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This study investigated the scalability of a cognitive multiple-choice test through the Mokken package in the R programming language for statistical computing. A 2019 mathematics West African Examinations Council (WAEC) instrument was used to gather data from randomly drawn K-12 participants (N = 2866; Male = 1232; Female = 1634; Mean age = 16.5 years) in Education District I, Lagos State, Nigeria. The results showed that the monotone homogeneity model (MHM) was consistent with the empirical dataset. However, it was observed that the test could not be scaled unidimensionally due to the low scalability of some items. In addition, the test discriminated well and had low accuracy for item-invariant ordering (IIO). Thus, items seriously violated the IIO property and scalability criteria when the HT coefficient was estimated. Consequently, the test requires modification in order to provide monotonic characteristics. This has implications for public examining bodies when endeavouring to assess the IIO assumption of their items in order to boost the validity of testing.