Knowledge points in junior high school mathematics textbooks
mathematical function
1 and three expressions of quadratic function
General formula: y = ax 2+bx+c (a, b and c are constants, and a≠0).
Vertex: y = a(x-h)2+k[ vertex p(h, k) of parabola]
Intersection point: y=a(x-x? )(x-x？ ) [only when it is related to the x axis a(x? , 0) and b(x? 0) parabola]
Note: Among these three forms of mutual transformation, there are the following relations:
h=-b/2ak=(4ac-b^2)/4ax？ ，x？ =(-b √b^2-4ac)/2a
2. Quadratic function image
Making the image of quadratic function y = x 2 in the rectangular coordinate system of mathematical plane, we can see that the image of quadratic function is a parabola.
Four. Properties of parabola
1. The mathematical parabola is an axisymmetric figure. The symmetry axis is a straight line x=-b/2a.
The only intersection of the mathematical symmetry axis and the parabola is the vertex p of the parabola. Especially when b=0, the symmetry axis of the parabola is the Y axis (that is, the straight line x=0).
2. The parabola has a vertex p, and its coordinates are: p(-b/2a, (4ac-b 2)/4a) When -b/2a=0, p is on the Y axis; When δ = b 2-4ac = 0, p is on the x axis.
3. Mathematical quadratic coefficient A determines the opening direction and size of parabola.
When a>0, the parabola opens upwards; When a<0, the parabola opens downward. The larger the |a|, the smaller the opening of the parabola.
4. Both the linear coefficient b and the quadratic coefficient a*** determine the position of the symmetry axis.
When A and B have the same number (ab>0), the symmetry axis is on the left side of Y axis;
When a and b have different numbers (i.e. AB
5. The constant term c determines the intersection of parabola and Y axis.
The parabola intersects the Y axis at (0, c)
Mathematics knowledge points in the new semester of grade three
One-dimensional linear equation:
(1) In an equation, there is only one unknown, and the exponent of this unknown is
1, such an equation is called a linear equation.
② Adding or subtracting or multiplying or dividing (non-0) an algebraic expression on both sides of the equation at the same time, the result is still an equation.
Steps to solve a linear equation with one variable:
Denominator is removed, items are shifted, similar items are merged, and the unknown coefficient is changed to 1.
Binary linear equation: An equation that contains two unknowns and all terms are 1 is called binary linear equation.
Binary linear equations: The equations composed of two binary linear equations are called binary linear equations. A set of unknown values suitable for binary linear equation is called the solution of this binary linear equation. The common * * * solution of each equation in a binary linear system of equations is called the solution of this binary linear system of equations.
Methods of solving binary linear equations: substitution elimination method/addition and subtraction elimination method.
2. Inequality and unequal groups
Inequality:
Formulas connected by "=" symbols are called inequalities.
② Add or subtract the same algebraic expression on both sides of the inequality, and the direction of the inequality remains unchanged.
③ Both sides of inequality are multiplied or divided by a positive number, and the direction of inequality remains unchanged.
④ Both sides of inequality are multiplied or divided by the same negative number, and the unequal numbers are in opposite directions.
Solution set of inequality;
(1) can make the value of an unknown inequality known as the solution of inequality.
(2) All solutions of an inequality with unknowns constitute the solution set of this inequality.
③ The process of finding the solution set of inequality is called solving inequality.
One-dimensional linear inequality: an inequality with algebraic expressions on both sides and only one unknown number of degree 1 is called one-dimensional linear inequality.
One-dimensional linear inequality system;
(1) Several linear inequalities about the same unknown quantity are combined into a linear inequality group.
② The common part of the solution set of each inequality in a linear inequality group is called the solution set of this linear inequality group.
③ The process of finding the solution set of inequality group is called solving inequality group.
Induction of ninth grade mathematics knowledge points
1. Proportional Theorem of Parallel Lines and Its Inference:
Theorem: Three parallel lines cut two straight lines, and the corresponding line segments are proportional.
2. Inference: A straight line parallel to one side of a triangle is directly proportional to the corresponding line segment obtained by cutting the other two sides (or extension lines of both sides).
3. Inference inverse theorem: If the corresponding line segment obtained by cutting two sides of a triangle (or the extension lines of two sides) is proportional, then this line segment is parallel to the third side of the triangle.
Second, the similar preparation theorem:
A straight line parallel to one side of a triangle and intersecting with the other two sides, the three sides of the cut triangle are directly proportional to the three sides of the original triangle.
Third, similar triangles:
1. Definition: A triangle with equal corresponding angles and proportional corresponding sides is called similar triangles.
2. Properties: (1) The angles corresponding to similar triangles are equal;
(2) The line segments corresponding to similar triangles (side, height, midline and angular bisector) are proportional;
(3) The perimeter ratio of similar triangles is equal to the similarity ratio, and the area ratio is equal to the square of the similarity ratio.
