Mathematics in Shandong college entrance examination in 2023 is more difficult. Shandong college entrance examination uses the national 1 volume, and this year the national 1 volume math problem is more difficult. Many candidates complain that they didn't do this year's math problems and couldn't understand them, which made people unable to grasp the clue.
Whether the math test is difficult or not must be a hot topic for candidates to discuss. Some people find it difficult, while others find it difficult. The fourth question of Shandong college entrance examination mathematics examination questions in 2023 examines the volume calculation of the platform, but does not directly examine it. Instead, we should integrate this knowledge into the real life background, examine students' mathematical modeling ability, and abstract practical problems into mathematical problems to solve.
In 2023, the probability statistics of 20 questions in the mathematics test questions of Shandong college entrance examination were also investigated based on the real situation of the relationship between a certain disease and health habits, which all reflected that the college entrance examination proposition paid attention to application.
First, the trigonometric function problem
Pay attention to the correctness of normalization formula and induction formula (when transforming into trigonometric function with the same name and the same angle, apply normalization formula and induction formula (singular change, even invariance; When symbols look at quadrants, it is easy to make mistakes because of carelessness! One careless move will lose the game! )。
Second, a series of questions
1. When proving that a series is an arithmetic (proportional) series, the arithmetic (proportional) series with the first item and the tolerance (common ratio) should be written in the final conclusion;
2. When proving the inequality in the last question, if one end is a constant and the other end is a formula containing n, the scaling method is generally considered; If both ends are formulas containing n, mathematical induction is generally considered (when using mathematical induction, when n=k+ 1, the assumption when n=k must be used, otherwise it is incorrect. After using the above assumptions, it is difficult to convert the current formula into the target formula, and generally it will be scaled appropriately. The concise method is to subtract the target formula from the current formula and look at the symbols to get the target formula. When drawing a conclusion, you must write a summary: it is proved by ① ②;
3. When proving inequality, sometimes it is very simple to construct a function and use the monotonicity of the function (so you should have the consciousness of constructing a function).
Third, solid geometry problems
1. It is easy to prove the relationship between line and surface, and it is generally unnecessary to establish a system;
2. It is best to establish a system when solving the problems such as the angle formed by lines on different planes, the included angle between lines and planes, the dihedral angle, the existence of geometry, the height, the surface area and the volume.
3. Pay attention to the relationship between the cosine value (range) of the angle formed by the vector and the cosine value (range) of the angle (symbol problem, obtuse angle problem, acute angle problem).