The second volume of the second day of junior high school mathematics knowledge points
1. Definition of fraction: If A and B represent two algebraic expressions, and B contains letters, then this formula is called a fraction.
The meaningful condition of a fraction is that the denominator is not zero, the numerator of the fractional value is zero, and the denominator is not zero.
2. The basic nature of the fraction: the numerator of the fraction is multiplied by the denominator or divided by the algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.
3. General and approximate scores of scores: the key is to decompose the factors first.
4. Fractional operation:
Law of fractional multiplication: fractional multiplication, the product of molecules is the numerator of the product, and the product of denominator is the denominator.
Law of fractional division: a fraction is divided by a fraction, and the numerator and denominator of the divisor are in turn multiplied by the divisor.
Fractional power law: Fractional power should be numerator and denominator respectively.
Addition and subtraction of fractions: addition and subtraction of fractions with the same denominator and addition and subtraction of molecules 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.
Mixed operation: The operation sequence is the same as before. It can be simplified by the operation speed.
5. The zeroth power of any number that is not equal to zero is equal to 1, that is; When n is a positive integer,
6. The operation property of positive integer exponential power can also be extended to integer exponential power (m, n is an integer).
(1) The power of the same base:;
(2) the power of power:
(3) the power of the product:
(4) Power division with the same base: (a ≠ 0);
(5) Power of quotient: (b≠0)
7. Fractional equation: an equation with a fraction and an unknown number in the denominator-fractional equation.
The process of solving the fractional equation is essentially to multiply both sides of the equation by an algebraic expression (the simplest common denominator) and transform the fractional equation into an integral equation.
When solving a fractional equation, when both sides of the equation are multiplied by the simplest common denominator, the simplest common denominator may be 0, which increases the root, so the fractional equation must be tested.
Steps to solve the fractional equation: (1) Simplify first and then simplify; (2) Multiplying both sides of the equation by the simplest common denominator, and transforming it into an integral equation;
(3) solving the integral equation; (4) Root inspection.
There are two conditions to add a root: one is that its value should make the simplest common denominator 0, and the other is that its value should be the root of the whole equation after removing the denominator.
Test method of fractional equation: bring the solution of the whole equation into the simplest common denominator. If the value of the simplest common denominator is not 0, the solution of the whole equation is the solution of the original fractional equation; Otherwise, this solution is not the solution of the original fractional equation.
What are the steps of applying the equation? (1) trial; (2) setting; (3) column; (4) solutions; (5) answer.
There are several types of application problems; What is the basic formula? There are basically four kinds:
(1) Travel problem: basic formula: distance = speed × time. Travel problems are divided into meeting problems and chasing problems.
(2) The number topic should master the representation of decimals in the number topic.
(3) The basic formula of engineering problems: workload = working time × working efficiency.
(4) Countercurrent problem: downstream = v still water +v water. V countercurrent =v still water -v water.
8. Scientific notation: The notation for expressing a number in one form (where n is an integer) is called scientific notation. When the absolute value of an n-bit integer is greater than 10, the exponent of 10 is
In scientific notation, when the absolute value is less than 1, the exponent of 10 is the number of zeros before the first non-zero number (including the zero before the decimal point).
Summary and induction of mathematical knowledge points in the first volume of the second day of junior high school
Congruent triangle
I. Knowledge framework
Two. The concept of knowledge
1. congruent triangles: When two triangles have the same shape and size, one of them can be translated, rotated and symmetrical to make it coincide with the other. These two triangles are called congruent triangles.
2. The nature of congruent triangles: the corresponding angles and sides of congruent triangles are equal.
3. The axiom and inference of triangle congruence are:
(1) "corner" is abbreviated as "SAS"
② The abbreviation of "corner" is "ASA"
(3) "Edge" is abbreviated as "SSS"
(4) The abbreviation of "corner edge" is "AAS"
(5) Two right-angled triangles (HL) with equal hypotenuse and right-angled side.
4. Inference from the bisector of the angle: the points with equal distance from the inside of the angle to both sides of the angle are on the bisector.
5. The basic method steps to prove the congruence of two triangles or to prove the equality of line segments or angles with it: ①. Determine the known conditions (including implied conditions, such as common * * * edge, common * * * angle, diagonal, bisector of angle, median line, height, isosceles triangle and other implied angular relations. ); 2. Review the triangle judgment and find out what else we need; ③.
When learning triangle congruence, teachers should start from the real life graphics, lead to congruence graphics, and then lead to congruent triangles. Through intuitive understanding and comparison, we can discover the mystery of congruent triangles. Stimulate students' collective thinking and inspire them. By exploring the bisector and midline of the triangle, students can realize the true charm of the collection.
Review knowledge points of eighth grade mathematics
square
The concept of 1 square
A group of parallelograms with equal adjacent sides and a right angle is called a square.
2, the nature of the square
(1) has all the properties of parallelogram, rectangle and diamond;
(2) All four corners of a square are right angles and all four sides are equal;
(3) The two diagonals of a square are equal and vertically bisected, and each diagonal bisects a set of diagonals;
(4) A square is an axisymmetric figure with four axes of symmetry;
(5) A diagonal line of a square divides the square into two isosceles right triangles, and two diagonal lines divide the square into four isosceles right triangles;
(6) The distance from one point on one diagonal of a square to both ends of the other diagonal is equal.
3. Determination of the square
(1) The main basis for judging whether a quadrilateral is a square is definition, and there are two ways:
First prove that it is a rectangle, and then prove that a group of adjacent sides are equal.
First prove that it is a diamond, and then prove that an angle is a right angle.
(2) The general order of judging a quadrilateral as a square is as follows:
First prove that it is a parallelogram;
Then prove to be a diamond (or rectangle);
It turned out to be a rectangle (or a diamond).
Articles about knowledge points in the eighth grade mathematics semester;
★ 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
★ Summary of the Mid-term Examination of Mathematics in Senior Two.
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Summary of algebraic key knowledge at the end of the second day of mathematics.
★ Review and arrangement of mathematics knowledge points in Grade Two.
★ Sort out and summarize the knowledge points of Grade 2 mathematics.
★ Summary of mathematics knowledge points in senior two.
★ Important knowledge points of mathematics in the second day of junior high school
★ Summary of Mathematics Knowledge Points in Senior Two.