Summarize the knowledge points of mathematics (practical) in the first grade of junior high school.
The concept of (1) number axis: The straight line defining the origin, positive direction and unit length is called number axis.
Three elements of the number axis: origin, unit length and positive direction.
(2) Points on the number axis: All rational numbers can be represented by points on the number axis, but not all points on the number axis represent rational numbers. Generally, the right direction is the positive direction, and the points on the number axis correspond to any real number, including irrational numbers.
(3) Compare the size with the number axis: Generally speaking, when the number axis is to the right, the number on the right is always greater than the number on the left.
Countdown knowledge point
(1) The concept of antipodal: Only two numbers with different symbols are called antipodal.
(2) The meaning of opposites: Grasp that opposites appear in pairs and cannot exist alone. From the number axis, except 0, they are two mutually opposite numbers, both on both sides of the origin, and the distance from the origin is equal.
(3) Simplification of multiple symbols: No matter the number of "+",the odd number of "﹣" is negative and the even number of "﹣" is positive.
(4) Summary of conventional methods: The way to find the reciprocal of a number is to add "﹣" in front of this number. For example, the reciprocal of A is ﹣a, and the reciprocal of m+n is ﹣(m+n). At this time, m+n is a whole. When you put a minus sign before an integer, use parentheses.
The Function of Triangle Mean Value Theorem
Position relation: It can be proved that two straight lines are parallel.
Quantitative relationship: it can prove the doubling relationship of line segments.
Common conclusion: Any triangle has three median lines, from which there are:
Conclusion 1: Three median lines form a triangle, and its circumference is half that of the original triangle.
Conclusion 2: Three median lines divide the original triangle into four congruent triangles.
Conclusion 3: Three median lines divide the original triangle into three parallelograms with equal areas.
Conclusion 4: A midline of the triangle is equally divided with the intersecting midline.
Conclusion 5: The included angle between any two median lines in a triangle is equal to the vertex angle of the triangle corresponding to this included angle.
Note: Important auxiliary lines: (1) and the midpoint of the midpoint form the midline; (2) Double the center line; (3) Add auxiliary parallel lines.
Properties of isosceles triangle
The property theorem of (1) isosceles triangle and its inference;
Theorem: The two base angles of an isosceles triangle are equal (abbreviated as equilateral corners).
Inference 1: The bisector of the top angle of an isosceles triangle bisects the bottom and is perpendicular to the bottom. That is, the bisector of the top angle of the isosceles triangle, the median line on the bottom edge and the height coincidence on the bottom edge.
Inference 2: All angles of an equilateral triangle are equal, and each angle is equal to 60.
(2) Other properties of isosceles triangle:
① The two base angles of an isosceles right triangle are equal, equal to 45.
② The base angle of an isosceles triangle can only be an acute angle, not an obtuse angle (or a right angle), and the top angle can be an obtuse angle (or a right angle).
③ Trilateral relationship of isosceles triangle: Let the waist length be A and the bottom length be B, then
④ Triangle relation of isosceles triangle: Let the top angle be ∠A and the bottom angles be ∠B and ∠C, then ∠ A = 180-2 ∠ B, ∠ B = ∠ C.
Judgement Theorem of Triangle Congruence
(1) Edge Theorem: Two edges and two triangles with identical included angles (abbreviated as "edge" or "SAS").
(2) Angle theorem: Two triangles have two angles, and their clamping edges are congruent (can be abbreviated as "angle" or "ASA").
(3) Edge Theorem: Two triangles corresponding to three equal sides are congruent (can be called "edge" or "SSS" for short).
Determination of congruence of right triangle;
For special right-angled triangles, there is also HL theorem (hypotenuse and right-angled edge theorem): two right-angled triangles with hypotenuse and a right-angled edge are the same (can be abbreviated as "hypotenuse, right-angled edge" or "HL").
Expanding reading: methods and skills of previewing mathematics learning.
In the unit preview, we can read roughly, understand the learning content in the recent stage, read carefully in the classroom preview, pay attention to the formation process of knowledge, and record the concepts, formulas and laws that are difficult to understand, so that we can listen to the class with questions.
Listen carefully in class.
Listening to lectures should include listening, thinking and remembering. Listen, listen to the ins and outs of the formation of knowledge, listen to the key and difficult points, and listen to the answers and requirements of examples. Thinking, one is to be good at association, analogy and induction, and the other is to dare to question and ask questions. Taking notes means taking notes in class-methods, doubts, requirements and precautions.
earnestly solve a problem
Classroom exercises are the most timely and direct feedback, and must not be missed. Don't rush to finish your homework, look at your notebook first, review your learning content, deepen your understanding and strengthen your memory.
Timely error correction
Classroom exercises, homework, tests and feedback should be consulted in time, the causes of wrong questions should be analyzed, and relevant calculation training should be strengthened when necessary. Ask your classmates and teachers if you don't understand. Don't let the problem hang in the air. Get into the good habit of doing things today.
Learn to summarize
Mathematics and mathematics are closely related, and so is knowledge. Summing up by stages can not only play a role in reviewing and consolidating, but also find the connection between knowledge, so as to achieve a thorough understanding.
Learn to manage
Manage your notebook, exercise book, correction book, and all the exercises and papers you have done. Teacher Feng said that this is the most useful material for reviewing the final exam and must not be ignored.
To improve the quality of lectures, it is necessary to cultivate the habit of listening and understanding lectures. Pay attention to the learning emphasis emphasized by the teacher in each class, the introduction and derivation methods and processes of theorems, formulas and rules, the tips and treatment methods of key parts of examples, the explanation of difficult problems, and the final summary of a class. In this way, grasping the important and difficult points and attending classes along the process of knowledge development can not only improve the efficiency of attending classes, but also change from "listening" to "listening".