What was the result of the 20 14 math exam in Hebei province?

20 14 Analysis of Mathematics Test Paper for Senior High School Entrance Examination in Hebei Province

First, the overall characteristics of the test questions

Hebei province 20 14 senior high school entrance examination paper is similar to 20 13 senior high school entrance examination paper in form, but it is quite different from 20 13 senior high school entrance examination paper in terms of examination content and examination angle, and the overall difficulty of the paper is lower than 20 13 senior high school entrance examination paper. It can be said that it is a non-test attempt under the test paper.

From the examination form, the mathematics examination paper of 20 14 senior high school entrance examination is still three sections: multiple-choice questions, fill-in-the-blank questions and solution questions. The score is 42,12,66, and the number of questions is16,4,6. The difference is that the scores of the answers have changed from 9, 10, 10,1,12, 14 last year to 10,/kloc-this year.

Judging from the examination content and examination, the changes in the mathematics examination paper of the 20 14 senior high school entrance examination mainly include the following aspects:

1.

Canceling the traditional function application problems, the whole set of problems has no application problems, which will make many students very uncomfortable. In recent years, the function application problem will be produced at the finale of the simulation problem of the senior high school entrance examination all over the country, and students have become accustomed to producing a big problem from an application problem. 20 14 The mathematics test paper for the senior high school entrance examination in Hebei Province presents application questions in the form of short answer questions, and the multiple-choice questions No.9, No.22, No.3 and No.26 use the idea of solving application questions, and the application questions appear in the form. This form of examination involves a wide range of knowledge, involving the application of linear function and quadratic function, and involving the application of profit, travel and transportation. Examination is comprehensive and basic. For example, the solution of right triangle involved in the third question of 22 questions and the second question of 25 questions is also the traditional examination form of big questions.

2. The core test center is flat.

This feature is reflected in the fact that there is no special examination center for solving equations and inequalities by numbers and formulas, quadrilateral properties in space graphics, circle properties, tangent judgment, combination of functions and space graphics, dynamic geometry problems, etc., and the small incision proposition and the point proposition for solving problems are selected. But the last question involves less core test sites, and the last big question involves less pure mathematics knowledge.

3. Make mathematics knowledge come alive.

As an applied subject, mathematics mainly solves practical problems. The previous conventional functions are combined with spatial graphics, and dynamic geometry problems are more based on mathematical knowledge to solve mathematical problems. In fact, the 26 questions in this set combine mathematical knowledge with common sense of life to investigate and solve practical problems in life, which strongly refutes the popular arguments in recent years, such as the uselessness of mathematics and the inability to buy food with functions. The essence of returning to mathematics learning is thinking learning, which is to improve students' logical thinking ability and inductive analysis ability.

From these changes, it can be seen that it is a great exploration for the proposition group to try to explore an exam that examines mathematical knowledge and ability without taking the exam in this baton-like selective exam.

Second, the typical test evaluation

1, multiple choice questions

1- 16 is a multiple-choice question, 1~6 is 2 points for each small question, paying attention to the basic examination; 7~ 16 3 points each, pay attention to the flexible use of basic knowledge. Multiple-choice questions involve a wide range of knowledge, most of which are small incision propositions within a large framework. Except for questions 8, 12 and 15, which are flexible and need to be transformed, the other questions are not difficult and the overall difficulty is low.

