smc-1200-10-Linear

Algebra, STD2 A1 2024 HSC 10 MC

Consider the formula \(s=w t+\dfrac{p}{2}\).

Which of the following correctly shows \(p\) as the subject of the formula?

\(p=2 w t-s\)
\(p=2 w t-2 s\)
\(p=2 s-w t\)
\(p=2 s-2 w t\)

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\(D\)

Show Worked Solution

	\(s\)	\(=w t+\dfrac{p}{2}\)
	\(\dfrac{p}{2}\)	\(=s-w t\)
	\(p\)	\(=2(s-w t)\)
		\(=2s-2w t\)

\(\Rightarrow D\)

EXAMCOPY Algebra, STD1 A1 2019 HSC 34

Given the formula `C = (A(y + 1))/24`, calculate the value of `y` when `C = 120` and `A = 500`. (3 marks)

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

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`4.76`

Show Worked Solution

`text(Make)\ \ y\ \ text(the subject:)`

`C`	`= (A(y + 1))/24`
`24C`	`= A(y + 1)`
`y + 1`	`= (24C)/A`
`y`	`= (24C)/A-1`
	`= (24 xx 120)/500-1`
	`= 4.76`

Algebra, STD1 A1 2019 HSC 34

Given the formula `C = (A(y + 1))/24`, calculate the value of `y` when `C = 120` and `A = 500`. (3 marks)

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

Show Answers Only

`4.76`

Show Worked Solution

`text(Make)\ \ y\ \ text(the subject:)`

`C`	`= (A(y + 1))/24`
`24C`	`= A(y + 1)`
`y + 1`	`= (24C)/A`
`y`	`= (24C)/A-1`
	`= (24 xx 120)/500-1`
	`= 4.76`

Algebra, STD2 A2 2022 HSC 14 MC

Which of the following correctly expresses `x` as the subject of `y=(ax-b)/(2)` ?

`x=(2y+b)/(a)`
`x=(y+b)/(2a)`
`x=(2y)/(a)+b`
`x=(y)/(2a)+b`

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`A`

Show Worked Solution

`y`	`=(ax-b)/(2)`
`2y`	`=ax-b`
`ax`	`=2y+b`
`:.x`	`=(2y+b)/a`

`=>A`

Algebra, STD2 A1 SM-Bank 12

Make `F` the subject of the equation `C = 5/9(F - 32)`. (2 marks)

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`F = (9C)/5 + 32`

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`C`	`= 5/9(F – 32)`
`9C`	`= 5(F – 32)`
`(9C)/5`	`= F – 32`
`:.F`	`= (9C)/5 + 32`

Algebra, STD2 A1 2019 HSC 11 MC

Which of the following correctly expresses `y` as the subject of the formula `3x-4y-1 = 0`?

`y = 3/4 x-1`
`y = 3/4 x + 1`
`y = (3x-1)/4`
`y = (3x + 1)/4`

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`C`

Show Worked Solution

♦ Mean mark 50%.

`3x-4y-1`	`= 0`
`4y`	`= 3x-1`
`:. y`	`= (3x-1)/4`

`=> C`

Algebra, STD2 A1 SM-Bank 6

Make `p` the subject of the equation `c = 5/3p + 15`. (2 marks)

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`p = 3/5 c – 9`

Show Worked Solution

`c`	`= 5/3p + 15`
`5/3p`	`= c – 15`
`p`	`= 3/5 (c – 15)`
	`= 3/5 c – 9`

Algebra, STD2 A1 2016 HSC 24 MC

Which of the following correctly expresses `Q` as the subject of `e = iR + Q/C`?

`Q = Ce + CiR`
`Q = Ce-CiR`
`Q = (e + iR)/C`
`Q = (e-iR)/C`

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`=> B`

Show Worked Solution

`e`	`= iR + Q/C`
`Q/C`	`= e-iR`
`:. Q`	`= C(e-iR)`
	`= Ce-CiR`

`=> B`

Algebra, STD2 A1 2015 HSC 28d

The formula `C = 5/9 (F-32)` is used to convert temperatures between degrees Fahrenheit `(F)` and degrees Celsius `(C)`.

Convert 3°C to the equivalent temperature in Fahrenheit. (2 marks)

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

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`37.4\ text(degrees)\ F`

Show Worked Solution

`C`	`= 5/9(F-32)`
`F-32`	`= 9/5C`
`F`	`= 9/5C + 32`

`text(When)\ \ C = 3,`

`F`	`= (9/5 xx 3) + 32`
	`= 37.4\ text(degrees)\ F`

Algebra, STD2 A1 2007 HSC 19 MC

Which of the following correctly expresses `T` as the subject of `B = 2pi (R + T/2)`?

`T = B/pi-2R`
`T = B/pi-R`
`T = 2R-B/pi`
`T = B/(4pi)-R/2`

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`A`

Show Worked Solution

`B`	`= 2pi (R + T/2)`
`B/(2pi)`	`= R + T/2`
`T/2`	`= B/(2pi)-R`
`T`	`= B/pi-2R`

`=> A`

Algebra, STD2 A1 2010 HSC 18 MC

Which of the following correctly express `x` as the subject of `a=(nx)/5` ?

`x=(an)/5`
`x=(5a)/n`
`x=(a-5)/n`
`x=5a-n`

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`B`

Show Worked Solution

`a`	`=(nx)/5`
`nx`	`=5a`
`x`	`=(5a)/n`

`=> B`

Algebra, STD2 A1 2013 HSC 21 MC

Which equation correctly shows `r` as the subject of `S=800(1-r)`?

`r=(800-S)/800`
`r=(S-800)/800`
`r=800-S`
`r=S-800`

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`A`

Show Worked Solution

♦♦♦ Mean mark 27%

`S`	`=800(1-r)`
`1-r`	`=S/800`
`r`	`=1-S/800`
	`=(800-S)/800`

`=>\ A`