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v1 Measurement, STD2 2012 HSC 26g

Milly purchases a new container of Gutho's Fertilizer which holds 25 kg.

The container comes with a small cup that holds 350 grams of fertilizer when full.
 

Milly has 5 pot plants that each receive 1.5 cups of fertilizer on the 1st day of the month and 1 cup each in the middle of the month.

Milly begins using this new container on the first day of October.

In what month will her fertilizer run out? Justify your answer with calculations.   (3 marks)

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 `text(March)`

Show Worked Solution

`text(Cups used per month)= 5 xx (1.5 + 1)=12.5`

`text(Fertiliser used per month)= 12.5 xx 350 = 4375\ text(g)`

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

`text(Time it will last)= (25\ 000)/4375= 5.71…\ text{months}`

`:.\ text(The container will run out in March.)`

v1 Measurement, STD2 M1 2012 HSC 26g

Deirdre purchases a weed killer product that contains 12 litres of solution.

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

  • Use 400 mL per 10 m² of lawn on 1st application of the week
  • Use 300 mL per 10 m² of lawn on 2nd application of the week

If Deirdre's lawn is 30 m² in area, how many full weeks will the weed killer last?   (2 marks)

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`text(8 full weeks.)`

Show Worked Solution

`text{Using  100 mL = 0.1 L:}`

`text{Total weekly usage} = 3 xx(0.4+0.3) = 2.1\ text{litres}`

`text{Total solution} = 18\ text{L}`

`text{Weeks it will last} = 18/2.1=8.57…`

`:.\ text{The bottle will last 8 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. 40 000
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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`

 
`:. 0.004\ \text{m}^2= 0.004 xx 1\ 000\ 000= 4000\ \text{mm}^2`

`⇒ D`

v1 Measurement, STD2 M1 2020 HSC 2 MC

What is 0.0004782 expressed in standard form with two significant figures?

  1. `4.8 xx 10^(-4)`
  2. `4.78 xx 10^(-4)`
  3. `4.8 xx 10^(-5)`
  4. `4.78 xx 10^(-5)`
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`A`

Show Worked Solution

♦ Mean mark 39%.
COMMENT: Students often round incorrectly when converting to standard form.
`0.0004782` `= 4.782 xx 10^(-4)`
  `= 4.8 xx 10^(-4)\ \ \ text{(to 2 sig fig)}`

`⇒ A`

v1 Measurement, STD2 M1 2015 HSC 12 MC

A sprinter’s reaction time at the start of a race was recorded as 0.25 seconds, correct to the nearest hundredth of a second.

What is the percentage error in this measurement, correct to one significant figure?

  1. 0.5%
  2. 1%
  3. 2%
  4. 3%
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`C`

Show Worked Solution
♦ Mean mark 43%.

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.01 = 0.005\ text{s}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.005/0.25 xx 100%`  
  `=2%`  

 
`⇒ C`

v1 Measurement, STD2 M1 2016 HSC 1 MC

What is  0.04967  correct to two significant figures?

  1. 0.049
  2. 0.050
  3. 0.0496
  4. 0.0497
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`B`

Show Worked Solution

`text(We are rounding 0.04967 to 2 significant figures.)`

• `text(First 2 significant digits: 4 and 9)`

• `text(Next digit is 6 → round **up**)`

• `text(0.04967 rounds to 0.050 (2 sig. fig.))`

`=> B`

v1 Measurement, STD2 M1 2015 HSC 1 MC

The distance from Earth to the Moon is approximately 384 400 km.

What is this distance in standard form correct to two significant figures?

  1. `3.84 × 10^5\ \text{km}`
  2. `3.8 × 10^5\ \text{km}`
  3. `3.9 × 10^5\ \text{km}`
  4. `3.84 × 10^6\ \text{km}`
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`C`

Show Worked Solution

`384\ 400`

`= 3.844 × 10^5`

`\text(Rounded to 2 significant figures)  →  3.9 × 10^5\ \text{km}`

 
`⇒ C`