1. rational number

The meaning of (1) rational number

(2) Use points on the number axis to represent rational numbers, their opposites and absolute values.

(3) Comparison of rational numbers

(4) Find the reciprocal and absolute value of rational numbers (absolute value does not contain letters)

(5) the meaning of power

(6) addition, subtraction, multiplication, division, multiplication and mixing of rational numbers (mainly divided into three steps)

2. Real numbers

The concepts of (1) square root, arithmetic square root, cubic root and quadratic root.

(2) Square roots and cube roots are represented by root signs.

(3) Roots and powers are reciprocal operations.

(4) Find the arithmetic square root of some non-negative numbers and the cube root of real numbers.

(5) The concepts of irrational number and real number

(6) There is a one-to-one correspondence between real numbers and points on the number axis.

(7) Reasonably explain and infer the information with a large number of figures.

(8) Estimate the approximate range of irrational numbers with rational numbers.

(9) Concepts of divisor and significant number

(10) Divison's law of addition, subtraction, multiplication and division and quadratic root.

Simple four operations of (1 1) real numbers

3. Algebraic expressions

(1) Use letters to indicate the meaning of numbers.

(2) Using algebraic expressions to express the quantitative relationship of simple problems.

(3) Explain the actual background or geometric meaning of some simple algebraic expressions.

(4) Find the value of the algebraic expression

(5) The meaning and basic properties of integer exponential power.

(6) using scientific notation to represent numbers

(7) The concepts of algebra and fraction.

(8) Simple algebraic addition, subtraction, multiplication and division (polynomial multiplication only refers to linear multiplication).

(9) Derivation and application of square difference and complete square formula.

(10) Extract the common factor method and the formula method (use the formula no more than twice, and the index is a positive integer) for factorization.

(1 1) Use the basic properties of fractions for reduction and division.

(12) Simple fractional addition, subtraction, multiplication and Divison.

4. Equations and equations

(1) List equations or equations according to the quantitative relationship in specific problems.

(2) Solve linear equations with one variable and linear equations with two variables.

(3) The solution can be reduced to a fractional equation of linear equation (there are no more than two fractions in the equation)

(4) Using factorization method, formula method and collocation method to solve the quadratic digital coefficient equation.

(5) Estimate the solution of the equation through observation, drawing or calculation.

(6) according to the practical significance of specific problems, whether the test results are reasonable.

5. Inequality and unequal groups

The meaning of (1) inequality

(2) Basic properties of inequality

(3) Solve the unary linear inequality and the inequality group consisting of two unary linear inequalities, and express the solution set on the number axis.

(4) Simple application of inequality and inequality group

6. Function

The meaning of (1) constant and variable

(2) Give examples of functions.

(3) The concept of function and three representations of function.

(4) Analyze the functional relationship in simple practical problems with images.

(5) Find the range of independent variables of simple algebraic expressions, fractions and simple practical problems.

(6) Find the function value

(7) Describe the relationship between variables in some practical problems with proper function representation.

(8) Combined with the analysis of function relation, try to make a preliminary prediction on the variation law of variables.

(9) Meaning of linear function, inverse proportional function and quadratic function

(10) Determine the representation of linear function and inverse proportional function according to known conditions.

(1 1) Determine the quadratic function expression by analyzing the actual problem.

(12) Draw an image of a function and an inverse proportional function.

(13) Trace points to draw quadratic function images.

(14) Understand the properties of linear functions and inverse proportional functions.

(15) Understanding the Properties of Quadratic Function through Images

(16) Determine the vertex, opening direction and symmetry axis of the image according to the formula (the formula needs no memory).

(17) Use the image of linear function to find the approximate solution of binary linear equations.

(18) Using the image of quadratic function to find the approximate solution of quadratic equation in one variable.

(19) Use linear function, inverse proportional function and quadratic function to solve practical problems.

