Summary of Mathematics Knowledge Points in Volume II of Grade One of Beijing Normal University Edition
intersection line
One vertex has a common * * *, one side has a common * * *, and the other side is an extension line opposite to each other. Such two angles are called adjacent complementary angles.
There are four pairs of adjacent complementary angles when two straight lines intersect.
There is a vertex with a common * * *, and both sides of the corner are opposite extension lines. These two angles are called antipodal angles.
Two straight lines intersect and have two opposite angles.
The vertex angles are equal.
Two straight lines intersect, and one of the four corners is a right angle, so the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection point is called the vertical foot.
Parallel lines and their determination
Property 1: Two straight lines are parallel and equal to the complementary angle.
Property 2: Two straight lines are parallel and the internal dislocation angles are equal.
Property 3: Two straight lines are parallel and complementary.
Properties of parallel lines
Property 1 Two parallel lines are cut by a third line, and the congruence angles are equal. To put it simply: two straight lines are parallel and have the same angle.
Property 2 Two parallel lines are cut by a third straight line, and their internal angles are equal. To put it simply: two straight lines are parallel and their internal angles are equal.
Property 3 Two parallel lines are cut by a third straight line and complement each other. Simply put, two straight lines are parallel and complementary.
translate
Translate one unit length to the left and you can get the corresponding point (x-a, y).
Translate b unit lengths upwards, and you can get the corresponding point (x, y+b).
By translating down by b unit lengths, the corresponding point (x, y-b) can be obtained.
The second volume of the first day of junior high school mathematics review materials
1, monomial: The product of numbers and letters is called monomial.
2. Polynomial: The sum of several monomials is called polynomial.
3. Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.
4. The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.
5. Degree of Polynomial: The degree of the degree term in a polynomial is the degree of this polynomial.
6. Complementary angle: The sum of two angles is 90 degrees, and these two angles are called complementary angles.
7. Complementary angle: The sum of two angles is 180 degrees, and these two angles are called complementary angles.
8. Relative vertex angles: two corners have a common vertex, and two sides of one corner are opposite to the extension lines of two sides of the other corner. These two angles are antipodal angles.
9. Common angle: In the "three-line octagon", the angles at the same position are common angles.
10, internal angle: in the "three-line octagon", the angle sandwiched between two straight lines is the internal angle.
1 1, ipsilateral inner angle: in "trilinear octagon", the angle on the same side of trilinear is ipsilateral inner angle.
12, significant number: an approximation, starting with the first number on the left that is not 0 and ending with the exact 1, all numbers are significant numbers.
13, probability: the probability of an event is the probability of this event.
14, triangle: A figure composed of three line segments that are not on the same line is called a triangle.
15, Angle bisector of triangle: In a triangle, the angle bisector of an inner angle intersects its opposite side, and the line segment between the intersection of the vertex and this angle is called the angle bisector of triangle.
16, triangle midline: the line segment connecting the vertex and the midpoint of the opposite side of the triangle is called the midline of the triangle.
17. Height line of triangle: Draw a vertical line from one vertex of triangle to the line where its opposite side is located, and the line segment between vertex and vertical foot is called height line of triangle.
18, congruent graphics: two graphics that can overlap are called congruent graphics.
19, variable: the number of changes is called variable.
20. Independent variable: If there is an active change in the amount of change, it is called an independent variable.
2 1, dependent variable: the quantity that changes passively with the change of independent variables is called dependent variable.
22. Axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then this figure
This is called an axisymmetric figure.
23. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.
24. perpendicular bisector: The line segment is an axisymmetric figure, and its symmetry axis is perpendicular to this line segment and divides it into two parts. Such a straight line is called the midline of this line segment. (refers to the middle vertical line)
Six methods and skills to learn math well in grade one.
1, get ready:
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.
2. Listen carefully:
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.
3. Seriously solve the 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.
4, 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.
5, learn to summarize:
Teacher Feng said: "Mathematics is closely related, and knowledge is closely related. 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.
6, 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.
At present, junior high school students have a serious problem in learning mathematics, that is, they are not good at reading mathematics textbooks and often memorize them. Paying attention to reading methods is very important to improve junior high school students' learning ability. To learn a new chapter, first read it roughly, that is, browse the branches of what you have learned in this chapter, then tick while reading, get a general understanding of the content of the textbook and its key points and difficulties, and mark the places you don't understand. Then read carefully, that is, according to the learning requirements of each chapter after the festival, read the content of the textbook carefully, understand the essence of mathematical concepts, formulas, laws and thinking methods and their causal relationship, grasp the key points and break through the difficulties. Read it again as a researcher, that is, discuss the context, structural relationship and arrangement intention of knowledge from the perspective of development, summarize the main points, finish reading the book, form a knowledge network and improve the cognitive structure. When students master these three reading methods and form habits, they can essentially change their learning methods and improve their learning efficiency.
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".
Asking questions is an effective way to improve learning efficiency. In the process of learning, when encountering problems, take the time to ask teachers and classmates, and master the knowledge that you don't understand or learn in the shortest time. Set up your own error book and read it often to remind yourself not to make the same mistake twice. So as to improve the learning efficiency.
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