Description: ① The area ratio of equal-height triangle is equal to the ratio of bottom, and the area ratio of equal-bottom triangle is equal to the ratio of height; ② Pay attention to the correspondence between two graphic elements.
3. Decision theorem:
(1) Two angles are equal and two triangles are similar;
(2) The two sides are correspondingly proportional, the included angle is equal, and the two triangles are similar;
(3) Three sides are proportional and two triangles are similar;
(4) Two right-angled triangles are similar if the hypotenuse and one right-angled side of one right-angled triangle are directly proportional to the hypotenuse and one right-angled side of another right-angled triangle.
Knowledge points of mathematics review in grade three
Rational number, addition and subtraction of algebraic expression, linear equation of one variable, preliminary understanding of graphics.
(1) rational number: it is the basic content of junior high school mathematics. The scores of the questions in the senior high school entrance examination are about 3-6 points, which mostly appear in the form of multiple-choice questions, fill-in-the-blank questions and calculation questions. The difficulty is simple.
Investigate complex numbers and mixed operations (midterm and final exams), axis, reciprocal, absolute value and reciprocal (multiple choice questions, fill-in-the-blank questions).
(2) Addition and subtraction of algebraic expressions: the score in the middle exam is about 4 points, mainly multiple-choice questions and fill-in-the-blank questions, which are relatively difficult.
Survey content
The concept and simple operation of (1) algebraic expression, mainly the concept and simplified evaluation of similar terms.
② The geometric meaning of complete square formula and square variance formula.
(3) factorization by common factor method and formula method.
(3) One-dimensional linear equation: it is the key content of junior one learning. The main learning contents include (induction, summary and extension) application questions, thinking, steps and questions, and seeking the unknown according to known conditions. The score of the senior high school entrance examination is about 1-3, and the main types of questions are multiple-choice questions and fill-in-the-blank questions, with fewer short answers and easier difficulty.
Survey content
① The concept of equation and its solution
(2) According to the meaning of the question, do a linear equation.
(3) Solve linear equations. Question types: pursuit, encounter, the relationship between time, speed and distance, discount sales, profit formula.
(4) Geometry: angles and line segments, laying the foundation for learning triangles in the next volume.
Collect and describe intersecting lines and parallel lines, real numbers, plane rectangular coordinate systems, binary linear equations, inequalities and inequality groups and databases.
(1) intersection line and parallel line: intersection line and parallel line are common test sites for senior high school entrance examinations over the years. Usually in the form of fill-in-the-blank questions and multiple-choice questions The score is 3-4, which is easy.
Survey content
① Properties of parallel lines (axiom)
② Discrimination method of parallel lines
③ Construct parallel lines and use the properties of parallel lines to solve problems.
(2) Plane rectangular coordinate system: the score in the middle school exam is about 3-4 points, and the multiple-choice questions and fill-in-the-blank questions are the main ones, which are relatively easy.
Survey content
① Coordinate characteristics of inspection points in plane rectangular coordinate system.
(2) The range of the function independent variable and the value of the spherical function.
③ Using images to investigate and analyze the functional relationships in simple practical problems.
(3) Binary linear equations: the score of the senior high school entrance examination is about 3-6 points, which is mainly based on multiple-choice questions and answers, and the difficulty is moderate.
Survey content
(1) Solve the equation, solve the equation.
(2) According to the meaning of the question, a set of binary linear equations is established to solve economic problems.
(4) Inequality and inequality group: the score in the middle school exam is about 3-8 points, and the main points are selection, filling in the blanks and solving problems.
Survey content:
(1) One-dimensional linear inequality (group) solution, number axis representation of inequality (group) solution set, integer solution of inequality (group), etc. , and the question type is mainly to choose and fill in the blanks.
(2) column inequality (group) to solve economic problems, deployment problems, etc. , mainly to solve the problem.
③ Pay attention to the combination of inequality (group) and function image.
(5) Collection and description of database
The general score is 6- 10. In recent years, questions mainly appear in the form of solving problems, and occasionally in the form of choosing to fill in the blanks. The difficulty is moderate.
Summary of knowledge points in the first volume of mathematics teaching materials for grade three;
★ Summary of important knowledge points in the first volume of ninth grade mathematics
★ Summary of mathematical knowledge points in the first volume of Grade Three
★ Summarize the knowledge points of junior high school mathematics.
★ Summarize the knowledge points of mathematics in the first volume of the ninth grade.
★ Summary of mathematical knowledge points in the first volume of the third grade.
★ Summary of mathematics knowledge points in the first volume of the ninth grade
★ Summary of essential knowledge points of junior high school mathematics Chapter I and Chapter II of junior high school mathematics
★ Summary of last semester's study of mathematics in Grade Three.
★ ninth grade mathematics knowledge point book 1
★ Mathematics knowledge points in the first volume of the third grade
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