The knowledge and methods you have learned are likely to be forgotten. If you want to master them firmly and form your own ability, you must review them scientifically and effectively in order to achieve the purpose of reviewing the old and learning new things! Next, I sorted out the basic knowledge of high school mathematics for you. I hope you like it!

Basic knowledge of high school mathematics 1

Definition of ball:

The first definition: The rotation body formed by taking the straight line where the diameter of the semicircle is located as the rotation axis and the semicircle surface rotates once is called a sphere, which is called a ball for short.

The center of the semicircle is called the center of the ball, the radius of the semicircle is called the radius of the ball, and the diameter of the semicircle is called the diameter of the ball.

The second definition: a sphere is a set of all points in space, and the distance between these points and a fixed point is equal to a fixed length.

Ball:

Taking the straight line with the diameter of the semicircle as the rotation axis, the rotating body formed by one rotation of the semicircle surface is called a solid ball, which is called a ball for short.

Basic knowledge of high school mathematics II

Subject 1: assembly

Basic operation of test center 1:set

Test site 2: the relationship between sets

Topic 2: Function

Test Center 3: Functions and Their Representation

Test Site 4: Basic Properties of Functions

Test site 5: linear function and quadratic function.

Test Site 6: Exponent and Exponential Function

Test site 7: Logarithms and Logarithmic Functions

Test site 8: power function

Test center 9: function image

Test location 10: functional range and maximum value

Test center 1 1: Application of function

Topic 3: A Preliminary Study of Solid Geometry

Test center 12: structure, three views and straight views of space geometry

Test center 13: surface area and volume of space geometry.

Test center 14: the positional relationship between points, lines and surfaces.

Test center 15: the nature and judgment of parallel lines and planes

Test Center 16: Measurement and characteristics of vertical lines and planes.

Test center 17: space corner

Test center 18: space vector

Basic knowledge of high school mathematics III

1. New Content Proposition Trend of Senior High School Mathematics

New contents: basic knowledge and application of vector, basic knowledge and application of probability and statistics, derivative and application of elementary function.

Proposition trend: the test paper covers new content as much as possible; The difficulty control is synchronized with the deepening of middle school education reform, which requires gradual improvement; Attach importance to the unique role of new content in solving problems.

Three-level (1) derivative test questions

The first level: the concept, formula and law of derivative;

The second level: the simple application of derivative, including finding the extreme value and monotonous interval of function, proving the increase and decrease of function, etc.

The third level: comprehensive examination, including solving application problems, combining derivative content with inequality and monotonicity of functions in traditional content.

(2) Inspection requirements for plane vectors

A. Examine the properties, algorithms and basic operation skills of plane vectors. Candidates are required to master the operations of sum, difference, number multiplication and inner product of plane vectors, understand their intuitive geometric meaning and perform the operations correctly.

B. Investigate the coordinate representation of vectors and the linear operation of vectors.

C. Combining with other mathematical contents, such as basic knowledge of functions, curves, series, etc., the ability of comprehensive application of mathematical knowledge such as logical reasoning and operational ability to solve problems is investigated. The examination of basic knowledge and skills is generally from shallow to deep, and it is not difficult to start, but it requires strict logical reasoning and accurate calculation to successfully complete the answer.

(3) Probability statistics.

Basic questions: probability questions of equal possible events, probability questions of one occurrence in mutually exclusive events, probability questions of mutually independent events, and probability questions of independent repeated tests. The above four problems are combined with numerical characteristic calculation to form a comprehensive problem.

Review suggestions: firmly grasp the basic concepts; Correct analysis of random test; Familiar with common probability models; Correctly calculate the numerical characteristics of random variables.

2. The knowledge backbone of high school mathematics

Basic theoretical application of function, solution, proof and comprehensive application of inequality, basic knowledge and application of sequence; Trigonometric function and trigonometric transformation; The positional relationship between straight line and plane, plane and plane; The solution of curve equation, the nature and position relationship of straight line and conic curve.

3. Propositional changes and basic trends of traditional backbone knowledge

(1) function, sequence, inequality

A. Changes in functional inspection

The power function is removed from the function, and the contents such as "solution of unreasonable inequality, solution of exponential inequality and solution of logarithmic inequality" are removed from the exponential equation, logarithmic equation and inequality. The propositional heat of this kind of problem will get cold, but it may still appear in the form of equality or inequality.

