The response rate of ex-core detectors depends on the power level, power distribution, and reactor configuration. For the analysis of the detector response rate for various core power distributions, it is important to generate spatial weighting functions that are insensitive to small changes in the core power distribution and determined by the reactor configuration. Two-dimensional discrete ordinates adjoint transport calculations are used to calculate the core axial weighting functions. The effects of the reactor operating conditions on the core axial weighting functions are analyzed, and it is found that the soluble boron concentration in the reactor coolant has little effect while the core power level affects the core axial weighting functions significantly. A comparison between the results of the adjoint and forward transport calculations shows an excellent agreement. However, the adjoint transport method provides more detailed data and requires less computing time than the forward transport method.