Resistance and magnetization measurements have been carried out as a function of temperature, applied field, and transport current (resistance only) on a series of dilute In-Bi alloy foils (0.45<κ1<0.75, thickness d>=0.002 cm). The data enable the determination of Hc2, HcB, κ1(T), and κ2(T) over most of the superconducting temperature range (t>~0.3). It is found that In-1.25 at.% Bi [κ1(Tc)~0.64], and In-1.15 at.% Bi [κ(Tc)~0.62]-both of which are bulk type-II superconductors at temperatures well below Tc-exhibit mixed-state-like behavior as foils in a transverse applied field at all temperatures below Tc. Specifically, at thicknesses less than approximately 0.005 cm, the transverse-field magnetization exhibits an apparent second-order transition at Hc2<HcB, the parallel transition field. The Hc2(T) and κ1(T) values thus determined are in good agreement with the dirty-limit-theory temperature dependence. Moreover, the κ2(T) values which are determined from the slope of the transverse-field magnetization by the formula -4πM=(Hc2-H0)[(2κ22- 1)β+1] are in good agreement with the κ1 values near Tc and exhibit similar temperature dependence. It is found that the critical fields of the magnetization curves can be identified with characteristic features of the resistive transition curves.