Inverse proportional function of ninth grade mathematics knowledge points
A function in the form of y = k/x (where k is a constant, k≠0, x≠0, y≠0) is called an inverse proportional function.
The range of the independent variable x is all real numbers that are not equal to 0.
Inverse proportional function image properties:
The image of the inverse proportional function is a hyperbola.
Since the inverse proportional function belongs to odd function, let f(-x)=-f(x), and the image is symmetrical about the origin.
In addition, from the analytical formula of inverse proportional function, it can be concluded that any point on the image of inverse proportional function is perpendicular to two coordinate axes, and the rectangular area surrounded by this point, two vertical feet and the origin is a constant, which is ∣k∣.
When K>0, the inverse proportional function image passes through one or three quadrants, which is a decreasing function (that is, Y decreases with the increase of X).
When k < 0, the inverse proportional function image passes through two or four quadrants, which is increasing function (that is, y increases with the increase of x).
Because the independent variable and dependent variable of the inverse proportional function cannot be zero, the image can only approach the coordinate axis infinitely, and cannot intersect the coordinate axis.
1. Any point on the inverse proportional function image is a vertical line segment of two coordinate axes, and the area of the rectangle surrounded by these two vertical line segments and coordinate axes is |k|.
2. For hyperbola y=k/x, if you add or subtract any real number on the denominator (that is, y = k/x (x m) m is constant), it is equivalent to translating the hyperbola image to the left or right by one unit. (When adding a number, move to the left, and when subtracting a number, move to the right)
Factorial decomposition method of mathematics review materials in grade three
1. cross multiplication
(1) decompose quadratic coefficient and constant term into factors respectively;
(2) try the cross chart, so that the sum of the numbers obtained by multiplying the cross lines is the first-order coefficient;
(3) Determine the appropriate crossplot and write the results of factorization;
(4) inspection.
2. Common factor method
(1) Find the common factor;
(2) Put forward the common factor and determine another factor;
① To find the common factor, we can first determine the coefficient, and then determine the letters according to the method of determining the common factor;
(2) common factor and determining another factor. When determining another factor, you can divide the original polynomial by the common factor, and the obtained quotient is the quotient left after dividing one factor by the common factor. You can also divide each term of the original polynomial by the common factor to find the remaining other factor.
(3) After extracting the common factor, the number of terms of another factor is the same as that of the original polynomial.
3. The undetermined coefficient method
(1) The general analytical formula for determining the undetermined coefficient;
(2) According to the identity condition, a group of undetermined coefficient equations are listed;
(3) Solve the equation or eliminate the undetermined coefficient, thus solving the problem.
Math learning methods and skills: Math learning method one in grade three.
Let's go to class Prepare textbooks, notebooks and other stationery needed for class before class, and take time to simply recall and review what you learned last class. We should go to class with a strong thirst for knowledge, hoping to learn new knowledge from teachers and solve new problems in class. You should listen attentively in class. As soon as the bell rings, you should immediately enter an active learning state and consciously eliminate all kinds of distractions. When listening to the class, you should look up, keep your eyes on the teacher's every move, and listen attentively to every word of the teacher. We should firmly grasp the teacher's thinking, pay attention to the logic of the teacher's narration of the problem, how the problem is raised, and analyze the methods and steps to solve the problem. Classroom is the key link to understand and master basic knowledge, skills and methods. "Learning is not enough", students who have taught themselves before class can concentrate more, and they know where to be detailed and where to omit; Where to carve carefully, where to pass by and where to record, instead of copying all the records, pay attention to one thing and lose another.
Listening in class is very important, and 45 minutes should be effective: don't think I'm joking, who can't listen in class? Actually, it's not. By listening, I mean listening completely, seriously and carefully. For every formula and theorem that the teacher talks about in class, we should go deep into its source, so that even if we forget the formula in the exam, we can solve the problem well and avoid inner panic and tension. In addition, we should make full use of the short 45 minutes in class and try our best to absorb the knowledge learned in class, so as to further carry out the next step of study after returning home and save time.
Math learning methods of grade three II
It is also important to be careful when reading the questions. I think everyone has this experience. When I did the problem, I didn't work it out for a long time. Perhaps I inadvertently glanced at the question, or was reminded by my teachers and classmates, and suddenly found that there were some conditions or relationships. Therefore, the questions will be easily solved soon. Unclear examination of the questions will often lead to wrong results or waste of time, especially in the exam, when time is wasted, it is very likely that the questions are not finished, resulting in loss of points.
Consolidate the foundation in an all-round way: grasp the problem-solving law of choosing fill-in-the-blank questions and ensure that the basic part gets full marks in previous exams, that is, get the full marks you deserve. In a round of review, all students should concentrate on getting through the basic barrier of choosing fill-in-the-blank questions, otherwise the college entrance examination will be very sad 100. In reality, many students have devoted themselves to aimless, varied and varied questions from the beginning. In order to achieve this goal in a round of review, students with poor foundation can take the initiative to give up large-scale complex exercises and put the saved time and energy back into choosing fill-in-the-blank questions to further consolidate their foundation; Students with a good foundation should not focus too much and mainly on solving problems in a large area, but should study one or two big problems in detail in a small amount every day, but by topic and stage, and gradually accumulate experience and rules in solving problems, and must not spread out a lot. We should know that the accumulation of problem-solving experience and law is a long process from quantitative change to qualitative change, and persistence is more important than influence.
Math learning method three in grade three
Read more examples: careful friends will find that after explaining the basic content, the teacher will always give us some extra-curricular examples and exercises, which is of great benefit. The concepts and theorems we learn are generally abstract. To concretize them, we need to apply them to the theme. Because we have just come into contact with this knowledge, we are not skilled enough to use it. At this time, examples will be of great help to us. You can look at examples. Let the understanding of knowledge be more profound and thorough, because the examples added by teachers are very limited, so we should also find some examples ourselves, and pay attention to the following points:
You can't just look at the skin, not the connotation. When we look at examples, we should really master their methods and establish a broader idea of solving problems. If we look at something, we will lose its original meaning. Every time we look at a topic, we should sort out its thinking and master its thinking method. When we encounter similar topics or topics of the same type, we will have a general impression in our hearts and it will be easy to do it.
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