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Measurement, STD2 M7 2025 HSC 16

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

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

Show Worked Solution

\(\text{Cost of 4 litre cans:}\)

\( C_1=\dfrac{80}{4} \times 90=$1800 \)

\(\text{Cost of 10 litre cans:}\)

\( C_2=\dfrac{80}{10} \times 205=$1640\)

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

Measurement, STD2 M7 2025 HSC 7 MC

There are 960 students at a high school.

Using stratified sampling, 240 students from the whole school are to be chosen for a survey.

If there are 200 students in Year 12, how many Year 12 students should be chosen?

  1. 4
  2. 5
  3. 50
  4. 60
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Stratified sampling}\ \ \Rightarrow\ \ \text{Fraction of Y12 in school = same fraction in sample}\)

\(\text{Yr 12 students in school}\ =\dfrac{200}{960} = \dfrac{5}{24}\)

\(\text{Number in sample}\ = \dfrac{5}{24} \times 240 = 50\)

\(\Rightarrow C\)

v1 Measurement, STD2 M7 2018 HSC 27a

Alex used a cloud storage service for one month.

The plan has a base monthly cost of $25. The service also charges 45 cents per GB uploaded and 12 cents per GB downloaded.

During the month, Alex uploaded 180 GB and downloaded 350 GB.

What was the total bill for the month?   (2 marks)

Show Answers Only

`$148.00`

Show Worked Solution

`text(Upload charge = 180 × 45c = $81.00)`

`text(Download charge = 350 × 12c = $42.00)`

`:.\ text(Total bill)` `= 25 + 81 + 42`
  `= $148.00`

v1 Measurement, STD2 M7 2014 HSC 17 MC

A child who weighs 22 kg needs to be given 12 mg of medicine for every 2 kg of body weight. 

Every 10 mL of this medicine contains 150 mg. 

What is the correct dosage for the child? 

  1. 7.0 mL 
  2. 8.8 mL 
  3. 10.2 mL 
  4. 11.5 mL 
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Dosage needed}\ = \dfrac{22}{2} \times 12 = 132\ \text{mg}\) 

\(\text{Since there is 150 mg in 10 mL:} \) 

\(\text{Volume (132 mg)}\ =\dfrac{132}{150} \times 10 = 8.8\ \text{mL}\) 

\(\Rightarrow B\)

v2 Measurement, STD2 M7 2016 HSC 9 MC

An old air conditioner uses 2.8 kW of electricity per hour. A new air conditioner uses 1.2 kW per hour. How much electricity is saved each year if the air conditioner runs for 5 hours per day for 200 days using the new model?

  1. 1200 kWh
  2. 1600 kWh
  3. 2400 kWh
  4. 2800 kWh
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Electricity used by old air conditioner}\ = 2.8 \times 5 \times 200 = 2800\ \text{kWh}\)

\(\text{Electricity used by new air conditioner}\ = 1.2 \times 5 \times 200 = 1200\ \text{kWh}\)

\(\therefore\ \text{Electricity saved} = 2800-1200 = 1600\ \text{kWh}\)

\(\Rightarrow B\)

v1 Measurement, STD2 M7 2016 HSC 9 MC

An old dishwasher uses 45 L of water per cycle. A new dishwasher uses 15 L per cycle. How much water is saved each year if three cycles are run each week using the new dishwasher?

  1. 2340 L
  2. 3640 L
  3. 4680 L
  4. 7020 L
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Water used by old dishwasher}\ = 45 \times 3 \times 52 = 7020\ \text{L}\)

\(\text{Water used by new dishwasher}\ = 15 \times 3 \times 52 = 2340\ \text{L}\)

\(\text{Water saved}\ = 7020-2340 = 4680\ \text{L}\)

\(\Rightarrow C\)

v1 Measurement, STD2 M1 2009 HSC 23c

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

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

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $60. 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 floor.   (2 marks)

Show Answers Only

i.    `17\ text(m²)`

ii.   `$1140`

Show Worked Solution
i.
`text(Area)` `=\ text(Area of big square – Area of 2 cut-out squares`
  `= (3 + 2) xx (3 + 2)\-2 xx (2 xx 2)`
  `= 25\-8`
  `= 17\ text(m²)`

 

ii. `text(Tiles required)` `= (17 +10 text{%}) xx 17`
    `= 18.7\ text(m²)`

 

 `=>\ text(19 boxes are needed)`

`:.\ text(Total cost of boxes)` `=19 xx $60`
  `= $1140`

Measurement, STD2 M7 2024 HSC 33

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

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

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

 

\(\therefore\ \text{Time to run 150m}\) \(=\dfrac{150}{11.11…}\)  
  \(=13.5\ \text{seconds}\)  

Measurement, STD2 M7 2020 HSC 17

Ayla wishes to estimate the number of trees on a square block of land measuring 1000 m by 1000 m. She counts the number of trees on a 5 m by 5 m section of the block and finds there are 8 trees.

