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Year 12 Mathematics sample

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Question 1 of 5 Number and arithmetic

A household pays $2700 to have solar panels fitted. The panels cut $400 off the power bills in the first year, and because power prices keep climbing the saving is $40 bigger in each year than in the year before. At the end of which year has the total saving first covered what the panels cost?

Solar quote and first year saving
What it coversAmount
Cost of fitting the panels$2700
Saving in year 1$400
Extra saving in each later year$40
Question 2 of 5 Space and geometry

A ferry leaves the wharf and runs 5 km on a bearing of 050, then turns and runs 16 km on a bearing of 110. How far is the ferry from the wharf when the second leg ends?

Ferry log for the two legs
LegDistance runBearing held
Wharf to the turning buoy5 km050
Turning buoy to the island16 km110
Question 3 of 5 Number and arithmetic

A bakery keeps two flours: a strong one that is 13 per cent protein and a soft one that is 8 per cent protein. The head baker wants 40 kg of a blend that comes out at 9 per cent protein. How much of the strong flour goes in?

Question 4 of 5 Measures and units

A survey drone drains its battery at a steady rate, plotted here for one flight. Safety rules say it must land with at least 15 per cent charge still in the battery. One survey run over the paddock takes 8 minutes of flying. How many complete runs fit into one fully charged battery?

Charge left on one flight02468101214161820022446688110Minutes flownCharge left15 min: 555 minutes across10 per cent up
Question 5 of 5 Chance and data

A surf club sells every one of its 600 raffle tickets at $6 each. It pays out one major prize of $720 and three runner up prizes of $60 each. Averaged over all the tickets, how much of a single ticket price does the club keep?

Raffle book and prize list
ItemAmount
Tickets printed and sold600
Price of one ticket$6
Major prize$720
Each runner up prize (three of them)$60
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