Space and graphics

7. Understanding of graphics

(1) Understanding Points, Lines and Faces

(2) the concept and representation of angle

(3) Recognition of degrees, minutes and seconds, and simple conversion of degrees, minutes and seconds.

(4) Angle comparison or estimation.

(5) Calculation of Angle Sum and Difference

(6) Angular bisector and its properties

8. Intersecting lines and parallel lines

(1) concepts such as complementary angle, complementary angle and right angle.

(2) Equal complementary angle, equal complementary angle and equal antipodal angle.

(3) Concepts such as vertical line and vertical line segment, and understand that the vertical line segment is the shortest.

(4) The distance from a point to a straight line and the distance between two parallel lines.

(5) There is one and only one straight line perpendicular to the known straight line.

(6) Draw a straight line perpendicular to a point with a triangular ruler or protractor.

(7) The midline of the line segment and its properties.

(8) Two straight lines are parallel and have the same angle.

(9) At a point outside the straight line, there is one and only one straight line parallel to the known straight line.

Outline of Changchun Junior Middle School Mathematics Joint Examination

Inspection scope and requirements

I. Number and Algebra (I) Number and formula 1, real number

(1) rational numbers can be used to estimate the approximate range of an irrational number, and the sizes of rational numbers will be compared. (2) Understand the concepts of square root, arithmetic square root and cube root.

(3) Master the operations of addition, subtraction, multiplication, division, multiplication and root of real numbers, and simplify the operations by using the algorithm. (4) Be able to reasonably explain and infer information containing numbers, express numbers with larger or smaller absolute values by scientific notation, and understand the concepts of divisor and significant number.

(5) Understand the corresponding relationship between points on the number axis and real numbers, and use the number axis to understand the meaning of the opposite number and absolute value (the absolute value symbol does not contain letters) 2. Algebraic expression.

(1) Algebraic expression According to the actual situation, we can explain the practical significance of simple algebraic expression and find the value of algebraic expression. (2) Understand the concept of algebraic expression, and perform simple algebraic addition, subtraction, multiplication and division operations (polynomial multiplication is limited to linear multiplication).

(3) I will derive the multiplication formula, and I will use the multiplication formula for simple operations (using the formula directly for no more than two times). (4) I will use the common factor method and the formula method (directly using the formula for no more than two times) for factorization.

(5) To understand the concept of fractions, we can use the basic properties of fractions to perform subtraction and division, and we can also perform simple operations of addition, subtraction, multiplication and division of fractions.

(6) Understand the concept of quadratic radical. (2) Equations and inequalities 1, equations and equations

(1) can be used to solve linear equations of one variable, simple linear equations of two variables and fractional equations that can be transformed into linear equations of one variable (there are no more than two fractions in the equations).

(2) We can use factorization method, formula method and collocation method to solve a simple quadratic equation with digital coefficients.

(3) According to the quantitative relationship of specific problems, equations or equations can be listed, and empirical equations are effective mathematical models to describe the real world.

(4) According to the practical significance of specific problems, the solution of an equation (group) can be estimated by observation, drawing or calculation, which will test whether the result is reasonable. 2. Inequalities and inequality groups (1) Understand the basic properties of inequalities.

(2) Can solve simple linear inequalities (groups), and can indicate that the solutions are set on the number axis.

(3) According to the quantitative relationship of specific problems, one-dimensional linear inequalities can be listed to solve simple practical problems (3) Function 1, function.

(1) will discuss the quantitative relationship and variation law in specific problems. (2) Understand the concept of function.

(3) Simple functional relationships with practical significance can be expressed by one or more of list method, image method and analytical method.

(4) We can determine the range of independent variables of a function in simple practical problems and find the function value; (5) To be able to make a preliminary prediction of the variation law of variables in combination with the function relationship; 2. Linear function.

(1) Understand the meaning of the linear function, and determine the analytical formula of the linear function according to the known conditions and specific conditions. (2) Draw the image of the linear function, understand the image of the linear function and its properties. (3) Find the approximate solution of the equations according to the image of the linear function. (4) Use the knowledge of the linear function to solve practical problems. (3) Inverse proportional function.

