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Measurement, STD1 M4 2025 HSC 28

The table provides information about a $2 coin and a $5 note.

\begin{array} {|c|c|c|}
\hline \text{Coin/note} & \text{Quantity needed to} & \text{Mass of this number} \\ & \text{make \$1000} & \text{of notes/coins}  \\& & \text{(kg)} \\
\hline \$2  & 500 &  3.3 \\
\hline \$5  & 200 & 0.157  \\
\hline \end{array}

  1. Calculate the mass of a $2 coin in grams, correct to 1 decimal point?   (2 marks)
  3. Suppose the $2 coin is to be replaced with a note that has the same mass as a $5 note.
  4. What is the mass of $1000 in $2 notes in grams? Give your answer correct to the nearest gram.   (2 marks)
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a.    \( 6.6\ \text{g}\)

b.    \( 393\ \text{g (nearest gram)}\)

Show Worked Solution

a.    \(\text{Using 1 kg = 1000 grams:}\)

\(\text{Mass of \$2 coin}=\dfrac{3.3\times 1000}{500}=6.6\ \text{g}\)
 

b.    \( \text{Number of \$2 notes}=\dfrac{1000}{2}=500\)

\(\text{Mass of one \$5 note} = \dfrac{0.157}{200}=0.000785\ \text{kg}\)

\(\text{Since \$2 note weighs the same as \$5 note:}\)

\(\text{Mass of 500 \$2 notes}\) \(=500\times 0.000785\)
  \(=0.3925\ \text{kg}\)
  \(=393\ \text{g (nearest gram)}\)

v1 Measurement, STD2 M1 2012 HSC 26g

A new weed killer bottle contains 18 litres of solution.

It is used to spray the lawn twice a week. The instructions state:

  • Use 1.5 litres on the first application of the week
  • Use 1 litre on the second application of the week

How many full weeks will this bottle last? (2 marks)

Show Answers Only

`text(7 full weeks.)`

Show Worked Solution
`text{Total weekly usage}` `= 1.5 + 1 = 2.5\ \text{litres}`
`text{Total amount available}` `= 18\ \text{litres}`

MARKER’S COMMENT: Most students handled the decimal calculation well but some forgot to round down to full weeks.
`text{Weeks it will last}` `= 18 / 2.5 = 7.2`

`:.` The bottle will last 7 full weeks.

v1 Measurement, STD2 M1 2009 HSC 12 MC

How many square millimetres are in 0.004 square metres?

  1. 4
  2. 40
  3. 4000
  4. 40000
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`D`

Show Worked Solution
`text{Since 1 m}^2` `= 1000\ text{mm} xx 1000\ text{mm}`
  `= 1\ 000\ 000\ \text{mm}^2`

♦♦ Mean mark 27%.
`:. 0.004\ \text{m}^2` `= 0.004 xx 1\ 000\ 000`
  `= 4000`
  `= 4000\ \text{mm}^2`

`⇒ D`

v1 Measurement, STD2 M1 2004 HSC 13 MC

During a study break, Sam is walking while Alex is sitting.
 

Sam breathes in air at a rate of 30 litres per minute while walking. Alex breathes in air at a rate of 8 litres per minute while sitting.

During a 20-minute break, how much more air would Sam breathe than Alex?

  1. 220 Litres
  2. 440 Litres
  3. 460 Litres
  4. 600 Litres
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`=>\ B`

Show Worked Solution
`text{Sam’s total}` `= 30 × 20 = 600\ \text{L}`
`text{Alex’s total}` `= 8 × 20 = 160\ \text{L}`
`text{Difference}` `= 600 − 160 = 440\ \text{L}`

`=>\ B`

Measurement, STD2 M1 2006 HSC 11 MC

Peter rides his bike at a speed of 27 km/h.

What is this speed in m/s?

  1.  `7.5`
  2. `18.75`
  3. `97.2`
  4. `450`
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`A`

Show Worked Solution
`text(27 km/h)` `= 27\ 000\ text(metres per hour)`
  `= (27\ 000)/60\ text(metres per minute)`
  `= (27\ 000)/(60 xx 60)\ text(metres per second)`
  `=7.5\ text(m/s)`

`=>  A`

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 2014 HSC 2 MC

A measurement of  72 cm is increased by 20% and then the result is decreased by 20%. 

What is the new measurement, correct to the nearest centimetre?

  1. 46 cm
  2. 69 cm
  3. 72 cm
  4. 104 cm
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`B`

Show Worked Solution
STRATEGY: Students confident in this area could save time in the calculations as follows: `72 xx 1.2 xx 0.8“ = 69.12`

`text(72 increased by 20%)`

`= 72 + (text(20%) xx 72) = 86.4\ text(cm)`

`text(86.4 decreased by 20%)`

`= 86.4\ – (text(20%) xx 86.4) = 69.12\ text(cm)`

`=>  B`

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)

Show Answers Only

 `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.)`