Stage 8 - Q1 - 2 marks
A ticket office charges USD 4 per ticket. Write the cost c for n tickets.
Hint
There is no fixed charge.
Stage 8 - Q2 - 2 marks
A booking costs USD 9 plus USD 6 per hour. Write c in terms of h.
Hint
Separate the time-dependent and fixed parts.
Stage 8 - Q3 - 2 marks
Use \(c=8h+11\) to find the cost for 4 hours.
Hint
Multiply before adding.
Stage 8 - Q4 - 2 marks
A plant is 12 cm tall and grows 3 cm per week. Write its height H after w weeks.
Hint
At zero weeks, the function should give 12.
Stage 8 - Q5 - 2 marks
A tank contains 35 L and loses 5 L per minute. Write \(V\left(t\right)\) and state when it becomes empty.
Hint
The initial value is the constant term.
Stage 8 - Q6 - 2 marks
A hire bill follows \(c=7h+10\) USD. The bill is USD 59. Find the hours.
Hint
Use the inverse operations.
Stage 8 - Q7 - 3 marks
A linear service costs USD 17 for one item and USD 29 for four items. Find the fixed and per-item charges.
Hint
The difference removes the fixed charge.
Stage 8 - Q8 - 3 marks
A pupil models a USD 20 fixed fee and USD 3 per hour as \(c=20h+3\). Explain and correct the error.
Hint
Test the meaning of the bill at \(h=0\).
Stage 8 - Q9 - 4 marks
Create a realistic fictional situation represented by \(y=40-2.5x\). State units and a useful domain.
Hint
A decreasing physical quantity must stop at zero.
Stage 8 - Q10 - 5 marks
Challenge: plan A costs USD 15 plus USD 6 per hour. Plan B costs USD 3 plus USD 9 per hour. Find when the costs match, and explain which is cheaper for shorter and longer bookings.
Hint
Compare both the fixed charges and rates, then solve the crossing point.