2026 CCHMS P2 Q3

A weather station recorded the temperature of a city, \(T\) in degrees Celsius, at various times between 8.30 p.m. on 15 July and 3.30 a.m. on 16 July.

Let \(t\) be the time, in hours, measured relative to midnight at the start of 16 July.

Some of the recorded temperatures are shown in the table below.

For example: \(t=-3\) corresponds to 9 p.m. on 15 July.

The temperature can be modelled by the equation \(T=k(t+3)(t-p)(t-q)\) where \(k\), \(p\) and \(q\) are constants.

1. On the grid opposite, plot the points given in the table and join them with a smooth curve.[3]
2. Using your graph, estimate the values of \(p\) and \(q\).[2]
3. By drawing a tangent, find the gradient of the curve at \(t=-2\) and state the units in your answer.[3]
4. A warning is issued whenever \(T\leq-1.5\). Using your graph, estimate the duration for which the warning would have been active.[1]