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Numbers of Any Magnitude, SMB-024 MC

The first three days of the Brisbane cricket test had the following attendances:

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex}\text{Day 1}\rule[-1ex]{0pt}{0pt} & 20\ 156\\
\hline
\rule{0pt}{2.5ex}\text{Day 2}\rule[-1ex]{0pt}{0pt} & 18\ 397\\
\hline
\rule{0pt}{2.5ex}\text{Day 3}\rule[-1ex]{0pt}{0pt} & 29\ 981\\
\hline
\end{array}

What was the total crowd over the first 3 days, to the nearest 1000?

  1. `68\ 000`
  2. `69\ 000`
  3. `70\ 000`
  4. `71\ 000`
Show Answers Only

`B`

Show Worked Solution

`20\ 156 + 18\ 397 + 29\ 981`

`= 68\ 534`

`= 69\ 000\ text{(nearest 1000)}`
 

`=>B`

Numbers of Any Magnitude, SMB-023

A red blood cell and a white blood cell have a combined total mass of `4.2 xx 10^-11` grams.

If the red blood cell has a mass of `2 xx 10^-12` grams, what is the mass of the white blood cell?  (2 marks)

Show Answers Only

`4.0 xx 10^-11\ text(grams)`

Show Worked Solution
`text{Mass}` `=4.2 xx 10^-11-2 xx 10^-12`  
  `= 4.0 xx 10^-11\ text{(by calculator)}`  

Numbers of Any Magnitude, SMB-021

An insect expert estimates that an anthill 30 cm high contains `10^8` ants.

He also estimates that a 25 cm high anthill contains `10^7` ants.

If his estimations are correct, how many more ants live in the 30 cm high anthill than the 25 cm high one?  (2 marks)

Show Answers Only

`text(90 million)`

Show Worked Solution

`text(The extra ants in the 30 cm high anthill)`

`= 100\ 000\ 000-10\ 000\ 000`

`=90\ 000\ 000`

`=90\ text(million)`

Numbers of Any Magnitude, SMB-015

The width of red blood cell is 8 nanometres or `8 xx 10^{-9}` metres.

How many red blood cells, lined up side by side in straight line, would it take to form a 1 cm distance.  (2 marks)

Show Answers Only

`1.25 xx 10^6`

Show Worked Solution

`text{Convert cm to metres:}`

`text{100 cm = 1 m}\ => \ text{1 cm = 0.01 m}`

`text{Number of cells}` `=0.01/(8xx10^{-9})`  
  `=1\ 250\ 000`  
  `=1.25 xx 10^6`  

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 scientific notation, what is the approximate mass in grams of one microbe?   (2 marks)

Show Answers Only

`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)`

Numbers of Any Magnitude, SMB-008 MC

A person's height is measured as 1.7 metres.

What is the absolute error of this measurement?

  1. 1 centimetre
  2. 5 centimetres
  3. 10 centimetres
  4. 50 centimetres
Show Answers Only

`B`

Show Worked Solution

`text{1 metre = 100 cm}\ => \ text{0.1 metre = 10 cm}`

`text(A)text(bsolute error)` `= 1/2 xx\ text(precision)`
  `= 1/2 xx 0.1\ text(m)`
  `= 1/2 xx 10\ text(cm)`
  `= 5\ text(cm)`

 
`=> B`

Numbers of Any Magnitude, SMB-007

The capacity of a bottle is measured as 1.35 litres correct to the nearest 10 millilitres.

What is the percentage error for this measurement, correct to two significant figures?   (2 marks)

Show Answers Only

`text(0.37%)`

Show Worked Solution

`text{1.35 litres = 1350 milliliters (mL)}`

`text(A) text(bsolute error) = 1/2 xx\ text{precision} = 1/2xx10=5\ text(mL)`

`:.\ text(% error)` `= 5/1350 xx 100`
  `=0.3703… %`
  `=0.37%\ text{(to 2 sig.fig.)}`

Numbers of Any Magnitude, SMB-006

A dinosaur fossil is measured to be 1.3 metres in length.

What is the percentage error in this measurement, giving your answer correct to two decimal places?  (2 marks)

Show Answers Only

`3.85%`

Show Worked Solution

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

`%  text(error)` `= frac(0.05)(1.3) xx 100`
  `= 3.84615%`
  `=3.85%\ text{(to 2 d.p.)}`

Numbers of Any Magnitude, SMB-005

A puppy's weight is measured at 5.2 kilograms, to the nearest 100 grams.

Calculate the percentage error in this measurement, correct to one significant figure?  (3 marks)

Show Answers Only

`1%`

Show Worked Solution

`text{Using  1 kilogram = 1000 grams}`

`=>\ text{5.2 kilograms = 5200 grams}`

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 100 = 50\ text{g}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=50/5200 xx 100%`  
  `=0.961… %`  
  `=1%\ text{(to 1 sig. fig.)}`  
TIP: Convert all measurements to either grams or kilograms before applying formula.

Numbers of Any Magnitude, SMB-004

The height of palm tree is measured at 8 metres, to the nearest metre.

What is the percentage error in this measurement?  (2 marks)

Show Answers Only

`6.25%`

Show Worked Solution

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

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/8 xx 100%`  
  `=6.25%`  

Numbers of Any Magnitude, SMB-003

The width of a hockey field is measured to be 45 metres, correct to the nearest metre.

What is the upper limit for the width of the hockey field?  (2 marks)

Show Answers Only

`45.5\ text(m)`

Show Worked Solution

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

`=>\ text{True length could lie 0.5 metres either side of 45 m measurement.}`

`:.\ text(Upper limit)` `= 45+0.5`
  `= 45.5\ text(m)`

Numbers of Any Magnitude, SMB-002 MC

The width of a soccer field is measured to be 50.60 metres, correct to the nearest centimetre.

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

  1. 50.55 m
  2. 50.59 m
  3. 50.595 m
  4. 50.599 m
Show Answers Only

`C`

Show Worked Solution

`text{1 cm = 0.01 metre}`

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

`:.\ text(Lower limit)` `= 50.60-0.005`
  `= 50.595\ text(m)`

 
`=>C`

Numbers of Any Magnitude, SMB-001

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?  (2 marks)

Show Answers Only

`5.25\ text(cm)`

Show Worked Solution

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

`=>\ text{True length could lie 0.05 cm either side of 5.2 cm measurement.}`

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

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
Show Answers Only

`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 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 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 2016 HSC 1 MC

What is  208.345  correct to two significant figures?

  1. 208
  2. 210
  3. 208.34
  4. 208.35
Show Answers Only

`B`

Show Worked Solution

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

♦♦ Mean mark 36%!!

`=> B`

 

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 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)`
Show Answers Only

`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 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.`