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Algebra, STD2 A2 2021 HSC 9 MC

A student is thinking of a number. Let the number be `x`.

When the student subtracts 8 from this number and multiplies the result by 3, the answer is 2 more than `x`.

Which equation can be used to find `x`?

`3(x-8)=2x`
`3x-8=2x`
`3(x-8)=x+2`
`3x-8=x+2`

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`C`

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`text(The description defines the following equation:)`

`(x-8) xx 3`	`= x + 2`
`3(x-8)`	`=x+2`

`=>C`

Algebra, STD2 A2 2020 HSC 6 MC

Suppose `y = -1-2x`.

When the value of `x` increases by 5, the value of `y` decreases by

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`D`

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`text(Strategy 1)`

`text(If) \ \ x\ \ text(increases by) \ 5`

`=> y \ \ text(decreases by) \ \ 2x = 2 xx 5 = 10`

`text(Strategy 2)`

`text(Test) \ 2 \ text(values:)`

`text(If) \ \ x = 0 , \ y = -1`

`text(If) \ \ x = 5 , \ y = -1-10 = -11`

`:.\ y \ text(decreases by) \ 10.`

`=>D`

Algebra, STD2 A2 SM-Bank 6 MC

Renee went bike riding 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) & 18 & 24 & 30 & 36 & 42 \\
\hline \end{array}

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

`C = 12 + 6h`
`C = 6 + 12h`
`C=18 + 12h`
`C=12 + 18h`

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`A`

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`text(Consider Option 1:)`

`12 + (6 xx 1) = 12+6=18`

`12 + (6 xx 2) = 12+12=24`

`12 + (6 xx 3) = 12+18=30\ \ \ \ text(etc …)`

`:.\ text(The linear equation is:)\ \ C = 12 + 6h`

`=>A`

Algebra, STD2 A4 2017 HSC 17 MC

The graph of the line with equation `y = 6 - 2x` is shown.

When the graph of the line with equation `y = x + 3` is also drawn on this number plane, what will be the point of intersection of the two lines?

A. `(0, 6)`

B. `(1, 4)`

C. `(2, 2)`

D. `(3, 0)`

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`text(B)`

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`text(Solution 1)`

`text(From graph, intersection at (1,4))`

`=>B`

`text(Solution 2)`

`y`	`= 6 – 2x`	`…\ (1)`
`y`	`= x + 3`	`…\ (2)`

`text{Substitute (2) into (1)}`

`x + 3`	`= 6 – 2x`
`3x`	`= 3`
`x`	`= 1`

`text(When)\ \ x = 1, y = 4`

`=>B`

Algebra, STD2 A2 2005 HSC 17 MC

The total cost, `$C`, of a school excursion is given by `C = 2n + 5`, where `n` is the number of students.

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

`$6`
`$11`
`$15`
`$16`

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`A`

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`C = 2n + 5`

`text(If)\ n\ text(increases to)\ n + 3`

`C`	`= 2(n + 3) + 5`
	`= 2n + 6 + 5`
	`= 2n + 11`

`:.\ text(Total cost increases by $6)`

`=> A`

Algebra, STD2 A1 2009 HSC 16 MC

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

Which of the following graphs shows this relationship?

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`A`

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`T`	`prop 1/S`
`T`	`= k/S`

`text{By elimination:}`

`text(As S) uarr text(, T) darr => text(cannot be B or D)`

♦ Mean mark 38%

`text(C is incorrect because it graphs a linear relationship)`

`=> A`

Algebra, STD2 A2 2009 HSC 14 MC

If `A = 6x + 10`, and `x` is increased by 2, what will be the corresponding increase in `A` ?

`2x`
`6x`
`2`
`12`

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`D`

Show Worked Solution

♦ Mean mark 50%.
STRATEGY: Substituting real numbers into the equation can work well in these type of questions. eg. If `x=0,\ A=10` and when `x=2,\ A=22`.

`A = 6x + 10`

`text(If)\ x\ text(increases by 2)`

`A\ text(increases by)\ 6 xx 2 = 12`

`=> D`