Junior high school students should pay attention to the summary of knowledge points in the process of learning mathematics. The following summarizes the knowledge points of the first volume of senior two mathematics for your reference.

Location and coordinates 1. Determine the location.

In a plane, two data are usually needed to determine the position of an object.

2. Plane rectangular coordinate system

Meaning: In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.

(2) Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, and the vertical axis is called Y axis and vertical axis, both of which are collectively called coordinate axes, and their common origin O is called the origin of rectangular coordinate system.

③ Establish a plane rectangular coordinate system, and the points on the plane can be represented by a set of ordered real number pairs.

(4) In the plane rectangular coordinate system, two coordinate axes divide the coordinate plane into four parts, the upper right part is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant counterclockwise, and the points on the coordinate axes are not in any quadrant.

⑤ In the rectangular coordinate system, for any point on the plane, there is a unique ordered real number pair (that is, the coordinates of the point) corresponding to it; Conversely, for any ordered real number pair, there is a unique point on the plane corresponding to it.

3. Axisymmetry and coordinate changes

Regarding the coordinates of two points about the axis symmetry of X, the abscissa is the same, and the ordinate is opposite; With regard to the coordinates of two points symmetrical about the Y axis, the ordinate is the same, and the abscissa is opposite.

The linear function (1) is one of the functions, and its general form is y=kx+b(k, b is a constant, k≠0), where x is the independent variable and y is the dependent variable. Especially when b=0, y=kx+b(k is constant, k≠0), and y is called the proportional function of x.

(B) the three elements of function

1. domain: let x and y be two variables, and the range of the variable x is d. If for each number x∈D, the variable y always has a certain value corresponding to it according to a certain law, it is said that y is a function of x, and it is denoted as y=f(x), x∈D, where x is called an independent variable and y is called a dependent variable.

2. In the classical definition of a function, the range of values changed due to the change of variables is called the range of values of the function, while in the modern definition of a function, it refers to the set of all images corresponding to all elements in the definition domain under a corresponding law. If f(x)=x, then the range of f(x) is the range of function f(x).

3. Correspondence rule: Generally speaking, in the function symbol y=f(x), "f" represents the correspondence rule, and the equation y=f(x) shows that for any value of x in the definition domain, the unique value of y in the value domain can be obtained under the action of the correspondence rule "f".

(3) Representation method of linear function

1. analytic method: the method of expressing a function with independent variable x is called analytic method.

2. List method: The method of tabulating a series of function values y corresponding to x values to express the function relationship is called list method.

3. Image method: the method of expressing functional relationship with image is called image method.

(4) Properties of linear functions

The change value of 1.y is in direct proportion to the change value of x, and the ratio is K. That is, y=kx+b(k≠0)(k is not equal to 0, and k and b are constants).

2. When x=0, b is the intersection point of the function on the Y axis, and the coordinate is (0, b). When y=0, the coordinate of the intersection of the function image on the X axis is (-b/k, 0).

3.k is the slope of the linear function y=kx+b, and k=tanθ (the angle θ is the included angle between the linear function image and the positive direction of the X axis, θ ≠ 90).

4. When b=0 (y=kx), the image of a linear function becomes a proportional function, which is a special linear function.

5. Function image properties: when k is the same and b is not equal, the images are parallel; When k is different and b is equal, the images intersect on the y axis; When k is negative reciprocal, two straight lines are perpendicular.

6. When translating: add top and bottom at the end, and add left and right in the middle.

Congruent triangles 1. After flipping and translating, two triangles that can completely overlap are called congruent triangles, and the three sides and three angles of the two triangles are equal.

2. Determination of triangle congruence

(1)SSS (side by side)

A triangle with three equal sides is congruent triangles.

(2)SAS (edge)

A triangle with two equal corners is congruent triangles.

(3)ASA (corner)

Two angles and their sides correspond to the congruence of a triangle.

(4)AAS (corner)

The opposite sides of two angles and one angle correspond to congruences of equal triangles.

(5)RHS (right angle, hypotenuse, edge)

In a pair of right-angled triangles, the hypotenuse is equal to the other right-angled side.

3. Angle dividing line

(1) Draw a ray from the vertex of an angle and divide it into two identical angles. This ray is called the bisector of this angle.

(2) Nature

The two angles of the bisector of the (1) angle are equal, both equal to half the angle.

② The distance between the point on the bisector of the angle and both sides of the angle is equal.

Fraction (1) Fraction Operation

Keywords fractional four operations, sequential multiplication, division, addition and subtraction,

Multiplication and division are at the same level, and the sign of division must be changed (multiplication).

Keywords multiplication simplification, factorization priority,

Molecules and denominators meet and then operate.

The addition and subtraction denominator should be the same, and the product of denominator is the key.

It is not difficult to find that simpl common ground,

The sign must be changed in two places, and the result is the simplest.

(2) the algorithm of score

(1) approximate score

(1) If the numerator and denominator of a fraction are both monomials or products of several factors, their common factors are removed.

(2) The numerator and denominator of a fraction are polynomials, which are decomposed into factors respectively, and then the common factor is removed.

(2) Common factor extraction method

The coefficient takes the greatest common divisor of the coefficient of the numerator denominator, the letter takes the letter of the numerator denominator * * *, and the index takes the smallest exponent of the letter of the public denominator * * *, which is their common factor.

(3) division

Divide two fractions, invert the numerator and denominator of the divisor, and then multiply by the divisor.

(4) Power

Multiply the numerator by the numerator and the denominator by the denominator to simplify the complex.

Translation and rotation of graphics 1. Translation means that all points on a graph move equidistantly along a straight line in the same plane. This kind of graphic movement is called graphic translation movement, which is called translation for short.

2. Translation attributes

The shape and size of (1) graph have not changed before and after translation, but the position has changed.

(2) After the graphic is translated, the line segments connected by the corresponding points are parallel (or on the same straight line) and equal.