# Senior One # Introduction After entering high school, many freshmen have such a psychological gap. There are many people who are better than themselves, and few people notice their existence, so they are psychologically unbalanced. This is normal psychology, but they should enter the learning state as soon as possible. The Senior One Channel has compiled "Five Necessary Knowledge Points of Senior One Mathematics" for you who are studying hard. I hope it helps you!

1. Five required knowledge points in senior one mathematics.

Function model and its application This section mainly includes knowledge points such as function model and function application. Mainly to understand the general steps of function to solve application problems, and flexibly use functions to solve practical application problems.

1. Common function models include linear function model, quadratic function model, exponential function model, logarithmic function model and piecewise function model.

2. The basic steps to solve application problems with functions are:

(1) Read and understand the meaning of the question. The key is the actual meaning of data and letters;

(2) quantitative modeling;

(3) solving the function model;

(4) Simply answer practical questions.

Common test methods:

This section has various forms of knowledge examination, with high frequency, including multiple-choice questions, fill-in-the-blank questions and solutions. It is difficult to examine the maximum value of piecewise function and more complex function, which is a high-level problem.

Misunderstanding reminder:

1. When solving practical problems, we should not only consider the definition domain of the function itself, but also understand the range of independent variables in combination with practical problems.

2. When solving application problems, we should first make clear the meaning of the questions, distinguish the conditions and conclusions, grasp the key words and quantities, straighten out the quantitative relationship, and then transform the written language into mathematical language and establish the corresponding mathematical model.

2. Five compulsory knowledge points of senior one mathematics.

I. Axioms, Theorems, Inferences and Inverse Theorems:

1. The accepted true proposition is called axiom.

2. Prove the correctness of other true propositions by reasoning, and the proved true propositions are called theorems.

3. A theorem directly derived from an axiom or theorem is called the inference of this axiom or theorem.

4. If the inverse proposition of a theorem is true, then this inverse proposition is called the inverse theorem of the original theorem.

Second, analogical reasoning:

A mathematical problem consists of three elements: known conditions, solutions and conclusions to be proved, which can be regarded as the attributes of mathematical examination questions. If two mathematical problems are similar in a series of attributes, or one comes from another problem, then we can infer that the attributes of one problem also have the same or similar attributes in the other problem by analogy.

Third, prove that:

1. The process of reasoning about a proposition is called proof, including cognition, verification and proof.

2. The general steps of proof:

(1) Review the meaning of the topic, and clarify the conditions and conclusions;

(2) Draw a picture according to the meaning of the question;

(3) according to the conditions and conclusions, combined with graphics, write the known verification;

(4) Analysis conditions and conclusions;

(5) According to the analysis, write the proof process.

3. Common methods of proof: synthesis, analysis and reduction to absurdity.

Fourth, the application of auxiliary lines in proof:

In the proof of geometric problems, sometimes, in order to prove, some lines are added to the original graphics. These line segments are called auxiliary lines and are usually represented by dotted lines. Write the addition process at the beginning of the proof, and the auxiliary lines added in the proof can be used as known conditions to participate in the proof.

3. Five compulsory knowledge points of senior one mathematics.

(1) If the series {a} is a geometric series with a common ratio of q, then the sum of the first n terms is S=

That is to say, the sum of the first n terms of the geometric series whose common ratio is q is a series of function values of the piecewise function of q, and the boundary of the piecewise function is q= 1. Therefore, it is necessary to find out whether the common ratio q may be equal to 1 by using the formula of the first n terms and geometric series. If q may be equal to 1, it is necessary to divide it by Q = 1.

(2) When a, q and n are known, the formula S =；; When a, q and a are known, the formula S= is used.

(3) If S is a geometric series whose common ratio is q, then S = S+QS. (2).

(4) If the sequence {a} is geometric progression, then S, S-S, S-S, ... still become geometric series.

5. If the geometric series of 3n terms (q≦- 1) has the first n-term sum and the first n-term product s and t, and the second n-term sum and the second n-term product s and t, respectively, then s, s and s are geometric series, and t and t are also geometric series.

Universal formula: sin2α = 2tanα/( 1+tan 2α) (note: tan 2α refers to tan squared α).

cos2α=( 1-tan^2α)/( 1+tan^2α)tan2α=2tanα/( 1-tan^2α)

4. Five compulsory knowledge points of senior one mathematics

quadratic function

I. Definition and definition of expressions

Generally speaking, there is the following relationship between independent variable X and dependent variable Y: Y = AX 2+BX+C.

(a, b, c are constants, a≠0, a determines the opening direction of the function, a >；; 0, the opening direction is upward; A0, the parabola opens upwards; A0, 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 double zeros or second-order zeros.

(3)△