The problem 1 is a fixed rational number base; The second question simply and directly examines the nature of the neutral line; The third question has changed the traditional examination method of algebraic expression operation, allowing candidates to choose the operation result instead of the correct option, which is the same as the question number in 20 12 is not in the solution set of inequality group. The fourth question has a unique angle, which requires students to have certain transformation ability to examine the external angle in non-closed graphics. The fifth problem is the conventional real number estimation; Question 6 examines the determination of slope according to the image of a linear function, which involves solving the inequality group and representing the solution set of the inequality group on the number axis. The examination content is basically comprehensive; The seventh problem is fractional simplification, which is a common problem in Hebei province for many years. The denominator is the same and it is not difficult. Question 8: The key to cutting a rectangle into a square is to find a way to cut two lines into three sections and determine the feasibility of 3, 4 and 5. Question 9 can be understood as an application of a small question to determine the coefficients of quadratic function according to known conditions; The question 10 can be folded. If you change the D option, some candidates may not read the questions carefully. 1 1 The question is calculated by combining probability and frequency, 1 The question depends on four calculations; 12 followed the multiple-choice question of 20 12 to investigate the nature of the vertical line in ruler drawing, and reached the conclusion that PA=PB is the key; 13 to examine the judgment of similar graphics, it is necessary to grasp the proportion of edges of similar graphics; The problem 14 is brought into the evaluation to determine the k value of the inverse proportional function, which needs to be discussed in classification; 15 has a novel examination angle, which requires students to be familiar with the characteristics of regular hexagon and evaluate it as a whole; 16 question examines the definition of median and mode by determining other numbers in a set of data according to median and mode. Good angle, not difficult.

Step 2 fill in the blanks

17-20 is a blank question. Fill-in-the-blank questions are not difficult except that the 20 th question is easy to be miscalculated.

The issue 17 is the topic of real number operation, and the basis for comparison; Question 18, the operation with value, absolute value and square number, has been tested in many non-negative junior high schools, and students are familiar with it. 17 and 18 can be understood as the decomposition of real number mixed operation in the calculation of conventional solution 1 problem; 19 questions examine the formula for calculating the fan-shaped area, and candidates can remember this formula for calculation; Question 20 is the inductive conjecture of the last test of fixed multiple-choice questions, which can be expressed step by step by scientific counting method, and the calculated result has no operational error.

Step 3 answer questions

The title of 2 1-26 is problem solving.

2 1 the topic examines the matching solution of quadratic equation in one variable, the definition of square root, and the formula for finding the root of quadratic equation in one variable. The derivation and application of mathematical formula is the focus of mathematics learning, but it is rarely involved in teaching and examination. Students can derive the formula for finding the root of a quadratic equation with one variable, Vieta theorem of the formula for finding the root, and the relationship between the discriminant of the root and the number of roots. This question follows the examination method of Question 22 of 20 13, so that students can find their own mistakes in places where they are prone to make mistakes in daily life and ask questions from a better angle. Generally speaking, it is an examination of basic formulas, definitions and calculations. The prototype of this question is 20 13 Baoding junior high school mathematics teacher qualification certificate written test topic.

Question 22 is the fixed statistical probability test, which examines the calculation of the average, the fan-shaped statistical chart and the solution of the right triangle. The combination of statistical probability and other subjects' knowledge has been accepted by many provincial and municipal middle school entrance examination questions in recent two years. Without changing the proportion of statistical probability scores, it can make the examination scope wider and the topic scores more reasonable. This set of questions examines the probability and statistics in 1 1 and 16 respectively. 1 The problem is calculated directly according to the definition of the average value, the second problem is a conventional statistical graph problem, and the third problem can be understood as a small application problem, which can be calculated numerically. This question is not difficult, so it is based on comparison.

Question 23 is the proof of spatial graphics. 1 The congruence of the question and the angle of the second question are better. This is proved by simple conventional methods. The third question is to grasp the progressive proof idea of proving parallelogram first and then rhombus. The angle of the second question is equal to parallelism, and then the other side is combined with congruence parallelism. The third question has some difficulty in thinking. The gradient of this problem is obvious. 1 and 2 questions are compared, and the third question reflects the discrimination of the test questions.

Question 24 mainly investigates the method of undetermined coefficient to find the quadratic resolution function. Question 1, question 2, the undetermined coefficient method can be set with two columns, three solutions and four circles, can be used to find the vertex, can be used to verify whether the point is on the image, and the third question can directly get the number of parabolas that meet the conditions according to the characteristics of parabolas. The overall difficulty of the test questions is not great, and it is relatively basic from examination to thinking and calculation. Combined with the moving point problem, we can further investigate the distance and shortest distance between two points on the same side of the line and a point on the line, the calculation of the length of the line segment perpendicular to the coordinate axis, the area problem and the existence of the point.

