1, multiple choice questions
In the mathematics test questions of the college entrance examination, multiple-choice questions pay attention to the small synthesis of multiple knowledge points, infiltrate various mathematical thinking methods, and reflect the orientation of paying attention to examining "three basics". Whether you can get high marks on multiple-choice questions has a great influence on the mathematics scores of the college entrance examination. Multiple choice questions mainly examine the understanding of basic knowledge, the proficiency of basic skills, the accuracy of basic calculation, the application of basic methods, the rigor of considering problems and the speed of solving problems. The basic strategy of answering multiple-choice questions is to make full use of the information provided by topic setting and branch selection to make judgments. Generally speaking, if you can make a qualitative judgment, you won't use complicated quantitative calculation; If we can use special numerical values to judge, we don't need to use conventional solutions; If you can use indirect solutions, you don't have to use direct solutions; We should eliminate obvious negative choices as soon as possible and narrow the scope of choices; For those who have many ways to solve problems, they should choose the simplest solution. When solving problems, we should carefully examine the questions, analyze them in depth, deduce them correctly, and beware of omissions; Check carefully after the primary election to ensure accuracy. From the examination point of view, it is enough to choose the right answer to multiple-choice questions. It doesn't matter what "strategy" and "means" are used, and people can "do whatever it takes". However, when you usually do the problem, you should try to find out the correct reason and the wrong reason for each choice. In addition, when solving a multiple-choice question, it is often necessary to use several methods for analysis and reasoning at the same time. Only in this way can we make full use of the information provided by the questions themselves in the college entrance examination, turn routine into special, avoid making a mountain out of a molehill, and truly achieve accuracy and speed.
In short, to solve multiple-choice questions, we should not only see that the problem-solving ideas of various conventional questions can guide the answers of multiple-choice questions in principle, but also fully tap the "personality" of the questions, seek simple solutions, make full use of the suggestive role of choosing branches, and make correct choices quickly. This can not only get the correct answer quickly and accurately, but also improve the speed of problem solving and save time for subsequent problem solving.
Step 2 fill in the blanks
Fill-in-the-blank questions and multiple-choice questions belong to objective questions, and they have many common characteristics: short and pithy forms, focused examination objectives, short and clear answers, no need to fill in the problem-solving process, and objective, fair and accurate grading. But there is a qualitative difference between fill-in-the-blank questions and multiple-choice questions. First of all, there is no substitute for filling in the blanks. Therefore, the answer has the advantage of not being disturbed by induced errors, and it also lacks the help of hints. Candidates' ability to think and solve problems independently will be higher. For a long time, the correct answer rate of fill-in-the-blank questions has been lower than that of multiple-choice questions, which may be an important reason Secondly, the structure of fill-in-the-blank questions is often in a correct proposition or judgment, in which some contents (both conditions and conclusions) are removed, leaving room for candidates to fill in independently and the examination method is more flexible. In reading comprehension of topics, it sometimes seems more difficult than multiple-choice questions. Of course, this is not always the case, it will depend on the design intention of the proponent.
Fill-in-the-blank problem in mathematics is an objective problem, and only the result needs to be written, not the problem-solving process. There should be reasonable analysis and judgment when solving problems, each step of reasoning operation should be correct, and the answer expression should be accurate and complete. Reasonable reasoning, optimized thinking and less thinking will be the basic requirements for solving fill-in-the-blank questions quickly and accurately.
Math fill-in-the-blank questions are mostly computational (especially inferential calculation) and conceptual (qualitative) judgment questions, which can only be answered by actual calculation or logical deduction and judgment according to rules. The basic strategy to solve the fill-in-the-blank problem is to work hard accurately, skillfully and quickly.
Step 3 answer questions
Although the answers are flexible and changeable, the mathematical knowledge, methods and basic mathematical ideas remain unchanged, and the setting of the topic form is relatively stable, which has the outstanding characteristics of stability. Continue to strengthen the double basics, examine the ability, highlight the backbone, and conduct a comprehensive examination.
The methods to solve the problem are flexible and diverse, with wide entrance, easy deviation and difficult full score. Almost every question has a gradient and a grade is set, which can better distinguish the ability level of candidates. Operation and reasoning permeate each other, reasoning proof and calculation are closely combined, and the strength of operation ability has a great influence on the success or failure of solving problems. When examining logical reasoning ability, it is often combined with operational ability, and the conclusion of the problem is often deduced and proved through specific operations; In the calculation problem, logical reasoning is also more mixed in it, reasoning and calculation, paying attention to the examination of inquiry ability and innovation ability. Exploratory test questions are good materials to test this ability, so they occupy an important position in the test paper.
