Answer test and answer analysis of national mathematics volume B
Thinking method of answering mathematics questions in college entrance examination
The topic of 1. function, equation or inequality should be directly considered first, and then the relationship between them should be established.
Consider the domain first, and then use the "three-in-one theorem".
2. If there is a transcendental expression in an equation or inequality, the thinking method of combining numbers and shapes is preferred;
3. In the face of elementary functions with parameters, we should grasp the invariance of the parameters when learning.
As a fixed point, the symmetry axis of quadratic function or ...;
4. Fill in the blanks with inequality questions and choose the special value method;
5. To find the range of parameters, we should establish an equation or inequality about parameters, and use the definition or range of functions or solve inequalities. In the process of formula deformation, the method of separating parameters is optimized;
6. The problem of constant establishment or its opposite can be transformed into a maximum problem. Pay attention to the application of quadratic function, flexibly use the maximum value on the closed interval, and discuss the idea of classification. Classification discussion should not be repeated or omitted;
7. The topic of conic curve should be clear first, and the problem of intersection between straight line and conic curve should be solved. If it is related to the chord midpoint, we should choose the method of setting instead of finding the point difference, and if it is not related to the chord midpoint, we should choose the method of Vieta theorem formula. When using Vieta theorem, we should first consider whether it is the discriminant of quadratic sum root;
8. To solve the problem of curve equation, if you know the shape of the curve, you can choose the undetermined coefficient method. If you don't know the shape of the curve, the steps used are to establish the system, set the points and simplify the list (pay attention to remove the special points that do not meet the conditions);
9. Find the eccentricity of ellipse or hyperbola, and establish the relation equation of A, B and C;
10. To find the period, monotone interval or maximum value of trigonometric function, first consider transforming it into a chord function with the same angle, and then use the auxiliary angle formula to solve it; To solve the triangle problem, pay attention to the use of internal angle sum theorem; For vector-related topics, pay attention to the range of vector angles;
1 1. The title of the series is related to sum, and the formula of sum and the method of difference are preferred; Pay attention to the proof after induction and conjecture; The direction of conjecture is two special series; When solving, pay attention to the idea of understanding the equation by using the general term formula and the first n term summation formula;
12. If the first problem of solid geometry is to build a system, it must be completed by traditional methods. If not, you can build the system from the first question. Note that vector angle is different from line angle, line angle and plane angle, and master the transformation of trigonometric function values between them skillfully; The calculation attention coefficient of cone volume is 1/3, while the calculation attention coefficient of triangle area is1/2; It is also necessary to prevent problems related to the ball. Pay attention to connecting the "heart distance" to create a right triangle to solve the problem;
13. The topic of derivative is generally not difficult, but attention should be paid to the level and steps of solving the problem. If you want to prove inequality with constructor, you can find a breakthrough from the known or previous question and give up if necessary; Pay attention to the application of geometric meaning and whether the point is on the curve;
14. If the probability problem has a solution, set an event first, and then write the reason for using the formula. Of course, you should pay attention to the number of steps to determine the details of the solution; If there is a distribution table, the probability sum is 1, which is an important method to test whether it is correct or not.
15. In the three-out-of-three questions, pay attention to the transformation method for polar coordinates and parameter equations, pay attention to the geometric meaning of Cauchy sum absolute value for inequality questions, and pay attention to the known product related to the circle for plane geometry, and can be measured if necessary;
16. When encountering a complex formula, you can use the substitution method. When using the substitution method, we must pay attention to the scope of S $. If Pythagorean theorem is known, it can be done by trigonometric substitution.
17. Pay attention to the binomial distribution in probability distribution, the use and assignment method of general formula in binomial theorem, the enumeration method in permutation and combination, the negative writing of full name and proper name proposition, whether the endpoint of the solution of value norm or inequality can be verified separately, and whether there is slope when using point oblique or oblique equations.
18. Absolute value problem gives priority to absolute value removal, and absolute value removal gives priority to using definitions;
19. Regarding translation, please note that the formula "left plus right minus, up plus down minus" is only used for functions, and the translation along the vector must be completed by the translation formula;
20. With regard to central symmetry, it is only necessary to use the formula of midpoint coordinates. Regarding axis symmetry, pay attention to the application of two equations: one is vertical, and the other is that the midpoint is on the axis of symmetry.
Three Skills of Mathematics Review in College Entrance Examination
1 There are three main points in grasping the foundation.
(1) Ensure the number of comprehensive training questions, complete the training of sets of questions in a limited time, and make efforts to be fast, accurate and standardized.
(2) "Raise your head to do the problem", starting from a clear problem-solving idea, optimize the problem-solving steps and find the best tangent λ point.
(3) Correcting mistakes, trapping and gleaning in time.
2 Follow-up and promotion from the perspective of ability requirements
(1) Train the transformation of three mathematical languages (mathematical language, mathematical symbol language and mathematical graphic language).
(2) Strengthen the serious and rigorous test habits.
(3) Strengthen training and solve problems quickly and flexibly.
(4) Make efforts to determine a reasonable operation direction, choose a reasonable operation mode, optimize the rules of the combination formula, and form a flexible problem strategy.
(5) Appropriate training should also be given to practical application, open inquiry, solving multiple-choice questions and filling in the blanks.
3 do a good job of psychological adjustment
In addition to mathematical ability, excellent psychological quality is also the main factor affecting the success or failure of the exam. The educator of Xueda University pointed out that candidates should find their own position, establish reasonable reference targets, always see their own achievements and positive psychological effects, and improve their review efficiency and later test-taking ability.
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