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Proper assessment leads to adequate judgement of examinees performance in external examinations. The method employed by any public examining bodies such as National Examinations Council (NECO) might be adduced to one of the reasons examinees' performances in Mathematics were fluctuating. Extant literature showed that NECO only established item and person parameters of their dichotomous and polytomous items using Classical Test Theory (CTT) which is sample-dependent, without exploring efficient frameworks by Item Response Theory (IRT) considering its efficacy for accurate calibration and ranking. This study, therefore, developed dichotomous (60) items and polytomous (5) items through IRT based calibration. Concurrent true ability indices and relative efficacy of IRT and CTT in ranking of scores were also estimated.The study was anchored to Item Response Theory (modern psychometrics theory), while instrumentation approach and counterbalance design were adopted. The study was conducted in two phases: Validation and calibration of multiple choice and constructed response items of Mathematics Achievement Test (MAT).