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Algebra, STD2 A1 SM-Bank 7

If  `S = V_0 (1 - r)^n`, find `S` given  `V_0 = $42\ 000, r = 0.16 and n = 4`. (give your answer to the nearest cent)  (2 marks)

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`$20\ 910.60\ text{(to nearest cent)}`

Show Worked Solution
`S` `= V_0 (1 – r)^n`
  `= 42\ 000 (1 – 0.16)^4`
  `= 42\ 000 (0.84)^4`
  `= $20\ 910.597…`
  `= $20\ 910.60\ \ text{(to nearest cent)}`

Algebra, STD2 A1 2017 HSC 7 MC

It is given that  `I = 3/2 MR^2`.

What is the value of  `I`  when  `M = 26.55`  and  `R = 3.07`, correct to two decimal places?

A.     `375.35`

B.     `3246.08`

C.     `9965.45`

D.     `14\ 948.18`

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`A`

Show Worked Solution
`I` `= 3/2 xx 26.55 xx (3.07)^2`
  `= 375.346…`

 

`=> A`

Algebra, STD2 A1 SM-Bank 2

If   `A = P(1 + r)^n`, find  `A`  given  `P = $300`,  `r = 0.12`  and  `n = 3`  (give your answer to the nearest cent).  (2 marks)

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`$421.48\ \ text{(nearest cent)}`

Show Worked Solution
`A` `= P(1 + r)^n`
  `= 300(1 + 0.12)^3`
  `= 300(1.12)^3`
  `= 421.478…`
  `= $421.48\ \ text{(nearest cent)}`

Algebra, STD2 A1 2004 HSC 3 MC

If  `K = Ft^3`, `F = 5`  and  `t = 0.715`, what is the value of `K` correct to three significant figures?

  1. `1.82`
  2. `1.827`
  3. `1.828`
  4. `1.83`
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`D`

Show Worked Solution
`K` `= Ft^3`
  `= 5 xx (0.715)^3`
  `= 1.8276…`
  `= 1.83\ \ text{(3 sig figures)}`

 
`=> D`

Algebra, STD2 A1 2007 HSC 28b

This shape is made up of a right-angled triangle and a regular hexagon.
 

 

The area of a regular hexagon can be estimated using the formula  `A = 2.598H^2`  where  `H`  is the side-length.

Calculate the total area of the shape using this formula.   (3 marks)

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`22.784\ text(cm²)`

Show Worked Solution

`text(Area) = 2.598H^2`

`text(Using Pythagoras)`

`H^2` `= 2^2 + 2^2`
  `= 8`
`H` `= sqrt 8`
`:.\ text(Area of hexagon)` `= 2.598 xx (sqrt 8)^2`
  `= 20.784\ text(cm²)`
`text(Area of triangle)` `= 1/2 bh`
  `= 1/2 xx 2 xx 2`
  `= 2\ text(cm²)`

 

`:.\ text(Total Area)` `= 20.784 + 2`
  `= 22.784\ text(cm²)`

Algebra, STD2 A1 2008 HSC 9 MC

What is the value of  `sqrt ( (x + 2y)/(8y) )`  if  `x = 5.6`  and  `y = 3.1`, correct to 2 decimal places? 

  1. `0.69`
  2. `2.62`
  3. `2.83` 
  4. `4.77`  
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`A`

Show Worked Solution
`sqrt ( (x + 2y)/(8y) )` `= sqrt ( (5.6 + (2 xx 3.1))/((8 xx 3.1)) )`
  `= sqrt (11.8/24.8)`
  `= 0.6897…`

`=>  A`