In recent days, the research on student’s intelligence level modelling is a challenging Artificial Intelligence (AI) task, which gains more attraction because it provides actionable insights to the tutor by analyzing the intelligence level of the learners. Each learner’s knowledge, comprehension, and intellectual capacities are unique. It is critical to identify these capacities and provide learners, particularly slow learners, with the necessary knowledge. Cognitive Performance Test (CPT) is an essential component for assessing the knowledge level of students. The reasoning level or coefficient deals with the analysis of the thinking capability in a logical way. It also reflects the child’s learning potential. The main aim of the proposed system is to design a Cognitive Knowledge Representation Model (CKRM), which fuses Cognitive Performance Metrics (CPM) calculation and Reasoning Coefficient Calculation (RCC) algorithms to assess the student’s intelligence level. The result of the proposed system is stratification of students to three different ranges of reasoning coefficient. The CKRM consists of the following phases: data collection, statistical Exploratory Data Analysis (EDA), model building and analysis, which involve the assessment of the knowledge level using CPT and calculation of reasoning coefficient using First Order Logic (FOL), and finally model evaluation using cognitive evaluation metrics. CPM and RCC algorithms have been proposed in this paper to calculate the student’s reasoning coefficient by using the forward chaining FOL inference engine. The dataset is a real time data which consists of the academic and cognitive performance details of school students from classes 1 to 6 for the year 2019 to 2020. The academic data are collected from the Educational Management Information System (EMIS) maintained by the school. The cognitive performance data are collected by conducting the tests for the students using the memory training application called Lumosity. The proposed system’s performance is evaluated using ten Machine Learning (ML) algorithms in which the Quadratic Discriminant Analysis achieved an accuracy of 0.97 for classes 1, 2, and 3. For classes 4, 5, and 6, nearly twelve ML algorithms are evaluated in which Random Forest (RF) Classifier achieved an accuracy of 0.98. Six math expert committee teachers concluded that the reasoning coefficient value was acceptable with an average accuracy of 0.92 for classes 1, 2, 3 and 0.9 for classes 4, 5, 6. In comparison to the pre-existing models employed in the prior research, it was determined that the created CKRM (academic and cognitive) was superior. The cognitive metrics such as taskability, Response Time (RT), knowledge capacity and utilization has also been evaluated. The average values of taskability, RT, knowledge capacity and knowledge utilisation are 0.85, 0.81, 0.55, and 0.44. The ultimate goal is to make customised teaching easier; hence, this article involves determining a student’s cognitive level by estimating their reasoning coefficient. The suggested approach analyses and categorises students’ cognitive abilities, such as memory, reasoning, problem solving, thinking, and logical reasoning, using three different reasoning coefficients. This approach assists teachers in determining the degree of intelligence of their students.