1. Multiple choice strategy-straight line, line, number, specialty and estimation
Mathematics multiple-choice questions in college entrance examination consist of three parts: required language; Interrogative stem; Options. Candidates' solutions to multiple-choice questions can be summarized as "straight, ranked, counted, specialized and evaluated".
Direct-direct method. In other words, we can draw the correct conclusion directly through calculation or reasoning. Most multiple-choice questions in the college entrance examination are solved in this way. Therefore, we should attach great importance to the direct method.
Exclusion-exclusion method. That is, deny the wrong options one by one to achieve the goal of "choosing one from three".
Combination of numbers and shapes. That is, intuitive judgment is made by combining the relationship between numbers and quantities. There are more than three multiple-choice questions in the annual college entrance examination questions that can be answered in this way, and we should focus on mastering them.
Special method. On the premise of not affecting the conclusion, the conditions for setting the topic are specialized, so as to draw the correct conclusion.
Estimation-estimation method. According to the information provided by the stem and options, the approximate range of the required quantity can be estimated, and the other three options can be excluded, so as to achieve the goal.
The above five important methods are not used in isolation. When solving problems, they may be the comprehensive application of several methods. Most multiple-choice questions are low-scoring questions in the college entrance examination, so don't "make a mountain out of a molehill" when solving multiple-choice questions. Otherwise, taking up too much time will cause "potential loss of points".
2. Fill in the blanks strategies-straight lines, numbers and special.
Fill in the blanks is an objective question. Compared with multiple-choice questions, it has no options as a reference. Compared with solving problems, it is not necessary to write reasoning and operation process, but only to give accurate results. Most of the fill-in-the-blank questions are intermediate, but the scores are either full marks or zero. The common methods of solving fill-in-the-blank problems can be summarized as "straight, numerical and special"
Direct-direct method. That is, starting from the conditions of the topic, using knowledge such as definition, nature, theorem and formula. Through deformation, reasoning, calculation, etc. We can draw the desired conclusion directly. Direct method is the most commonly used method to solve fill-in-the-blank problems.
Combination of numbers and shapes. According to the geometric meaning of the condition, draw an auxiliary diagram of the problem, and then draw a correct conclusion through the intuitive analysis of the diagram. This is also an important way to answer the fill-in-the-blank questions in the college entrance examination.
Special-special value method. When the information provided in the question conditions implies that the answer is a fixed value, some special values or positions can be taken to determine this fixed value, thus improving the efficiency of solving problems.
When answering fill-in-the-blank questions, we should pay attention to rationality, accuracy and speed in choosing methods. In view of the fact that fill-in-the-blank questions only pay attention to the results rather than the process, in order to ensure the correctness of the answers, we must carefully examine the questions, make clear the requirements, clarify the concepts, calculate clearly and express correctly.
3. Problem solving strategies
Examine the meaning of the problem and seek the best way of thinking.
Among the three types of mathematics test questions in the college entrance examination, the number of answers is not as much as that of multiple-choice questions, but it accounts for a large proportion of the scores and occupies a very important position in the test paper.
Check the meaning of the question. This is the most critical step to solve the problem. We must examine the key words, figures and symbols thoroughly, make clear the conditions (including implied conditions) given in the question and their various equivalent deformations, correctly understand the relationship between conditions and objectives, and reasonably design the problem-solving program. Therefore, the examination of questions should be slow and the writing process can be accelerated appropriately.
Seek the best way to solve the problem. While taking the first step, it is another key step to explore different ideas according to the characteristics of solving problems. Because the solution design of college entrance examination questions is flexible, we should pay attention to the problem from many directions and angles when doing the questions, and we can't mechanically apply the model. When seeking ideas to solve problems, we must follow the following four basic principles: familiarity principle; Principle of concretization; Principle of simplification; Principle of harmony. It should be noted that the application of the above four principles is based on analysis and synthesis, and the use of analysis and synthesis to solve comprehensive problems means continuous transformation and regression, so that problems can be "turned into small things".
Common thinking strategies for solving problems. Specifically, it is: language conversion strategy-the basis of understanding the meaning of the problem; The strategy of advancing and retreating simultaneously-learn to find the starting point of thinking; The strategy of combining numbers and shapes-learn to put forward a guess or find the direction of solving problems from the perspective of shape, and then scientifically prove it from the quantitative relationship; Classification discussion strategy-the method of breaking the whole into parts; Dialectical thinking strategy-look at the problem from the particularity or negative side; Analogy and induction strategies-a bridge from the special to the general.
