SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, STD2 EQ-Bank 24

The area of a semicircle is given by  \(A=\dfrac{1}{2}\pi r^2\)  where \(r\) is the radius of the semicircle.

If the area of a semicircle is 250 cm², find the radius, to 1 decimal place.   (3 marks)

Show Answers Only

\(12.6\ \text{cm}\)

Show Worked Solution

\(A=\dfrac{1}{2}\pi r^2\ \ \Rightarrow \ \ r^2=\dfrac{2A}{\pi}\)

   
\(\text{When}\ \ A = 250:\)

\(r^2\) \(=\dfrac{2\times 250}{\pi}=\dfrac{500}{\pi}=159.154…\)
\( r\) \(=\sqrt{159.154…}=12.615…=12.6\ \text{cm (to 1 d.p.)}\)

Algebra, STD2 EQ-Bank 3 MC

If  \(w=4y^2-5\), what is the value of \(y\) when  \(w=43\)?

  1. \(3\)
  2. \(-3\)
  3. \(\sqrt{3}\)
  4. \(-2\sqrt{3}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{When}\ w=43:\)

\(w\) \(=4y^2-5\)
\(43\) \(=4y^2-5\)
\(4y^2\) \(=48\)
\(y^2\) \(=\dfrac{48}{4}=12\)
\(y\) \(=\pm 2\sqrt{3}\)

 
\(y=-2\sqrt{3}\ \text{(only possibility given options)}\)

\(\Rightarrow D\)

Algebra, STD2 A1 2005 HSC 24c

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

Show Answers Only

`± 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 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`