It is a written material that reviews, analyzes and objectively evaluates the work, research or thoughts of a certain period in the past. You can make clear the direction of the next work, make fewer detours, make fewer mistakes and improve work efficiency. Why don't you calm down and write a summary? So how to write a summary in a new way? The following is a summary of senior one mathematics knowledge points compiled by Bian Xiao for reference only. Welcome to reading.

Summary of Mathematics Knowledge Points in Senior One 1

Related concepts of set

1) Set: set some specified objects together to form a set. Each object is called an element.

Note: 1 set and its elements are two different concepts, which are given by description in textbooks, similar to the concepts of points and lines in plane geometry.

2 The elements in the set are deterministic (A? A and a? A, the two must be one), different from each other (if a? A, b? A, then a≠b) and disorder ({a, b} and {b, a} represent the same set).

A set has two meanings, that is, all eligible objects are its elements; As long as it is an element, you must sign the condition.

2) Representation methods of sets: enumeration method, description method and graphic method are commonly used.

3) Classification of sets: finite set, infinite set and empty set.

4) commonly used number sets: n, z, q, r, n.

Concepts such as subset, intersection, union, complement, empty set and complete set.

1) subset: if x∈A has x∈B, then AB (or AB);

2) proper subset: AB has x0∈B but x0A is marked as AB (or, and).

3) intersection: A∩B={x|x∈A and x∈B}

4) and: A∪B={x|x∈A or x∈B}

5) Complement set: CUA={x|xA but x∈U}

Note: a, if A≦? And then what? a；

If sum, then A=B (equal set)

Sets and elements

Master related terms and symbols, especially the following symbols: (1) and? Difference; (2) the difference between and; (3) The difference between and.

Several equivalence relations of subsets

1A∩B = AAB； 2A∪B = BAB； 3ABCuACuB

4A∩CuB= empty set CuAB5CuA∪B=IAB.

Properties of intersection and union operations

1A∩A=A，A∩？ =? ，A∩B = B∩A； 2A∪A=A，A∪？ =A，A∪B = B∪A；

3Cu(A∪B)= CuA∪CuB，Cu(A∪B)= CuA∪CuB；

Number of finite subsets:

Let the number of elements in set A be n, then A has 2n subsets, 2n- 1 nonempty subset and 2n-2 nonempty proper subset.

Exercise questions:

Given the set m = {x | x = m+, m ∈ z}, n = {x | x =, n ∈ z}, p = {x | x =, p ∈ z}, then m, n and p satisfy the relation ().

a)M = NPB MN = PC)MNPD)NPM

Analysis 1: Start with judging the uniqueness and difference of elements.

Answer 1: For the set M:{x|x=, m ∈ z}; For the set N:{x|x=, n∈Z}

For the set P:{x|x=, p∈Z}, because 3(n- 1)+ 1 and 3p+ 1 both represent numbers divided by 3, and 6m+ 1 represents numbers divided by 6.

Summary of mathematics knowledge points in senior one and two

Equation definition of circle:

In the standard equation (X-A) 2+(Y-B) 2 = R2 of a circle, there are three parameters A, B and R, that is, the center coordinates are (A, B). As long as a, b and r are found, the equation of the circle is determined, so three independent conditions are needed to determine the equation of the circle, in which the coordinate of the center of the circle is the positioning condition of the circle and the radius is the circle.

The positional relationship between a straight line and a circle:

1. The first way to judge the positional relationship between a straight line and a circle is the viewpoint of equations, that is, the equations of a circle and a straight line are combined into equations, and the positional relationship is discussed by using the discriminant δ.

1δ& gt； 0, line and circle intersect, 2 δ = 0, line and circle are tangent, 3 δ.

The second method is the geometric point of view, that is, the distance d from the center of the circle to the straight line is compared with the radius R.

1dR, straight line and circle are separated,

2. The straight line is tangent to the circle. This kind of problem is mainly to find the tangent equation of the circle. The tangent equation of a circle can be divided into two cases: the known slope k or the points on the known straight line, and the points on the known straight line can be divided into the points on the known circle and the points outside the circle.

