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Measurement, STD1 M2 2025 HSC 18

Ramon took 1.25 hours to travel the length of a freeway. The length of the freeway is 100 km.

  1. Ramon’s total travel time was made up of:
    • 20 minutes to travel to the start of the freeway
    • the time taken to travel the length of the freeway
    • 35 minutes after exiting the freeway to get to his destination.
  1. What was the total time Ramon spent travelling? Give your answer in hours and minutes.   (2 marks)
  1. What was Ramon’s average speed on the freeway?   (1 mark)
Show Answers Only

a.    \(2\ \text{hours}\ 10\ \text{minutes}\)

b.    \(80\ \text{km/h}\)

Show Worked Solution
a.     \(\text{Total time}\) \(=20+75+35\)
    \(=130\ \text{minutes}\)
    \(=2\text{ h }10\text{ min}\)

Mean mark (a) 54%.
b.     \(\text{Average speed}\) \(=\dfrac{\text{distance}}{\text{time}}\)
    \(=\dfrac{100}{1.25}\)
    \(=80\ \text{km/h}\)

♦♦ Mean mark (b) 43%.

Measurement, STD1 M4 2025 HSC 17

Paint is sold in two sizes at a local shop.

  • Four-litre cans at $90 per can
  • Ten-litre cans at $205 per can

Mina needs to purchase 80 litres of paint.

Calculate the amount of money Mina will save by purchasing only ten-litre cans of paint rather than only four-litre cans of paint.    (2 marks)

Show Answers Only

\(\text{Saving}=$160\)

Show Worked Solution

\(\text{4 litre cans needed}\ =\dfrac{80}{4}=20\)

\(\text{Cost using 4 litre cans}\ =20\times $90=$1800\)

\(\text{10 litre cans needed}\ =\dfrac{80}{10}=8\)

\(\text{Cost using 10 litre cans}\ =8\times $205=$1640\)
 

\(\therefore\ \text{Saving}\ =$1800-$1640=$160\)

Measurement, STD1 M4 2025 HSC 12

Vijay’s heart rate before and after his morning run is shown.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex} \text{Before run} \rule[-1ex]{0pt}{0pt} & \text{72 beats per minute} \\
\hline
\rule{0pt}{2.5ex} \text{After run} \rule[-1ex]{0pt}{0pt} & \text{126 beats per minute} \\
\hline
\end{array}

What is the percentage increase in Vijay’s heart rate?    (2 marks)

Show Answers Only

\(75\%\)

Show Worked Solution
\(\text{% increase}\) \(=\Big[\dfrac{\text{Change in HR}}{\text{Original HR}}\Big]\times 100\%\)
  \(=\Big[\dfrac{126-72}{72}\Big]\times 100\%\)
  \(=75\%\)

♦♦ Mean mark 45%.

Measurement, STD1 M4 2024 HSC 31

Wombats can run at a speed of 40 km/h over short distances.

At this speed, how many seconds would it take a wombat to run 150 metres?   (3 marks)

Show Answers Only

\(\text{13.5 seconds}\)

Show Worked Solution

\(\text{Convert km/h to m/sec:}\)

\(\text{40 km/h}\) \(=40\,000\ \text{m/h}\)  
  \(=\dfrac{40\,000}{60 \times 60}\ \text{m/s}\)  
  \(=11.11\ \text{m/s}\)  

 

\(\therefore\ \text{Time to run 150m}\) \(=\dfrac{150}{11.11…}\)  
  \(=13.5\ \text{seconds}\)  
♦♦♦ Mean mark 25%.

Measurement, STD1 M4 2023 HSC 10 MC

A tap is dripping at the rate of 4 mL per minute.

Which expression shows how many litres this would amount to in one year?

  1. \(\dfrac{4 \times 1000}{60 \times 24 \times 365}\)
  2. \(\dfrac{4 \times 60 \times 24 \times 365}{1000}\)
  3. \(\dfrac{60 \times 24 \times 365}{4 \times 1000}\)
  4. \(\dfrac{1000}{4 \times 60 \times 24 \times 365}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Rate}\Rightarrow 4 \text{ mL} / \text{minute}\)

\(\text{Litres in 1 year}\) \(=\dfrac{4}{1000}\times 60\times 24\times365\)
  \(=\dfrac{4 \times 60 \times 24 \times 365}{1000}\)

 
\(\Rightarrow B\)

♦ Mean mark 47%.

Financial Maths, STD1 F1 2023 HSC 6 MC

A delivery truck was valued at $65 000 when new. The value of the truck depreciates at a rate of 22 cents per kilometre travelled.

