First, based on the discipline foundation, highlight the main knowledge.
According to the curriculum standards and examination instructions, the importance of returning to basic knowledge and skills is emphasized, such as liberal arts 1-9, science 1-7, liberal arts11-3, etc. Focus on the understanding and application of concepts and formulas, and examine candidates' understanding of the essence of mathematics. The ninth question of liberal arts and the seventh question of science not only examine the application of the volume formula of the rotating body, but also examine the examinee's understanding of the structure and generation process of the rotating body. Some questions in the test paper come directly from the examples and exercises in the textbook, which are adapted and integrated appropriately, giving people a feeling of deja vu, such as questions 3, 5 and 9 in science, questions 4, 5 and 12 in liberal arts, and questions (ⅲ) in 20, which fully embodies the concept of "from the textbook, higher than the textbook" and is very good for middle school mathematics teaching.
The examination paper comprehensively examines the basic knowledge of mathematics, and at the same time highlights the core content of the mathematics subject system in middle schools, reaching the necessary depth. The main knowledge of trigonometric function, solid geometry, probability statistics, sequence, function and derivative, analytic geometry and so on are fully examined in the whole paper. For example, for the content of functions and derivatives, there are 3, 7, 8, 10, 20 questions in liberal arts, and 10,12 1 questions in science. The examination of solid geometry focuses on the understanding, imagination and reasoning of the relationship between lines, lines and surfaces in graphics. Analytic geometry focuses on the geometric meaning and properties of conic curves, the combination of numbers and shapes and motion transformation. The topic design takes key knowledge as the core, combines knowledge with ability, and has a strong sense of mathematics. It tries to design test questions at the intersection of several knowledge levels from the overall height of the subject, so as to test whether candidates have an orderly networked knowledge system, and can extract relevant information from it and solve problems flexibly.
Second, pay attention to the way of thinking and deepen the ability of conception.
Mathematical thinking method is the abstraction and generalization of mathematical knowledge at a higher level, which is contained in the process of occurrence, development and application of mathematical knowledge and is an important bridge from knowledge to ability. Common mathematical ideas in middle school mathematics, such as functions and equations, classification and integration, combination of numbers and shapes, transformation and reduction, are vividly reflected in this year's mathematics test paper. For example, questions 7, 13, 20 in liberal arts and 4, 5, 8, 9, 15, 17, 2 1 in science examined the idea of combining numbers with shapes; Question liberal arts 10, 15, science 10,14,21etc. The idea of classification integration is studied. Question liberal arts 19, 20, 2 1, science 10, 12, 20, 2 1, etc. , examines the ideas of functions and equations; The subjects of liberal arts 20, 2 1, science 17, 19, 20, 2 1 examined the transformation and transformation ideas. Most of the test questions have low design threshold and wide entrance, and the thinking methods used are hierarchical and gradient, thus effectively distinguishing the ability levels of candidates at different levels. This design embodies the requirements of knowledge as the carrier, method as the support and ability as the purpose, improves the discrimination of test questions and is conducive to the selection of talents in colleges and universities.
The two papers of arts and sciences pay attention to the examination of spatial imagination, abstract generalization, reasoning, data processing, operational solution and application consciousness. The test paper focuses on abstract generalization ability and reasoning ability, examines candidates' exploration, discovery and creation ability, and tests students' learning potential. For example, the sixth question of liberal arts is based on the temperature situation in A and B, and the basic form of stem and leaf diagram is used as the carrier to design related statistical questions to investigate the application of "probability statistics" knowledge in real life. The test questions are close to life and the background is fair, and the data processing ability and application consciousness of the candidates are examined. Another example is the science question 1 1. With binomial expansion as the background and exponential power operation and combinatorial number operation as the knowledge carriers, the mathematical thinking and inductive reasoning ability of candidates are examined.
Third, attach importance to rational thinking and highlight the function of choice.
Test design knowledge meets, methods interweave and abilities cross. The examination questions are exquisite, unique and rich in coverage, which embodies the characteristics of mathematical rational thinking. A comprehensive investigation is made from the aspects of hierarchy, profundity and innovative thinking, which highlights the selection function of college entrance examination questions.
The test questions pay attention to generality and methodology, and at the same time leave enough room for candidates with higher thinking level, and pay full attention to the differences of candidates' thinking level. For example, for liberal arts 2 1 questions and science 20 questions, the area that candidates can directly seek can also be converted into the sought area according to the proportional relationship suggested in the previous question, which simplifies the operation and makes the thinking level clear. The examination questions are comprehensive and pay attention to the profound examination of thinking. For example, science 19 takes the counting principle as the carrier and the application of mathematics as the background, and examines the candidates' mathematical application consciousness, abstract thinking ability, mathematical modeling ability, problem analysis and problem solving ability. If the examinee does not form the comprehensive application ability of knowledge and the depth of thinking can not meet the examination requirements of this question, it is difficult to answer this question completely.
Fourth, the difficulty design is reasonable, which reflects humanistic care.
The difficulty design of the test questions is reasonable, from easy to difficult, with distinct levels, which conforms to the cognitive law and learning characteristics of candidates. There are three short questions for 20 questions in science, 20 questions in liberal arts and 2 1, with clear gradient and step by step, which is beneficial for candidates to eliminate nervousness and play normally. Question (1) has a low thinking starting point, which makes it easy for candidates to get started, giving more chances for candidates to score. The thinking starting point of questions (2) and (3) is gradually rising, which requires candidates to have strong exploration ability and creative problem-solving ability.
The expression of the test questions is concise and accurate, the scene blends, the knowledge and ability are equally important, it conforms to the mathematical law, and the proportion of thinking and calculation is appropriate, which reflects the humanistic care for the candidates. The examination questions fully consider the different characteristics of the thinking of the candidates of arts and sciences and meet their respective cognitive requirements. There are only two identical questions and four sister questions in the liberal arts and science examination paper. The examination of the same knowledge points is presented in different ways, which reflects the humanistic care for liberal arts candidates. For example, the science 17 question is exactly the same as the liberal arts 18 question. The first question (1) is the proof that the line is parallel to the plane, and the second question (2) is the proof that the liberal arts are vertical, while the science seeks the dihedral angle on the basis of proving that the line is vertical to the plane. For another example, liberal arts question 2 1 examines the same subjects as science question 20, while liberal arts question (1) examines candidates' familiarity with solving elliptic equations by undetermined coefficient method, and science question (1) examines candidates' exploration of ellipse generation process and graphic characteristics under geometric background, and strengthens reasoning by combining numbers and shapes. On the premise of ensuring effective distinction, the difficulty design of liberal arts and science examination questions is reasonable, which embodies the new curriculum concept of "people-oriented".
In a word, the mathematics test questions in Shandong Paper of 20 15 college entrance examination are clear in thinking, concise in expression, rich in connotation, stable in change, innovative in change and accurate in positioning, which is conducive to selection. While fully examining the subject ideas and methods, it pays attention to humanities, embodies the characteristics of Shandong, and well implements the new curriculum concept.