Operational properties and images of exponential, logarithmic and power functions

Several major elements of the 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.

2. Application of functions

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 there must be 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.

3. Space geometry

It is not difficult to draw three views and straight views, but it takes a strong sense of space to restore objects from three views for calculation. To draw the object in your mind slowly from the three plans, students, especially those with weak sense of space, are required to read more illustrations in the book, combine the object plan with the plan plan, skillfully push forward first, and then slowly push back (it is recommended 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.

4. The positional relationship between points, lines and surfaces.

In this chapter, except for the intersection of faces, the requirements for the concept of space are not strong, 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.

5. Circle sum equation

You can skillfully convert general equations into standard equations. 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, you should pay attention to the definition after the prescription or the limitation of the value range. 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.

6, trigonometric function

The exam must be given here, 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.

7. Plane vector

The operational nature of vectors and the rules of triangles and parallelograms are not difficult, as long as you remember that "vectors have the same starting point" when calculating, it will be OK. 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.

8. Trigonometric identity transformation

There are many formulas in this chapter, and aberration 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.

9, triangle solution

Master sine and cosine formulas and their variants, inferences and triangle area formulas.

10, sequence

The general formula of arithmetic and geometric series, the first n terms and some properties often appear in filling in the blanks and solving problems. 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.

1 1, inequality

This chapter generally examines students in the form of linear programming, which is usually related to practical problems. Therefore, students should be able to read the questions, find inequalities from the questions, draw a linear programming diagram, and then find the maximum value according to the limitations of practical problems.