| Excellent | Good | Acceptable | Not acceptable |
Achievement 1 | Understand the nature of mapping. | Understand the nature of sets. | Understand the basic concepts of sets and maps. | Insufficient understanding of sets and maps. |
Achievement 2 | Understand the concept of order relations. | Understand the concept of equivalence relations. | Understand the basic concepts of equivalence relations and order relations. | Insufficient understanding of equivalence relations and order relations. |
Achievement 3 | Mastered indirect proof methods such as kinematic pair method, reductio ad absurdum, and counterexample method. | Logical symbols can be used. | Understand the basic nature of logic. | Insufficient understanding of logic and proof methods. |
Achievement 4 | Propositions can be proved using various variations of mathematical induction. | Propositions can be proved using basic mathematical induction. | Understand mathematical induction. | Insufficient understanding of basic mathematical induction. |
Achievement 5 | Understand and use the idea of the multinomial theorem. | Understand and use the idea of the binomial theorem. | Understand the idea of the number of combinations. | Insufficient understanding of the number of combinations. |
Achievement 6 | Understand the nature of prime numbers. | Understand the least common multiple, the greatest common divisor and their properties. | Understand the principle of division. | Insufficient understanding of the nature of elementary integers. |