Knowledge of mathematical conic curve
formula
Parabola: y = ax+bx+c
Y equals ax plus bx plus c squared.
When a> is 0, the opening is upward.
When a< is 0, the opening is downward.
When c = 0, the parabola passes through the origin.
When b = 0, the axis of symmetry of parabola is the Y axis.
Vertex y = ax+h+k
That is, y equals a times x+h squared+k.
-h is x of vertex coordinates.
K is y of vertex coordinates.
Generally used to find the maximum and minimum.
Parabolic standard equation: y 2 = 2px
It means that the focus of the parabola is on the positive semi-axis of X, the focal coordinate is p/20, and the equation of the directrix is x=-p/2.
Since the focus of parabola can be on any semi-axis, * * has the standard equation y 2 = 2px y 2 =-2px x 2 = 2py x 2 =-2py.
Circle: volume = 4/3 PIR 3
Area = PIR 2
Perimeter = 2 pairs
The standard equation of a circle x-a2+y-b2=r2 Note: ab is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4F0.
Solving skills of mathematical conic curve
1 Make full use of geometry
The research object of analytic geometry is geometric figures and their properties, so when dealing with analytic geometry problems, besides using algebraic equations, fully mining geometric conditions and combining plane geometry knowledge can often reduce the amount of calculation.
2 Make full use of Vieta's theorem and the strategy of "setting without seeking"
We often set the coordinates of the endpoint of a chord instead of looking for it, but solve it by combining Vieta's theorem. This method is often used for slope, midpoint and other problems.
3 Make full use of the equation of curve system
Using the equation of curve system can avoid finding the intersection of curves, so it can also reduce the amount of calculation.
4. Make full use of the parametric equation of ellipse.
The parametric equation of ellipse involves sine and cosine. By using the boundedness of sine and cosine, we can solve the related problems of finding the maximum value, that is, the triangle replacement method we often say.
Methods of learning mathematics well
1. Mathematics requires skilled calculation ability, so there are enough exercises after class. Only by doing exercises can you have calculation ability.
2. Do a good preview before class, so that we can better digest and absorb the unknown knowledge points in math class.
3. Mathematical formulas must be memorized and deduced.
4. Mathematics focuses on understanding. When you begin to learn knowledge, you must understand it. So listen carefully in class and see how the teacher explains it.
5. Mathematics scores 80% from basic knowledge and 20% from difficulty, so it is not difficult to test 120.
6. Mathematics needs to be done by heart. It is difficult for impetuous people to learn mathematics well, and it is the last word to do the problems in a down-to-earth manner.
7. If you want to learn math well, you can't do it without thinking. You can't hide when you encounter problems, and you can't stop until you figure it out.
8. The most important thing in mathematics is the problem-solving process. It is important to know mathematical thinking. With clear thinking, mathematics will naturally be easy to handle.
9. Mathematics is not for seeing, but for calculating. Maybe I have no idea for a second. When you pick up the pen and start calculating, you will be suddenly enlightened.
10. One of the reasons why I can't do math problems is that I don't understand the examples, so I must not let go of the examples in the math book.
1 1. There is nothing wrong with math, but the problem is that you only do problems without summarizing them. What's the use of doing so many problems?
12. The effective way to learn mathematics well is to be good at correcting mistakes, correct mistakes in time, and do relevant exercises to consolidate training.
13. The most important thing in learning mathematics is the ability to solve problems. If you want to do math problems, you must have a lot of practical accumulation and know the steps and methods to solve various problems. If you do more questions, you will feel it. If you come up with similar questions, you will have a solution idea.
14. Draw inferences and draw inferences to cultivate the breadth and depth of mathematical thinking. Simply put, it is the vertical and horizontal connection between training knowledge and multiple solutions to one problem, which lays the foundation for establishing your own mathematical knowledge system.
15. Plan the time to study math every day. Only when time is guaranteed can we improve our academic performance. Don't be careless, study when you have time, and don't touch when you don't have time. If you don't learn well.
16. If you still can't learn math, you can look at some math learning experiences, methods and notes. Why not use the experience summarized by predecessors?
17. Learn to summarize when you finish the problem. We should be good at classifying and summarizing the problems we have done and those we have done wrong, and then analyze similar problems to know where the problems are easy to occur, and then try to avoid them. At the same time, in the process of doing the questions and summarizing, we should learn to draw inferences from others and seize the test sites for review.
18. In addition to some learning methods and tricks, mathematics should also pay attention to strategies and will not give up decisively.
19. allocate the answer time reasonably during the exam, answer multiple-choice questions and big questions as planned, and do the next question if the time is not calculated.
20. There are some famous stories to read in math, which are very interesting and helpful for math learning.
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