(1) Understand the meaning of inverse proportional function, and determine the relationship of inverse proportional function according to the known conditions and specific conditions. (2) Draw a schematic diagram of the inverse proportional function image, and use the image to understand the properties of the quadratic function and determine the top of the function.

Point, opening direction and symmetry axis

(3) We can use the image of quadratic function to find the approximate solution of quadratic equation in one variable. (4) We can use the knowledge of quadratic function to solve simple practical problems.

Second, space and graphics (4) Understanding of graphics 1, a preliminary understanding of graphics

(1) will compare and estimate the size of angles, and calculate the sum and difference of angles, conversion degree and points. (2) Understand the bisector of the angle and its properties.

(3) Understand complementary angles, complementary angles, right angles and related properties.

(4) Understand the vertical lines, vertical line segments, median vertical lines of line segments and their properties (5) Grasp the properties and judgment methods of parallel lines.

(6) Understand the meaning of the distance between two points, the distance between a point and a straight line and the distance between two parallel lines, and measure or calculate these distances. Step 2: Triangle

(1) Understand the related concepts of triangle (inner angle, outer angle, midline, height, angle bisector and midline) and master the related properties (2) Understand the relationship among the three sides of triangle and the stability of triangle and its simple application (3) Understand the concept of congruent triangles and master the properties and judgment methods of two congruent triangles.

(4) Understand the concepts of isosceles triangle, equilateral triangle and right triangle, and master the related properties and discrimination methods. (5) Solving simple practical problems with Pythagorean theorem and its inverse theorem. 3. Quadrilateral

(1) Understand the formula of the sum of internal angles and external angles of multiple deformations, and understand the concept of regular polygons.

(2) Grasp the concepts of parallelogram, rectangle, rhombus and square, their related properties and discrimination methods; (3) Understand trapezoid and its related concepts, the properties and discrimination methods of isosceles trapezoid; (4) Understand the instability of quadrilateral and its simple application, and understand the relationship between special quadrilaterals; (5) You can use triangle, quadrilateral or regular hexagon for simple mosaic design. 4.

(1) Understand the circle and its related concepts, the relationship between arc, chord and central angle, and the positional relationship between point and circle, straight line and circle, and circle and circle.

(2) Understand the relationship between fillet and central angle, and understand the relative characteristics of fillet and diameter.

(3) Understand the inner and outer centers of triangles

(4) Understanding the concept of tangent and mastering the relationship between tangent and tangent radius will determine whether a straight line is tangent to a circle.

(5) can calculate the arc length and the area of the fan, and can calculate the transverse area and the total area of the cone. 5. Drawing and scale drawing (1).

With the help of straightedge, triangular ruler, protractor and other tools, complete the following figure: (1) Draw a vertical line after one point; Draw a parallel line of this straight line through a point outside the known straight line; Can draw the bisector, midline and height of any triangle; Tangent line of a circle passing through a point on the scale (2).

Will use a ruler to draw to complete the following basic drawing; Make a line segment equal to a known line segment; Make an angle equal to a known angle; The bisector of the angle; Perpendicular bisector as a line segment; Can draw and make simple plane figures with a ruler (you don't have to write what you know, how to do it, how to do it, just leave traces of painting) 6. Views and development diagrams.

(1) can draw three views of basic geometry (straight prism, cylinder, cone and sphere), judge three views of simple objects, and describe basic geometry or physical prototype according to the three views.

(2) Understand the plane development diagram of the cube, understand the side development diagram of the right-angled prism and cone, and identify the three-dimensional figure according to the development diagram.

(3) Understand the relationship between basic geometry and its three views, expanded drawings (except spheres) (5) Graphics and transformation.

Axis symmetry, translation and rotation of 1. graph

(1) Understand the symmetry, translation and rotation, and understand their basic properties. (2) Explore the transformation relationship between simple figures.

