Summary of high school mathematics knowledge points

High school mathematics includes set and function, trigonometric function, inequality, sequence, complex number, permutation, combination, binomial theorem, solid geometry, plane analytic geometry and so on. The specific summary is as follows:

1, sets and functions

Content intersection and complement set, and power exponential pair function. Parity and increase and decrease are the most obvious observation images. When the compound function appears, the law of property multiplication is distinguished. To prove it in detail, we must grasp the definition. Exponential function and logarithmic function are reciprocal functions. Cardinality is not a positive number of 1, and 1 increases or decreases on both sides. The domain of the function is easy to find. Denominator cannot be equal to 0, even roots must be non-negative, and zero and negative numbers have no logarithm. The tangent function angle is not straight, and the cotangent function angle is uneven; The real number sets of other functions have intersection in many cases.

2. Trigonometric function

Trigonometric functions are functions, and quadrant symbols are labeled. Function image unit circle, periodic parity increase and decrease. The same angle relation is very important, and both simplification and proof are needed. At the vertex of a regular hexagon, the number 1 is recorded at the chord cutting center from top to bottom to connect the vertex triangles; The sum of squares of a downward triangle, the reciprocal relationship is diagonal, and any function of the vertex is equal to the division of the latter two. The inductive formula is good. After the negative is positive, it becomes bigger and smaller, and it becomes a tax angle, which is convenient for table lookup and essential for simplification. Semi-integer multiple of two, the odd parity is unchanged, the latter is regarded as an acute angle, and the symbol is judged by the original function. The cosine of the sum of two angles is converted into an angle for evaluation.

3. Inequality

The solution to inequality is to use the properties of functions. The unreasonable inequality of the opposite side is transformed into a rational inequality. From high order to low order, step-by-step transformation should be equivalent. The mutual transformation between numbers and shapes helps to solve problems. The method of proving inequality is powerful in real number property. Difference is compared with 0, and quotient is compared with 1. Comprehensive method with good direct difficulty analysis and clear thinking. Non-negative common basic expressions, positive difficulties are reduced to absurdity. There are also important inequalities and mathematical induction. Graphic function help, drawing modeling construction method.

4. "series"

Arithmetic ratio two series, the sum of n terms in the general formula. Two finites seek the limit, and four operations are the other way around. The problem of sequence is changeable, and the equation is simplified as a whole calculation. It is difficult to sum series, and it is easy to transform and offset, learn from each other's strengths and calculate the sum formula of split terms. Inductive thinking is very good, just do a procedural thinking: one counts two or three associations, and guessing proves indispensable. There is also mathematical induction, and the steps of proof are programmed: first verify and then assume, from k plus 1 to k, the reasoning process must be detailed and affirmed by the principle of induction.

5. Complex number

As soon as the imaginary unit I came out, the number set was expanded into a complex number. A complex number and a logarithm, the real and imaginary parts of horizontal and vertical coordinates. Corresponding to a point on the complex plane, the origin is connected with it in the form of an arrow. The axis of the arrow is opposite to the X axis, and the resulting angle is a radial angle. The length of the arrow shaft is a model, and the numbers are often combined. Algebraic geometric triangles, try to transform each other. The essence of algebraic operation is I polynomial operation. The positive integer of I is the second time, and there are four numerical periods. Some important conclusions, cleverly remember the results. The ability of mutual transformation between reality and reality is great, and complex number equals transformation.

Extended data:

1. Many concepts in senior high school mathematics are closely related, such as parallel lines and parallel vectors, plane angles and space angles, equations and inequalities, mappings and functions, opposing events and mutually exclusive events. In teaching, we should be good at discovering and analyzing their connections and differences, which will help students grasp the essence of concepts.

2. For another example, there are two definitions of the concept of function. One is the definition given by junior high school, which is from the point of view of motion change, and the corresponding relationship is to correspond each value of independent variables with a unique function value; The other is the definition given by high school, which is based on the viewpoint of set and correspondence, in which the correspondence is to correspond each element in the original image set with the only determined element in the image set.

References:

High School Mathematics-Baidu Encyclopedia