smc-5233-10-Substitute

v1 Algebra, STD2 A1 2010 HSC 7 MC

If $M=-8$, what is the value of $\dfrac{4M^2+3M}{8}$

$-1027$
$-35$
$29$
$125$

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$C$

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♦♦ Only 31% of students answered correctly!

$\dfrac{4M^2+3M}{8}$	$=\dfrac{4\times (-8)^2+3\times (-8)}{8}$
	$=\dfrac{4\times 64-24}{8}$
	$=\dfrac{232}{8}$
	$=29$

$\Rightarrow C$

v1 Algebra, STD2 A1 2008 HSC 9 MC

What is the value of $\sqrt{\dfrac{2x + y}{5x}}$ if $x=5.1$ and $y=3.7$, correct to 2 decimal places?

$0.13$
$0.74$
$3.74$
$3.80$

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$B$

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$\sqrt{\dfrac{2x+y}{5x}}$	$=\sqrt{\dfrac{2\times 5.1+3.7}{5\times 5.1}}$
	$=\sqrt{\dfrac{13.9}{25.5}}$
	$= 0.7383\dots$

$\Rightarrow B$

v1 Algebra, STD2 A1 2007 HSC 28b

This shape is made up of a right-angled triangle and a regular hexagon.

The area of a regular hexagon can be estimated using the formula $A=2.598H^2$ where $H$ is the side-length.

Calculate the total area of the shape using this formula. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

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$51.264\ \text{cm}^2$

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$\text{Area}=2.598H^2$

$\text{Using Pythagoras}$

$H^2$	$= 3^2+3^2$
	$=18$
$H$	$=\sqrt{18}$

$\therefore\ \text{Area of hexagon}$	$=2.598\times {\sqrt {18}}\ ^2$
	$=46.764\ \text{cm}^2$

$\text{Area of triangle}$	$=\dfrac{1}{2}bh$
	$=\dfrac{1}{2}\times 3\times 3$
	$=4.5\ \text{cm}^2$

$\therefore\ \text{Total Area}$	$=46.764+4.5$
	$=51.264\ \text{cm}^2$

v1 Algebra, STD2 A1 2005 HSC 2 MC

What is the value of $\dfrac{x-y}{6}$, if $x=184$ and $y=46$?

$6$
$23$
$176$
$552$

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$B$

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$\dfrac{x-y}{6}$	$=\dfrac{184-46}{6}$
	$=23$

$\Rightarrow B$

v1 Algebra, STD2 A1 2006 HSC 2 MC

If $V=\dfrac{4}{3}\pi r^3$, what is the value of $V$ when $r = 5$, correct to two decimal places?

$20.94$
$53.05$
$104.72$
$523.60$

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$D$

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$V =\dfrac{4}{3}\pi r^3$

$\text{When}\ r = 2,$

$V$	$=\dfrac{4}{3}\pi\times 5^3$
	$=523.598\dots$

$\Rightarrow D$

v1 Algebra, STD2 A1 2004 HSC 3 MC

If $K=Ft^3$, $F=9$ and $t=0.829$, what is the value of $K$ correct to three significant figures?

$5.12$
$5.127$
$5.128$
$5.13$

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$D$

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$K$	$=Ft^3$
	$=9\times 0.829^3$
	$=5.1275\dots$
	$=5.13\ \text{(3 sig figures)}$

$\Rightarrow D$

v1 Algebra, STD2 A1 SM-Bank 1

What is the value of $4m^2-n$, if $m=−3$ and $n=1$. (2 marks)

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$35$

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$4m^2-n$	$=4(−3)^2-1$
	$=4\times 9-1$
	$=35$

v1 Algebra, STD2 A1 SM-Bank 2

If $A=P(1 + r)^n$, find $A$ given $P=$500$, $r=0.09$ and $n=5$ (give your answer to the nearest cent). (2 marks)

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$$769.31\ \text{(nearest cent)}$

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$A$	$=P(1 + r)^n$
	$=500(1 + 0.09)^5$
	$=500(1.09)^5$
	$=769.311\dots$
	$=$769.31\ \text{(nearest cent)}$

v1 Algebra, STD2 A1 2017 HSC 7 MC

It is given that $I=\dfrac{3}{2}MR^2$.

What is the value of $I$ when $M =19.12$ and $R = 1.02$, correct to two decimal places?

$13.26$
$29.84$
$119.35$
$570.52$

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$B$

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$I$	$=\dfrac{3}{2}\times 19.12\times 1.02^2$
	$=29.84$

$\Rightarrow B$

v1 Algebra, STD2 A1 SM-Bank 7

If $S = V_0(1 - r)^n$, find $S$ given $V_0 = $57\ 000$, $r = 0.12$ and $n=5$. (give your answer to the nearest cent). (2 marks)

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$$30\ 080.72\ \text{(to nearest cent)}$

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$S$	$=V_0(1 – r)^n$
	$=57\ 000 (1-0.12)^5$
	$=57\ 000 (0.88)^5$
	$=$30\ 080.719\dots$
	$=$30\ 080.72\ \text{(to nearest cent)}$

v1 Algebra, STD2 A1 SM-Bank 8

What is the value of $\dfrac{x+y}{xy}$ if $x=-4.3$ and $y=-2.4$, correct to 1 decimal place? (2 marks)

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$-0.6\ \text{(1 d.p.)}$

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$\dfrac{x+y}{xy}$	$=\dfrac{-4.3+(-2.4)}{-4.3\times -2.4}$
	$=\dfrac{-6.7}{10.32}$
	$=-0.649\dots$
	$\approx-0.6\ \text{(1 d.p.)}$

\(\dfrac{4M^2+3M}{8}\)	\(=\dfrac{4\times (-8)^2+3\times (-8)}{8}\)
	\(=\dfrac{4\times 64-24}{8}\)
	\(=\dfrac{232}{8}\)
	\(=29\)

\(\sqrt{\dfrac{2x+y}{5x}}\)	\(=\sqrt{\dfrac{2\times 5.1+3.7}{5\times 5.1}}\)
	\(=\sqrt{\dfrac{13.9}{25.5}}\)
	\(= 0.7383\dots\)

\(H^2\)	\(= 3^2+3^2\)
	\(=18\)
\(H\)	\(=\sqrt{18}\)

\(\text{Area of triangle}\)	\(=\dfrac{1}{2}bh\)
	\(=\dfrac{1}{2}\times 3\times 3\)
	\(=4.5\ \text{cm}^2\)

\(K\)	\(=Ft^3\)
	\(=9\times 0.829^3\)
	\(=5.1275\dots\)
	\(=5.13\ \text{(3 sig figures)}\)

\(\therefore\ \text{Area of hexagon}\)	\(=2.598\times {\sqrt {18}}\ ^2\)
	\(=46.764\ \text{cm}^2\)

\(\therefore\ \text{Total Area}\)	\(=46.764+4.5\)
	\(=51.264\ \text{cm}^2\)

\(\dfrac{x-y}{6}\)	\(=\dfrac{184-46}{6}\)
	\(=23\)

\(V\)	\(=\dfrac{4}{3}\pi\times 5^3\)
	\(=523.598\dots\)