Induction of mathematical knowledge points in the last semester of senior two.
Axisymmetric graphics:
A figure is folded in half along a straight line, and the parts on both sides of the straight line can completely overlap. This straight line is called the axis of symmetry. Points that coincide with each other are called corresponding points.
1, axisymmetric:
Two figures are folded in half along a straight line, and one of them can completely coincide with the other. This straight line is called the axis of symmetry. Points that coincide with each other are called corresponding points.
2, the difference and connection between axisymmetric graphics and axisymmetric:
(1) difference. Axisymmetric graphics discuss "the symmetrical relationship between graphics and straight lines"; Axisymmetry discusses "the symmetrical relationship between two figures and a straight line".
(2) contact. Axisymmetric figures are defined as "the parts on both sides of the axis of symmetry are regarded as two figures". Axisymmetric "two figures as a whole" is an axisymmetric figure.
3, the essence of axial symmetry:
(1) Two symmetric graphs are congruent.
(2) The symmetry axis is perpendicular to the line segment connecting the corresponding points.
(3) The distances from the corresponding points to the symmetry axis are equal.
(4) The connecting lines of the corresponding points are parallel to each other.
Third, use coordinates to represent the axis symmetry.
1, and the coordinates of the point (x, y) which is symmetrical about x axis are (x,-y);
2. The coordinates of the point (x, y) about the Y axis symmetry are (-x, y);
3. The coordinates of the point (x, y) symmetrical about the origin are (-x, -y).
4. About the symmetry of the bisector of the coordinate axis.
The point P(x, y) is symmetrical about the bisector y=x of the first and third quadrant coordinate axes, and the coordinate of this point is (y, x).
The point P(x, y) is symmetrical about the bisector y=-x of the second and fourth quadrant coordinate axes, and the coordinate of this point is (-y, -x).
Knowledge point induction in the second volume of mathematics in the second day of junior high school
The first chapter scores
The numerator and denominator of 1 fraction and their basic properties are multiplied (or divided) by an algebraic expression that is not equal to zero at the same time, but the fraction remains unchanged.
Fractional operation of 2
(1) The law of multiplication, division and multiplication of fractions: Fractions are multiplied by fractions, the product of molecules is the numerator of the product, and the product of denominator is the denominator of the product. Law of division: a fraction is divided by a fraction, and the numerator and denominator of division are multiplied by the divisor in turn.
(2) Law of fractional addition and subtraction: fractional addition and subtraction with the same denominator, and numerator addition and subtraction with the same denominator; Fractions with different denominators are added and subtracted, first divided by fractions with the same denominator, and then added and subtracted.
Addition, subtraction, multiplication and division of exponential powers of three integers
4- Fractional Equation and Its Solution
Chapter II Inverse Proportional Function
Expressions, images and properties of 1 inverse proportional function
Image: hyperbola
Expression: y=k/x(k is not 0)
Nature: the increase and decrease of the two branches are the same;
2 the application of inverse proportional function in practical problems
Chapter III Pythagorean Theorem
Pythagorean Theorem of 1: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.
2 Pythagorean Theorem Inverse Theorem: If the sum of squares of two sides in a triangle is equal to the square of the third side, then the triangle is a right triangle.
The fourth chapter quadrilateral
1 parallelogram
Attribute: equilateral; Diagonally equal; Divide diagonally.
Judgment: two groups of quadrangles with equal opposite sides are parallelograms;
Two groups of quadrangles with equal diagonal are parallelograms;
Quadrilaterals whose diagonals bisect each other are parallelograms;
A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
Inference: The midline of a triangle is parallel to the third side and equal to half of the third side.
Special parallelogram: rectangle, diamond and square.
(1) rectangle
Properties: All four corners of a rectangle are right angles;
Diagonal lines of rectangles are equal;
A rectangle has all the characteristics of a parallelogram.
Judgment: a parallelogram with a right angle is a rectangle; Parallelograms with equal diagonals are rectangles;
Inference: The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
(2) The nature of the diamond: all four sides of the diamond are equal; Diagonal lines of the rhombus are perpendicular to each other, and each diagonal line bisects a set of diagonal lines; A diamond has all the characteristics of a parallelogram.