Question 25 is about the calculation of a circle. 1 The question is about finding the chord center distance according to the vertical diameter theorem and the OBP angle according to the perpendicularity of the tangent. The second question is about finding the angle to solve the right triangle according to the tangent property, and the third question is about using the limit method according to the tangent definition. Pay attention to convert the included angle between AB and ABP into angle. The overall difficulty of this problem is moderate, which requires students to flexibly use trigonometric functions to transform the relationship between corners.

Question 26 is the moving point problem of spatial graphics, but it is presented in the form of life examples. This kind of problem-solving form has appeared more in the right triangle problem in recent two years, but rarely in the moving point problem. Grasping the relative symmetry of the position of two cars about CA is the key to determine the simultaneous position of two cars. The first question focuses on the classification and discussion of problems. The second problem can be solved by understanding the movement process and combining the symmetry of two cars about CA. The third problem needs to find out the position of 1 when tourists just missed the No.2 car and the position of No.2 car when they just missed the No.2 car. Furthermore, we can get the distance from 1 and No.2 to point A. The longer the distance, the longer the time. Fourth, to understand the meaning of just meeting No.2 head-on, determine the approximate positions of 1 and No.2 and compare them with the remaining distance. According to PA, the distance and time required for walking and riding 1 can be calculated, and the scheme selection can be discussed. The gradient of this question is obvious, which requires students to have strong logical thinking ability and spatial imagination ability, and can turn real life problems into travel time problems. At the same time, the ability of students to establish mathematical models to solve mathematical models is investigated.

Third, the distribution of knowledge points and scores

Title number

Examination content

Key points of solving problems

Related knowledge points

Methods and skills

score

difficulty

Question 1

Rational number base

Understand the definition of reciprocal

Only two numbers with different symbols are opposite.

exclusive method

2

easy

Question 2

Neutral line attribute

According to the midpoint of the center line

The center line of a triangle is equal to half of the third side.

Measurement method

2

easy

Question 3

formula for the difference of square

Understand the square difference formula

exclusive method

2

easy

Question 4

Exterior angle attribute

Find the external angle relationship

The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

Measurement method

2

easy

Question 5

Real number estimation

Convert to a square relationship

exclusive method

2

easy

Question 6

Linear function image

Determine the positive and negative values of k according to the image.

Linear function k

exclusive method

2

easy

Question 7

Fractional simplification

Factor decomposition of molecules

exclusive method

three

easy

Question 8

Region splicing

pythagorean theorem

Determine the side length of a square

exclusive method

structured approach

three

easy

Question 9

quadratic function

Square area

Determine the analytical formula of y about x

exclusive method

three

easy

Question 10

Plane expansion diagram of three-dimensional graphics

Fold the expanded chart back to the cube.

Plane expansion diagram of three-dimensional graphics

structured approach

three

easy

Question 1 1

Frequency calculation

Calculate the probability and frequency of statistical charts.

P(A)=m/n, where m represents the number of results of event A and n represents all possible numbers.

Estimation method

three

easy

Question 12

Midline attribute

According to the meaning of the question, PA=PB

The point on the middle vertical line is equal to the distance between the two ends of the line segment.

change

three

easy

Question 13

Determination of similar numbers

Judging according to the similarity judgment theorem

Side-length ratio of similar figures

Measurement method

three

easy

Question 14

Inverse proportional function image

According to the new definition, a and b are replaced by 2 and x respectively.

K>0, the inverse proportional function is in the first and third quadrants.

When k < 0, the inverse proportional function is in two or four quadrants.

Classified discussion

three

easy

Question 15

Properties of Regular Hexagons and Regular Triangles

Put two blank triangles together to form an equilateral triangle with one side of a regular hexagon.

Two adjacent vertices and the center of a regular hexagon form an equilateral triangle with sides.

Graphic stitching

three

easy

Question 16

Median and mode

According to the median and the mode, the other two numbers are determined to be less than 6 and not equal.

Median is the middle number in order of size, and mode is the number that appears most frequently in a set of data.

exclusive method

three

easy

Question 17

Real operational

According to the radical multiplication algorithm operation or radical simplified evaluation.

or

three

easy

Question 18

Non-negativity of absolute value and square number, power of negative exponent and power of 0.

