Quadratic root of knowledge point induction in the first volume of mathematics in grade three
1, quadratic radical
The formula is called quadratic radical, which must satisfy the following requirements: it contains quadratic radical sign ""; The root sign a must be non-negative.
2. The simplest quadratic radical
If the square root satisfies: the factor of the square root is an integer and the factor is an algebraic expression; The square root number contains no factor or can be completely opened. Such a quadratic root is called the simplest quadratic root.
Methods and steps of transforming quadratic form into simplest quadratic form;
(1) If the square root of the quotient is a fraction (including decimals) or a fraction, first use the nature of the arithmetic square root of the quotient to write it in the form of a fraction, and then simplify it with the denominator.
(2) If the number of roots is integer or algebraic expression, first decompose them into factors or factors, and then extract the factors or factors that can be opened to the maximum extent.
3. Similar quadratic roots
After several quadratic roots are transformed into the simplest quadratic roots, if the number of roots is the same, these quadratic roots are called similar quadratic roots.
4. Properties of quadratic roots
5. Quadratic radical mixed operation
The mixed operation of quadratic root is in the same order as that in real number. Multiply first, then divide, and finally add and subtract. If there are brackets, count them first (or remove them first).
monadic quadratic equation
One-dimensional quadratic equation
1, unary quadratic equation
An integral equation with an unknown number and the highest degree of the unknown number is 2 is called a quadratic equation.
2. The general form of quadratic equation with one variable
It is characterized in that there are eleven quadratic polynomials on the left side of the equation about the unknown x, and the right side of the equation is zero, which is called quadratic term, and a is called quadratic term coefficient; Bx is called a linear term, and b is called a linear term coefficient; C is called a constant term.
Second, the solution of a quadratic equation
1, direct Kaiping method
2. Matching method
Matching method is an important mathematical method, which is not only suitable for solving quadratic equations with one variable, but also applied in mathematics.
3. Formula method
4, factorization method
Factorization is to find the solution of the equation by factorization. This method is simple and easy to use, and it is the most commonly used method to solve the quadratic equation of one variable.
Thirdly, the discriminant of the root of a quadratic equation with one variable.
discriminant
Fourthly, the relationship between the roots and coefficients of a quadratic equation with one variable.
Radial
First, rotation
1, definition
The graphic transformation that rotates a graph by an angle around a certain point o is called rotation, where o is called rotation center and the rotation angle is called rotation angle.
2. Nature
(1) The distance from the corresponding point to the rotation center is equal.
(2) The included angle of the connecting line between the corresponding point and the rotation center is equal to the rotation angle.
Second, the center is symmetrical.
1, definition
Rotate the graph around a point 180. If the rotated figure can coincide with the original figure, then this figure is called a central symmetric figure, and this point is its symmetric center.
2. Nature
(1) Two graphs that are symmetric about the center are congruent.
(2) For two graphs with symmetrical centers, the connecting lines of symmetrical points pass through the symmetrical centers and are equally divided by the symmetrical centers.
(3) With respect to two figures with symmetrical centers, the corresponding line segments are parallel (or on the same straight line) and equal.
3. Judges
If a straight line connecting the corresponding points of two graphs passes through a point and is bisected by the point, then the two graphs are symmetrical about the point.
4. Centrally symmetric figure
Rotate the figure around a point 180. If the rotated graph can coincide with the original graph, then this graph is called a central symmetric graph, and this shop is its symmetric center.
Characteristics of symmetrical points in coordinate system;
1, the characteristics of points symmetrical about the origin
When two points are symmetrical about the origin, the signs of their coordinates are opposite, that is, the symmetrical point of point P(x, y) about the origin is P'(-x, -y).
2. About the characteristics of the axisymmetrical point of X axis.
When two points are symmetrical about X axis, in their coordinates, X is equal, and the sign of Y is opposite, that is, the symmetrical point of point P(x, y) about X axis is P'(x, -y).
3. On the characteristics of the point of Y axis symmetry
When two points are symmetrical about Y, Y is equal, and the sign of X is opposite in its coordinates, that is, the point where P(x, y) is symmetrical about Y is P'(-x, y).
Expanding Reading: How to Quickly Improve the Refinement of Time Allocation in Junior Middle School Mathematics
The review of mathematics in senior high school entrance examination should be planned and arranged in advance, and teachers should make detailed and feasible plans according to the teaching practice of the school and the characteristics of students. Generally, new teaching tasks are completed at the end of March, and review for the senior high school entrance examination begins at the beginning of April. At the end of April, complete the first round of "fixed edition" review, comprehensively and systematically review, divide the textbook into units and chapters, review according to the curriculum standards and the instructions for the senior high school entrance examination, strengthen the training of knowledge points, unit chapters and test sites, consolidate the foundation and cultivate basic skills; At the end of May, the second round of "special training" review was completed, laying a solid foundation, building a knowledge network, being organized and systematic, strengthening plate synthesis and special knowledge training, breaking through key and difficult points, highlighting the flexible use of knowledge, and cultivating the ability to solve practical problems. At the same time, we will check the blind spots of knowledge and strengthen training. From the first ten days of June to the senior high school entrance examination, the third round of "comprehensive test" review is completed, with kickbacks and double bases, checking points and filling vacancies, emphasizing comprehensive simulation, strengthening students' test-taking skills and problem-solving methods, and reducing non-intellectual factors.
Recitation of the instructions for the senior high school entrance examination
As a teacher, we should thoroughly study the instructions of the senior high school entrance examination and master the knowledge points and difficulties in the examination outline. When reviewing, teachers should take the requirements in the exam instructions as the basis, pay attention to the review of basic knowledge, do not blindly emphasize the training of difficult questions or digression, but conduct targeted review according to the characteristics of the difficulty of the proposition.
Selection of review materials
Choose good materials and make good use of them when reviewing. At the beginning of review, the teacher will carefully select several materials for students, and after comparison, determine one or two materials with complete knowledge points and moderate difficulty as review books in class. Students should not have too much review materials at hand. If there are too many, they will be confused, which will easily lead to the feeling that they have not finished so much, which will easily lead to the omission of knowledge points and make students feel annoyed. Therefore, teachers should carefully select review materials for students, so that students can understand that math review materials should be precise but not rare.
Basic concept exercises
The review of mathematical concepts is not a simple repetition, but an organic connection between concepts, not a rote memorization, but a solution to practical problems. For example, there are many concepts related to formulas in junior high school mathematics, such as algebra, algebra, monomial, polynomial, similar term, fraction, rational formula, simplest fraction, quadratic root, simplest quadratic root and so on. But one thing is worth affirming. If you want to use these concepts to solve problems, you must first memorize them.