First, the college entrance examination mathematics multiple-choice proposition law is as follows:
1, functions and derivatives
2-3 small questions, 1 big questions, objective questions mainly focus on the basic properties of the function, the image and transformation of the function, the geometric significance of the zero and derivative of the function, definite integral and so on. It is also possible to make a comprehensive investigation with knowledge such as inequality; Solving problems mainly uses derivatives as tools to solve application problems such as functions, equations and inequalities.
2. Trigonometric function and plane vector
Generally speaking, small questions mainly examine the images and properties of trigonometric functions, and use the simplified evaluation of inductive formula and differential angle formula, double angle formula, sine and cosine theorem, and the basic properties and operations of plane vectors. In the big topic, we mainly take sine and cosine theorems as the knowledge framework, and rely on triangles (pay attention to the examination in practical problems) or the combination of vectors and triangles to examine the simplified evaluation, images and properties of trigonometric functions. In addition, vectors may also be combined with analytical knowledge.
Step 3: Order
2 small questions or 1 big questions, small questions mainly examine the concept, nature, general formula, N items before the series, and formulas, which belong to middle and low-level questions; The solution is mainly to examine the general formula and summation formula of arithmetic (ratio) sequence, dislocation subtraction summation, simple recursion.
4. Analytic geometry
2 as small as 1. Small questions are mainly about the properties of straight lines, circles and conic curves, which can be easily solved with the help of graphics. Generally speaking, a big problem is based on the positional relationship between a straight line and a conic curve, combined with the knowledge of functions, equations, series, inequalities, derivatives, plane vectors, etc., to investigate the problem of solving trajectory equations, explore the nature, parameter range, maximum value, fixed value and existence of curves.
5. Solid geometry
2 Small 1 large, small questions must be tested, generally focusing on the relationship between lines, lines and surfaces, surfaces and surfaces, and the calculation of spatial angle, distance, area and volume in spatial geometry. In addition, special attention should be paid to the investigation of the combination of balls. The goal of solving problems is parallelism, verticality, included angle and distance. The geometric shapes are quadrangular prism, quadrangular pyramid, triangular prism and triangular pyramid.
6. Probability and statistics
2 Small 1 large and small questions generally mainly examine frequency distribution histogram, stem leaf diagram, numerical characteristics of samples, independence test, geometric probability and classical probability, sampling (especially stratified sampling), permutation and combination, binomial theorem and several important distributions. The examination point of solving problems is relatively fixed, and the distribution list, expectation and variance of discrete random variables are generally examined. The focus is still on the application problems closely related to real life, reflecting.
7. Inequality
Small questions generally examine the basic properties and solutions of inequalities (generally involving other knowledge, such as sets, piecewise functions, etc.) ), the application of basic inequalities and linear programming; General problem solving is based on other knowledge (such as sequence, analytic geometry, function, etc. ), and it is generally difficult to comprehensively examine inequality as a tool.
8. Algorithms and reasoning
The program block diagram appears once a year, and it is generally difficult to combine functions, sequences and other knowledge. Reasoning questions occasionally appear.
Two, the college entrance examination mathematics multiple-choice questions six answering skills
Answer formula:
(1), make a mountain out of a molehill
(2) Don't ignore the options.
(3), can qualitative analysis, not quantitative calculation.
(4) The energy characteristic method does not need conventional calculation.
(5) If it can be solved indirectly, don't solve it directly.
(6) Narrowing the selection range can be ruled out.
(7) Choose the option directly after analyzing and calculating half.
(8), three similarities choose similarity.
1, special value method
Methods: Take special values to improve the speed of solving problems. The general situation in the problem must meet our special situation of taking values, so we choose appropriate special values according to the meaning of the problem to help us eliminate wrong answers and choose correct options.
2. Estimation method
Methods: When there is a big gap between the options and there is no suitable solution, the approximate range or approximate value of the answer can be estimated by appropriately enlarging or narrowing some data, and then the option closest to the estimated value can be selected.
[Note]: When comparing dimensions with root signs or looking for approximate values, square them to reduce errors.
3. Inverse method
Methods: Giving full play to the function of options, observing the characteristics of options and making special solutions to problems can greatly simplify the steps of solving problems and save time. Remember not to ignore the options when making multiple-choice questions.
4. Special case analysis method
Methodological thinking: when there is no limited situation in the question, we can start with the most special situation, which can often help us eliminate some options, and then analyze the [excessive] (bigger and smaller) from the special situation to the general situation to choose the correct answer.
5. Algorithm simplification
Methods: Qualitative analysis replaces quantitative calculation, and the calculation process is simplified according to the question structure, which helps us to speed up the problem solving to some extent.
Through the explanation of the following examples, we should not only master the method, but more importantly, understand and use this idea.
6. Special reasoning