Failure is the mother of success, and repetition is the mother of learning. Learning needs to be repeated constantly, repeating what you have learned and deepening your impression. In fact, the learning methods of any subject are constantly repeated. The following are some eighth-grade math knowledge points I have compiled for you, hoping to help you.

Induction of mathematical knowledge points in the last semester of senior two.

I. Pythagorean Theorem

1, Pythagorean theorem

The sum of squares of two right angles A and B of a right triangle is equal to the square of hypotenuse C, that is, a2+b2=c2.

2. Inverse theorem of Pythagorean theorem

If all three sides of a triangle have this relationship, then the triangle is a right triangle.

3. The number of Pythagoras

The three positive integers satisfied are called Pythagoras numbers.

Common Pythagorean arrays are: (3,4,5); (5, 12, 13); (8, 15, 17); (7,24,25); (20,2 1,29); (9,40,4 1); ..... (multiples of these pythagorean arrays or pythagorean numbers).

Second, prove

1. Sentences that judge things are called propositions. That is, a proposition is a sentence that judges one thing.

2. Theorem of the sum of the internal angles of a triangle: the sum of the three internal angles of a triangle is equal to 180 degrees.

(1) The idea of proving the theorem of the sum of internal angles of a triangle is to put three angles in the original triangle together to form a right angle. Generally need assistance.

(2) The outer angle of a triangle and its adjacent inner angle are complementary angles.

3. The relationship between the outer angle of a triangle and its non-adjacent inner angle.

(1) The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

(2) The outer angle of a triangle is larger than any inner angle that is not adjacent to it.

4. The basic steps to prove the proposition is true.

(1) Draw a picture according to the meaning of the question.

(2) according to the conditions and conclusions, combined with graphics, write the known and verified.

(3) Through analysis, find out the proof method of known derivation and write the proof process. It should be noted that: ① Under normal circumstances, the analysis process does not need to be written. (2) Every step of reasoning in the proof should have a basis. If both lines are parallel to the third line, then the two lines are also parallel to each other.

Eighth grade mathematics knowledge point book 1

(A) the use of formula method

We know that algebraic multiplication and factorization are inverse deformations of each other. If the multiplication formula is reversed, the polynomial is decomposed into factors. So there are:

a2-b2=(a+b)(a-b)

a2+2ab+b2=(a+b)2

a2-2ab+b2=(a-b)2

If the multiplication formula is reversed, it can be used to factorize some polynomials. This factorization method is called formula method.

(2) Variance formula

formula for the difference of square

Equation (1): a2-b2=(a+b)(a-b)

(2) Language: the square difference of two numbers is equal to the product of the sum of these two numbers and the difference of these two numbers. This formula is the square difference formula.

(3) Factorization

1. In factorization, if there is a common factor, first raise the common factor and then decompose it further.

2. Factorization must be carried out until each polynomial factor can no longer be decomposed.

(4) Complete square formula

(1) Reversing the multiplication formula (a+b)2=a2+2ab+b2 and (a-b)2=a2-2ab+b2, we can get:

a2+2ab+b2=(a+b)2

a2-2ab+b2=(a-b)2

That is to say, the sum of squares of two numbers, plus (or minus) twice the product of these two numbers, is equal to the square of the sum (or difference) of these two numbers.

Equations a2+2ab+b2 and a2-2ab+b2 are called completely flat modes.

The above two formulas are called complete square formulas.

(2) the form and characteristics of completely flat mode

① Number of projects: three projects.

② Two terms are the sum of squares of two numbers, and the signs of these two terms are the same.

A term is twice the product of these two numbers.

(3) When there is a common factor in the polynomial, the common factor should be put forward first, and then decomposed by the formula.

(4) A and B in the complete square formula can represent monomials or polynomials. Here as long as the polynomial as a whole.

(5) Factorization must be decomposed until every polynomial factor can no longer be decomposed.

Induction of Mathematics Knowledge Points in Grade Two of Junior High School

The first chapter scores

The numerator and denominator of 1 fraction and their basic properties are multiplied (or divided) by an algebraic expression that is not equal to zero at the same time, and the fraction remains unchanged.

Fractional operation of 2

(1) The law of multiplication, division and multiplication of fractions: Fractions are multiplied by fractions, the product of molecules is the numerator of the product, and the product of denominator is the denominator of the product. Law of division: a fraction is divided by a fraction, and the numerator and denominator of division are multiplied by the divisor in turn.

(2) Law of fractional addition and subtraction: fractional addition and subtraction with the same denominator, and numerator addition and subtraction 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.

Addition, subtraction, multiplication and division of exponential powers of three integers

4- Fractional Equation and Its Solution

Chapter II Inverse Proportional Function

Expressions, images and properties of 1 inverse proportional function

Image: hyperbola

Expression: y=k/x(k is not 0)

Nature: the increase and decrease of the two branches are the same;

2 the application of inverse proportional function in practical problems

Summary of knowledge points in the first volume 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 knowledge points in the first volume of the second grade mathematics.

★ Sort out and summarize the knowledge points of eighth grade mathematics.

★ Summary of knowledge points in the first volume of eighth grade mathematics

★ Summarize the knowledge points of mathematics in the first volume of the second day.

★ Knowledge points of the first volume of mathematics in the second day of junior high school

★ Summary of knowledge points in the first volume of eighth grade mathematics

★ Summary of the knowledge points in the first volume of the second grade mathematics.

★ People's Education Edition for Summarizing Knowledge Points in the First Volume of Mathematics in the Second Day of Junior High School

★ The first volume of mathematics knowledge points induction of the second grade teaching edition.