According to the nonnegativity of absolute value and square number, the values of m and n are obtained, and the values are used for operation.

change

three

easy

Question 19

Sector area calculation

Determine the arc length of the sector according to the meaning of the question.

change

three

easy

Question 20

Inductive conjecture

Using scientific counting method to represent OA,

length

Scientific notation

N is an integer

Rule induction

three

easy

Question 2 1

Solving quadratic equation with one variable by matching method

The definition of square root, the formula for finding the root of quadratic equation in one variable and the matching method

(a & gt0)

Method of completing a square

10

easy

Question 22

Average calculation

Fan statistics chart

Solving right triangle

Find out the percentage and total number of a place,

Find AB length

10

easy

Question 23

Congruence judgment, sum of internal angles of triangle, parallelogram judgment

SAS proves congruence, and by summing the inner angles of triangles, the parallel parallelogram is used to find ACE.

The sum of the internal angles of a triangle is 180 degrees, and the quadrilateral with equilateral and equilateral parallel sides is a parallelogram.

Progressive proof

1 1

easy

Question 24

Quadratic function image and its properties

Power of-1

Solving quadratic resolution function by undetermined coefficient method,

Classified discussion

method of undetermined coefficients

1 1

easy

Question 25

Vertical diameter theorem, tangent property, rotation property, solution of right triangle

Calculate the chord center distance according to the vertical diameter theorem, and calculate the vertical OBP angle according to the tangent.

Limit method

1 1

middle

Question 26

Fixed point problem, scheme selection

Determine the relationship according to the meaning of the question and grasp the relative symmetry of the positions of the two cars to determine the position of the two cars at the same time.

Classified discussion

13

difficult

Chapter IV Proportional Analysis

chapters and sections

20 14 senior high school entrance examination

20 13 senior high school entrance examination

20 12 senior high school entrance examination

chapters and sections

Occupation integral

Share ratio

Occupation integral

Share ratio

Changes in the proportion of 20 14 senior high school entrance examination

Occupation integral

Occupation integral

proportion

Changes in the proportion of 20 14 senior high school entrance examination

Number sum formula

Equations (groups) and inequalities (groups)

3 1

25.8%

29

24.2%

↑ 1.6%

29

24.2%

↑ 1.6%

function

27

22.5%

28

23.3%

↓0.8%

34

28.3%

↓5.8%

Statistics and probability

13

10.8%

13

10.8%

_______

13

10.8%

_______

Space and graphics

Forty nine

40.9%

50

4 1.7%

↓0.8%

Forty-four

36.7%

↑4.2%

Overall evaluation of verb (abbreviation of verb) test questions

It can be seen from the changes of the mathematics examination paper of the senior high school entrance examination in Hebei Province in recent two years that the proposition group has been seeking changes, breakthroughs and innovations, and seeking the essence of mathematics learning and examination. This is a great challenge to students' study and teachers' teaching.

From the students' point of view, although the candidates will not be completely unprepared for the 20 14 Hebei Senior High School Entrance Examination Paper, as the previous candidates did for the 20 13 Hebei Senior High School Entrance Examination Paper, the changing examination forms this year will still make some students uncomfortable, which requires students to have good psychological quality, strong adaptability and knowledge transfer ability. At the same time, we should think and understand the essence and practical significance of mathematical theorems and formulas in our usual study. At the same time, we need to find the knowledge system, tap the context of knowledge, truly understand the application of knowledge points, and improve the ability to use knowledge and solve practical problems.

From the teaching point of view, the changes in the mathematics test papers of the senior high school entrance examination in Hebei Province in the past two years will also make teachers uncomfortable. The irregular changes in the test questions make the modular routine teaching and preparation for the exam more and more unable to adapt to the development of the senior high school entrance examination. Teaching staff can't predict what will be in the exam, which will bring some confusion to teachers' teaching. But only in this way can we really teach students the thinking method of mathematics learning from mathematics teaching and improve their logical thinking ability. Only in this way can we really let students think and solve problems independently, and let them have the ability to summarize and analyze independently, so as to realize the real purpose of learning mathematics.