In the process of learning, the summary of knowledge is often very important, so what are the induction of mathematics knowledge points in senior one? The following is a summary of the knowledge points of senior one mathematics compiled by me for your reference only. You are welcome to read it.

Chapter 1: The concepts of set and function.

I. Collection of related concepts

The meaning of 1. set

2. Three characteristics of elements in a set:

The certainty of (1) element is as follows: mountains in the world;

(2) The mutual anisotropy of elements, such as the set of happy letters {h, a, p, y }；;

(3) The disorder of elements: for example, {a, b, c} and {a, c, b} represent the same set.

3. Representation of assembly: {…} such as {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean and Arctic Ocean};

(1) Set is expressed in Latin letters: A={ basketball players in our school}, b = {1, 2, 3, 4, 5};

(2) Representation of sets: enumeration and description.

Note: Common number sets and their expressions: XKb 1. Com

The set of non-negative integers (that is, the set of natural numbers) is recorded as: n;

Positive integer set: N* or n+;

Integer set: z;

Rational number set: q;

Real number set: r;

1) enumeration: {A, b, c ...};

2) Description: describes the common attributes of the elements in the set, and is written in braces to indicate the set {x? r | x-3 & gt； 2}，{ x | x-3 & gt； 2};

3) Language description: Example: {a triangle that is not a right triangle};

4) Venn diagram:

4, the classification of the set:

(1) finite set contains a set of finite elements;

(2) An infinite set contains an infinite set of elements;

(3) An example of an empty set without any elements: {x | x2 =-5}.

Second, the basic relationship between sets

1. "Inclusive" relation-subset

Note: There are two possibilities.

(1)A is a part of B;

(2)A and B are the same set.

On the other hand, set A is not included in set B, or set B does not include set A, so it is recorded as AB or BA;

2. "Equality" relation: A=B(5≥5, and 5≤5, then 5=5) holds.

Example: let a = {x | x2-1= 0} b = {-1,1} "Two sets are equal if their elements are the same".

Namely:

(1) Any set is a subset of itself.

② proper subset: If AíB and A 1B, then set A is the proper subset of set B, and it is recorded as AB (or BA).

③ If aí b and bí c, aí c;

(4) If AíB is accompanied by BíA, then A = B；;

3. A set without any elements is called an empty set and denoted as φ;

It is stipulated that an empty set is a subset of any set and an empty set is a proper subset of any non-empty set.

4. Number of subsets:

A set of n elements, including 2n subsets, 2n- 1 proper subset, 2n- 1 nonempty subset and 2n- 1 nonempty proper subset.

Third, the operation of the set.

The operation types intersect and set the complement set;

Define a set consisting of all elements belonging to A and B, which is called the intersection of A and B, and it is marked as AB (pronounced as' A-B'), that is, AB={x|xA, and XB }；;

A set consisting of all elements belonging to set A or set B is called the union of A and B, and is written as AB (pronounced as' A and B'), that is, AB={x|xA, or XB});

Chapter 2: Basic elementary functions

I exponential function

(A) the operation of exponent and exponent power

The concept of 1. radical: generally, if, then it is called n-th root, where >: 1 and ∈ *.

When it is an odd number, the power root of a positive number is a positive number and the power root of a negative number is a negative number. At this point, the power root of is represented by a symbol. The formula is called radical, here is called radical component, and here is called radical.

When it is an even number, a positive number has two power roots, and the two numbers are opposite. At this time, the positive power roots of positive numbers are represented by symbols, and the negative power roots are represented by symbols. Positive and negative power roots can be combined into +(>: 0). It can be concluded that negative numbers have no even roots; Any power root of 0 is 0, which is recorded as.

Note: When it is odd, it is even.

2. Power of fractional exponent

The meaning of the power of the positive fractional index stipulates:

The positive fractional exponential power of 0 is equal to 0, and the negative fractional exponential power of 0 is meaningless;

It is pointed out that after defining the meaning of fractional exponent power, the concept of exponent is extended from integer exponent to rational exponent, and the operational nature of integer exponent power can also be extended to rational exponent power.

