1. An image forming apparatus comprising: an image forming unit that forms an image on a recording medium; a post-processing unit that performs a post-processing on the recording medium on which the image is formed by the image forming unit; a post-processing controller that controls the post-processing unit to perform the post-processing, or to inhibit the post-processing for calibration, at an end of a predetermined print job according to whether an image requested by a user or a test image is formed on the recording medium; and a plurality of discharge trays that carry the recording medium on which the image is formed by the image forming unit, wherein the test image is printed on the recording medium for calibration, the post-processing is a discharge processing of the recording medium, the post-processing controller determines the discharge tray to discharge the recording medium on which the test image is formed, based on the discharge tray to discharge the recording medium on which the requested image is formed, and issues an instruction to discharge the recording medium on which the requested image is formed and the recording medium on which the test image is formed to the trays different from each other, and the post-processing unit discharges the recording medium on which the requested image is formed and the recording medium on which the test image is formed to the discharge trays different from each other according to the instruction of the post-processing controller.