smc-5240-50-Other

v1 Algebra, STD2 A2 2009 HSC 14 MC

If $C=5x+4$, and $x$ is increased by 3, what will be the corresponding increase in $C$ ?

$3$
$15$
$3x$
$5x$

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$B$

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$C=5x+4$

$\text{If}\ x\ \text{increases by 3}$

$C\ \text{increases by}\ 5\times 3=15$

$\Rightarrow B$

♦ Mean mark 50%.
STRATEGY: Substituting real numbers into the equation can work well in these type of questions. eg. If $x=0,\ C=4$ and when $x=3,\ C=19$.

v1 Algebra, STD2 A2 2005 HSC 17 MC

The total cost, $$C$, of a school excursion is given by $C=4n+9$, where $n$ is the number of students.

If five extra students go on the excursion, by how much does the total cost increase?

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$B$

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$C=4n+9$

$\text{If}\ n\ \text{increases to}\ n+5$

$C$	$=4(n+5)+9$
	$=4n+20+9$
	$=4n+29$

$\therefore \text{Total cost increases by }$20$

$\Rightarrow B$

v1 Algebra, STD2 A4 2017 HSC 17 MC

The graph of the line with equation $y=5-x$ is shown.

When the graph of the line with equation $y=2x-1$ is also drawn on this number plane, what will be the point of intersection of the two lines?

$(0, 5)$
$(1, 2)$
$(2, 3)$
$(5, 0)$

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$C$

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$\text{Method 1: Graphically}$

$\text{From graph, intersection is at} (2,3)$

$\text{Method 2: Algebraically}$

$y$	$=5-x$	$…\ (1)$
$y$	$=2x-1$	$…\ (2)$

$\text{Substitute (2) into (1)}$

$2x-1$	$=5-x$
$3x$	$=6$
$x$	$=2$

$\text{When}\ \ x=2,\ y=5-2=3$

$\Rightarrow C$

v1 Algebra, 2ADV F1 2018 HSC 3 MC

What is the $x$-intercept of the line $x-4y+8=0$?

$(-2, 0)$
$(-8, 0)$
$(0, -8)$
$(0, -2)$

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$B$

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$x\text{-intercept occurs when}\ y = 0:$

$x-4y+8$	$=0$
$x$	$=-8$

$\therefore\ x\text{-intercept is}\ (-8, 0)$

$\Rightarrow B$

v1 Algebra, STD2 A2 SM-Bank 6 MC

Hannah went paddle boarding on a holiday.

The hiring charges are listed in the table below:

\begin{array} {|l|c|c|}
\hline \text{Hours hired} \ (h) & 1 & 2 & 3 & 4 & 5 \\
\hline \text{Cost} \ (C) & 15 & 23 & 31 & 39 & 47 \\
\hline \end{array}

Which linear equation shows the relationship between $C$ and $h$?

$C=8+7h$
$C=7+8h$
$C=15+8h$
$C=8+15h$

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$B$

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$\text{Consider Option 2:}$

$7+8\times 1=7+8=15$

$7+8\times 2=7+16=23$

$7+8\times 3=7+24=31\ \ \ \ \text{etc …}$

$\text{The linear equation is:}\ \ C=7+8h$

$\Rightarrow B$

v1 Algebra, STD2 A2 2020 HSC 6 MC

Suppose $y=-2-3x$.

When the value of $x$ increases by 4, the value of $y$ decreases by

$1$.
$4$.
$12$.
$14$.

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$C$

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$\text{Strategy 1}$

$\text{If}\ \ x\ \ \text{increases by} \ 4$

$\rightarrow y\ \text{decreases by} \ \ 3x=3\times 4 = 12$

$\text{Strategy 2}$

$\text{Test}\ 2\ \text{values:}$

$\text{If} \ \ x=0 , \ y=-2$

$\text{If}\ \ x=4 , \ y =-2-3\times 4=-14$

$\therefore\ \ y \ \text{decreases by} \ 12.$

$\Rightarrow C$

v1 Algebra, STD2 A2 2021 HSC 9 MC

Marty is thinking of a number. Let the number be $n$.

When Marty subtracts 4 from this number and multiplies the result by 7, the answer is 8 more than $n$.

Which equation can be used to find $n$?

$7n-4=8n$
$7(n-4)=8n$
$7n-4=n+8$
$7(n-4)=n+8$

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$D$

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$\text{The description defines the following equation:}$

$(n-4)\times 7$	$=n+8$
$7(n-4)$	$=n+8$

$\Rightarrow D$

v1 Algebra, STD2 A1 2009 HSC 16 MC

The time for a train to travel a certain distance varies inversely with its speed.

Which of the following graphs shows this relationship?

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$C$

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$T$	$\propto \dfrac{1}{S}$
$T$	$=\dfrac{k}{S}$

$\text{By elimination:}$

$\text{As Speed} \uparrow \ \text{, Time}\downarrow\ \Rightarrow\ \text{cannot be A or B}$

$\text{D is incorrect because it graphs a linear relationship}$

$\Rightarrow C$

♦♦ Mean mark 38%.

\(C\)	\(=4(n+5)+9\)
	\(=4n+20+9\)
	\(=4n+29\)

\(y\)	\(=5-x\)	\(…\ (1)\)
\(y\)	\(=2x-1\)	\(…\ (2)\)

\(2x-1\)	\(=5-x\)
\(3x\)	\(=6\)
\(x\)	\(=2\)

\(x-4y+8\)	\(=0\)
\(x\)	\(=-8\)

\((n-4)\times 7\)	\(=n+8\)
\(7(n-4)\)	\(=n+8\)

\(T\)	\(\propto \dfrac{1}{S}\)
\(T\)	\(=\dfrac{k}{S}\)