Every parent knows the importance of olympiad in junior high school entrance examination! It can be said that Olympiad directly and indirectly affects students' test scores! Especially in the senior high school entrance examination of key middle schools in Ningbo, the written mathematics test is directly the Olympiad. If you can't do the Olympiad, then you can say that you left the key middle school! In the last issue, we summarized 33 knowledge points of the Olympic Mathematics, among which we made another summary, and concluded that the Olympic Mathematics test is nothing more than four points: number, line, shape and calculation.

What is "number, line, shape and calculation", that is, number theory, line, diagram and calculation. The difficulty of number theory lies in abstraction, which is the key to distinguish top students from ordinary students; The complexity of travel problem lies in its application. Children do this kind of problem, not only need to think, but also need to express. Graphic problem (geometric problem) is complex and difficult, and the key requirement is the calculation of area, which is the beginning of middle school education; Calculation is the foundation and the necessary guarantee for children to get high marks.

Because these four questions are easy for students to get started, but they are not skilled and often make mistakes, so they have become the focus of examinations in key middle schools in recent years. According to statistics, in recent years, about 80% of these big questions are' test questions', and the sixth grade of the middle school attached to Beijing Normal University and Renhua School are also very particular about these questions. The study of number theory and travel itinerary is the most important, often accounting for 50% of a test paper. How to review these four aspects?

For graphics, what we want to say is to cultivate children's thinking in images, with the focus on the calculation of area. The skills and methods of calculation have also been summarized and strengthened. This paper mainly introduces the review methods of number theory and travel questions.

Number Theory In the study of number theory, students are often prone to make the following mistakes:

1, dyslexia. The description of number theory topics is often only a few sentences or even a line, but these short sentences express many meanings. If students can't understand the meaning of the topic, the topic will usually be wrong.

2. Knowledge is rigid. Because the problem of number theory is very abstract, most students often "digest" what they have learned by rote, which leads to familiar knowledge points, but they are at a loss when they encounter practical problems. For example, as soon as we mentioned parity, we knew what was going on, and immediately began to recite: "Odd number+odd number = even number …", but when we did the problem, it was unexpected.

See only the trees, but not the forest. Lack of flexible application of number theory theorem. The mentioned theorems can be memorized word by word, but there is a lack of overall understanding and grasp of various concepts and properties, let alone understanding the internal relations between various knowledge points.

Knowledge system:

Divisibility problem:

Divisible characteristics of (1) number (content of routine examination in junior high school)

(2) the application of the bit value principle (using letters and numbers to represent multiple numbers)

Composite number of prime numbers:

(1) Concepts and Judgments of Prime Numbers and Composite Numbers (II) Decomposition of Prime Factors (Emphasis)

Approximate multiple:

(1) greatest common divisor least common multiple (2) Rules for judging the number of factories (the content of junior high school students' common test)

Remaining problems:

Understanding and application of (1) formula with remainder: (2) The nature and application of congruence; (3) parity of China's remainder theorem: (1) parity and four operations; (2) The application of parity in practical problem solving: (1) the judgment and properties of the complete square number; (2) the application of the complete square number and the decomposition and splitting of the score (key and difficult points).

;