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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 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 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 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`

Measurement, STD2 M1 2023 HSC 9 MC

The length and width of a rectangle are measured to be 8 cm and 5 cm respectively, to the nearest centimetre.

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

  1. `text{28 cm}^2\ text{and 54 cm}^2`
  2. `text{36 cm}^2\ text{and 42 cm}^2`
  3. `text{38.25 cm}^2\ text{and 41.25 cm}^2`
  4. `text{33.75 cm}^2\ text{and 46.75 cm}^2`
Show Answers Only

`D`

Show Worked Solution

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

`text{8 cm side: upper limit = 8.5 cm, lower limit = 7.5 cm}`

`text{5 cm side: upper limit = 5.5 cm, lower limit = 4.5 cm}`

`text{Rectangle upper limit}\ =8.5xx5.5=46.75\ text{cm}^2`

`text{Rectangle lower limit}\ =7.5xx4.5=33.75\ text{cm}^2`

`=>D`

♦♦♦ Mean mark 29%.

Measurement, STD2 M1 2020 HSC 5 MC

A plant stem is measured to be 16.0 cm, correct to one decimal place.

What is the percentage error in this measurement?

  1.  0.3125%
  2.  0.625%
  3.  3.125%
  4.  6.25%
Show Answers Only

`A`

Show Worked Solution

♦ Mean mark 41%.

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

`%  text(error)` `= frac(0.05)(16.0) xx 100`
  `= 0.3125%`

 
`=> \ A`

Measurement, STD2 M1 2019 HSC 8 MC

A person's weight is measured as 79.3 kg.

What is the absolute error of this measurement?

  1. 10 grams
  2. 50 grams
  3. 100 grams
  4. 500 grams
Show Answers Only

`B`

Show Worked Solution

♦ Mean mark 46%.

`text(A)text(bsolute error)` `= 1/2 xx\ text(precision)`
  `= 1/2 xx 0.1\ text(kg)`
  `= 1/2 xx 100\ text(grams)`
  `= 50\ text(grams)`

 
`=> B`

Measurement, STD2 M1 SM-Bank 25 MC

A cockroach is measured in a school science experiment and its length is recorded as 5.2 cm.

What is the upper limit of accuracy of this measurement?

  1.  5.21 cm
  2.  5.25 cm
  3.  5.5 cm
  4.  5.9 cm
Show Answers Only

`=>\ B`

Show Worked Solution

`text(A)text(bsolute error = 0.05 cm)`

`text(Upper limit)` `= 5.2 + 0.05`
  `= 5.25\ text(cm)`

 
`=>\ B`

Measurement, STD2 M1 2018 HSC 18 MC

The length of a window is measured as 2.4 m.

Which calculation will give the percentage error for this measurement?

  1. `0.05/2.4 xx 100`
  2. `0.05/100 xx 2.4`
  3. `0.5/2.4 xx 100`
  4. `0.5/100 xx 2.4`
Show Answers Only

`A`

Show Worked Solution

`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%`  
  `=0.05/2.4 xx 100%`  

 
`=>A`

Measurement, STD2 M1 2017 HSC 21 MC

The length of a netball court is measured to be 30.50 metres, correct to the nearest centimetre.

What is the lower limit for the length of the netball court?

  1. 30.45 m
  2. 30.49 m
  3. 30.495 m
  4. 30.499 m
Show Answers Only

`C`

Show Worked Solution
`text(A)text(bsolute error)` `= 0.5\ text(cm)`
  `= 0.005\ text(m)`

 

`:.\ text(Lower limit)` `= 30.50-0.005`
  `= 30.495\ text(m)`

 
`=>C`

Measurement, STD2 M1 2015 HSC 12 MC

The length of a fish was measured to be 49 cm, correct to the nearest cm.

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

  1. 0.01%
  2. 0.5%
  3. 1%
  4. 2%
Show Answers Only

`C`

Show Worked Solution
♦ Mean mark 41%.

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

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/49 xx 100%`  
  `=1.020… %`  
  `=1%\ \ text{(to 1 sig fig)}`  

 
`=>C`

Measurement, STD2 M1 2008 HSC 23b

The capacity of a bottle is measured as 1.25 litres correct to the nearest 10 millilitres.

What is the percentage error for this measurement?   (1 mark)

Show Answers Only

`text(0.4%)`

Show Worked Solution

`text(A) text(bsolute error) = 5\ text(mL)`

`:.\ text(% error)` `= 5/1250 xx 100`
  `=\ text(0.4%)`

Measurement, STD2 M1 2014 HSC 10 MC

The top of the Sydney Harbour Bridge is measured to be 138.4 m above sea level. 

What is the percentage error in this measurement?

  1. 0.036%
  2. 0.050%
  3. 0.072%
  4. 0.289%
Show Answers Only

`A`

Show Worked Solution
 
♦ Mean mark 48%

`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%`  
  `=0.05/138.4 xx 100%`  
  `=0.036%`  

 
`=>  A`

Measurement, STD2 M1 2013 HSC 27d

A rectangular wooden chopping board is advertised as being 17 cm by 25 cm, with each side measured to the nearest centimetre.

  1. Calculate the percentage error in the measurement of the longer side.   (1 mark)

  2. Between what lower and upper limits does the actual area of the top of the chopping board lie?     (2 marks)

Show Answers Only
  1. `text(2%)`
  2. `404.25\ text{cm}^2 and 446.25\ text{cm}^2`
Show Worked Solution

i.    `text(Longer side) = 25\ text(cm)`

♦♦ Mean mark 23%
MARKER’S COMMENT: Be aware that measurements accurate to the nearest cm have an absolute error for calculation purposes of 0.5 cm.

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

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/25 xx 100%`  
  `=2%`  

 

ii.   `text(Area) = l xx b`

♦ Mean mark 35%
`text{Area (upper)}` `=25.5 xx 17.5`
  `=446.25\ text{cm}^2`

 

`text{Area (lower)}` `=24.5 xx 16.5`
  `=404.25\ text{cm}^2`

 
`:.\ text{Area is between 404.25 cm}^2\ text{and 446.25 cm}^2.`