2016 Mathematics HSC 3 Unit
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1)
a
D
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2)
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B
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3)
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A
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4)
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C
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5)
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6)
a
D
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7)
a
C
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8)
a
B
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9)
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A
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10)
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A
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11a)
a
$y=(x+2)^{\frac13}$
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11b)
a
$\frac25(x-4)^{\frac52}+\frac83(x-4)^{\frac32}+C$
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11c)
a
$\frac{6}{1+4x^2}$
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11d)
a
$\frac23$
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11e)
a
$x<-3$, $-\frac52
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11fi)
a
$\frac{36}{125}$
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11fii)
a
$\frac{2997}{3125}$
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12ai)
a
$r=\frac h4$
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12aii)
a
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12aiii)
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12aiv)
a
$-0.2$cm$^3$ per second
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12bi)
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12bii)
a
$A=500$
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12ci)
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12cii)
a
$\alpha\approx0.76$
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13ai)
a
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13aii)
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$11:22:30$am
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13bi)
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13bii)
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13biii)
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$2.5$ seconds
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13biv)
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$25$m
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13ci)
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13cii)
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14ai)
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14bi)
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14bii)
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14biii)
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14ci)
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14cii)
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14ciii)
a
$\frac a4$
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14civ)
a
$t=\pm\sqrt2$
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Answers
1) D
2) B
3) A
4) C
5) A
6) D
7) C
8) B
9) A
10) A
11a) $y=(x+2)^{\frac13}$
11b) $\frac25(x-4)^{\frac52}+\frac83(x-4)^{\frac32}+C$
11c) $\frac{6}{1+4x^2}$
11d) $\frac23$
11e) $x<-3$, $-\frac52
11fi) $\frac{36}{125}$
11fii) $\frac{2997}{3125}$
12ai) $r=\frac h4$
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12aiii) show that question
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12aiv) $-0.2$cm$^3$ per second
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12bii) $A=500$
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12cii) $\alpha\approx0.76$
13ai) explain question
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13aii) $11:22:30$am
13bi) proof question
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13biii) $2.5$ seconds
13biv) $25$m
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13cii) proof question
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14ai) show that question
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14aii) proof question
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14bi) show that question
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14bii) show that question
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14biii) show that question
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14ci) show that question
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14cii) show that question
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14ciii) $\frac a4$
14civ) $t=\pm\sqrt2$
Solutions
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11a)
11b)
11c)
11d)
11e)
11fi)
11fii)
12ai)
12aii)
12aiii)
12aiv)
12bi)
12bii)
12ci)
12cii)
13ai)
13aii)
13bi)
13bii)
13biii)
13biv)
13ci)
13cii)
14ai)
14aii)
14bi)
14bii)
14biii)
14ci)
14cii)
14ciii)
14civ)
