Primary school mathematics teacher recruitment questions

Zhejiang’s primary school test questions (and reference answers)

1. Multiple-choice questions (this major question has 10 small questions, each question is 3 points, ***30 points ): Only one of the four alternative answers listed in each question meets the question requirements. Please fill in its code in the brackets after the question. No points will be awarded for incorrect selections, multiple selections or no selections.

(1) " " is " "--------------------------------- --------------------------( )

A. Sufficient but unnecessary condition B. Necessary but insufficient condition

C. Necessary and sufficient conditions D. Neither sufficient nor necessary conditions

(2) Suppose in a quadrilateral, , and, then this quadrilateral is----( )

A. Parallelogram B. Rectangle C. Isosceles trapezoid D. Rhomboid

(3) It is known that, , and, then the range of real numbers is ---------- -------------------------------------------------- ------------------------------------------------( )

A. B. C. D.

(4) There are planes that are equidistant from four points on different surfaces of space ------------------- -----------------------------( )

A. 4 B. 5 C. 6 D. 7

(5) The inequalities that hold for any real numbers are--------------------------------- ------------------( )

A. B.

C. D.

(6) Suppose it is equal to The sum of the first n terms of the difference sequence, if, then-----------------------------( )

A. B. C. D.

(7) It is known that the total area of ??a cone is three times the area of ??the base, then the central angle of the sector of the side expansion diagram of the cone is ( )

A. B. C. D.

(8) One cube root of a complex number is, and its other two cube roots are--------------------------------- --( )

A. B. C. D.

(9), then the value is ( )

A. B. C. D.

(10) Set to double The two foci of the curve, P is a point on the hyperbola, and, then the area is--------------------------------- -------------------------------------------------- -( )

(A) (B) (C) (D)

2. Fill-in-the-blank questions (this major question has 5 small questions, each question is worth 4 points, ***20 points): Fill in the answer directly on the horizontal line.

(11) The teaching objectives of mathematics classroom teaching should generally include three aspects: process and method.

(12) "General High School Mathematics Curriculum Standards (Experimental)" believes that students' mathematics learning activities should not be limited to acceptance, memory, imitation and practice, but should also advocate, hands-on practice, reading and self-study, etc. learning style.

(13) If , then the maximum value of is .

(14) If 4 pairs of shoes are randomly selected from 5 pairs of shoes of different sizes, then the probability that these 4 shoes can be matched into at least one pair of shoes is .

(15) The inverse matrix of matrix .

3. Answer questions (this major question has 5 small questions, each question is 6 points, 30 points maximum): The answer should be written with a written explanation to prove the process or calculation steps.

(16) How to understand the abstract nature of mathematics? How to implement the principle of combining concreteness and abstraction in mathematics teaching?

(17) is a function defined on the real number set , and is the inverse function of . Student A thinks: "If the images of and do not overlap, but there are common points, then all common points are on the straight line." Please judge whether Student A's view is correct. If correct, please provide proof; if incorrect, please provide counterexample.

(18) Each term is a sequence of positive real numbers , the sum of its preceding terms is , and , find the general term .

(19) In the plane Cartesian coordinate system, find the area of ??the plane area enclosed by and .

(20) Assume function , constant and . If , , verify that is established.

4. Discussion or case design questions (this major question has 2 small questions, each of 10 points, 20 points): the discussion, analysis or design should clearly indicate the point of view and logic Clear, appropriate evidence, and well-founded.

(21) Concept assimilation is one of the basic ways for students to acquire mathematical concepts. Try to explain the meaning and psychological process of concept assimilation, and give examples of its application in teaching mathematical concepts.

(22) Write a lecture script with the content of "Monotonicity of Functions".

Reference answers and scoring standards

1. Multiple-choice questions (this major question has 10 small questions, each question is 3 points, ***30 points)

(1)C (2)B (3)D (4)A (5)A

(6)D (7)A (8)B (9)D (10)C

2. Fill-in-the-blank questions (this major question has 5 small questions, each question is 4 points, 20 points)

(11) Hands-on practice (2 points) , self-study in reading (2 points)

(12) Innovation awareness (2 points), mathematical model (2 points)

(13) 179

(14 )

(15) 2

3. Answer questions (this major question has 5 small questions, each question is 6 points, ***30 points)

(16) The selection of mathematics teaching methods is mainly based on the following four aspects

①Based on the purpose of mathematics teaching; ②Based on the content of mathematics teaching; (3 points)

③Based on students situation; ④Based on the teacher’s own quality conditions. (3 points)

(17) Abstraction is the basic characteristic of mathematics. In order to conduct research in a relatively pure state, mathematics often ignores other characteristics of objective objects and only abstracts its quantitative relationships and spatial forms for research. The abstraction of mathematics is mainly reflected in the following aspects: the content of mathematics is highly abstract formal structure and quantitative relationships; the method of mathematics is also highly abstract; the abstraction of mathematics also shows the characteristics of layer by layer progression; the abstraction of mathematics can Reach areas that people's perception cannot reach. (3 points)

Concreteness is the basis of mathematical abstraction, and abstraction must take concreteness as its destination.

In teaching, we should pay attention to the following aspects: use vivid, vivid, concrete and intuitive realistic materials and teaching language to introduce and clarify new mathematical knowledge; and then give full play to the leading role of teachers in a timely manner to guide students to summarize abstract and general knowledge. Mathematical concepts and conclusions; abstract mathematical knowledge and theories should be applied to specific practices, solve specific problems, and explain specific phenomena. (3 points)

(18) = (3 points)

,

So . (3 points)

(19) Because, (3 points)

obtain a special solution, corresponding to the basic solution system of the homogeneous linear equations,

So, the general solution of a system of linear equations is any constant. (3 points)

(20) Suppose, from the midline theorem, we get

,

and, , (3 points)

Two The squares of the equations are added together, so, ,

, so the hyperbola equation is. (3 points)

IV. Discussion or case design questions (this major question has 2 small questions, each of 10 points, ***20 points)

(21 ) The teaching of mathematical concepts is generally divided into three stages: introducing concepts to enable students to perceive concepts and form representations; enabling students to understand and clarify concepts through analysis, abstraction and generalization; enabling students to consolidate and apply concepts through examples and exercises. (3 points)

① Common methods of introducing concepts: introducing new concepts based on perceptual materials; introducing new concepts based on the relationship between old and new concepts; introducing new concepts in the form of "questions"; starting from concepts Introducing new concepts into the process of occurrence.

②Clear the connotation and denotation of the concept, and correctly express the essential attributes of the concept. Methods that can be adopted: comparison and analogy; appropriate use of counterexamples; rational use of variations; formation of a conceptual system.

③ When consolidating and applying concepts, attention should be paid to: timely review; hierarchical application of concepts; broad application of concepts. (4 points)

Appropriate example analysis. (3 points)

(22) Talk about teaching materials (2 points); talk about learning situation (2 points); talk about teaching methods (2 points); talk about teaching process (2 points); talk about teaching evaluation (2 points) point).