MedVision ad

Search results

  1. I

    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $By the way, to simplify this, we should consider things as a function of $\tan \alpha$ instead of $\alpha$. I.e. the area is $A=f(\tau)=\frac{\left(2\tau +1 \right)^2}{2\tau}$, (assuming your functions are all correct), where...
  2. I

    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $What were your functions you got?$
  3. I

    Interesting mathematical statements

    $\noindent Another really nice one is Bayes' Billiard Ball argument that proves that $\int _0 ^1 \binom{n}{k}x^k (1-x)^{n-k}\text{ d}x=\frac{1}{n+1}$ without needing to do any integration at all. The 18$^{\text{th}}$ century probabilist Bayes essentially proved this by considering two equivalent...
  4. I

    HSC 2016 MX2 Integration Marathon (archive)

    Re: MX2 2016 Integration Marathon $\noindent Here's a pretty nice result that's easy to prove.$ $\underline{QUESTION}$ $\noindent Let $f$ be a function that is differentiable and invertible on $[a,b]$ and suppose $f(a)=a$ and $f(b)=b$ (\small{i.e. $a$ and $b$ are \textit{fixed points} of...
  5. I

    Best textbooks and sources for chemistry

    For HSC Chemistry textbooks, Jacaranda and Conquering Chemistry are considered to be the most useful I think.
  6. I

    Advanced Courses?

    What about if you didn't get 65+ in everything, but your average mark was above 65?
  7. I

    Advanced Courses?

    It's equivalent to a Credit (weighted) average: https://en.wikipedia.org/wiki/Academic_grading_in_Australia#Grade_point_average (Check the column there with "UWS" in it.)
  8. I

    what proofs do we need to know

    Yeah, proof by contradiction is a way to prove that radius one. A proof is here on ProofWiki: https://proofwiki.org/wiki/Radius_at_Right_Angle_to_Tangent $An alternative proof is obtained via calculus. Use implicit differentiation to find the slope of the tangent at $P(x_0,y_0)$ to the circle...
  9. I

    what proofs do we need to know

    Oh, and for the radius is perpendicular to tangent one, that's one that's meant to have its proof discussed in class, but the reproduction of its proof is not needed by students according to the syllabus. So maybe that's why your teacher didn't bother proving it.
  10. I

    what proofs do we need to know

    People who don't read the syllabus could be in trouble if the HSC exam ended up asking for a proof of one of the circle geometry theorems. But you're right, it'd be quite surprising if the HSC exam asked for a proof of such a theorem.
  11. I

    what proofs do we need to know

    Probably. Everything has guidance nowadays. Anyway, here is the syllabus for Mathematics 2U/3U Year 11-12: http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths23u_syl.pdf On page 28, for circle geometry, it says: "3 Unit students will be expected to be able to prove any of the...
  12. I

    what proofs do we need to know

    Iirc there are things students are technically expected to be able to prove, e.g. certain circle geometry theorems, but they rarely get asked.
  13. I

    what proofs do we need to know

    You don't need to know the proofs for Simpson's rule of Trapezoidal rule I think (to be absolutely sure, check the syllabus on the BOSTES site, but they never ask about those). Trapezoidal rule formula is easy to prove though, it's just the area of a trapezium. And what are your referring to by...
  14. I

    Scaling

    They don't scale too well (compared to other common NSW HSC subjects).
  15. I

    Log Help 2

    $\underline{QUESTION 1}$ $We have$ $$\begin{align*}C&= A \log_{200} 5 + B \log_{200}2 \\ &= \log_{200} \left(5^A\right) + \log_{200} \left(2^B \right) \\ &= \log_{200} \left(5^A\times 2 ^B\right)\\ \Rightarrow 200^C &=5^A\times 2 ^B , \text{but }200 = 2^3 \times 5^2 \text{ so} \\ \left(2^3...
  16. I

    Griffith Med Sci question

    Someone got in last year with 99.5 ATAR I think, to Nathan campus. Check out this thread: http://community.boredofstudies.org/332/medicine-medical-health-studies/333245/anyone-receive-offer-griffith-med.html
  17. I

    Series and Sequences

    $The $(n+1)^{\text{th}}$ term $t_{n+1}$ is$ $$\begin{align*}t_{n+1} &= S_{n+1}-S_n \\ &= 7(2^{n+1}-1) - 7(2^n-1) \\ &= 7 \times 2^{n+1} - 7\times 2^n \\ &= 7\times 2^n \left(2-1 \right) \\ &=7\times 2^n . \end{align*}$$ $Hence$ $$\begin{align*}S_n &=7\left(2^n-1\right) \\ &= 7\times 2^n - 7...
  18. I

    HSC 2016 MX2 Marathon ADVANCED (archive)

    Re: HSC 2016 4U Marathon - Advanced Level I and another user were also a bit confused by this so we asked some questions about it on the thread where it was first posted, so you might want to read those posts...
  19. I

    How to do really well in 3 unit

    Just avoid silly mistakes.
  20. I

    HSC 2016 MX2 Marathon ADVANCED (archive)

    Re: HSC 2016 4U Marathon - Advanced Level $\noindent I don't know if he did it this way, but one way would be to look at the divided equation he has. He then noticed what are the only integer pairs that make the L.H.S. an integer. Then, just test these ones to see if they are solutions. This...
Top