In free response choice tasks, decision making is often modeled as a first-passage problemfor a stochastic differential equation. In particular, drift-diffusion processes withconstant or time-varying drift rates and noise can reproduce behavioral data (accuracyand response-time distributions) and neuronal firing rates. However, no exact solutionsare known for the first-passage problem with time-varying data. Recognizing the importanceof simple closed-form expressions for modeling and inference, we show that an interrogationor cued-response protocol, appropriately interpreted, can yield approximatefirst-passage (response time) distributions for a specific class of time-varying processesused to model evidence accumulation. We test these against exact expressions for theconstant drift case and compare them with data from a class of sigmoidal functions. Wefind that both the direct interrogation approximation and an error-minimizing interrogationapproximation can capture a variety of distribution shapes and mode numbersbut that the direct approximation, in particular, is systematically biased away from thecorrect free response distribution.