2026 ZHSS P1 Q1

The Richter scale is used to measure the magnitude of an earthquake.

The magnitude, \(M\), is related to the amplitude, \(A\) mm, of the seismic wave recorded by a seismograph according to the model.

\[M=\lg\left(\frac{A}{0.001}\right)\]

It was observed that two earthquakes happened within a month.

1. Find the magnitude of the first earthquake where the amplitude of the seismic wave was recorded at 1200 mm.[1]
2. The second earthquake has a magnitude of 4.6, find the amplitude, \(A\) mm, of the seismic wave recorded.[2]
3. A researcher proposed a new model to measure the magnitude of an earthquake.
   \(M=\log_3\left(\dfrac A9\right)\)
   Using this new model, find the magnitude of the first earthquake with an amplitude of 1200 mm.[2]