Induction of mathematical knowledge points in the last semester of senior two.
fractional equation
I. Understanding the definition
1. Fractional equation: an equation with a fraction and an unknown number in the denominator-fractional equation.
2, the idea of solving the fractional equation is:
(1) Multiplies the simplest common denominator on both sides of the equation, removes the denominator, and becomes an integral equation.
(2) Solve the whole equation.
(3) Bring the root of the whole equation into the simplest common denominator to see if the result is zero, so that the root of the simplest common denominator is the additional root of the original equation and must be discarded.
(4) Write the root of the original equation.
"Four summaries of one transformation, two solutions and three experiments"
3. Root addition: The root addition of fractional equation must meet two conditions:
(1) Finding the root is the simplest, and the common denominator is 0; (2) Increasing root is the root of integral equation formed by fractional equation.
4, the solution of fractional equation:
(1) Simplification before simplification (2) Multiply both sides of the equation by the simplest common denominator and turn it into an integral equation;
(3) solving the integral equation; (4) Root inspection;
Note: When solving the 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.
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.
5. Fractional equation solves practical problems.
Steps: Examining questions-setting unknowns-listing equations-solving equations-testing-writing answers. Pay attention to the test equation itself and practical problems when testing.
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.
Important knowledge points of eighth grade mathematics
Probabilistic preliminary
23. 1 deterministic events and random events
1. A phenomenon that must occur under certain conditions is called an inevitable event.
2. A phenomenon that will never occur under certain conditions is called an impossible event.
3. Necessary events and impossible events are collectively referred to as definite events.
4. Those phenomena that may or may not appear under certain conditions are called random time, also called the possibility of uncertain events.
23.3 time probability
1. The number used to represent the probability of an event is called the probability of the event.
2. Use 0 as the probability of impossible events; Probability with 1
3. The probability of event A is recorded as p (a); For random event a, 0 is known.
4. If the repeatable test has the following characteristics:
The results of (1) test are limited, and the chances of possible results are equal;
(2) Any two results cannot appear at the same time.
Then such a test is called equal possibility test.
5. Generally speaking, if an experiment * * * has n equal possible results and event A contains k results, then the probability of event p (a) = the number of possible results contained in event A/the total number of all possible results = k/n.
6. Enumeration, Tree Diagram and List
23.4 example of probability calculation
Summary of the necessary knowledge points of eighth 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 published by People's Education Press
★ Summarize and sort out the knowledge points of junior two mathematics.
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Summary of Mathematics Knowledge Points in Grade 8 of Junior Middle School
★ Summarize and sort out the math knowledge points in Grade Two.
★ Summary of basic knowledge points of mathematics in senior two.
★ Summary of the knowledge points in the first volume of the second grade mathematics.
★ Sort out and summarize the knowledge points of Grade 2 mathematics.
★ Arrangement of Mathematics Knowledge Points in Senior Two