Judgment: A set of parallelograms with equal adjacent sides is a diamond; Parallelograms with diagonal lines perpendicular to each other are rhombic; A quadrilateral with four equilateral sides is a diamond.
(3) Square: It is both a special rectangle and a special diamond, so it has all the properties of a rectangle and a diamond.
Trapezoid: right-angled trapezoid and isosceles trapezoid.
Isosceles trapezoid: two angles on the same bottom of isosceles trapezoid are equal; The two diagonals of isosceles trapezoid are equal; A trapezoid with two equal angles on the same base is an isosceles trapezoid.
Math learning skills in grade two of junior high school
The cultivation of self-study ability is the only way to deepen learning.
When learning new concepts and operations, teachers always make a natural transition from existing knowledge to new knowledge, which is the so-called "reviewing the past and learning the new". Therefore, mathematics is a subject that can be taught by itself, and the most typical example of self-study is mathematician Hua.
We listen to the teacher's explanation in class, not only to learn new knowledge, but more importantly, to subtly influence the teacher's mathematical thinking habits and gradually cultivate our own understanding of mathematics.
The stronger the self-study ability, the higher the understanding. With the growth of age, students' dependence will be weakened, while their self-learning ability will be enhanced. So we should form the habit of previewing.
Therefore, solid mathematics learning in the past laid the foundation for future progress, and it is not difficult to learn new lessons by yourself. At the same time, when preparing a new lesson, it goes without saying that it is great to listen to the teacher explain the new lesson with questions when you encounter any problems that you can't solve.
Learn to learn, knowledge is still someone else's. The test of whether you can learn math well is whether you can solve problems. Understanding the definitions, rules, formulas and theorems related to memory is only a necessary condition for learning mathematics well, and being able to solve problems independently and correctly is the symbol of learning mathematics well.
Confidence can make you stronger.
In the exam, I always see that some students have a lot of blanks in their papers, but they haven't done a few questions at all. Of course, as the saying goes, art is bold, art is not timid. However, it is one thing to fail, and it is another thing to fail. The solution and result of a slightly more difficult math problem are not obvious at a glance. It is necessary to analyze, explore, draw, write and calculate. After tortuous reasoning or calculation, some connection between conditions and conclusions will be revealed and the whole idea will be clear.
When solving a specific problem, we must carefully examine the problem, firmly grasp all the conditions of the problem, and don't ignore any one. There is a certain relationship between a problem and a class of problems. We can think about the general idea and general solution of this kind of problem, but it is more important to grasp the particularity of this problem and the difference between this problem and this kind of problem. There are almost no identical problems in mathematics, and there are always one or several different conditions, so the process of thinking and solving problems is not the same. Some students and teachers can do the questions they have talked about, while others can't. They just talk about the matter and stare at some small changes in the problem, and they can't start.
The topics of mathematics are infinite, but the ideas and methods of mathematics are limited. As long as we learn the basic knowledge well and master the necessary mathematical ideas and methods, we can successfully deal with endless problems. The topic is not to do more, the better. The ocean of topics is endless, and you will never finish reading it. The key is whether you have cultivated good mathematical thinking habits and mastered the correct mathematical problem-solving methods.
Solving problems requires rich knowledge and more confidence. Without self-confidence, you will be afraid of difficulties and give up; With self-confidence, we can forge ahead, not give up easily, study harder, and hope to overcome difficulties and usher in our own spring.
Articles about the knowledge points of mathematics in the eighth grade of junior high school;
★ Sort out and summarize the knowledge points of eighth grade mathematics.
★ Summary of knowledge points in the first volume of eighth grade mathematics published by People's Education Press
★ Mathematics knowledge points in the first volume of the eighth grade of junior high school
★ Summary and induction of mathematics knowledge points in the first volume of the eighth grade of junior high school
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★ Review and arrangement of mathematics knowledge points in Grade Two.
★ The arrangement of mathematics knowledge points in the first volume of the eighth grade
★ The first volume of eighth grade mathematics knowledge points