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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)

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\(12.6\ \text{cm}\)

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

   
\(\text{When}\ \ A = 250:\)

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

Algebra, STD1 A1 2020 HSC 18

The distance, `d` metres, travelled by a car slowing down from `u` km/h to `v` km/h can be obtained using the formula

`v^2 = u^2-100 d`

What distance does a car travel while slowing down from 70 km/h to 40 km/h?   (2 marks)

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`33 \ text{metres}`

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`u = 70 \ , \ v = 40`

`v^2` `= u^2-100d`
`40^2` `= 70^2-100d`
`100d` `= 70^2-40^2`
`:. d` `= frac{70^2-40^2}{100}`
  `= 33 \ text{metres}`

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)

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`4.76`

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`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 A1 EQ-Bank 25

For adults (18 years and older), the Body Mass Index is given by

`B = m/h^2`  where  `m = text(mass)`  in kilograms and  `h = text(height)`  in metres.

The medically accepted healthy range for  `B`  is  `21 <= B <= 25`.

What is the minimum weight for a 163 cm adult female to be considered healthy?   (2 marks)

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`55.8\ text(kg)`

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`B = m/h^2`

`h = 163\ text(cm) = 1.63\ text(m)`
  

`text(Given)\ \ 21 <= B <= 25,`

`=>B = 21\ \ text(for minimum healthy weight.)`

`21` `= m/1.63^2`
`:. m` `= 21 xx 1.63^2= 55.794…= 55.8\ text(kg)\ text{(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`

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`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`

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 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)

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`3.6\ text(seconds)`

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`D = t/3`

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

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