Stage 8 - Q1 - 2 marks
Find y when \(x=2\) in \(y=15-3x\).
Hint
Keep the order of subtraction.
Stage 8 - Q2 - 2 marks
For \(y=18-2x\), state the y-intercept.
Hint
Set the input to zero.
Stage 8 - Q3 - 4 marks
Complete the table, then plot the straight line on the grid.
Hint
A negative coefficient makes y fall as x rises.
Stage 8 - Q4 - 4 marks
Complete the table, then plot the straight line on the grid.
Hint
Check the sign of each product before subtracting.
Stage 8 - Q5 - 2 marks
A 42 L tank loses 6 L per minute. Find the emptying time and the valid time interval.
Hint
A physical volume cannot become negative under this model.
Stage 8 - Q6 - 2 marks
A decreasing line passes through \(\left(0,\ 28\right)\) and \(\left(7,\ 0\right)\). Find its equation.
Hint
Use the two intercepts.
Stage 8 - Q7 - 3 marks
The model \(V=32-4t\) is used for a draining tank. A pupil predicts \(-8\) L at \(t=10\). Explain the mathematical value and the physical limitation.
Hint
Separate algebraic extension from the allowed physical domain.
Stage 8 - Q8 - 3 marks
A container drops from 50 L to 26 L in 6 minutes at a constant rate. Find its volume rule and emptying time.
Hint
Recover the rate before extending the model.
Stage 8 - Q9 - 4 marks
Two tank graphs have the same initial volume. One falls twice as steeply. Compare their emptying times if both losses remain constant.
Hint
Use amount divided by loss rate.
Stage 8 - Q10 - 5 marks
Challenge: tank A contains 36 L and loses 3 L per minute. Tank B contains 12 L and gains 1 L per minute. When are the volumes equal? What is that volume, and is A still within its valid draining interval?
Hint
Solve the equality and separately test whether the physical models still apply.