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Algebra, STD2 A1 2012 HSC 21 MC v1

Which of the following correctly expresses \(r\) as the subject of  \(V=\pi r^2+x\) ?

  1. \(r=\pm\sqrt{\dfrac{V}{\pi}}-x\)
  2. \(r=\pm\sqrt{\dfrac{V}{\pi}-x}\)
  3. \(r=\pm\sqrt{\dfrac{V-x}{\pi}}\)
  4. \(r=\pm\dfrac{\sqrt{V-x}}{\pi}\)
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\(C\)

Show Worked Solution
\(V\) \(=\pi r^2+x\)
\(\pi r^2\) \(=V-x\)
\(r^2\) \(=\dfrac{V-x}{\pi}\)
\(\therefore\ r\) \(=\pm\sqrt{\dfrac{V-x}{\pi}}\)

\(\Rightarrow C\)

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 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}`
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`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`
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`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 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`
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`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)`
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`A`

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

 
`=>  A`