The test paper of this senior one exam is moderately difficult, basically covering all the knowledge points that students have learned this semester, with various forms of examination, such as filling in the blanks, connecting lines and calculating. The topic is flexible and the difficulty is moderate, which reflects the problem that students are prone to make mistakes. It can be said that this test paper can largely reflect the children's learning situation and the teachers' teaching situation, and comprehensively examine the children's basic knowledge and application ability.

Data expansion:

Many mathematical objects, such as numbers, functions, geometry, etc., reflect the internal structure of continuous operation or the relationships defined therein. Mathematics studies the properties of these structures.

For example, number theory studies how integers are represented under arithmetic operations. In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.

Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra. Because abstract algebra has great universality, it can often be applied to some seemingly unrelated problems.

For example, some old problems in ruler drawing were finally solved by Galois theory, which involves domain theory and group theory. Another example of algebraic theory is linear algebra, which makes a general study of vector spaces with quantitative and directional elements. These phenomena show that geometry and algebra, which were originally considered irrelevant, actually have a strong correlation. Combinatorial mathematics studies the method of enumerating several objects satisfying a given structure.

space

The study of space originated from Euclidean geometry. Trigonometry combines space and numbers, including the famous Pythagorean theorem, trigonometric function and so on. Now the research on space has been extended to high-dimensional geometry, non-Euclidean geometry, topology and graph theory.

Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold. Algebraic geometry has the description of geometric objects such as polynomial equation solution set, which combines the concepts of number and space; There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change.