In an online learning environment, it is important to establish a suitable assessment approach that can be adapted on the fly to accommodate the varying learning paces of students. At the same time, it is essential that assessment criteria remain compliant with the expected learning outcomes of the relevant education standard which predominantly utilizes a competency-based curriculum such as in Indonesia. The aim of the research in this paper is to improve the adaptiveness of questions in the existing Computerized Adaptive Testing (CAT) model by taking into consideration multiple aspects of user context. We propose a context-based question selection model based on competency evaluation by merging four methods of Classical Test Theory, Rasch Model, Linear and Quadratic models, and the combination of branching and item adaptive methods to select questions of suitable difficulty for each individual student. To evaluate the proposed model, we conducted experiments based on a real dataset of 689 elementary school students in Indonesia. The experiment results prove the effectiveness of the proposed model in terms of accuracy in predicting the appropriateness of the questions in relation to the students' ability. This adaptive assessment method which accurately builds upon the students' competency level will support students' success in the online learning environment.