Looking at the content of junior high school mathematics involves about 200 knowledge points. Specifically, we can start from the following four aspects:

I. Numbers and algebra

1. Sum of numbers

(1) rational number, number axis, reciprocal, absolute value of number, comparison of rational number, addition, subtraction, multiplication and division, power of rational number, arithmetic of addition, subtraction, multiplication and division, simple mixed operation of rational number.

(2) Real numbers:

Square root, arithmetic square root, cube root, irrational number, real number, four operations of real number, divisor, significant number, quadratic root, properties of quadratic root, simplest quadratic root, addition and subtraction of similar quadratic root, multiplication and division of quadratic root, rationalization of denominator.

(3) Algebraic formula:

Algebraic expression. The value of an algebraic expression.

(4) Algebraic expressions and fractions:

Algebraic expression. Merge similar terms. Remove the bracket. Addition and subtraction of algebraic expressions. Multiplication and division of algebraic expressions. Integer exponential power. Scientific symbols.

Multiplication formula: (a+b) (a-b) = A2-B2; (a+b)2= a2+2ab+b2。

Factorization (common factor method, formula method).

Scores. Basic properties of fractions. Scores, general scores. Addition, subtraction, multiplication and Divison of fractions.

2. Equality and inequality

(1) equations and equations;

Equation and its solution. One-dimensional linear equations and their solutions and applications. Two-dimensional linear equations and their solutions and applications. One-dimensional quadratic equation and its solution and application.

Fractional equations that can be reduced to linear equations with one variable (no more than two fractions in the equation) and fractional equations that can be reduced to quadratic equations with one variable (no more than two fractions in the equation).

(2) Inequality and unequal groups:

Inequality. Basic properties of inequality. Solution set of inequality.

One-dimensional linear inequality and its solution and application. One-dimensional linear inequality and its solution and application.

3. Function

(1) function:

Constants, variables, functions and their representations.

(2) A function:

Linear function. Images and properties of linear functions. Approximate solutions of binary linear equations.

(3) Inverse proportional function:

Inverse proportional function. Images and properties of inverse proportional function.

(4) Quadratic function

Quadratic function. Images and properties of quadratic function. Application of quadratic function.

Approximate solution of quadratic equation in one variable.

Second, graphics and geometry.

1. Understanding of graphics

(1) Point, line, surface and angle:

The bisectors of points, lines, surfaces, angles and angles and their properties.

(2) Intersecting lines and parallel lines:

Make up the angle Make up the angle Diagonal

Vertical line. Distance from point to straight line. Perpendicular bisector of line segment and its properties.

Parallel lines. The distance between parallel lines. The nature and judgment of two parallel lines.

(3) Triangle:

Triangle. Angle bisector, median line and height of triangle. The center line of a triangle.

Congruent triangles. Judgement and properties of triangle congruence.

Judgments and properties of isosceles triangle, equilateral triangle, right triangle, pythagorean theorem and inverse theorem.

(4) quadrilateral:

Polygon. The sum of the inner and outer angles of multilateralism. Regular polygon.

Concepts, judgments and properties of parallelogram, rectangle, diamond, square and trapezoid. Mosaic of plane graphics.

(5) Circle:

Round. Symmetry of a circle. The relationship between arc, chord and central angle. The positional relationships between points and circles, straight lines and circles, and circles and central angles. The relationship between the angle of circle and the angle of center. The inner and outer centers of a triangle. The nature and judgment of tangent. Arc length. Sector area. The lateral area and total area of a cone.

(6) ruler drawing:

Basic figures. Draw a triangle with basic drawing method. One point, two points and three points that are not on a straight line intersect to make a circle.

(7) Views and predictions:

Three views of simple geometry. The sides of straight prisms and cones are unfolded. Viewpoint, visual angle, blind area. Central projection and parallel projection.

2. Graphics and transformations

Axis symmetry, translation and rotation of (1) graph;

Axisymmetric. Translation. Spin.

(2) Similarity of graphics:

The basic nature of proportion. The ratio of line segments. Proportional segment.

Similarity and properties of graphs. Judgement and properties of triangle similarity. Similarity of graphs.

Sharp trigonometric function. Trigonometric function values 30, 45, 60. Solve right triangle.

3. Graphics and coordinates

Plane rectangular coordinate system.

