3.2.2 Algebra and Functions (A-level only)

A geophysicist is monitoring the normalized amplitude $A$ of two different seismic waves over time $t$ . Given that $k$ is a positive constant,

on separate diagrams, sketch the graph with equation

(i) $A = 3 k - 2∣ t ∣$

(ii) $A = ∣5 t - k ∣$

Show on each sketch the coordinates, in terms of $k$ , of each point where the graph meets or cuts the axes.

[4]

Hence determine, in terms of $k$ , the values of $t$ for which

∣5 t - k ∣ = 3 k - 2∣ t ∣

giving your answers in simplest form.

[4]

3.2.2 Algebra and Functions (A-level only) Questions