Induction of knowledge points in the first volume of mathematics in grade three
Binary linear equations
1. Definition: An integral equation with two unknowns whose degree is 1 is called a binary linear equation.
2. The solution of binary linear equations
(1) substitution method
The equations composed of a quadratic equation and a linear equation are usually solved by method of substitution, which is the basic method of elimination and simplification.
(2) Factor decomposition method
In binary quadratic equation, when at least one equation can be decomposed, it can be solved by factorization, eliminating elements and reducing order.
(3) Matching method
A formula, or a part of a formula, is transformed into a completely flat road or the sum of several completely flat roads through constant deformation.
(4) Vieta's law.
Through the inverse theorem of Vieta's theorem, we can use the sum-product relation of two numbers to construct a quadratic equation with one variable.
(5) Constant elimination method
When the first term is missing in both equations, it can be solved by eliminating the constant term.
Solve a quadratic equation with one variable
The basic idea of solving quadratic equations with one variable is to simplify them into two quadratic equations with one variable.
1, direct Kaiping method:
The equation in the form of (x-m)2=n(n≥0) is solved by direct Kaiping method, and its solution is x = m. 。
Direct Kaiping method is the inverse operation of square, and the result is usually expressed by root sign.
2. Matching method
The method of obtaining the root of a quadratic equation by matching it completely flat. The solution of this unary quadratic equation is called collocation method, and the formula is based on the complete square formula.
(1) transformation: transform the quadratic equation of one variable into the form of ax 2+bx+c = 0 (that is, the general form of the quadratic equation of one variable).
(2) Coefficient 1: convert the quadratic term into 1.
(3) Move the term: move the constant term to the right of the equal sign.
(4) Formula: The left and right sides of the equal sign are added with the square of half of the first coefficient.
(5) Deformation: Write the algebraic expression on the left of the equal sign as a complete square.
(6) Square root: simultaneous square root.
(7) Solution: The root of the original equation can be obtained by sorting.
The induction of mathematics knowledge points in the second volume of the ninth grade
1. Proportional Theorem of Parallel Lines and Its Inference:
Theorem: Three parallel lines cut two straight lines, and the corresponding line segments are proportional.
2. Inference: A straight line parallel to one side of a triangle is directly proportional to the corresponding line segment obtained by cutting the other two sides (or extension lines of both sides).
3. Inference inverse theorem: If the corresponding line segment obtained by cutting two sides of a triangle (or the extension lines of two sides) is proportional, then this line segment is parallel to the third side of the triangle.
Second, the similar preparation theorem:
A straight line parallel to one side of a triangle and intersecting with the other two sides, the three sides of the cut triangle are directly proportional to the three sides of the original triangle.
Third, similar triangles:
1. Definition: A triangle with equal corresponding angles and proportional corresponding sides is called similar triangles.
2. Properties: (1) The angles corresponding to similar triangles are equal;
(2) The line segments corresponding to similar triangles (side, height, midline and angular bisector) are proportional;
(3) The perimeter ratio of similar triangles is equal to the similarity ratio, and the area ratio is equal to the square of the similarity ratio.
Description: ① The area ratio of equal-height triangle is equal to the ratio of bottom, and the area ratio of equal-bottom triangle is equal to the ratio of height; ② Pay attention to the correspondence between two graphic elements.
3. Decision theorem:
(1) Two angles are equal and two triangles are similar;
(2) The two sides are correspondingly proportional, the included angle is equal, and the two triangles are similar;
(3) Three sides are proportional and two triangles are similar;
(4) Two right-angled triangles are similar if the hypotenuse and one right-angled side of one right-angled triangle are directly proportional to the hypotenuse and one right-angled side of another right-angled triangle.
Mathematics review materials for grade three
Factorization method
1. cross multiplication
(1) decompose quadratic coefficient and constant term into factors respectively;
(2) try the cross chart, so that the sum of the numbers obtained by multiplying the cross lines is the first-order coefficient;
(3) Determine the appropriate crossplot and write the results of factorization;
(4) inspection.
2. Common factor method
(1) Find the common factor;
(2) Put forward the common factor and determine another factor;
① To find the common factor, we can first determine the coefficient, and then determine the letters according to the method of determining the common factor;
(2) common factor and determining another factor. When determining another factor, you can divide the original polynomial by the common factor, and the obtained quotient is the quotient left after dividing one factor by the common factor. You can also divide each term of the original polynomial by the common factor to find the remaining other factor.
(3) After extracting the common factor, the number of terms of another factor is the same as that of the original polynomial.
3. The undetermined coefficient method
(1) The general analytical formula for determining the undetermined coefficient;
(2) According to the identity condition, a group of undetermined coefficient equations are listed;
(3) Solve the equation or eliminate the undetermined coefficient, thus solving the problem.
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