What is the value of the truck after it has travelled a total distance of 132 600 km?

  1. $35 828
  2. $29 172
  3. $14 872
  4. $14 300
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Depreciation} = 132\ 600\times\dfrac{22}{100}=\$29\,172\)

\(\text{Value} = 65\,000-29\,172=\$35\,828\)

\(\Rightarrow A\)

Financial Maths, STD2 F1 2023 HSC 4 MC

A delivery truck was valued at $65 000 when new. The value of the truck depreciates at a rate of 22 cents per kilometre travelled.

What is the value of the truck after it has travelled a total distance of 132 600 km?

  1. $35 828
  2. $29 172
  3. $14 872
  4. $14 300
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Depreciation}=0.22\times 132\ 600=$29\ 172\)

\(\text{Truck value}=65\ 000-29\ 172=$35\ 828\)

   
\(\Rightarrow A\)

Measurement, STD1 M4 2021 HSC 22

A tap is leaking water. It leaks 1 drop every 4 seconds, and 15 of these drops make up 1 mL.

  1. Find the amount of water leaked in a 24-hour period. Give the answer in litres.  (3 marks)

  2. A bucket can hold 9 litres of water. How long will it take for the leaking tap to completely fill this empty bucket?  (1 mark)

Show Answers Only
  1. `1.44\ text(L)`
  2. `6.25\ text(days)`
Show Worked Solution

a.   `text(Drops per minute) = 60/4 = 15`

♦ Mean mark part (a) 50%.

`text(Volume per minute = 1 mL)`

`:.\ text(Volume in 24 hours)` `= 1 xx 60 xx 24`
  `= 1440\ text(mL)`
  `= 1.44\ text(L)`
♦♦ Mean mark part (b) 32%.

 

b.    `text(Time to fill bucket)` `= 9/1.44`
    `= 6.25\ text(days)`

Measurement, STD1 M4 2020 HSC 12

Two painters each provide a quote for painting an area of 1500 square metres. Painter A charges $100 per 30 square metres. Painter B charges $80 per hour and bases their quote on painting 25 square metres per hour.

Calculate how much will be saved by choosing the cheaper quote.   (3 marks)

Show Answers Only

`$200`

Show Worked Solution

`text{Painter A cost:}`

`C_A = frac{1500}{30} xx 100 = $5000`
 

`text{Painter B cost:}`

`text(Hours)\ = frac{1500}{25} = 60`

`C_B = 60 xx 80 = $ 4800`
 

`therefore \ text{Savings by using Painter B}`

`= 5000 – 4800`

`=  $200`

Measurement, STD2 M7 2018 HSC 27a

Jenny used her mobile phone while she was overseas for one month.

Her mobile phone plan has a base monthly cost of $50. While overseas, she is also charged 33 cents per SMS message sent and 26 cents per MB of data used.

During her month overseas, Jenny sent 120 SMS messages and used 1400 MB of data.

What was her mobile phone bill for the month overseas?  (2 marks)

Show Answers Only

`$453.60`

Show Worked Solution

`text(SMS charge = 120 × 33c = $39.60)`

`text(Data charge = 1400 × 26c = $364.00)`
 

`:.\ text(Total bill)` `= 50 + 39.60 + 364`
  `= $453.60`

Measurement, STD2 M7 2018 HSC 26g

A field diagram of a block of land has been drawn to scale. The shaded region `ABFG` is covered in grass.
 

 
The actual length of `AG` is 24 m.

  1. If the length of `AG` on the field diagram is 8 cm, what is the scale of the diagram?  (1 mark)

  2. How much fertiliser would be needed to fertilise the grassed area  `ABFG`  at the rate of 26.5 g /m²?  (3 marks)

Show Answers Only
  1. `text(1 : 300)`
  2. `5008.5\ text(grams)`
Show Worked Solution

♦♦ Mean mark 32%.

i.    `text(Scale    8 cm)` `\ :\ text(24 m)`
  `text(1 cm)` `\ :\ text(3 m)`
  `1` `\ :\ 300`

 

ii.   `text(Area of rectangle)\ ABFE`

`= 6\ text(cm × 3 cm)`

`= 18\ text(m × 9 m)`

`= 162\ text(m²)`
 

`text(Area of)\ DeltaEFG`

`= 1/2 xx 3\ text(cm) xx 2\ text(cm)`

`= 1/2 xx 9 xx 6`

`= 27\ text(m²)`
 

`:.\ text(Fertiliser needed)` `= (162 + 27) xx 26.5`
  `= 5008.5\ text(grams)`

Measurement, STD2 M7 2017 HSC 26b

Toby’s mobile phone plan costs $20 per month, plus the cost of all calls. Calls are charged at the rate of 70 cents per 30 seconds, or part thereof. There is also a call connection fee of 50c per call.

