Compulsory knowledge points of high school mathematics 1
Mandatory 1
The first chapter is the basic concepts of set and function. The mistakes in this chapter are all focused on the concept of empty set, and the topic selection of each exam basically involves this concept. If you are not careful, you will lose points. The secondary knowledge point is the Wayne diagram and drawing ability of the set. Mastering these, the "combination, complement, intersection and opposition" of the set will be solved.
There are also concepts such as the domain of function and monotonicity, increase and decrease of function, which are the basis of function and are not difficult to understand. In the first round of review, you must remember these concepts again and again. The best way is to write them down in a notebook and read them at least once a day.
The second chapter is the operational nature of basic elementary functions-exponential, logarithmic and power functions. Several major elements of image function and related test sites are basically reflected in the function image, such as monotonicity, increase and decrease, extreme value, zero point and so on. Regarding the operation formulas of these three functions, it is basically no problem to remember more and do more exercises.
Function image is the most difficult point in this chapter, and the image problem can not be solved by memory. You must understand and skillfully draw function images, such as domain, range, zero and so on. For power function, it is also necessary to understand the relationship between the difference of images and the function value when the exponential power is greater than 1 less than 1, which is also a common test site. In addition, the opposition between exponential function and logarithmic function and how to transform it need to focus on textbook examples.
Chapter III Application of Function This chapter mainly investigates the combination of function and equation, which is actually the zero point of function, that is, the intersection of function image and X axis. The transformation relationship between the three is the focus of this chapter. Only by learning to transform flexibly can we solve the problem most simply. As for the method of proving zero, there must be zero in the direct calculation, and zero in the continuous function if it is defined above and below the X axis. We should remember the proof methods corresponding to these difficulties and practice more. The δ discrimination method of the zero point of quadratic function requires you to understand the definition, draw more pictures and do more problems.
Compulsory knowledge points of high school mathematics II
compulsory 2
In the first chapter of space geometry, it is not difficult to draw three views and straight views, but it takes a strong sense of space to recover objects from three views for calculation. To draw the objects in your mind slowly from three plans, students, especially those with weak sense of space, are required to read more illustrations in books, combine the objects with the plan, skillfully push forward first, and then slowly push back (it is suggested to make a cube with paper to find the feeling).
Do the problem with a sketch, not just by imagination. The formulas of surface area and volume of cone, cylinder and platform are not difficult to remember.
The second chapter is the positional relationship of point, line and surface. In this chapter, except for the intersection of faces, the concept of space is not high, and most of them can be drawn directly, which requires students to look at pictures more. It is a normative problem to pay strict attention to the solid line and dotted line when sketching yourself.
For the content of this chapter, keep in mind that several theorems and properties of straight line and straight line, face to face, straight line and face intersection, verticality and parallelism can be expressed by graphic language, written language and mathematical expression at the same time. As long as all this is over, this chapter will solve more than half. The difficulty of this chapter lies in the concept of dihedral angle. Even if most students know this concept, they can't understand how dihedral angles make this angle. In this case, we must start with the definition, remember the definition first, and then do more and see more. There is no shortcut.
Chapter III Straight Line and Equation This chapter mainly talks about the positional relationship between slope and straight line. As long as the parallel and vertical slopes of the straight line are clear, the problem can't be wrong. It should be noted that when the straight line is vertical, the slope does not exist, which is a common test site in the exam. In addition, the general formulas involved in several forms of linear equations can be used without high requirements. As long as the formulas are directly applied, there is no difficulty in the distance between points, between points and straight lines, and between straight lines.
The fourth chapter can skillfully transform the general equation into the standard equation. The usual form of examination is that one side of the equation contains the root sign and the other side does not. At this time, we should pay attention to the limitation of definition or value range after prescription. Use the distance from point to point, the distance from point to straight line and the radius of circle to judge the positional relationship between point and circle, straight line and circle, and circle and circle. In addition, pay attention to the tangency and intersection caused by the symmetry of the circle, and list several symmetrical forms yourself. It is not difficult to understand if you think about it more.
Compulsory knowledge points of high school mathematics 3
Compulsory 3
Generally speaking, this book is not difficult and complicated. It needs patience to draw and calculate. The combination of program block diagram and three algorithm statements, as well as the algorithm representation of block diagram, should not be understood in conventional language, otherwise you will stumble in this kind of problem. Qin's algorithm is the key, so we should remember the formula of the algorithm. Statistics is a pile of data processing, and the exam is also based on calculation, which will calculate digital characteristics such as median from bar charts. For the regression problem, as long as you remember the formula, it is also a calculation problem. Probability is mainly geometric probability and classical probability. As long as the geometric probability can find the length and area of the requested event, the classical probability can only represent all events.
Compulsory knowledge points of high school mathematics 4
Required 4
The first chapter trigonometric function exam must give questions in this piece, and the number of questions is not small! It is not too difficult to summarize some properties of formulas and basic trigonometric function images, as long as you can draw pictures. The difficulty lies in the amplitude, frequency, period, phase and initial phase of trigonometric function, and the calculation of the values and periods of a and b according to the maximum value, as well as the changes of images and properties when constant changes occur. This part of knowledge is more and takes more time, so we should start with images and examples instead of defining dead buttons.
The second chapter is about the operational properties of plane vectors. The triangle rule and parallelogram rule are not very difficult. Just remember the "same starting point vector" when calculating. The mathematical expressions of vector * * * straight line and vertical line are commonly used in calculation. * * * Straight line theorem, basic theorem of vector and formula of quantity product. The vernal equinox coordinate formula is an important and difficult content, which needs to be memorized.
The third chapter is trigonometric identity transformation. There are many formulas in this chapter, and aberration double half-angle formulas often appear, so be sure to remember them. Because the amount is relatively large and difficult to remember, it is recommended to write it on paper and stick it on the table, and read it every day. It should be mentioned that the transformation of trigonometric identities is regular, and trigonometric functions can be set to remember.
Compulsory knowledge points of high school mathematics 5
Elective course 5
The first chapter is to solve the triangle and master the sine and cosine formula and its variants, inference and triangle area formula. The second chapter, the arithmetic of sequence, the general formula of geometric series, the first n terms and some properties often appear in fill-in-the-blank questions and problem solving. This part of the content is relatively simple to learn, but the test of its derivation, calculation and flexible application is deep, so we should be cautious. In the examination questions, the contents of general formula, the first n items and sum appear frequently, so it is no problem to deduce these questions purposefully after seeing them.
Chapter III Inequality This chapter generally examines students in the form of linear programming, which is usually related to practical problems, so you should be able to read the questions, find out the inequalities from the questions, draw a linear programming diagram, and then find the maximum value according to the constraints of practical problems.
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