Knowledge point induction in the second volume of mathematics in the second day of junior high school
linear function
First, the concept of proportional function and linear function:
Generally, a function in the form of y = kx (where k is a constant and k≠0) is called a proportional function, where k is called a proportional coefficient.
Generally, a function in the form of y = kx+b (where k and b are constants and k≠0) is called a linear function.
When b=0, y=kx+b is y=kx, so the proportional function is a special case of linear function.
Second, the image and properties of the proportional function:
(1) image: the image of the proportional function y=kx(k is a constant, k≠0) is a straight line passing through the origin, and we call it straight line y=kx.
(2) Properties: when k >; 0, the straight line y=kx rises from left to right through the third quadrant, that is, y increases with the increase of x; When k0, b>0 images pass through the first, second and third quadrants;
(2)k & gt； 0, b<0 image passes through the first, third and fourth quadrants;
(3)k & gt； 0, b=0 image passes through the first and third quadrants;
(4)k & lt； 0, b>0 image passes through the first, second and fourth quadrants;
(5)k & lt； 0, b<0 image passes through two, three and four quadrants;
(6)k & lt； 0, b=0 The image passes through two or four quadrants.
Determination of linear function expression
When solving the linear function y=kx+b(k and b are constants, k≠0), two points need to be determined; When finding the proportional function y=kx(k≠0), only one point is needed.
5. Linear functions and binary linear equations:
solve an equation
From the "number" point of view, when the independent variable (x) is a value, the values of the two functions are equal.
Find this function value
Solve the equation and determine the coordinates of the intersection of two straight lines from the perspective of shape.
data analysis
Representatives of data: mean, mode, median, range and variance.
Summary of eighth grade mathematics knowledge points
Function and its related concepts
1, variables and constants
In a certain change process, the quantity that can take different values is called a variable, and the quantity whose value remains unchanged is called a constant.
Generally speaking, there are two variables, X and Y, in a certain change process. If for each value of X, Y has a definite value corresponding to it, then X is an independent variable and Y is a function of X. ..
2. Resolution function
The mathematical formula used to express functional relationship is called resolution function or functional relationship.
The whole set of values of independent variables that make a function meaningful is called the range of independent variables.
3. Three representations of functions and their advantages and disadvantages.
(1) analysis method
The functional relationship between two variables can sometimes be expressed by an equation containing these two variables and the symbols of digital operations. This representation is called analytical method.
(2) List method
A series of values of the independent variable x and the corresponding values of the function y are listed in a table to represent the functional relationship. This representation is called list method.
(3) Image method
The method of expressing functional relations with images is called image method.
4. General steps of drawing images with resolution function.
(1) List: List gives some corresponding values of independent variables and functions.
(2) Point tracking: Take each pair of corresponding values in the table as coordinates, and track the corresponding points on the coordinate plane.
(3) Connection: according to the order of independent variables from small to large, connect the tracked points with smooth curves.
Mathematics learning methods and skills
orderly
Mathematics is an interlocking subject, and any link will affect the whole learning process. Therefore, don't be greedy when studying. You should pass the exam chapter by chapter, and don't leave questions that you don't understand or understand deeply easily.
Emphasize understanding
Concepts, theorems and formulas should be memorized on the basis of understanding. Every time you learn a new theorem, first try to do an example without looking at the answer to see if you can correctly apply the new theorem; If not, compare the answers to deepen the understanding of the theorem.
basic skill
You can't learn mathematics without training. Usually do more exercises with moderate difficulty. Of course, don't fall into the misunderstanding of dead drilling questions, be familiar with the questions of the college entrance examination, and be targeted in training.
Pay attention to mistakes
Booking the wrong book and collecting the wrong questions by yourself is often your weakness. When reviewing, this wrong book has become a valuable review material.
Mathematics learning is a step-by-step process, and it is unrealistic to dream of reaching the sky in one step. After reciting the contents of the book, carefully write the exercises at the back of the book. Some students may think that the exercises after the book are too simple to do. This idea is highly undesirable. The function of the exercises after the book is not only to help you remember the contents in the book, but also to help you standardize the writing format, make your problem-solving structure compact and tidy, make proper use of formulas and theorems, and reduce unnecessary marks in the exam.
Articles on knowledge points in the second volume of eighth grade mathematics published by Jiangsu Education Publishing House;
★ The final examination paper of the second volume of mathematics in the second day of junior high school of Jiangsu Education Edition.
★ Su Jiaoban Grade 8 Mathematics Volume 2 Final Examination Paper
★ The second volume of the eighth grade physics Su Jiaoban knowledge points.
★ Knowledge points of the third grade mathematics Su Education Edition
★ Encyclopedia of Mathematics Learning Methods in Different Grades
★ Jiangsu Education Press, eighth grade mathematics textbook, Volume II, answer reference.
★ Encyclopedia of Mathematics Learning Methods in Different Grades
★ The eighth grade mathematics teaching plan Volume II Su Jiaoban
★ Answers to exercises in the second volume of the eighth grade mathematics textbook published by Jiangsu Education Press