Recent content by Luukas.2

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    HSC+CSSA Trial Past Papers + Answers Sorted by topic

    @skepticalmiss... the CSSA take a strong stance on copyright and so have forced most places hosting their papers to take them down. HSC papers can be accessed only from NESA, who similarly object to anyone else posting their papers online. Likely that is why this old link no longer works.
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    Proofs q

    It's worth noting that this proof would not have established the maximum area at all without the equality part. Leaving out the equality part, the proof establishes that the area of any triangle with semi-perimeter s cannot be more than s2 / root 27, but that doesn't mean that a triangle with...
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    year 11 adv and ex1 math resources

    Bear in mind that the paper is an assessment task 1 from about April, not a yearly paper
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    Year 10 5.3: the sine rule for angles

    There are two answers to 5(a), but the second one is not 117o, it is 21o. If the third angle is x (say) then: \frac{\sin{x}}{8}=\frac{\sin{42^\circ}}{6} \qquad \implies \qquad \sin{x} = \frac{4}{3} \times \sin{42^\circ} \approx 0.892174 ... There are two possible solutions: \text{Answer 1: }...
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    Perms and combs

    Another approach: Arrange the IMION in 5! / 2! ways. Choose the 5 positions from 10 for the word PRESS in 10C5 = 10! / (5!)2 ways Total arrangements = 10! / (5!)2 times 5! / 2! = 10!5! / (5!)22! = 10! / 5!2! after cancelling Thus, the answer is indeed (B)
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    Is it assumed that dot product of 0 means perpendicular?

    It is NOT true to say that, just because the dot product of two vectors a and b is zero, it follows that a and b are perpendicular. The correct inference is that EITHER a and b are perpendicular OR at least one of the vectors a or b is the zero vector. Formally, once you have shown that a . b...
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    why isnt it A for q13

    The net effect in (A) has forward faster than reverse, though decreasing as it approaches equilibrium. The forward rate is increasing in (B) but the reverse rate is higher / faster so the net movement is to the left.
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    why isnt it A for q13

    For Q 13, adding aqueous NaOH to a saturated Mg(OH)2 solution will lead to further precipitation of Mg(OH)2 (s) and with a decrease in the concentration of magnesium ions and an increase in the concentration of hydroxide ions such that [Mg2+][OH-]2 remains constant. This assumes that the sodium...
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    why isnt it A for q13

    For the second one, shifting to the right means the rate of the forward reaction (A + B ---> C) is faster / higher than that of the reverse reaction. Prior to returning to equilibrium, graph A has rate forward > rate reverse (moving right) while (B) has rate reverse > rate forward.
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    Math year 10 5.3: trigonometric relations

    I am guessing that you are just starting to deal with angles of any magnitude, and thus that trig functions aren't always positive. In each case, the noted information is meant to tell you that the two angles are both acute and complementary... you need the (highlighted) complementary part to...
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    Question help plsplsplsplspls

    More likely that the answer is correct and the question is wrong... y = 8 leads to a messier answer, they probably meant it to be y = 9.
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    4u integration

    They were standard integrals on the old syllabus, but that's going back a way - see page 16 of the 2001 paper accessible from https://educationstandards.nsw.edu.au/wps/portal/nesa/resources-archive/hsc-exam-papers-archive/mathematics/mathematics-2001-hsc-exam-pack-archive, for example
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    ionisation energies q

    Since element B has the highest first IE amongst the four consecutive elements, it must be a noble gas. Thus: element A is a halogen (group 17) and forms an A- anion element C is in group 1 and forms a C+ cation element D is in group 2 and forms a D2+ cation Forming a D3+ cation requires much...
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    How would you solve double inequalities like this

    You can also find the boundary values by solving \begin{align*} |3x - 2| &= |x + 4| \\ \\ \textbf{Case 1:} \qquad 3x - 2 = x + 4 \qquad \implies \qquad 2x &= 6 \qquad \implies \qquad x = 3 \\ \\ \textbf{Case 2:} \qquad 3x - 2 = -(x + 4) \qquad \implies \qquad 4x &= -2 \qquad \implies \qquad x =...
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    Rate of Change Question

    Define a height axis, y, along the central axis of the cylinder, taking y = 0 at the top and placing the light source at y = h above the cylinder. When h > 0, the light casts a shadow of radius i cm from the axis. We are told that h is increasing at dh/dt = 3 cm/s, and r decreases as this...
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