Here is a record of all his calls in July.
 

How much is Toby’s mobile phone bill for July?  (2 marks)

Show Answers Only

`$27.10`

Show Worked Solution

`text(Call cost) = 0.70 + (2 xx 0.70) + (5 xx 0.70) = $5.60`

`text(Connection fees) = 3 xx 0.50 = $1.50`

`:.\ text(Total bill)` `= 5.60 + 1.50 + 20`
  `= $27.10`

Measurement, STD2 M7 2016 HSC 15 MC

Calls on a mobile phone plan are charged at the rate of 54 cents per 30 seconds, or part thereof.

What is the cost of a call lasting 2 minutes and 15 seconds?

  1.    $2.16
  2.    $2.32
  3.    $2.43
  4.    $2.70
Show Answers Only

`=> D`

Show Worked Solution

`5 xx 30\ text(second blocks)`

♦ Mean mark 44%.
`:.\ text(C)text(ost)` `= 5 xx 0.54`
  `= $2.70`

`=> D`

Measurement, STD2 M7 2016 HSC 9 MC

An old washing machine uses 130 L of water per load. A new washing machine uses 50 L per load.

How much water is saved each year if two loads of washing are done each week using the new machine?

  1.   2600 L
  2. 4160 L
  3. 5200 L
  4. 8320 L
Show Answers Only

`D`

Show Worked Solution

`text(Water used by old machine)`

`= 130 xx 2 xx 52`

`= 13\ 520\ text(L)`

`text(Water used by new machine)`

`= 50 xx 2 xx 52`

`= 5200\ text(L)`

`:.\ text(Water saved)` `= 13\ 520 – 5200`
  `= 8320\ text(L)`

`=> D`

Measurement, STD2 M7 2008 HSC 23c

An alcoholic drink has 5.5% alcohol by volume. The label on a 375 mL bottle says it contains 1.6 standard drinks.

  1. How many millilitres of alcohol are in a 375 mL bottle? (1 mark)

  2. It is recommended that a fully-licensed male driver should have a maximum of one standard drink every hour.

     

    Express this as a rate in millilitres per minute, correct to one decimal place.    (2 marks)

Show Answers Only
  1. `20.625\ text(mL)`
  2. `3.9\ text(mL/min)`
Show Worked Solution
i.    `text(Alcohol)` `= 5.5/100 xx 375`
    `= 20.625\ text(mL)`

 

ii.    `text(S)text(ince 1.6 standard drinks = 375 mL)`

`=>\ text(1 standard drink)`

`= 375/1.6`

`= 234.375\ text(mL)`
 

`:.\ text(Rate)` `= 234.375/60`
  `= 3.90625`
  `= 3.9\ text(mL/min)`

Measurement, STD2 M7 2014 HSC 17 MC

A child who weighs 14 kg needs to be given 15 mg of paracetamol for every 2 kg of body weight.

Every 10 mL of a particular medicine contains 120 mg of paracetamol.

What is the correct dosage of this medicine for the child?

  1. 5.6 mL
  2. 8.75 mL
  3. 11.43 mL
  4. 17.5 mL
Show Answers Only

`B`

Show Worked Solution

`text(Paracetamol needed)`

`= 14/2 xx 15\ text(mg)`

`= 105\ text(mg)`

 

`text(S)text(ince 120 mg is contained in 10 mL,)`

`=> 105\ text(mg is contained in)`

`105/120 xx 10\ text(mL)= 8.75\ text(mL)`

`=>  B`

Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a terrace which is to be tiled.
 

  1. Find the area of the terrace.   (2 marks)

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $55. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

     

    Find the total cost of the boxes of tiles required for the terrace.   (2 marks)

Show Answers Only

a.   `13.77\ text(m²)`

b.   `$880`

Show Worked Solution
a.
`text(Area)` `=\ text(Area of big square – Area of 2 cut-out squares`
  `= (2.7 + 1.8) xx (2.7 + 1.8)\-2 xx (1.8 xx 1.8)`
  `= 20.25\-6.48= 13.77\ text(m²)`

 

b.    `text(Tiles required)` `= (13.77 +10 text{%}) xx 13.77= 15.147\ text(m²)`

`=>\ text(16 boxes are needed)`

`:.\ text(Total cost of boxes)=16 xx $55= $880`