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  1. R

    HSC Biology Marathon 2015

    1. 20 cuttings of length 10cm were made from a Germanium plant. 2. Each cutting was embedded into a pot with standard potting mix one third of the way deep. 3. The cuttings were randomly allocated into two groups of 10. 4. The first group received water everyday, while the second group received...
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    HSC Biology Marathon 2015

    For optimal cell functioning. If there is an incorrect order of bases: different mRNA strand produced in transcription -> different amino acids and polypeptides produced in translation -> potentially impaired cell activity. Not sure if that is what the question was asking for.
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    HSC Biology Marathon 2015

    Contrast the movement of materials in the phloem tissue of plants with the movement of blood in the vascular system of mammals. (4 marks)
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    HSC Biology Marathon 2015

    That's pretty much it. You could have also mentioned that dialysis does not perform all the functions of the kidney (no hormonal control of blood pressure), and that is difficult to find donors for kidney transplants.
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    HSC Biology Marathon 2015

    Kidney disease is the 8th leading cause of death in the United States. An estimated 31 million people in the United States (10% of the population) have chronic kidney disease (CKD). CKD is more common among women, but men with CKD are 50% more likely than women to progress to kidney failure...
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    HSC Biology Marathon 2015

    Prions - non-cellular proteins that are capable of causing disease. They lack genetic material. Viruses - non-cellular pathogens made up a protein coat which encloses genetic material in the form of DNA or RNA. Protozoa - unicellular eukaryotes. Fungi - unicellular or multi-cellular eukaryotes...
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon \begin{align*}W&=W_0e^{0.02t} \\H&=H_0e^{-0.01t} \\\textup{When }t&=0 \to W=8000,~H=12000 \\8000&=W_0e^0 \to W_0=8000 \\12000&=H_0e^0 \to H_0=12000 \\\therefore W&=8000e^{0.02t},~H=12000e^{-0.01t} \\\textup{Populations are equal when }W&=H...
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    HSC Physics Marathon 2013-2015 Archive

    re: HSC Physics Marathon Archive .
  9. R

    Biology 2015 Predictions

    Here's what has been asked so far: 2001: Reproductive technologies 2002: First hand investigation (size of red blood cells), Contributions of Louis Pasteur and Robert Koch 2003: Designing an epidemiological study 2004: Planning an investigation (enzyme activity under certain conditions) 2005...
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon If you're using O, A, and (4,0) to make your triangle, it is not a triangle as a side would be curved - the one from A to (4,0).
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon Split it into two areas from x=0 to x=1 (point of intersection), and x=1 to x=2. The first part is the area under 4x-x2, while the second part is the area under 4-x2: A=\int^1_0~4x-x^2~\mathrm{d}x+\int^2_1~4-x^2~\mathrm{d}x. If you evaluate...
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon $1. Differentiate $\log_e{\left (\frac{\sqrt{x}}{2x+1} \right )}$. \\\indent 2. Calculate the volume of solid generated when the curve $y=\frac{1}{2} \left (e^{x}+e^{-x} \right )$ is rotated about the $x$-axis between $x=-3$ and $x=3$. \\\indent 3. Prove $\int^{e^2}_e...
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    HSC 2015 MX1 Marathon (archive)

    Re: HSC 2015 3U Marathon $Evaluate $\int^{3^5}_{2^5}~\frac{1}{x-x^\frac{3}{5}}~\mathrm{d}x$ using the substitution $u=x^{\frac{2}{5}}-1$.
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon $Given that $f(x)+2f(8-x)=x^2$ for all real $x$, find $f(2)$.
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon Let ABC be a triangle such that AB = 3, BC = 4, AC = 5. Let X be a point in the triangle. Find the minimal possible value of AX2 + BX2 + CX2.
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon There is a circular table with 6 chairs. Alice, Bob, and Eve each pick a random chair to sit down in. Compute the probability that each person has an empty chair on either side of them.
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    Factorisation

    It is easier if you consider the coefficient of x^3 in (1+x)^{m+n} and (1+x)^m(1+x)^n. You know that the coefficients of x^3 in each of these expansions will be equal as (1+x)^m(1+x)^n=(1+x)^{m+n}.
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    HSC 2015 Maths Marathon (archive)

    Re: HSC 2015 2U Marathon I'll label each corner of the staircase with B, C, D, E, ... So we have: $B$ \left (\cos{18}, ~ 0 \right ) $C$ \left (\cos{18}, ~ \cos^2{18} \right ) $D$ \left (\cos{18} + \cos^3{18}, ~ \cos^2{18} \right ) $E$ \left (\cos{18} + \cos^3{18}, ~ \cos^2{18} + \cos^4{18}...
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    HSC 2015 MX1 Marathon (archive)

    Re: HSC 2015 3U Marathon If you draw the circle as the question suggests ("13 cards (Ace through King in that order) in a circle."), you could try a random selection. For example, starting at the top (Ace) and skipping every second card (2, 4, 6, ...) so that we have every first flipped over...
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    HSC 2015 MX1 Marathon (archive)

    Re: HSC 2015 3U Marathon (1) I understood this part by actually testing it out. I'll refer to flipping as crossing out on the circle. I drew up the circle, crossed out the top card (the Ace on my circle) and then the one on the right (4). I then made an isolated card by skipping the third card...
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