2015 Mathematics HSC 3 Unit

Answers

1) A

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2) C

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3) B

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4) C

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5) A

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6) D

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7) B

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8) B

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9) D

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10) C

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11a) $\frac12x-\frac14\sin2x+c$

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11b) $\theta=\frac{\pi}{4}$ or $\theta=45^\circ$

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11c) $-3 < x\le 1$

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11d) $13\left(x+\tan^{-1}\left(\frac{12}{5}\right)\right)$

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11e) $\frac14\left(\ln3+\frac23\right)$

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11fi) show that question
look at solution

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11fii) $-1,3,4$

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12ai) $\angle ACB=60^\circ$

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12aii) $\angle ADX=30^\circ$

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12aiii) $\angle CAB=70^\circ$

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12bi) show that question
look at solution

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12bii) $\left(\frac{-a}{2},\frac{a}{16}\right)$

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12ci) show that question
look at solution

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12cii) $h\approx910$

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12di) show that question
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12dii) show that question
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12diii) $\approx2.57$

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13ai) $x=3,7$

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13aii) $\sqrt{11}$ms$^{-1}$

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13aiii) $a=2$, $c=5$, $n=\frac{\sqrt{11}}{2}$

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13bi) $a_2=\left(\begin{array}{cc} 18\\2\end{array}\right)\dfrac{2^{16}}{3^2}$

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13bii) $\left(\begin{array}{cc}18\\9\end{array}\right)\left(\dfrac23\right)^9$

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13c) proof question
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13di) proof question
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13dii) show that question
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14ai) show that question
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14aii) $\frac{\pi}{6}$ below the horizontal

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14aiii) downwards, for explanation see solution

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14bi) show that question
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14bii) $x=1-e^{-t}$

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14biii) $\lim_{t\to\infty}x=1$

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14ci) explain question
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14cii) $\left(\begin{array}{cc}4\\4\end{array}\right)\left(\dfrac12\right)^5+\left(\begin{array}{cc}5\\4\end{array}\right)\left(\dfrac12\right)^6+\left(\begin{array}{cc}6\\4\end{array}\right)\left(\dfrac12\right)^7$

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14ciii) proof question
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