Induction of mathematical knowledge points in the last semester of senior two.
Triangular knowledge concept
1, triangle: A figure composed of three line segments that are not on the same line end to end is called a triangle.
2. Trilateral relationship: the sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.
3. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.
4. midline: in a triangle, the line segment connecting a vertex and its relative midpoint is called the midline of the triangle.
5. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the vertex and the intersection of this angle is called the angular bisector of the triangle.
6. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
7. Polygon: On the plane, a figure composed of some line segments connected end to end is called polygon.
8. Interior Angle of Polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
9. Exterior angle of polygon: The angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
10, diagonal of polygon: the line segment connecting two non-adjacent vertices of polygon is called diagonal of polygon.
1 1, regular polygon: a polygon with equal angles and sides in a plane is called a regular polygon.
12, plane mosaic: a part of the plane is completely covered by some non-overlapping polygons, which is called covering the plane with polygons.
13, formula and properties:
(1) Sum of internal angles of triangle: The sum of internal angles of triangle is 180.
(2) the nature of the triangle exterior angle:
Property 1: One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it.
Property 2: The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
(3) The formula of the sum of polygon internal angles: Is the sum of polygon internal angles equal to? 180
(4) Sum of polygon external angles: the sum of polygon external angles is 360.
(5) Number of diagonal lines of a polygon: ① Starting from a vertex of a polygon, a diagonal line can be drawn to divide the polygon into triangles. ② The polygon * * * has a diagonal line.
Eight-grade mathematics knowledge points
Addition and subtraction of fractions
1. Although general fractions and reduction are aimed at fractions, they are two opposite variants. Reduction is for one score, while general scores are for multiple scores. The approximate fraction is a simplified fraction, and the general fraction is a simplified fraction, thus unifying the denominator of the fraction.
2. Both general score and approximate score are deformed according to the basic properties of the score, and their similarity is to keep the value of the score unchanged.
3. The general denominator is written in the form of unexpanded continuous product, and the numerator multiplication is written in polynomial to prepare for further operation.
4. Total score basis: the basic nature of the score.
5. The key to general division is to determine the common denominator of several fractions.
Usually, the product of the powers of all factors of each denominator is taken as the common denominator, which is called the simplest common denominator.
6. By analogy, get the total score of this score:
Changing several fractions with different denominators into fractions with the same mother equal to the original fraction is called the general fraction of fractions.
7. The rules for adding and subtracting fractions with the same denominator are: adding and subtracting fractions with the same denominator and adding and subtracting numerators with the same denominator.
Addition and subtraction of fractions with the same denominator, denominator unchanged, addition and subtraction of molecules, that is, the operation of fractions is transformed into the operation of algebraic expressions.
8. Fraction addition and subtraction law of different denominators: Fractions of different denominators are added and subtracted, first divided by fractions of the same denominator, and then added and subtracted.
9. Fractions with the same denominator are added and subtracted, and the denominator remains the same. Add and subtract molecules, but pay attention to each molecule as a whole, and put parentheses in due course.
10. For the addition and subtraction between the algebraic expression and the fraction, the algebraic expression is regarded as a whole, that is, it is regarded as a fraction with the denominator of 1, so as to divide.
1 1. For addition and subtraction of fractions with different denominators, first observe whether each formula is the simplest fraction. If the fraction can be simplified, it can be simplified first and then divided, which will simplify the operation.
12. As the final result, if it is a score, it should be the simplest score.
One-dimensional linear equation with letter coefficient
One-dimensional linear equation with letter coefficient
Example: A times (a≠0) of a number is equal to B, so find this number. This number is represented by X. According to the meaning of the question, the equation ax=b(a≠0) can be obtained.
In this equation, X is unknown, and A and B are known numbers in letters. For x, the letter a is the coefficient of x and b is a constant term. This equation is a one-dimensional linear equation with letter coefficients.
The solution of the letter coefficient equation is the same as that of the numerical coefficient equation, but special attention should be paid to: multiply or divide two sides of the equation with a letter, and the value of this formula cannot be equal to zero.
Math review method in junior two
orderly
Mathematics is an interlocking subject, and any link will affect the whole learning process. Therefore, don't be greedy when studying. You should pass the exam chapter by chapter, and don't leave questions that you don't understand or understand deeply easily.
Emphasize understanding
Concepts, theorems and formulas should be memorized on the basis of understanding. Every time you learn a new theorem, try to do an example without looking at the answer to see if you can correctly apply the new theorem; If not, compare the answers to deepen the understanding of the theorem.
basic skill
You can't learn mathematics without training. Usually do more exercises with moderate difficulty. Of course, don't fall into the misunderstanding of dead drilling questions, be familiar with the questions of the college entrance examination, and be targeted in training.
Pay attention to mistakes
Booking the wrong book and collecting the wrong questions by yourself is often your weakness. When reviewing, this wrong book has become a valuable review material.
Mathematics learning is a step-by-step process, and it is unrealistic to dream of reaching the sky in one step. After reciting the contents of the book, carefully write the exercises at the back of the book. Some students may think that the exercises after the book are too simple to do. This idea is highly undesirable. The function of the exercises after the book is not only to help you remember the contents in the book, but also to help you standardize the writing format, make your problem-solving structure compact and tidy, make proper use of formulas and theorems, and reduce unnecessary marks in the exam.
The usual mathematical research:
○ 1 preview carefully before class. The purpose of preview is to listen to the teacher better. Through preview, the mastery level should reach 80%. Listen to the teacher answer these questions with questions that you don't understand in the preview. Preview can also improve the overall efficiency of attending classes. Specific preview method: finish the topics in the book and draw the knowledge points. The whole process lasts about 10.
○2 Let math class combine with practice. It's no use just listening in math class. When the teacher asks the students to do calculus on the blackboard, they should also practice on the draft paper. You must ask questions you don't understand, or you may not do it if you encounter similar problems in the exam. When listening to the teacher's lecture, you must concentrate on the details, otherwise, "the embankment of a thousand miles will collapse in the ant nest."
○3 Review in time after class. After finishing your homework, sort out what the teacher said that day, and you can do extracurricular problems for about 25 minutes. You can choose the extracurricular books that suit you according to your own needs. The content of the extracurricular problem is probably today's class.
The fourth unit test is to test your recent study. In fact, the score represents your past. The key is to sum up and learn from each exam so that you can do better in the mid-term and final exams. Teachers often take exams without notice and review them in time after class.
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