1, order problem
(1) Master the properties of arithmetic, geometric series, general term formula and summation formula;
(2) Deeply understand how the sum formula of arithmetic and proportional series in textbooks is derived, and the problem-solving ideas such as "reverse addition" contained in it are often used in solving problems;
(3) Mastering the problem that denominator algebraic multiplication scores are converted into single fraction differences, and realizing the problem of "eliminating the middle and leaving two ends";
(4) Mastering the problem of extracting several terms satisfying a certain condition from the existing series (such as {An}) to form a new series (such as {Ank}), and then finding the sum of the general terms and the previous terms of the new series;
(5) Mastering the method of simplification or undetermined coefficient to solve problems and "scraping" irregular series into arithmetic or geometric progression;
(6) Master the principle of mathematical induction and apply it to solve the individual inquiry problems of "guessing before proving".
(7) Mastering the problem of finding the limit of sequence, especially making the exponent of denominator higher than the exponent of numerator through simplification, and making the score equal to 0 when n is infinite.
2. Conic curve problem
(1) It is the soul and essence of analytic geometry to master the geometric definition and directrix definition of conic curve and deeply understand the idea of "combination of numbers and shapes": to study geometric problems with algebraic ideas and realize quantitative solution;
(2) Using the ordinary equation of conic curve (ellipse, hyperbola, parabola) skillfully to solve the problems of line segment, the distance from point to line and the included angle between two lines;
(3) The parametric equation of conic curve is skillfully used to help solve problems, especially the parametric equation of ellipse and hyperbola is closely combined with trigonometric function, and the boundedness of trigonometric function is closely related to finding the maximum and minimum values of inequality.
(4) Because plane analytic geometry solves the problems in the plane, when solving the problems in solid geometry, if we can confirm that the distance from the point to the surface or dihedral angle can be solved in a certain plane, but it is not easy to remember from the point of view of pure geometry, then we can establish a coordinate system on a certain surface of the solid graph and turn the problems in solid geometry into problems in plane analytic geometry (the distance from the point to the line and the included angle of the line), which sometimes works well.
By the way, the following "mathematical ideas" are particularly important in the usual exams and college entrance examinations:
The idea of (1) equation: turn the unknown into a formal known, then find out the relationship and find out the known solution of this form;
(2) The idea of inequality: use the enlargement and contraction of inequality to judge the limit of variables or expressions and solve the maximum and minimum values;
(3) The idea of function: abstract the real problem into an algebraic problem, and dynamically investigate the changing law of function law according to the value range of variables;
(4) The idea of combining numbers with shapes: make full use of intuitive and vivid images to assist analysis and calculation;
(5) The idea of classified discussion: reflect the rigor of rational thinking and analyze the specific situation.
(6) the thought of reducing to absurdity: thinking in reverse, looking at the problem from the opposite angle;
(7) Mathematical induction thought: Try to explore the general law according to the limited data, and then verify the correctness of the guess through induction.
If you can conquer all the skills mentioned above, I believe you can handle these two problems easily.