Linear

Equations, SMB-012 MC

`y = 2x-3`

`y = 4x + 1`

Which value of `x` satisfies both of these equations?

`x = -2`
`x = -1`
`x = 1`
`x = 2`

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`A`

Show Worked Solution

`text(If)\ x = −2,`

`2(-2)-3`	`= -7`
`4(-2) + 1`	`= -7`

`:. x = -2\ \ text(satisfies both.)`

`=>A`

Equations, SMB-011

The daily energy requirement, `E` (kilojoules), for a person of mass `m` (kilograms) is calculated using the rule `E = 7m + 7300`.

For Elijah, `E = 7755`.

What is Elijah's mass? (2 marks)

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`65\ text{kgs}`

Show Worked Solution

`7755`	`= 7m + 7300`
`7 m`	`= 455`
`m`	`= 455/7`
	`= 65\ text(kilograms)`

Equations, SMB-005

`2(3p-5)-3=17`

Solve for `p`. (2 marks)

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`p=5`

Show Worked Solution

`2(3p-5)-3`	`=17`
`6p-10-3`	`=17`
`6p-13`	`=17`
`6p`	`=30`
`:.p`	`=5`

Equations, SMB-004

`17y+3(5-3y)-5=26`

What value of `y` makes this equation true? (2 marks)

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`y=2`

Show Worked Solution

`17y+3(5-3y)-5`	`=26`
`17y+15-9y-5`	`=26`
`8y+10`	`=26`
`8y`	`=16`
`:.y`	`=2`

Equations, SMB-003

`6(3a+4)-12=8a-18`

What value of `a` makes this equation true? (2 marks)

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`a=-3`

Show Worked Solution

`6(3a+4)-12`	`=8a-18`
`18a+24-12`	`=8a-18`
`10a`	`=-12-18`
`10a`	`=-30`
`:.a`	`=-3`

Equations, SMB-002

`2 (4x-2) + 1 +`

`= 9x-3`

What term makes this equation true for all values of `x`? (2 marks)

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

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`= x`

Show Worked Solution

`2(4x-2) + 1 +`	?	`= 9x-3`
`8x-4 + 1 +`	?	`= 9x-3`
`8x-3 +`	?	`= 9x-3`
	?	`= x`

Equations, SMB-001

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, 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, 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 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 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 2005 HSC 2 MC

What is the value of `(a-b)/4`, if `a = 240` and `b = 56`?

`4`
`46`
`226`
`736`

Show Answers Only

`B`

Show Worked Solution

`(a-b)/4`	`= (240-56)/4`
	`= 46`

`=> B`

Algebra, STD2 A1 2007 HSC 24b

The distance in kilometres (`D`) of an observer from the centre of a thunderstorm can be estimated by counting the number of seconds (`t`) between seeing the lightning and first hearing the thunder.

Use the formula `D = t/3` to estimate the number of seconds between seeing the lightning and hearing the thunder if the storm is 1.2 km away. (1 mark)

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

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`3.6\ text(seconds)`

Show Worked Solution

`D = t/3`

`text(When)\ \ D = 1.2,`

`t/3`	`= 1.2`
`t`	`= 3.6\ text(seconds)`

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 24a

Fred tried to solve this equation and made a mistake in Line 2.

\begin{array}{rl}
4(y+2)-3(y+1)= -3\ & \ \ \ \text{Line 1} \\
4y+8-3y+3= -3\ &\ \ \ \text{Line 2} \\
y+11 =-3\ &\ \ \ \text{Line 3} \\
y =-14& \ \ \ \text{Line 3}
\end{array}

Copy the equation in Line 1.

Rewrite Line 2 correcting his mistake. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Continue your solution showing the correct working for Lines 3 and 4 to solve this equation for `y`. (1 mark)

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

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`4y+8+3y-3=-3`
`y+5=-3`

`y=-8`

Show Worked Solution

i.	`4(y+2)-3(y+1)`	`=-3\ \ \ \ \ \ \ text(Line)\ 1`
	`4y+8-3y-3`	`=-3\ \ \ \ \ \ text(Line)\ 2`

ii.	`y+5`	`=-3\ \ \ \ \ \ \ text(Line)\ 3`
	`y`	`=-8\ \ \ \ \ \ \ text(Line)\ 4`

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`