Based on this, estimate the number of tress on the entire square block of land.   (2 marks)

Show Answers Only

`320\ 000`

Show Worked Solution
`text{Area of block}` `= 1000 xx 1000`
  `= 1\ 000\ 000 \ text{m}^2`

 

`8\ text{trees per} \ 25 text{m}^2`

`therefore \ text{Total trees}` `= 8 xx frac{1\ 000\ 000}{25}`
  `= 320\ 000`

Measurement, STD2 M7 SM-Bank 19

A laundromat can wash 12 loads of laundry in one hour at full capacity.

A standard load of laundry weighs 7 kilograms.

Here is some information about two different washing machines.
 


 

Working at full capacity, how many litres of water would the laundromat expect to save in one hour by using the front loader instead of the top loader?   (2 marks)

Show Answers Only

`text(315 L)`

Show Worked Solution

`text(Top loader water used (1 load))`

`= 7 xx 10.25`

`= 71.75\ text(L)`
 

`text(Front loader water used (1 load))`

`= 7 xx 6.5`

`= 45.5\ text(L)`
 

`:.\ text(Expected water saved)`

`= 12 xx (71.75 – 45.5)`

`= 315\ text(L)`

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 2015 HSC 27b

A patient requires 2400 mL of fluid to be delivered at a constant rate by means of a drip over 12 hours. Each mL of fluid is equivalent to 15 drops.

How many drops per minute need to be delivered?  (2 marks)

Show Answers Only

`50\ text(per minute)`

Show Worked Solution

`text(Fluid rate of delivery)`

`= 2400/12`

`= 200\ text(mL per hour)`

`= 200/60`

`= 3 1/3\ text(mL per minute)`

 
`text(S)text(ince each mL has 15 drops)`

`#\ text(Drops)` `= 15 xx 3 1/3`
  `= 50\ text(per minute)`

Measurement, STD2 M1 2004 HSC 23a

The diagram shows the shape of Carmel’s garden bed. All measurements are in
metres.

  1. Show that the area of the garden bed is 57 square metres.   (2 marks)

  2. Carmel decides to add a 5 cm layer of straw to the garden bed.

     

    Calculate the volume of straw required. Give your answer in cubic metres.   (2 marks)

  3. Each bag holds 0.25 cubic metres of straw.

     

    How many bags does she need to buy?   (2 marks)

  4. A straight fence is to be constructed joining point A to point B.

     

    Find the length of this fence to the nearest metre.   (2 marks)

Show Answers Only
  1. `text(Proof)\ \ text{(See Worked Solutions)}`
  2. `text(2.85 m³)`
  3. `text(She needs to buy 12 bags)`
  4. `8\ text{m  (nearest metre)}`
Show Worked Solution
i.  `text(Area of)\ Delta ABC` `= 1/2 xx b xx h`
  `= 1/2 xx 10 xx 5.1`
  `= 25.5\ text(m²)`
`text(Area of)\ Delta ACD` `= 1/2 xx 10 xx 6.3`
  `= 31.5\ text(m²)`

 

`:.\ text(Total Area)` `= 25.5 + 31.5`
  `= 57\ text(m² … as required)`

 

ii.  `V` `= Ah`
  `= 57 xx 0.05`
  `= 2.85\ text(m³)`

 

iii.  `text(Bags to buy)` `= 2.85/0.25`
  `= 11.4`

 
`:.\ text(She needs to buy 12 bags.)`

 

iv.  `text(Using Pythagoras,)`

`AB^2` `= 6.0^2 + 5.1^2`
  `= 36 + 26.01`
  `= 62.01`
`AB` `= 7.874…`
  `=8\ text{m  (nearest metre)}`

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

i.    `13.77\ text(m²)`

ii.   `$880`

Show Worked Solution
i.
`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)`

 

ii. `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`