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Measurement, STD2 EQ-Bank 01 MC

The sheets of paper Jenny uses in her photocopier are 21 cm by 30 cm. The paper is 80 gsm, which means that one square metre of this paper has a mass of 80 grams. Jenny has a pile of this paper weighing 25.2 kg.

How many sheets of paper are in the pile?

  1. 500
  2. 2000
  3. 2500
  4. 5000
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\(D\)

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\(1\ \text{square metre} = 100\ \text{cm}\times 100\ \text{cm}=10\,000\ \text{cm}^2\)

\(\text{Area of paper sheet}\ = \ 21\times 30=630\ \text{cm}^2\)

\(\text{Number of 80 gsm sheets in 25.2 kg}\ =\dfrac{25.2\times 1000}{80}=315\)

\(\therefore\ \text{Sheets in pile}\) \(=315\times\dfrac{10\,000}{630}\)
  \(=5000\)

  

Measurement, STD2 M1 2004 HSC 13 MC

During a ten-minute period, Kath is exercising and Jim is resting.

How much more air would Kath breathe than Jim during this time?

  1.  40 Litres
  2. 94 Litres
  3. 940 Litres
  4. 1060 Litres
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`C`

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`text(Kath’s air volume)`

`= 10 xx 100`

`=1000\ text(L)`

`text(Jim’s air volume)`

`= 10 xx 6`

`= 60\text(L)`
 

`:.\ text(Extra air that Kath breathes)`

`= 1000 – 60`

`= 940\ text(L)`

`=>  C`

Measurement, STD2 M1 2009 HSC 25b

The mass of a sample of microbes is 50 mg. There are approximately  `2.5 × 10^6` microbes in the sample.

In standard form, what is the approximate mass in grams of one microbe?   (2 marks)

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`2 xx 10^-8\ text(grams)`

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♦♦♦ Mean mark 20%.
IMPORTANT: Can you solve: 8 apples weigh 1kg, what does 1 apple weigh? This is exactly the same concept.
`text(We need to convert 50 mg into grams)`
`50\ text(mg) = 50/1000 = 0.05\ text(g) = 5 xx 10^-2\ text(grams)`

 

`:.\ text(Mass of 1 microbe)` `= text(mass of sample)/text(# microbes)`
  `= (5 xx 10^-2)/(2.5 xx 10^6)`
  `= 2 xx 10^-8\ text(grams)`

Measurement, STD2 M1 2012 HSC 26g

Bhawana purchases pool chlorine in a new container which holds 35 kg.
 

2012 26g

 
She begins using this new container on the first day of a week.

How many full weeks should this container last?     (2 marks)

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 `text(15 full weeks.)`

Show Worked Solution
`text(Cups used per week)` `= 3 + 6 = 9`
`text(Chlorine usage per week)` `= 9 xx 250text(g)`
  `= 2250 text(g)`

 
`text(Total chlorine available)\ = 35text(kg) = 35\ 000\  text(grams)`

MARKER’S COMMENT: Better answers converted all measurements to grams (rather than use decimals and kgs) and realised the answer should be in full weeks.
`text(Time it will last)` `= (35\ 000)/2250`
  `= 15.555…`

 

`:.\ text(The container will last 15 full weeks.)`