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Algebra, STD2 EQ-Bank 6 MC

Which graph shows a relationship that is a direct variation?
 

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\(B\)

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\(\text{Direct variation requires a linear relationship of the form }\ y = kx.\)

\(\text{Hence the line must be straight and pass through the origin.}\)

\(\text{By elimination:}\)

\(\text{Eliminate C and D – not linear}\)

\(\text{Eliminate A – linear but not passing through origin}\)

\(\Rightarrow B\)

Algebra, STD2 A2 2019 HSC 34

The relationship between British pounds `(p)` and Australian dollars `(d)` on a particular day is shown in the graph.
 

  1. Write the direct variation equation relating British pounds to Australian dollars in the form  `p = md`. Leave `m` as a fraction.   (1 mark)

  2. The relationship between Japanese yen `(y)` and Australian dollars `(d)` on the same day is given by the equation  `y = 76d`.

     

    Convert 93 100 Japanese yen to British pounds.   (2 marks)

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  1. `p = 4/7 d`
  2. `93\ 100\ text(Yen = 700 pounds)`
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a.   `m = text(rise)/text(run) = 4/7`

♦ Mean mark 42%.

`p = 4/7 d`
 

b.   `text(Yen to Australian dollars:)`

`y` `=76d`
`93\ 100` `= 76d`
`d` `= (93\ 100)/76= 1225`

 
`text(Aust dollars to pounds:)`

`p= 4/7 xx 1225= 700\ text(pounds)`

`:. 93\ 100\ text(Yen = 700 pounds)`

Algebra, STD2 A2 2007 HSC 24c

Sandy travels to Europe via the USA. She uses this graph to calculate her currency conversions.
  
  
     

  1. After leaving the USA she has US$150 to add to the A$600 that she plans to spend in Europe.

     

    She converts all of her money to euros. How many euros does she have to spend in Europe?    (3 marks)

  2. If the value of the euro falls in comparison to the Australian dollar, what will be the effect on the gradient of the line used to convert Australian dollars to euros?   (1 mark)

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a.    `480\ €`

b.   `text(If the value of the euro falls against the A$, then 1 A$)`

`text(will buy more euros than before and the gradient used)`

`text{to convert the currencies will steepen (increase).}`

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a.   `text(From graph:)`

`75\ text(US$)` `=\ text(100 A$)`
`=> 150\ text(US$)` `=\ text(200 A$)`

 
`:.\ text(Sandy has a total of 800 A$)`
 

`text(Converting A$ to €:)`

`text(100 A$)` `= 60\ €`
`:.\ text(800 A$)` `= 8 xx 60= 480\ €`

 

b.   `text(If the value of the euro falls against the A$, then 1 A$)`

`text(will buy more euros than before and the gradient used)`

`text{to convert the currencies will steepen (increase).}`

Algebra, STD2 A2 2012 HSC 13 MC

Conversion graphs can be used to convert from one currency to another.  
  

 
  

Sarah converted  60  Australian dollars into Euros. She then converted all of these Euros
into New Zealand dollars.

How much money, in New Zealand dollars, should Sarah have? 

  1. $26  
  2. $45
  3. $78
  4. $135
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`C`

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`text(Using the graphs)`

`$60\ text(Australian)=46\ text(Euro)`

`46 \ text(Euro)=$78\  text(New Zealand)`

`=>  C`