The periodicity of 1. function;
If f(x)=-f(x+k), then T = 2k.
If f(x)=m/(x+k)(m is not 0), then T = 2k If f(x)=f(x+k)+f(x-k), then T=6k.
note:
A. periodic function, the period must be infinite
A periodic function may have no minimum period, such as a constant function.
C. periodic function plus periodic function is not necessarily a periodic function.
On the symmetry problem
If on R (the same below): f(a+x)=f(b-x) is a constant and the symmetry axis is x = (a+b)/2;
The images of functions y=f(a+x) and y=f(b-x) are symmetric about x=(b-a)/2;
If f(a+x)+f(a-x)=2b, the image of f(x) is symmetrical about the center of (a, b).
2. Functional equivalence.
For odd function belonging to R, there is f (0) = 0;
For parametric functions, odd function has no even power term, and even functions have no odd power term.
3. Monotonicity of the function:
If the function is monotonous in the interval d, the function value increases (decreases) with the increase (decrease) of the independent variable.
4. Function symmetry:
If f(x) satisfies f(a+x)+f(b-x)=c, then the function is centrosymmetric about (a+b/2, c/2).
If f(x) satisfies f(a+x)=f(b-x), the function is symmetric about the straight line x=a+b/2.
5. The function y=(sinx)/x is an even function. It decreases monotonically at (0,) and increases monotonically at (-,0). Using the above attributes, you can compare sizes.
6. The function y=(lnx)/x monotonically increases at (0, e) and monotonically decreases at (e,+). In addition, y=x( 1/x) is consistent with the monotonicity of this function.
7. Composite function.
Parity of (1) composite function: the inner parity is even, and the inner parity is the same as the outer parity.
(2) Monotonicity of compound function: the same increase but different decrease.
8. Sequence law.
Arithmetic progression: S(n), S(2n)-S(n), S(3n)-S(2n) are arithmetic progression.
9. These projects cancel each other out. For Sn =1/(13)+1/(24)+1/(35)+? + 1/[n(n+2)]= 1/2[ 1+ 1/2- 1/(n+ 1)- 1/(n+2)]
Note: Four items are reserved every other item, namely the first two items and the last two items.
10. area formula: S= 1/2mq-np, where vector AB=(m, n) and vector BC=(p, q) Note: this formula can solve the problem of finding the area from the three-point coordinates of a known triangle!
1 1. In space solid geometry, the following propositions are all wrong.
Three different points in space define a plane;
Two lines perpendicular to the same line are parallel;
Two groups of quadrangles with equal opposite sides are parallelograms;
If a straight line is perpendicular to countless straight lines in the plane, it is perpendicular to the plane;
Two faces are parallel to each other, and the geometric shape of the parallelogram of the other two faces is a prism;
One face is a polygon, the other faces are triangles, and the geometry is a pyramid.
12. All pyramids with equal sides can be three, four or five pyramids.
13. Find f(x)=x- 1+x-2+x-3+? The minimum value of +x-n(n is a positive integer). The answer is: when n is odd, the minimum value is (n- 1)/4, and when x = (n+1)/2; When n is an even number, the minimum value is n/4, when x=n/2 or n/2+ 1.
14. area formula of focus triangle in ellipse: S=btan(A/2) In hyperbola: S=b/tan(A/2) Description: It is suitable for standard conic curve with focus on X axis. A is the included angle between two focal radii.
15. The tangent length l=(d-r)d represents the distance from a point outside the circle to the center of the circle, r is the radius of the circle, and d is the minimum distance from the center of the circle to a straight line.
16. For y=2px, the sum of two orthogonal chords AB and CD out of focus is at least 8p.
17. Error-prone point: If f(x+a)[a arbitrary] is odd function, then the conclusion is that the right side of the equation of f(x+a)=-f(-x+a) is not -f(-x-a). Similarly, if f(x+a) is an even function, we can get f (.
18. Vertex theorem of triangle.
Vector OH= vector OA+ vector OB+ vector OC(O is the outer center of the triangle and h is the vertical center.
If all three vertices of a triangle are on the image of the function y= 1/x, then its vertical center is also on the image of this function.
19. Theorems related to triangles:
In non-Rt, there are tana+tanbtana+tanb+tanc = tanatantbanc.
Projective theorem of arbitrary triangle (also known as the first cosine theorem): in ABC, a = bcosC+ccosB；; b = ccosA+acosC； c=acosB+bcosA
The radius of the inscribed circle of an arbitrary triangle r=2S/a+b+c(S is the area).
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