Problems that should be paid attention to in reviewing plane vector learning [examination requirements]
(1) Understand the concept of vector, master the geometric representation of vector, and understand the concept of * * * line vector.
(2) Master the addition and subtraction of vectors.
(3) Grasp the product of real number and vector, and understand the necessary and sufficient conditions of two vector lines.
(4) Understand the basic theorem of plane vector, understand the coordinate concept of plane vector, and master the coordinate operation of plane vector.
(5) Mastering the quantity product of plane vector and its geometric meaning, understanding the quantity product of plane vector can deal with the problems about length, angle and verticality, and master the conditions of vector verticality.
(6) Master the distance formula between two points on the plane, the coordinate formula of the bisector and midpoint of the line segment, and skillfully use and master the translation formula.
(7) Master sine theorem and cosine theorem, and use them to solve oblique triangle, and use calculator to solve the calculation problem of triangle solution.
Problems needing attention in plane vector learning review and the prospect of college entrance examination
Vector is a new content in the new textbook, which embodies modern mathematical thought.
Because of its "dual function" in geometric form and algebraic form, vector has become the intersection of middle school mathematics knowledge and the link to examine many contents. The college entrance examination questions mainly examine the relevant basic knowledge and highlight the instrumental role of vectors. Vector plays an important role in solving geometric and physical problems. In recent years, the scores of college entrance examination questions based on vectors account for about 10%.
The requirements for the examination of plane vectors are as follows: first, it mainly examines the nature, operation rules and basic operation skills of plane vectors, and examines students' mastery of the operation rules of sum, difference, multiplication and inner product of plane vectors, as well as their intuitive geometric significance and correct calculation; The second is to investigate the coordinate representation and linear operation of vectors; Third, combining with other mathematical knowledge, such as curves, series, functions, triangles, etc., are generally low-level questions.
In the science examination papers of the college entrance examination in recent four years, there are two questions every year, including four small questions, which examine the nature and operation law of vectors, multiplication of numbers, product of quantities, vectors of * * * lines and trajectories. The two major problems are based on vector form, and the conic curve problem is discussed.
It can be seen that vector has risen from an auxiliary tool for solving problems to one of the indispensable tools for analyzing and solving problems. In reviewing, we should pay attention to the position of this chapter in the college entrance examination. It mainly solves the problems of "parallelism, verticality, bisector and included angle" in plane geometry, analytic geometry, triangle and complex number. To solve these problems, we can properly use the knowledge of vectors. Using vectors to solve kinematics and mechanics problems in physics can not be ignored.
Problems needing attention in plane vector learning review