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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I need help with part b) I get y ' = -sinx/cosx + 1/cos^2 x - 1 Now I make this equal to 0 for stat pts but am unsure on the next step. I tried multiplying by cos^2 x to everything but there will be a sinxcosx .
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread i) Sketch the region in the complex plane which simulatenously satisfies: -pi/4 < or equal to arg(z + i) < or equal to pi/4 and |z - 2| < or equal to 1 ii) Find the maximun value of |z| iii) Find the minium values of arg(z)...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread There is a multiple choice question that says what is the range of g(x) = tan(1/2 inverse cos x) a) y less than 0 b) y all real c) 0 < y <1 D) y greater than or equal to 0 I choice b But the answer says D. Can someone...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I get part a) But am unsure on how to answer part b) using part a) part b) ii) answer says root 2 -1 = tan22.5 degrees
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Find the indefinite integral of the following; Integral of cos^2 (x/2) dx The answer says = 1/2 Integral of (cos x + 1) dx I don't get this part of the working.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Sorry, I also don't get part i) of the question Also, should I know that relationship? Don't remember learning it.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I don't get question 5 b) Mathematic Induction Q from this HSC Paper http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2000exams/hsc00_maths/97MAT3U.PDF Also if you go down to page 56 question 5b in the notes for this paper...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Thanks, I got it.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I thought the numerator had to be 1 to be able to use the standard formula to get tan^-1 ..... ( the one in the reference sheet) Also the question said to use the reverse chain rule, which is what I am confused about.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Stuck on question b) I let u = e^-x and got u' = - 1/e^x Is that correct? Not sure where to go now.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I do the normal integration and get up to tan^-1 3/5 - tan^-1 (-1/4) Not sure where to go from here.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I am stuck on part g) I have A = 2 Integral from 0 to infinity of 4/(x^2 + 4) dx I continued on but the problem is I get inverse tan of infinity on 2 Not sure where to go from here.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I understand how to do question a) and b). They are both odd so the area's cancel each other out and so the answer for both are 0. However I am unsure about question c). It has no symmetry. The answer says 3pi/4
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Having trouble with part b Using part a), I took the integral of both side and I got this Integral of tan^-1 x dx = xtan^-1 x - Integral of x/(1 + x^2) dx So I need to find the integral of x/(1 + x^2) Is this the...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Don't know how to do part b) Answer is 1 - 1/2 (3)^1/2 I have A = integral from 0 to pi/6 sin^2 y du Is that correct? then I got integral from 0 to pi/6 1/2 (1 - cos2y) dy I further continued on but got an...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread For part b), I get the answer they have in the question except for no absolute sign around the x in the denominator. Why is that? I used chain rule to differentiate the fn.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Could you explain how do find the domain. part a)
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Finally worked it out. Now stuck on the Show part of part c) in this question. Not sure how to do the branching of it.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I don't know that formula. I tried searching for it in the cambridge 3u textbook and can't find it. If I don't use the formula, is there another method to solving the question?
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Still very confused. I still am not getting the result. Also where does the 1/4 go now?
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