(3) Mastering the axial symmetry and related properties of isosceles triangle, rectangle, diamond, isosceles trapezoid, regular polygon and circle (4) Using axial symmetry, translation, rotation and their combinations to carry out simple pattern design (2) Similarity of graphics.

(1) Understand the basic properties of proportion, understand the proportion of line segments, and make proportional line segments.

(2) Understand similar figures and know that the corresponding angles of similar polygons are equal, the corresponding edges are multiplied by the ratio, and the area ratio is equal to the square of the corresponding edge ratio.

(3) Understand the concept of similarity between two triangles, master the conditions of similarity between two triangles, and use the similarity of graphics to solve a problem.

Some practical problems

(4) Understand the similarity of a graph and use it to enlarge or reduce a graph; (5) Understand the acute trigonometric function.

(6) Being able to use trigonometric functions to solve practical problems related to right triangles (6) Graphics and coordinates.

1. In the plane rectangular coordinate system, the position of the point will be tracked according to the coordinates, and its coordinates will be written from the position of the point. 2. A suitable plane rectangular coordinate system can be established on the grid paper to describe the position of the object. 3. In the same plane rectangular coordinate system, the coordinates of the transformed points will be determined. 4. The position of the object will be determined in different ways. (7) graphics and proof.

1. Understand the meaning of proof, the meaning of definitions, propositions and theorems, and the conditions and conclusions that can distinguish propositions. 2. Understand the concept of inverse proposition, and know two reciprocal propositions, and understand that the original proposition is true, but its inverse proposition is not necessarily true. 3. Master the format of comprehensive proof, understand the process of proof, and use the definitions, axioms and theorems related to straight lines, triangles and quadrangles to prove step by step.

Three. Statistics and Probability (8) Statistics

1, can sort out, describe and analyze the data, can point out the whole, individual and sample, and realize that different samples may get different results.

2. Know the mode, median, average, weighted average, range and variance of the sample, estimate the average and variance of the population with the average and variance of the sample, and explain the concentration and dispersion of the data with appropriate statistics. 3. Understand the concepts of frequency and frequency, and understand the significance and function of frequency distribution.

4. I can use fan-shaped statistical charts to represent data, draw fan-shaped statistical charts, bar-shaped statistical charts, frequency distribution histograms and frequency line charts, make frequency distribution tables, and use them to solve simple practical problems.

5. I will get data information from practical problems, express my opinions in the process of analyzing data, make reasonable judgments and predictions according to statistical results, and solve simple practical problems (9) Probability.

1. In order to understand the meaning of probability, we will use enumeration method (including list and tree diagram) to calculate the probability of simple time. 2. Understand that the frequency of repeated experiments can be used as an estimate of probability. We can use probability to solve relatively simple practical problems.

Examination form and examination paper structure

Examination form: closed-book written examination is adopted in mathematics academic examination. Test paper structure: full score of the whole paper 120, and examination time 120 minutes.

Test paper types include multiple-choice questions, fill-in-the-blank questions, solution questions (calculation questions, drawing questions, short-answer questions, argumentative questions, comprehensive questions, etc. ). The multiple-choice question is a single-choice question of "four choices"; Fill in the blanks directly with the results, without writing out the calculation process or reasoning process; Calculation questions require clear main calculation process and accurate calculation results; Drawing questions should be answered in concise and clear language; Argumentative questions require clear cause and effect of logical reasoning; The comprehensive questions will be asked in sections and answered step by step according to the meaning of the questions. All the answers are written on the answer sheet.

Numbers and algebra account for about 46%, space and graphics for about 42%, and statistics and probability account for about 12%. Practice and comprehensive application are included in the first three areas.

The test questions are divided into easy questions, difficult questions and difficult questions, and the score ratio is about 7: 2: 1.

You need to bring a ruler, a triangular ruler, a protractor and a compass for the math academic exam, and draw with a black gel pen.