The paper describes the results of a study whose main aim was to find the interrelationship between pupils' school grades in Czech language (native), mathematics, and physics and pupils' cognitive predispositions to problem-solving in science and mathematics diagnosed by the Lawson Classroom Test of Scientific Reasoning and the Culture of Problem Solving test. A total of 180 pupils from the Czech Republic aged 14-15 took part in this study. The results show that pupils with better grades in the monitored subjects achieve better results in both tests. It also turns out that there are generally statistically insignificant differences between the results of pupils assessed by grades 1 or 2 and between those assessed by grades 3 or 4. Pupils' performance in the two tests might help to strengthen the objectivization of grading at school. They might also help identify the indicators important for developing problem-solving skills. The research specifically points to the need to develop algebraic thinking, the conception of infinity, spatial imagination, geometric imagination in the plane, proportional reasoning, and the ability to control variables.