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Measurement, STD2 EQ-Bank 06

The distance between planets is measured in Astronomical Units (AU).

\(1\ \text{AU}\ \approx 1.496\times 10^8\) kilometres.

Given Venus is approximately 0.7 AU from Earth, calculate this distance in kilometres giving your answer in scientific notation, correct to 3 significant figures.  (2 marks)

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\(1.03\times 10^8\ \text{(3 sig. fig.)}\)

Show Worked Solution
\(\text{Distance}\) \(=0.7\times \left(1.496\times 10^8\right)\)
  \(=102\,830\,000\)
  \(=1.0283\times 10^8\)
  \(=1.03\times 10^8\ \text{(3 sig. fig.)}\)

Measurement, STD2 EQ-Bank 02 MC

Arrange the numbers \(5.6\times 10^{-2}\), \(4.8\times 10^{-1}\), \(7.2\times 10^{-2}\) from smallest to largest.

  1. \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  2. \(4.8\times 10^{-1}\),  \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\)
  3. \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  4. \(4.8\times 10^{-1}\),  \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\)
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\(A\)

Show Worked Solution

\(5.6\times 10^{-2}=0.052\)

\(4.8\times 10^{-1}=0.48\)

\(7.2\times 10^{-2}=0.072\)

\(\therefore\ \text{Correct order is: }\ 5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)

\(\Rightarrow A\)

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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\(D\)

Show Worked Solution

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

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

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

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

  

Measurement, STD1 M1 2022 HSC 4 MC

The area `(A)` of a circle is given by the formula `A=\pi r^2`, where `r` is the radius.

What is the value of `A`, correct to three significant figures, if `r=3.55` ?

  1. 39.5
  2. 39.6
  3. 39.591
  4. 39.592
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`B`

Show Worked Solution
`A` `=pi\r^2`  
  `=pi xx3.55^2`  
  `=39.591…`  
  `=39.6\ \ text{(3 sig fig)}`  

  
`=>B`


♦♦ Mean mark 30%.
COMMENT: Significant figures warrant attention.

Measurement, STD2 M1 2021 HSC 6 MC

Suppose  `a=b/7`, where  `b=22.`

What is the value of  `a`, correct to three significant figures?

  1. 3.14
  2. 3.15
  3. 3.142
  4. 3.143
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`A`

Show Worked Solution

`a=b/7=22/7=3.1428…`

`3.1428 = 3.14\ text{(to 3 sig fig)}`

`=>  A`

Measurement, STD2 M1 2020 HSC 2 MC

What is 0.002073 expressed in standard form with two significant figures?

  1. `2.07 xx 10^(-2)`
  2. `2.1 xx 10^(-2)`
  3. `2.07 xx 10^(-3)`
  4. `2.1 xx 10^(-3)`
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`D`

Show Worked Solution

♦♦ Mean mark 35%.
COMMENT: A notable knowledge gap flagged by this result.
`0.002073` `= 2.073 xx 10^(-3)`  
  `=2.1 xx 10^(-3)\ \ \ text{(to 2 sig fig)}`  

 
`=> D`

Measurement, STD2 M1 2016 HSC 1 MC

What is  208.345  correct to two significant figures?

  1. 208
  2. 210
  3. 208.34
  4. 208.35
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`B`

Show Worked Solution

`208.345 = 210\ (2\ text(sig. fig.))`

♦♦ Mean mark 36%!!

`=> B`

 

Measurement, STD2 M1 2015 HSC 1 MC

What is  1 560 200 km written in standard form correct to two significant figures?

  1. `1.56 × 10^4 \ text(km)`
  2. `1.6 × 10^5 \ text(km)`
  3. `1.56 × 10^6 \ text(km)`
  4. `1.6 × 10^6 \ text(km)`
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`D`

Show Worked Solution

♦♦ Mean mark 30%.
COMMENT: Incredibly, the first MC question in 2015 had the lowest mean mark of all MC questions in the exam!

`1\ 560\ 200`

`= 1.5602 xx 10^6`

`= 1.6 xx 10^6\ text(km)\ \ \ text{(2 sig fig)}`

 
`=> D`

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`

Show Worked Solution

`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 2007 HSC 1 MC

What is  `0.000\ 000\ 326`  mm expressed in scientific notation?

  1. `0.326 xx 10^-6\ \ text(mm)`
  2. `3.26 xx 10^-7\ \ text(mm)`
  3. `0.326 xx 10^6\ \ text(mm)`
  4. `3.26 xx 10^7\ \ text(mm)`
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`B`

Show Worked Solution

`0.000\ 000\ 326\ text(mm)`

`= 3.26 xx 10^-7\ \ text(mm)`

`=> B`

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)`

Show Worked Solution
♦♦♦ 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 2009 HSC 12 MC

How many square centimetres are in 0.0075 square metres? 

  1. 0.75 
  2. 7.5 
  3. 75
  4. 7500
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`C`

Show Worked Solution
`text{Since 1 m}^2` `= 100\ text(cm) xx 100\ text(cm)`
  `= 10\ 000\ text{cm}^2`

 

♦♦♦ Mean mark 19%.
`:.0.0075\ text{m}^2`  `= 0.0075 xx 10\ 000`
  `= 75\ text{cm}^2`

`=>  C`

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.)`