The implementation of "three basics" and "three basics" refers to the basic knowledge, basic skills and mathematical ideas contained in common mathematical methods in junior high school mathematics. To implement the "three basics", we must first understand the concept and master the connotation, extension and expression of mathematical concepts. The connotation of the concept is the essence of the concept, and the extension of the concept is the object it expresses; Every mathematical concept has its own mathematical symbol. Candidates should pay special attention to the concepts of arithmetic square root, absolute value, negative integer power of negative number, similarity term, central symmetric figure and axisymmetric figure, similarity and congruence of figure, piecewise function, trigonometric function, inner and outer center of triangle, median, mode and variance, which are easy to involve and difficult to grasp.
Second, we must firmly grasp theorems, formulas and laws. Important theorems can be described not only in written language, but also directly in pictures or accurately in mathematical symbolic language. Correctly apply theorems, formulas and laws without confusion, and make good use of them; Some formulas can be used in both positive and negative directions, and formula deformation can be carried out flexibly. Attention should be paid to: simplification rules of irrational numbers and fractions, Pythagorean theorem and its inverse theorem, midline properties of triangles and trapeziums, midline properties of hypotenuse of right-angled triangles, inner and outer angles of triangles and polygons, vertical diameter theorem, judgment and property theorem of tangents, secant theorem, tangent length theorem, area formula of isosceles trapezium with inner and outer angles and diagonal lines perpendicular to each other, complete square formula and arc length formula. Operation is one of the core contents of junior high school mathematics, and the strength of operation skills reflects the proficiency in using algorithms. When reviewing, try to give accurate, scientific, reasonable and quick answers to the calculation or deformation of simple numbers and formulas. Overcome the phenomenon of irregular writing, showing jumping steps, thus losing points; Pay attention to the algebraic simplification of letter range in the process of deformation; Remember the trigonometric function value of special angle skillfully; The identity transformation is carried out in strict accordance with the algorithm to prevent errors caused by wrong analogy or independent writing.
Fourth, we should have the habit of drawing reference pictures and master the drawing methods. Some questions have no reference map, so candidates are required to have a dynamic map in their minds and be able to freeze it into various possible States. If necessary, draw a schematic diagram of each situation and discuss it in categories. Some word problems or application problems need to use line charts, tables or direct diagrams to analyze the quantitative relationship or positional relationship, so as to find a breakthrough in solving problems. In the process of geometric calculation or proof, if auxiliary lines need to be added, they should be drawn in the drawing and expressed in words.
Fifth, we should be aware of estimation and master certain estimation methods. Estimation can predict the result or the range of the result, which is helpful to find out the idea of solving the problem or judge whether the solution is wrong. Remember some constants, such as the approximation of π, the sum of squares and cubes of some two digits; Master the changing trend of acute trigonometric function and the image characteristics of linear function, quadratic function and inverse proportional function.
Sixth, we should have the habit of inspection and master some inspection methods. Timely inspection can find and correct some mistakes in time and improve the scoring rate. In particular, the loss of points in many basic questions can be avoided. Commonly used inspection methods are: inverse operation inspection method; Back-substitution test; Conduct special value tests and experience tests.
Seventh, we should master the commonly used mathematical methods and understand the mathematical ideas contained in them. Scientific notation and graphic method are related to approximate method, which contains the idea of estimation; Collocation method is related to the evaluation of algebraic expression, the solution of quadratic equation in one variable and the properties of quadratic function, including the idea of limit; The undetermined coefficient method is often used to solve the resolution function, which contains the idea of modeling; In algebra, the whole substitution method is often used, which contains the idea of whole and part; Substitution method is often used to solve equations or algebraic expressions for simplification and evaluation, which contains the idea of transformation; Establishing equations to find unknown quantities is often used in application problems and geometry problems, which contains the idea of equations; When exploring problems in more than two situations, classified discussion is often used, which is the application of classified discussion thought; Geometric problems and algebraic problems are transformed into each other, which contains the idea of combining numbers with shapes; Geometric transformations such as similarity, translation, rotation, and axial symmetry in geometry can reveal the spatial positional relationship and quantitative relationship of points, lines, surfaces, or bodies, including corresponding ideas ... Eight, we should understand the new trends of the proposition in the senior high school entrance examination and focus on it while reviewing it comprehensively. With the deepening of curriculum reform and the maturity of practice, the form and content of test questions will be more reasonable. Geometric transformations such as reading comprehension, experimental operation, translation and folding, classification and discussion of moving points, scheme decision-making, and the connection with science and engineering students, other related disciplines and high school disciplines can all be seen in the simulated test questions of various districts or schools.
Pay attention to timeliness. Later math review should pay more attention to timeliness. There are three ways.
The first is limited training. The test questions in the senior high school entrance examination mathematics paper are arranged in a gradient cycle from easy to difficult, and the time of basic questions should be properly controlled. For example, multiple-choice questions take about eight minutes, fill-in-the-blank questions take six minutes, calculation questions take three minutes, simplification and evaluation questions take five minutes, geometric calculation and proof questions take eight minutes, application questions take eight minutes, and reading comprehension questions take ten minutes. Break down the comprehensive questions into small questions and control the time accordingly. Usually pay attention to the time spent on each question in the simulation exercise. It is not advisable to stay too long when you encounter problems in the exam. You put it aside and finish the following questions before you go back to solve the problem. Leave some time to check.
The second is simulation training. Do several sets of simulated test papers before the exam. In the simulation exercise, you should be independent and concentrate on answering questions, and control it to be completed within 90 minutes.
The third is to practice "old questions". Sort out the recent special training papers, monthly examination papers and simulation papers, and browse the "old questions". Revise past mistakes and redo unfinished problems. Summarize the best solution to similar problems. Reflection and improvement on old problems.