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    Inverse secant function?

    Does anyone recall seeing a Trial or HSC question that dealt with the inverses of sec, cosec, or cot? I saw one recently on sec-1x and am wondering if it was a one-off or if there are more that have appeared in past exams. Thanks
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    Challenging (?) Proof Question

    Prove that if M \notin \mathbb{Z} but M + \cfrac{1}{M} = \cfrac{M^2 + 1}{M} \in \mathbb{Z}, then M^n + \cfrac{1}{M^n} \in \mathbb{Z} for all n \in \mathbb{Z}^+. I am curious as to how Extension 2 students would approach this as a proof problem, and wondering if there are other approaches beyond...
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    Error in Help Section?

    At the end of the help section at there is help for latex codes that contains int_{1}^{2} x^{2} - 1 I think is meant to be an integral, and thus something like \int_{1}^{2} {x^2 - 1} dx Perhaps this could be fixed? Also, is there are a...
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    Worksheets and questions

    I was asked to post some more questions. The following are in no particular order, and focus on no particular topic, and vary in standard... 1. ABC is any triangle. Show that (a) tan A + tan B + tan C = tan A * tan B * tan C (b) sin A + sin B + sin C = 4cos(A / 2)cos(B / 2)cos(C / 2)...
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    CM_Tutor leaving

    for the snow for a week's holiday this weekend. :) So, the last time I'll be around before going will probably be Sat AM, and I won't be back until late on Sun 18th. If there are any things people want to ask about before I go, please post here. Also, if things come up while I'm away...
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    Some More Questions to Think About

    1. Consider the sequence a<sub>0</sub>, a<sub>1</sub>, a<sub>2</sub>, ... which is an increasing sequence of real numbers (ie a<sub>n</sub> < a<sub>n+1</sub> for all non-negative integers n), defined by a<sub>n+1</sub> = 2<sup>n</sup> - 3a<sub>n</sub>, for n = 0, 1, 2, ... (a) If the first...
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    Parametrics Questions

    In another thread, nike33 asked for some more interesting parametrics questions, so here we go... 1. P(2ap, ap<sup>2</sup>) and Q(2aq, aq<sup>2</sup>) are two points on the parabola x<sup>2</sup> = 4ay. The tangent at P and the line through Q parallel to the axis of the parabola meet at R...
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    Some Conics Questions

    Before I post any questions, I would like to make a couple of introductory comments about conics. Most students don't like conics, saying it is hard. I disagree. This is (conceptual) a relatively straight-forward topic, based mostly in simple co-ordinate geometry and calculus. What makes...
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    More questions from the ends of papers

    There has been a discussion of some of the harder stuff that can turn up at the ends of papers, so I thought I'd post some stuff from later questions of some 4u half-yearlies I have. I've skipped the motion, as people probably haven't done it yet, but please advise if I'm wrong... 1. (For...
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    Why do the subscript codes < sub > < /sub > (but without the spaces) not seem to work in some parts of the Chemistry forum. I just wrote a post using them in the Acidic Environment part of the forum, but they aren't working (thread on "Chemical Salts????????"). Can someone please have a look...
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    BOS University Guide: A Complete Guide to 1st Year Uni [A Work In Progress]

    I thought I might post a few pieces of advice that might benefit you all. Anybody with Uni experience, feel free to add add in some more hard won lessons. Lecturers know You might think that you are essentially anonymous in a lecture theatre of 150 people - unless you draw attention to...
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    Complex Numbers and Geometry

    Here are a few more questions for people to ponder. I know that each can be done algebraically, and this is better than not being able to solve them at all, but all are more easily done geometrically. 1. P and Q are points on the Argand Diagram representing the complex numbers z and w...
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    Challenge complex numbers problem for current students

    Suppose that z is a complex number with modulus 1 and argument @ (ie z = cos@ + isin@). (a) Show that z^n - 1 = 2i * sin(n@ / 2) * [cos(n@ /2) + isin(n@ / 2)], for n a positive integer. (b) Hence, or otherwise, show that z + z^2 + z^3 + ... + z^n = {sin(n@ / 2) / sin(@ / 2)] * [cos[(n +...
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    Challenge Polynomials problem for current students

    Here is a problem for current Extension 2 students to think about - it is not intended for those of use who are post-school to prove we can do it, because I'm sure we can. The polynomial ax^4 + bx^3 + cx + d = 0 has a triple root. (a) By proving that this root occurs at x = -b / 2a, or...