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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?

  1. \(p=2 w t-s\)
  2. \(p=2 w t-2 s\)
  3. \(p=2 s-w t\)
  4. \(p=2 s-2 w t\)
Show Answers Only

\(D\)

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

 
\(\Rightarrow D\)

♦♦ Mean mark 36%.

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)

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)` ?

  1. `x=(2y+b)/(a)`
  2. `x=(y+b)/(2a)`
  3. `x=(2y)/(a)+b`
  4. `x=(y)/(2a)+b`
Show Answers Only

`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`?

  1.  `y = 3/4 x-1`
  2.  `y = 3/4 x + 1`
  3.  `y = (3x-1)/4`
  4.  `y = (3x + 1)/4`
Show Answers Only

`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`?

  1. `Q = Ce + CiR`
  2. `Q = Ce-CiR`
  3. `Q = (e + iR)/C`
  4. `Q = (e-iR)/C`
Show Answers Only

`=> B`

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

 
`=> B`

Algebra, STD2 A1 SM-Bank 9

The volume of a sphere is given by  `V = 4/3 pi r^3`  where  `r`  is the radius of the sphere.

If the volume of a sphere is `\text{220 cm}^3`, find the radius, to 1 decimal place.   (3 marks)

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`3.7\ \ text{cm  (to 1 d.p.)}`

Show Worked Solution
`V` `= 4/3 pi r^3`
`3V` `= 4 pi r^3`
`r^3` `= (3V)/(4 pi)`

 

`text(When)\ \ V = 220`

`r^3` `= (3 xx 220)/(4 pi)`
  `= 52.521…`
`:. r` `=root3 (52.521…)`
  `= 3.744…\ \ \ text{(by calc)}`
  `= 3.7\ \ text{cm   (to 1 d.p.)}`

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)

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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 24c

Make  `L`  the subject of the equation  `T = 2piL^2`.   (2 marks)

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`± sqrt(T/(2pi))`

Show Worked Solution
`T` `= 2piL^2`
`L^2` `= T/(2pi)`
`:.L` `= ±sqrt(T/(2pi))`

Algebra, STD2 A1 2006 HSC 18 MC

What is the formula for `q` as the subject of `4p =5t + 2q^2`?

  1. `q = +- sqrt(5t - 4p)/2`
  2. `q = +- sqrt(4p + 5t)/2`
  3. `q = +- sqrt{(5t - 4p)/2}`
  4. `q = +- sqrt{(4p - 5t)/2}`
Show Answers Only

`D`

Show Worked Solution
`4p` `= 5t + 2q^2`
`2q^2` `= 4p – 5t`
`q^2` `= (4p – 5t)/2`
`q` `= +- sqrt{(4p – 5t)/2}`

 
`=>  D`

Algebra, STD2 A1 2004 HSC 11 MC

If  `d = 6t^2`, what is a possible value of `t` when  `d = 2400`?

  1. `0.05`
  2. `20`
  3. `120`
  4. `400`
Show Answers Only

`B`

Show Worked Solution
`d` `= 6t^2`
`t^2` `= d/6`
`t` `= +- sqrt(d/6)`

 
`text(When)\ \ d = 2400:`

`t` `= +- sqrt(2400/6)`
  `= +- 20`

 
`=> B`

Algebra, STD2 A1 2007 HSC 19 MC

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

  1. `T = B/pi-2R`
  2. `T = B/pi-R`
  3. `T = 2R-B/pi`
  4. `T = B/(4pi)-R/2`
Show Answers Only

`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` ?

  1. `x=(an)/5`
  2. `x=(5a)/n`
  3. `x=(a-5)/n`
  4. `x=5a-n`
Show Answers Only

`B`

Show Worked Solution
`a` `=(nx)/5`
`nx` `=5a`
`x` `=(5a)/n`

 
`=>  B`

Algebra, STD2 A1 2011 HSC 18 MC

Which of the following correctly expresses  `a`  as the subject of  `s= ut+1/2at^2 `?

  1. `a=(2(s-ut))/t^2`
  2. `a=(2s-ut)/t^2`
  3. `a=(1/2(s-ut))/t^2`
  4. `a=(1/2s-ut)/t^2`
Show Answers Only

`A`

Show Worked Solution
`s` `=ut+1/2at^2`
`1/2at^2` `=s-ut`
`at^2` `=2(s-ut)`
`a` `=(2(s-ut))/t^2`

 
`=>A`

Algebra, STD2 A1 2012 HSC 21 MC

Which of the following correctly expresses  `c`  as the subject of  `E = mc^2 + p` ? 

  1. `c = +-sqrt(\ \ (E-p)/m)` 
  2. `c = +-sqrt(E-p)/m` 
  3. `c = +- sqrt(\ \ E/m) -p` 
  4. `c = +- sqrt(\ \ E/m-p)`
Show Answers Only

`A`

Show Worked Solution
`E` `=\ mc^2 + p`
`mc^2` `=\ E-p`
`c^2` `=(E-p)/m`
`:.c` `= +-sqrt((E-p)/m)`

 
`=>  A`

Algebra, STD2 A1 2013 HSC 21 MC

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

  1. `r=(800-S)/800`
  2. `r=(S-800)/800`
  3. `r=800-S`
  4. `r=S-800`
Show Answers Only

`A`

Show Worked Solution
♦♦♦ Mean mark 27%
`S` `=800(1-r)`
`1-r` `=S/800`
`r` `=1-S/800`
  `=(800-S)/800`

 
`=>\ A`