4. Graphics and proofs

The meaning of (1) proof:

Definition, proposition, inverse proposition, theorem, theorem proof, reduction to absurdity.

(2) Basic facts:

① Determine a straight line at two points.

② The line segment between two points is the shortest.

There is one and only one straight line perpendicular to this straight line.

④ Two straight lines are cut by a third straight line. If congruent angles are equal, two straight lines are parallel.

⑤ There is one and only one straight line parallel to this straight line at a point outside the straight line.

⑥ A triangle with two sides and an equal included angle is congruent.

⑦ Two triangles with equal palm angles have equal sides.

Two triangles with three equal sides are congruent.

(3) Use the basic facts in (2) to prove the following propositions:

(1) Property theorem of parallel lines (internal dislocation angles are equal and internal angles on the same side are complementary) and judgment theorem (internal dislocation angles are equal or internal angles on the same side are complementary, then two lines are parallel).

(2) Theorem and inference of the sum of internal angles of a triangle (the external angle of a triangle is equal to the sum of two non-adjacent internal angles, and the external angle of a triangle is greater than any non-adjacent internal angle).

(3) Theorem for judging congruence of right triangle.

④ The property theorem and inverse theorem of angular bisector; The three bisectors of a triangle intersect at a point (center).

⑤ The property theorem and inverse theorem of the median vertical line; Perpendicular bisector of three sides of a triangle intersect at one point (outer center).

⑥ Triangle midline theorem.

⑦ Properties and judgment theorems of isosceles triangle, equilateral triangle and right triangle.

Properties and judgment theorems of parallelogram, rectangle, diamond, square and isosceles trapezoid.

Third, statistics.

Data. Data collection, collation, description and analysis.

Sampling. Population. Personal. Sample.

Fan chart, bar chart, line chart and histogram.

Weighted average. Concentration and dispersion of data. Range and variance.

Sample estimates the mean and variance of the population sample.

Statistics and decision making. Data information. The application of statistics in social life and science.

Fourth, probability

The probability enumeration method of events (including lists and drawing trees) calculates the probability of simple events.

Simulation experiment. Estimated value of event occurrence probability when a large number of experiments are repeated.

Using probability knowledge to solve practical problems.

The full mark of the mathematics senior high school entrance examination paper is 120, in which easy questions account for 60 points, intermediate questions account for 35 points and difficult questions account for 25 points, so the key and difficult test sites of the mathematics senior high school entrance examination are very clear.

The easier questions, the intermediate questions are the key points, and the more difficult questions are the difficulties. More than 200 knowledge points are test sites.

Let's analyze the previous senior high school entrance examination papers in Texas and the whole country. There are striking similarities in math test papers. There are several types of questions in the senior high school entrance examination:

1. Multiple choice questions; Fill in the blanks.

2. Algebraic calculation to simplify the evaluation questions.

3. Solve equations or inequalities; Solve equations or inequalities.

4. Equation type and inequality type application problems;

5. Function application questions; Statistical application questions;

6. Certificate congruence; Syndrome similarity;

7. Drawing questions (rarely tested);

8. Proof of equality (equal angle and equal line segment);

9. The evidence is relevant;

10. Parallel problem of syndrome; Longitudinal problem of syndrome;

1 1. Problems related to the relationship between roots and coefficients;

12. Solve the right triangle problem;

13. Calculation of geometry;

14. Comprehensive questions based on circles;

15. Comprehensive questions based on triangles and quadrilaterals;

16. Comprehensive questions based on functions.

The above type1-13 is the key, and14-16 is the difficulty.

In algebra, the senior high school entrance examination questions generally focus on equation-based application questions, linear functions and quadratic functions.

In geometry, the positional relationship between a straight line and a circle and the first part are both important and difficult. The position relationship between circles, the area of sectors and arches, and the surface area of cones and cylinders are essential contents, but they are not the key points.

Mathematics test questions in the senior high school entrance examination generally examine students' abilities in the following aspects:

(1) computing power;

② The ability to abstract practical problems into mathematical problems;

(3) the ability to combine shapes and numbers and transform each other;

④ Spatial imagination;

⑤ Ability to observe, experiment, compare, analyze and synthesize;

⑥ Ability to explore problems;

⑦ Innovation ability.

Among them, items ①-⑤ are the key abilities, and items ⑤ and ⑤ are the difficulties.