with both), and not feasible for series with many terms. You need to know how to sum general arithmetic and geometric series for the course anyway, so why not use this knowledge?
Yep thanks for your response.
I did some vector cross product before , a large chapter was devoted to that in Calculus Stewart book. I remember when I did 2nd year Engineering, I spent a lot of time doing those questions. It's a very efficient way of calculating an area.
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
If you were pedantic, then expressing your answer in years only is more appropriate since our question was with respect to years. i.e. maintain consistency of units
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:
Last edited by davidgoes4wce; 11 Mar 2017 at 12:58 AM.
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
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.
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
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..
Last edited by Drongoski; 18 Mar 2017 at 5:25 PM.
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