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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 2023 HSC 9 MC

The length and width of a rectangular pool are measured to be 13 m and 7.5 m respectively, correct to the nearest metre and nearest 0.1 metre.

What are the lower and upper bounds for the area of the pool?

  1. `text{94.25 m}^2\ text{and 101.25 m}^2`
  2. `text{93.125 m}^2\ text{and 101.925 m}^2`
  3. `text{92.5 m}^2\ text{and 102.5 m}^2`
  4. `text{93.75 m}^2\ text{and 100.75 m}^2`
Show Answers Only

`B`

Show Worked Solution
♦ Mean mark 35%.

`text{Length absolute error} = 1/2 xx 1 = 0.5\ \text{m}`

`text{Width absolute error} = 1/2 xx 0.1 = 0.05\ \text{m}`

`text{Length bounds: } 13 ± 0.5 = [12.5,\ 13.5]\ \text{m}`

`text{Width bounds: } 7.5 ± 0.05 = [7.45,\ 7.55]\ \text{m}`

`text{Lower bound area} = 12.5 xx 7.45 = 93.125\ \text{m}^2`

`text{Upper bound area} = 13.5 xx 7.55 = 101.925\ \text{m}^2`

`⇒ B`

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 2020 HSC 5 MC

A pencil is measured to be 12.8 cm long, correct to one decimal place.

What is the percentage error in this measurement?

  1. 0.20%
  2. 0.39%
  3. 0.78%
  4. 1.56%
Show Answers Only

`B`

Show Worked Solution

♦ Mean mark 44%.

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ \text{cm}`

`%  \text{error}` `= \frac{0.05}{12.8} xx 100`
  `= 0.390625%`
  `= 0.39%`

`⇒ B`

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)`
Show Answers Only

`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 2019 HSC 8 MC

A newborn baby’s length is recorded as 52.4 cm.

What is the absolute error of this measurement?

  1. 0.25 cm
  2. 0.5 cm
  3. 1 cm
  4. 2 cm
Show Answers Only

`B`

Show Worked Solution

♦ Mean mark 48%.

`text{Absolute error}` `= 1/2 xx\ text{precision}`
  `= 1/2 xx 1\ text{ cm}`
  `= 0.5\ text{ cm}`

`⇒ B`

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%
Show Answers Only

`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 2014 HSC 10 MC

The height of Mount Kosciuszko is measured to be 2228.1 m above sea level.

What is the percentage error in this measurement?

  1. 0.001%
  2. 0.002%
  3. 0.005%
  4. 0.011%
Show Answers Only

`B`

Show Worked Solution
 
♦ Mean mark 50%

`text{Absolute error}\ = 1/2 xx text{precision}\ = 1/2 xx 0.1 = 0.05\ text{m}`

`text{% error}` `= \frac{text{absolute error}}{text{measurement}} xx 100%`  
  `= 0.05 / 2228.1 xx 100%`  
  `= 0.0022%`  

 
`⇒  B`

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}`
Show Answers Only

`C`

Show Worked Solution

`384\ 400`

`= 3.844 × 10^5`

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

 
`⇒ C`

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
Show Answers Only

`=>\ 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`

v1 Measurement, STD2 M1 SM-Bank 25 MC

In a food technology class, a slice of bread is measured and its thickness is recorded as 1.6 cm.

What is the upper limit of accuracy of this measurement?

  1. 1.61 cm
  2. 1.64 cm
  3. 1.65 cm
  4. 1.7 cm
Show Answers Only

`=>\ C`

Show Worked Solution

`text{Absolute error} = 0.05\ \text{cm}`

`text{Upper limit}` `= 1.6 + 0.05`
  `= 1.65\ \text{cm}`

`=>\ C`