3. A straight line intersects a circle. This kind of problem is mainly to find the midpoint of chord length chord.

Properties of tangents

(1) The distance from the center of the circle to the tangent is equal to the radius of the circle;

(2) The radius of the tangent point is perpendicular to the tangent line;

(3) After passing through the center of the circle, the straight line perpendicular to the tangent must pass through the tangent point;

(4) After the tangent point, the straight line perpendicular to the tangent line must pass through the center of the circle;

When a straight line satisfies

(1) passes through the center of the circle;

(2) Over-tangent point;

(3) When two of the three properties are perpendicular to the tangent, the third property is also satisfied.

Tangent judgment theorem

The straight line passing through the outer end of the radius and perpendicular to the radius is the tangent of the circle.

Tangent length theorem

The two tangents of a circle drawn from a point outside the circle are equal in length, and the connecting line between the center of the circle and the point bisects the included angle between the two tangents.

Summary of Mathematics Knowledge Points of Grade One 3 in Senior High School

set operation

Complement set of intersection and union of operation types

Domain r domain r

Range > 0 Range > 0

It increases monotonically on R and decreases monotonically on R.

Nonsingular non-even function

All function images pass through a fixed point (0, 1). All function images pass through a fixed point (0, 1).

Note: Using the monotonicity of the function and combining with the image, we can also see that:

(1) on [a, b], the range is or;

(2) If yes, then; Take all positive numbers if and only if;

(3) For exponential function, there is always;

Second, the logarithmic function

(1) logarithm

The concept of 1. logarithm:

Generally speaking, if, then this number is called the logarithm of the base, written as: (―― base, ―― true number, ―― logarithmic formula).

Note: ○ 1 Pay attention to the limit of cardinal number, and;

○2 ;

3 pay attention to the writing format of logarithm.

Two important logarithms:

○ 1 common logarithm: logarithm based on 10;

○2 Natural Logarithm: Logarithm based on irrational numbers.

Reciprocity of exponential formula and logarithmic formula

Power real number

= N = b

cardinal number

Exponential logarithm

(B) the operational nature of logarithm

If,, and,, then:

○ 1 + ;

○2 - ;

○3 .

Note: the formula of bottoming: (,and; And; ).

The following conclusions are drawn by using the formula of changing the bottom: (1); (2) .

(3), the important formula 1, negative numbers and zero have no logarithm; 2,3, Logarithmic Identities

(2) Logarithmic function

1, the concept of logarithmic function: function, also called logarithmic function, where is the independent variable and the domain of the function is (0, +∞).

Note: The definition of ○ 1 logarithmic function is similar to that of exponential function, both of which are formal definitions. Pay attention to discrimination. For example, none of them are logarithmic functions, only logarithmic functions.

○2 restrictions of logarithmic function on cardinality:, and.

2, the nature of the logarithmic function:

a & gt 10

Defining domain x>0 domain x>0

The range of values is r, and the range of values is R.

Increase on r, decrease on r.

Function images all pass through the fixed point (1, 0). Function images all pass through the fixed point (1, 0).

(3) Power function

1. Definition of power function: Generally speaking, a shape function is called a power function, where is a constant.

2. Summarize the properties of power function.

(1) All power functions are defined at (0, +∞), and the image passes through (1,1);

(2) When the image of the power function crosses the origin, it is an increasing function in the interval. Especially, when the image of power function is convex; When the image of the power function is convex;

(3) The image of power function is a decreasing function in the interval. In the first quadrant, when moving from the right to the origin, the image is infinitely close to the positive semi-axis of the shaft on the right side of the shaft, and infinitely close to the positive semi-axis of the shaft above the shaft when moving to the origin.

Chapter IV Application of Functions

First, the root of the equation and the zero of the function.

1, the concept of function zero: for a function, the real number that makes it true is called the zero of the function.

2. The meaning of the zero point of the function: the zero point of the function is the real root of the equation, that is, the abscissa of the intersection of the image of the function and the axis.

That is, the image of the real root function of the equation has an intersection with the axis, and the function has a zero point.

3, the role of zero solution:

○ 1 (algebraic method) to find the real root of the equation;

○2 (Geometric method) For the equation that cannot be solved by the root formula, it can be linked with the image of the function, and the zero point can be found by using the properties of the function.

4. Zero point of quadratic function:

Quadratic function.

( 1)△& gt； 0, the equation has two unequal real roots, the image of the quadratic function has two intersections with the axis, and the quadratic function has two zeros.

(2)△=0, the equation has two equal real roots, the image of the quadratic function intersects with the axis, and the quadratic function has double zeros or second-order zeros.

(3)△

5. Functional model