1 The most difficult finale of college entrance examination mathematics-solid geometry
For solid geometry problems, pay attention to all kinds of proof methods (judgment theorem, property theorem) and introduce auxiliary lines, generally diagonal, midpoint, proportional point, midpoint of isosceles triangle, etc. In fact, it is possible to directly use the vector method when science cannot prove it. The calculation problem is mainly volume, pay attention to letter transposition (equal volume method);
The distance between a straight line and a plane is equal volume method. There are dihedral angles, line angles and plane angles in science. It is relatively simple to establish a spatial coordinate system (vector method). Pay attention to the calculation of coordinates of each point, and don't make mistakes.
Conic curve, 1 the most difficult final problem in mathematics in college entrance examination
Conic curve problem, the first problem is to find the curve equation, and pay attention to the methods (definition method, undetermined coefficient method, direct trajectory method, back calculation method, parameter equation method, etc.). Be sure to check whether the first question is correct or not, otherwise you will forget the second question.
Second, when a straight line intersects a conic curve, remember to use the same time when completing it. The first step, simultaneous, according to Vieta's theorem, the sum and difference of two roots generally intersect at two points, pay attention to verify the discriminant >; 0, pay attention to discuss whether there is a slope when setting a straight line.
The second and most crucial step is to use simultaneous interpretation. The key is how to use simultaneous interpretation, that is, how to transform the conditions in the question into x 1+x2 and x 1x2 you just completed, and then substitute the results. The problems usually involved are the relationship between chord length (substituted into chord length formula) and the fixed point (based on the proportional relationship, the relationship between three-point coordinates (abscissa or ordinate) is established. Then, according to the relationship between roots and coefficients, two relationships of coordinates of two points on a quadratic curve can be solved from these three relationships), point symmetry problem (using two conditions that two points are symmetrical about a straight line, that is, the connecting line of these two points is perpendicular to the symmetry axis, and the midpoint of these two points is on the symmetry axis), and fixed point problem (the straight line y=kx+b passes through a fixed point, that is, the relationship between K and B can be found.
1 Derivative, the most difficult finale in college entrance examination mathematics
The final test of derivative in college entrance examination is a comprehensive ability, and its content and methods are much higher than those in textbooks. The basic concepts involved are tangent, monotonicity, non-monotonicity, extreme value, extreme point, maximum value, constant establishment, arbitrariness and existence.
1. General topics will be described in a small amount of words, so it will involve simple translation of words.
2. The core description in the topic is various formulas: mainly common types: generally involving cubic functions, referring to logarithmic, fractional and absolute functions, and occasionally involving trigonometric functions; Special types: mainly including X 1, X2, F (X 1) and F (X2) types.
Thinking of solving problems: the process of text translation is generally simple, and the core is the deformation treatment of formula operation. For specific formulas, the template is mainly used to solve problems, focusing on the general formula operation deformation treatment strategy in the derivative finale problem, and it will also involve the ability to understand and draw some complex unfolded graphics quickly.