2016 Mathematics HSC 2 Unit

Answers

1) B

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2) C

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3) B

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4) A

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5) B

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6) A

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7) A

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8) D

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9) C

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10) D

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11a)

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11b) $-\frac{10}{(3x-4)^2}$

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11c) $-1\le x\le5$

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11d) $10$

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11e) Points of intersection are $(4,-21)$ and $(-2,3)$

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11f) Gradient of tangent is $1.17$

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11g) $x=\frac{\pi}{3},\frac{5\pi}{3}$

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12ai) Show that question.
Look at solution.

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12aii) $AD=\frac{19}{5}$

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12aiii) Area$=\frac{19}{2}$ square units

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12bi) Show that question.
Look at solution.

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12bii) $x=29$

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12c) $\theta=69^\circ$ to the nearest degree

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12di) $\frac{dy}{dx}=e^{3x}(1+3x)$

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12dii) $6e^6$

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13ai) Local maximum at $x=3$, ie at $(3,27)$

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13aii)

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13bi) Focal Length$=3$

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13bii) Focus $(2,2)$

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13ci) A$=10$

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13cii) $k=\frac{\ln\left(\frac12\right)}{-163}$
$\approx0.004252436$

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13d) $\frac{4}{\pi}-\frac12$ square units
or $\frac{8-\pi}{2\pi}$ square units

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14a) Area$\approx1.4$m$^2$

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14bi) Show that question.
Look at solution.

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14bii) Show that question.
Look at solution.

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14biii) $A_{14}\approx14500$

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14ci) Show that question.
Look at solution.

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14cii) Minimum length$=120$

at $x=12$, $\frac{d^2l}{dx^2}=\frac{1440}{12^3}>0$ therefore a minimum.

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14d) $5$

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14e) $45\log2$

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15a) $V=\frac{40\pi}{3}$

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15bi) Explain question.
Look at solution.

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15bii) $n=12$

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15ci) Show that question.
Look at solution.

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15cii) Show that question.
Look at solution.

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15ciii) $h=\frac{y}{x}$

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16ai) $v=-2$

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16aii) $a=1$ms$^{-2}$

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16aiii)

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16aiv) Distance travelled$=10+8\log2-4\log2^3$

or distance travelled$=10+8\log2-12\log2$

or distance travelled$=10-4\log2$

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16bi) Show that question.
Look at solution.

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16bii) $10\le y<200$

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16biii) Show that question.
Look at solution.

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16biv) Population growing fastest when population is $y=100$

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