3. Operational Properties of Exponential Power of Real Numbers

(B) Exponential function and its properties

1, the concept of exponential function: Generally speaking, a function is called an exponential function, where x is the independent variable and the domain of the function is R.

Note: The base range of exponential function cannot be negative, zero 1.

2. Images and properties of exponential function.

Chapter III: Chapter III Application of Functions

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. Namely:

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

3, the role of zero solution:

Find the zero point of a function:

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

(2) (Geometric method) For the equation that can't 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 (multiple roots), the image of the quadratic function intersects with the axis, and the quadratic function has a double zero or a second-order zero.

3)△& lt； 0, the equation has no real root, the image of the quadratic function has no intersection with the axis, and the quadratic function has no zero.

Expanding reading: how to learn high school mathematics well, read textbooks well and learn to study?

Some students who "feel good about themselves" often despise the study and training of basic knowledge, skills and methods in textbooks. They often forget what to do, but they are interested in difficult problems to show their "level". They aim too high, value "quantity" over "quality" and fall into the ocean of problems. They either make mistakes in calculation or give up halfway in formal homework or exams. Therefore, students should start from the first year of high school and enhance their awareness of learning from textbooks. We can treat every theorem and every example as an exercise, carefully re-prove, re-solve, and add some comments appropriately, especially through the explanation and analysis of typical examples. Finally, we should abstract the mathematical ideas and methods to solve such problems, do a good job of reflection after solving problems in writing, and summarize the general and special laws of solving problems in order to popularize and flexibly use them. In addition, students should solve problems independently as much as possible, because the process of solving problems is also a process of cultivating the ability to analyze and solve problems, and it is also a process of research.

Take notes and listen carefully in class.

First of all, it is very important to cultivate good listening habits in classroom teaching. Of course, listening is the main thing. Listening can help you concentrate. You should understand and listen to the key points of the teacher. Pay attention to thinking and analyzing problems when listening, but only listening without remembering, or just remembering without listening, it is inevitable to pay attention to one thing and lose sight of another, and the classroom efficiency is low. Therefore, we should take notes appropriately and purposefully to understand the main spirit and intention of the teacher in class. Scientific notes can improve the efficiency of a 45-minute class.

Secondly, to improve mathematics ability, of course, through the classroom, make full use of this position. The process of learning mathematics is alive, so is the object of teachers' teaching, which changes with the development of teaching process, especially when teachers pay attention to ability teaching, the teaching materials can not be reflected. Mathematical ability is formed simultaneously with the occurrence of knowledge. Whether forming a concept, mastering a law or doing an exercise, we should cultivate and improve it from different ability angles. Through the teacher's teaching in the classroom, we can understand the position of what we have learned in the textbook and the relationship with the previous knowledge. Only by mastering the teaching materials can we master the initiative in learning.

Finally, in math class, teachers usually ask questions and perform them, sometimes accompanied by discussion, so they can hear a lot of information. These questions are very valuable. For those typical problems, problems with universality must be solved in time, and the symptoms of the problems cannot be left behind or even solved. Valuable problems should be grasped in time, and the remaining problems should be supplemented in a targeted manner and pay attention to practical results.

Write a summary and grasp the law.

A person can constantly improve by constantly accepting new knowledge, encountering setbacks, having doubts and summing up. "Students who can't summarize will not improve their ability, and frustration experience is the cornerstone of success." The biological evolution process of survival of the fittest in nature is the best example. Learning should always sum up the rules, with the aim of further development. Through the usual contact and communication with teachers and classmates, the general learning steps are gradually summarized, including: making a plan, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and extracurricular learning, which are simply summarized as four links (preview, class, sorting and homework) and one step (review summary). Each link has profound content, strong purpose and pertinence, and should be put in place. Adhere to the study habit of "two before and two after a summary" (preview first, then listen to lectures, review first, then do homework, and write a summary of each unit).