B. the solution to the synthesis problem of inequality and recursive sequence

Simplify to solve the problem of arithmetic or geometric series; Solve it by teaching induction; Derive the general formula to solve; Inferring the properties of sequence directly by recursive formula.

C. The basic trend of function, sequence and inequality proposition: create new situations, use new forms and investigate basic concepts and their properties; Functions tend to be abstract, that is, the ability of abstraction is examined through functions; Intersection and fusion of functions, sequences and inequalities; Using derivatives to study the properties of functions and prove inequalities; The examination methods of induction and mathematical induction are changed from subjects to parts.

(2) Trigonometric function

Combining with practice, using a little trigonometric transformation (especially the application of cosine double angle formula and special case formula), the proposition of trigonometric function properties is examined; Combined with derivative, the properties and images of trigonometric function are studied. Taking triangle as the carrier, the ability of triangle transformation and the flexible application of sine theorem and cosine theorem are investigated. Investigate the ability to use knowledge flexibly by combining vectors.

(3) solid geometry

Focusing on examination, demonstration and calculation, we turn to examine not only the concept of space, but also the demonstration and calculation of geometry. From the formula and theorem as the carrier, to pay attention to observation, experiment, operation and design; Increase the application of vector tools; Ask questions in a different way.

(4) Analytic geometry

A. The amount of calculation is reduced, and the requirements for reasoning and argumentation are improved.

B. The scope of investigation has expanded from seeking the trajectory and discussing the properties of the curve itself to investigating the relationship between the curve and the point, the curve and the straight line, and the properties of the straight line related to the curve; Using the thought method of curve and equation, other curves except straight line and conic curve are studied. Determine the type of curve according to the definition.

C. Pay attention to proving geometric problems with algebra, and combine algebra, analytic geometry and plane geometry.

D. organically combine vectors, derivatives and analytic geometry.

4. Pay attention to the innovation of test questions

(1) The knowledge content is new: it may be manifested as a high viewpoint problem; Avoid hot issues and return to nature.

A. High-minded questions refer to questions related to advanced mathematics, which are based on advanced mathematics knowledge or reflect the mathematical thinking methods and reasoning methods commonly used in advanced mathematics. The starting point of high-viewpoint questions is high, but the setting point is low, that is, the so-called "high questions are low to do", that is, the design of the questions comes from advanced mathematics, but the solution is the elementary mathematics knowledge learned in middle school, so it is not necessary to introduce advanced mathematics into high school teaching. Candidates don't have to panic, as long as they face it calmly, it will be easier to break through.

B. Avoid hot issues and return to basics: Looking back at the test questions in recent years, the most influential ones are often unexpected and reasonable.

(2) Innovation in the form of examination questions: it may be manifested in the external forms of questions such as the creation of topic scenarios, the presentation of conditions, and the change of questioning angles.

Please also pay attention to the relationship between the content of the research topic and the content of the college entrance examination (college entrance examination news, college entrance examination), and the content and form of the applied questions.

(3) Innovation of problem-solving methods: It refers to solving old problems with derivative and vector methods in new textbooks.

5. Prospect of Mathematics Proposition in College Entrance Examination

The main contents focus on examination: comprehensive examination of basic knowledge, key examination of key knowledge, and desalination of special skills.

Adding new knowledge to the exam: the intensity of the exam and the proportion of scores will exceed the proportion of class hours, and it is a trend to combine new knowledge with traditional knowledge.

Thinking method is more in-depth: to investigate the basic method of connecting mathematical knowledge and the scientific method of solving mathematical problems.

Highlight the examination of thinking ability: mainly examine students' spatial imagination ability, learning ability, inquiry ability, application ability and innovation ability.

Write an article about knowledge reorganization: pay attention to the reorganization of information and the intersection of knowledge networks.

Computational ability has been improved: triviality is weakened, ability is emphasized, and students are encouraged to draw conclusions with concise methods.

Smooth transition of spatial imagination: the form will not change greatly, but it is a trend to solve solid geometry with vectors as tools.

The practical application ability is further strengthened: the application problems arising from practical problems are real application problems, and the test questions are only the main application problems in building models.

Examining innovative learning ability: Students can choose effective methods and means, have their own ideas and solve problems creatively.

Personality quality can be highlighted.