20 15 Shanghai college entrance examination mathematics paper basically follows the standard of "exam instructions" and does not exceed the outline. While paying attention to the basic knowledge and skills of mathematics in senior high school, we should highlight students' comprehensive mathematics quality, exploration spirit and innovation ability. Its main features are:
First, base on the foundation and pay attention to coverage.
Comprehensively examine basic knowledge, highlight the assessment of main knowledge, and strive to expand coverage. The big questions are still based on functions, triangles, series, analytic geometry, solid geometry and other knowledge points, while paying attention to the understanding of basic concepts and the examination of general methods.
For example, the science question 19, with a rectangular box as the carrier, mainly examines the reasoning and data processing ability of candidates. Low starting point, easy to cut. Deductive reasoning is directly used to prove, and space vector is used as a tool to complete the solution.
For example, the 20 questions of Shanghai liberal arts are also close to students' daily training, giving candidates a sense of intimacy. They examine the core content of the function that teachers often emphasize repeatedly-(monotonicity and parity). This is a good question, which not only stabilizes the "morale", but also gives the candidates a sense of accomplishment.
Second, strive to distinguish between strong choices
From basic questions, intermediate questions to ability questions, the test paper has obvious gradient and strong maneuverability, which is beneficial for candidates to climb the ladder and give full play to their strengths, so that the level of candidates at different levels can be reasonably evaluated.
For example, the design of 22 questions in science has a low starting point, a gentle slope and layered advancement, which can be described as ingenuity. Candidates of different levels can get started. Most of them say that candidates can get (1) small questions, and some candidates can get (2) and (3), which requires a certain degree of exploration ability and innovative spirit. This is the function of college entrance examination selection and the call of high school mathematics teaching reform.
Third, pay attention to discovering excellent abilities.
Based on the double bases of high school mathematics, relying on mathematical thinking and methods, and adhering to the concept of ability, this paper comprehensively examines the abilities of spatial imagination, abstract generalization, logical reasoning, operational solution, data processing, application and innovation. Instant learning and instant application
For example, Question 23 of Shanghai Science is an innovative question, which requires high ability. This paper mainly examines the ability of candidates to acquire knowledge independently, and completes the problem-solving under the background of the new definition through instant learning, instant understanding and instant application. It effectively examines the abstract generalization ability, rigorous logical reasoning demonstration and learning potential, and has strong discrimination and selection functions.