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Computerized Adaptive Testing (CAT) is a form of assessment test which requires fewer test questions to arrive at precise measurements of examinees' ability. One of the core technical components in building a CAT is mathematical algorithms which estimate examinees’ ability and select the most appropriate test questions for the estimation. Mathematical algorithms serve as a locomotive in operating the system of adaptive multiple-choice questions on computers. This research aims to develop essential mathematical algorithms for a computerized system of adaptive multiple-choice tests. A question bank of 500 multiple-choice questions standardized by IRT theory with the difficulty level following the normal distribution satisfying Kolmogorov-Smirnov test, to measure the mathematical ability of 10th graders is also built. The experimenting of the question bank shows that it satisfies the requirements of a psychometric model and the constructed mathematical algorithms meet the criteria for applying in computerized adaptive testing.
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