Item bank is one of the main components of adaptive tests. In this research, a test was made in order to design and calibrate items for Homogeneous Second Order Differential Equations. The items were designed according to the goal-content's table of the subject and the Bloom's taxonomy learning domain. Validity and reliability of these items was confirmed by academic staff who have taught the course for years. For calibrating items, 13 levels of ability were considered. By using Monte Carlo simulation, 32500 simulated examinees (2500 simulated examinees for each ability level) participated in the exam. Calibrating items were done by difficulty and discrimination parameters using item response theory and priory method. The results showed that chi-square indices of parameters is less than the standard chi-square indices, and therefore the estimated parameters are acceptable. These items can be used in adaptive tests in order to estimate examinee's ability level in this subject.