Summary of Mathematics Knowledge Points in Volume 2 of Grade One.
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, congruent graphics: two graphics that can overlap are called congruent graphics.
18, variable: the number of changes is called variable.
19, independent variable: the variable is called the independent variable.
20. Dependent variable: The quantity that changes passively with the change of independent variables is called dependent variable.
2 1, 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 is called an axisymmetric figure.
22. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.
The seventh grade volume 202 1 mathematical knowledge points
Probability; possibility
I. Events:
1. Events are divided into inevitable events, impossible events and uncertain events.
2. Inevitable events: events that will definitely happen in advance. In other words, the event must happen every time, and it is impossible not to happen, that is, what may happen is 100% (or 1).
3. Impossible events: events that will definitely not happen in advance. In other words, there is no chance at all, that is, the possibility of occurrence is zero.
4. Uncertain event: it is impossible to determine whether it will happen in advance, that is, the event may or may not happen, that is, the probability of occurrence is between 0 and 1.
Second, equal possibility: refers to the equal possibility of several events.
1. probability: it is a quantity that reflects the possibility of an event. It is a proportional number, generally expressed by p, and P(A)= the number of possible outcomes of event A/all possible outcomes.
2. The probability of the inevitable event is 1, and it is recorded as p (inevitable event) =1;
3. The probability of an impossible event is 0, and it is recorded as p (impossible event) = 0;
4. The probability of uncertain events is between 0 and 1, and it is recorded as 0.
Third, geometric probability.
1, the probability of the occurrence of event A is equal to the area of the possible result of this event A (expressed by SA) divided by the area of the graph of all possible results (expressed by S total), so the geometric probability formula can be expressed as P(A)=SA/S total, because the probability of the occurrence of events in each unit area is the same.
2. Find the geometric probability:
(1) Firstly, analyze the relationship between the area occupied by events and the total area;
(2) Then calculate the area of each part;
(3) Finally, the geometric probability is obtained by substituting into the formula.
Review method of mathematics in grade one of junior high school
Examination is different from homework logic:
Our exams are different from our homework. Some children's homework is ok, and the accuracy is quite high, but their exam results are not ideal. For example, after school, I will write my homework on the day I go home, but the exam is different. It is phased and comprehensive. For example, if you do your homework, you can read the information. If you can't, you can ask your classmates, but you have to rely on yourself in the exam. Also, when writing homework, the format may not be standardized, and it may not meet the standards, but the examination teacher will be very strict; In addition, some children are anxious about exams. Before the exam, mom and dad cheered their children up, but they didn't do well in the exam. Some children even have to go to the toilet before and after the exam to relieve stress and even affect their exam results.
That specifically involves the review of mathematics. I take Beijing Normal University Edition as an example, which is divided into four steps:
Summary of review methods
1 Return to books, organize chapters, conceptual formulas, property theorems, etc.
Just like building a house, whether the foundation of the house is solid or not. For example, in the review class, we ask our children to recite formulas, concepts such as monomials, polynomials and algebras, as well as the operation of powers and the multiplication and division of algebras. We must remember the square difference, complete square formula and deformation. Some children can memorize the complete square formula, but once they use it, they just don't need it. Because I am not skilled enough, I am afraid of making mistakes, so I use the most complicated formula to deduce it again, which is time-consuming and laborious, and always makes mistakes, and important formulas are even more unfamiliar.
For example, fill in the blanks with knowledge points:
Fill in the blanks with knowledge points
Our children usually do a lot of big questions at school and get some points in the exam, but they make mistakes in choosing to fill in the blanks. After the exam, they tried to watch it. The mistake is that the concept is unclear.
For example, how to define parallel lines, how many property theorems and how many judgment theorems are there? What are the connections and differences between them? In this chapter, where must we add the words "in the same plane"? Parents can let their children look for it.
For another example, the chapter of triangle involves the relationship between three sides and angles, as well as the important line segments of triangle and their properties, and the properties of isosceles equilateral triangle. These are definitely alternatives to the final multiple-choice question.
There are several ways to prove congruence, and the common auxiliary line method is the idea of geometric proof.
2. Break through the questions and summarize and practice the common hot issues in each chapter.
Our science subjects, such as mathematics and physics, are all about problems, not just problems. We must understand our thoughts.
You must analyze the types and difficulties of most children's exams, daily school assignments and weekly papers. You can mark the questions with different pens. For example, are questions 2 and 8 a kind of question type, a simplified evaluation or a deformed application of the formula? Through this analysis, children will find that in fact, exams are repeated practice. This is a very efficient learning method.
3. Familiar with routines and patterns
Common models of parallel lines: pencil model, trotter model, for example, I often tell you that parallel lines will be made when you meet an inflection point.
The common types of triangular chamfering are: 8-shaped, dart-shaped and angle-folded.
Triangle congruence model: natural model of angular bisector, isosceles right triangle model, three vertical model, folding (symmetry).
Learning these models well is equivalent to taking a toolbox exam, which is very efficient. Compared with other students, it saves the process of derivation and is fast and accurate. Of course, the premise is to master the basic content and not put the cart before the horse.
If the child can do all the previous steps well, master the basic knowledge points and questions, and can't make mistakes in calculation, then there must be no problem in your exam, except that some schools originally required it to be difficult, such as the finale, which is not to do too much, but to refine it. After finishing, continue to repeat the exam, say your thoughts in your own language and find out the logical relationship inside.
4. Insist on correcting the wrong questions
Bind the test papers of the whole semester together, spend half a day every week, correct the wrong questions, mark them with asterisks, and ask the teachers and classmates until they know, and continue to correct them next week to see if they really understand. For wrong questions, just like camels eating grass, children need to look at their ideas repeatedly to avoid repeating the mistakes of the same type of questions in the exam.
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