Memorizing methods of high school mathematics knowledge
1. Association method
Communication is a creative activity. Lenovo is characterized by its open mind, strong expansibility and flexibility. Lenovo can excite brain nerve cells and leave a clear mark on the cerebral cortex, so the memory is very strong. Persisting in using this memory method is helpful to develop imagination and cultivate creative spirit.
For example, in the section of high school textbook: elastic collision, the law of collision between a moving steel ball (m 1) and another static steel ball (m2) is described, and the velocity expression of two steel balls after collision is derived:
When dealing with practical problems, we can solve this kind of collision problem by remembering formulas ① and ②, and there is no need to re-derive the context of formulas ① and ② every time we solve the problem. Middle school students often confuse the footprints of molecular terms in these two formulas when discussing related issues. In order to clarify this confusion, we can relate the collision phenomenon to the formula. Since m 1 touches m2, we can regard the molecular term' m 1-m2' in the formula1as' m1? M2', that is, the minus sign'-'is visually regarded as an arrow'?' Read' m 1-m2' visually as' sports ball m1? (Touch) static ball m2' (or: active ball m 1? (Touching) the passive ball m2), after making such an association, even if it is described later that the moving ball B touches the static ball A, the expression can be written quickly and correctly. For the molecular term in formula (2), just remember that it is twice the momentum of the moving ball (2m 1v 1). In addition, the denominators of ① and ② are the same, so it is not difficult to remember.
2. Comparative method
Comparison is an important way to know things and an effective way to remember things. It can help us accurately identify memory objects and master their different characteristics for memory; It can also help us grasp the memory object from the connection between things; It can also help us understand the memory object.
For example, after learning the knowledge of mechanical resonance and electrical resonance, three periodic formulas can be listed and compared;
The difference is that the physical quantities L/g, m/k and LC in the root sign reflect the different inherent properties of the resonant system. In learning, when using the periodic formula of mechanical resonance, especially the periodic formula of spring oscillator, M and K in fK number are often filled backwards. Therefore, we can make such a comparison and association: associate L/g with the shape of a simple pendulum: cycloid L hangs on it (corresponding to writing L above the fractional line) and pendulum ball mg hangs below it (corresponding to writing G below the fractional line); Figuratively think of m/k as: just like a person with a mass of M sitting on a spring sofa, the stubbornness coefficient is K.
This comparative memory method is often used in physics teaching, such as: comparing the series-parallel characteristics of resistors (and capacitors); Compare electric field and gravity field; Compare weight and quality; Compare the left-handed rule with the right-handed rule; Compare? 、? 、? Rot; Compare several conservation laws and so on.
A student, only in the middle school stage, has to learn a lot of book knowledge and extracurricular knowledge, and recite a lot of concepts, laws, formulas and data. Take high school physics textbooks as an example. The number of physical formulas that students have to master and memorize is about 200 (including deduction formulas and conclusions), not to mention that students should keep pace with each other in all disciplines! Scattered and fragmented knowledge can never be remembered, nor can it last long. If we master their inherent laws and systematize our knowledge, we will remember them quickly and firmly. And this methodical and systematic method is to put clues on the beads of knowledge. In this way, I originally wanted to remember a lot of formulas, leaving only a few main formulas, just like a string of beads, threaded with a thread and hung all at once.
3. Conventional memory method
Using the law memory method can cultivate students' thinking ability, form a good habit of thinking about things together, grasping the essence through phenomena, and using their brains to reveal the internal laws of things, which is very beneficial to improve students' thinking level.
4. Homophonic method
Distance? Confused with letters with object distance of V, so just remember: What are the pronunciations of object distance and pinyin letters? Pronunciation is the same, whenever the object distance is mentioned, it is associated with phonetic alphabet homophonic? , so put? Distinguish clearly from the physical concept of v.
High school math formula jingle
I. Settings 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.
Two mutually inverse function have that same monotone property; The images are symmetrical with Y=X as the symmetry axis;
Solve the very regular inverse solution of substitution domain; The domain of inverse function, the domain of original function.
The nature of power function is easy to remember, and the index reduces the score; Keywords exponential function, odd mother and odd son odd function,
Even function with odd mother and even son, even mother non-parity function; In the first quadrant of the image, the function is increased or decreased to see the positive and negative.
Second, trigonometric functions
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 the regular hexagon, cut the chord from top to bottom;
The numb 1 records that triangle connecte the vertices in the center; The sum of the squares of the downward triangle, the reciprocal relationship is diagonal,
At the apex, we can slowly throw the S-shaped ridge of Zhu Tuo Reef. ? nbsp
It is easy to look up the table when it becomes a tax corner, and it is essential to simplify the proof. Half of the integer multiple of two, odd complementary pairs remain unchanged,
The latter is regarded as an acute angle, and the sign is judged as the original function. The cosine of the sum of two angles is converted into a single angle, which is convenient for evaluation.
Cosine product minus sine product, angular deformation formula. Sum and difference products must have the same name, and the complementary angle must be renamed.
The calculation proves that the angle is the first, pay attention to the name of the structural function, the basic quantity remains unchanged, and it changes from complexity to simplicity.
Guided by the principle of reverse order, the product of rising power and falling power and difference. The proof of conditional equality, the idea of equation points out the direction.
Universal formula is unusual, rational formula is ahead. The formula is used in the right and wrong direction, and the deformation is used skillfully;
1 add cosine to think of cosine, 1 subtract cosine to think of sine, power-on angle is halved, and power-on and power-off is a norm;
The inverse function of trigonometric function is essentially to find the angle, first to find the value of trigonometric function, and then to determine the range of angle value;
Using right triangle, the image is intuitive and easy to rename, and the equation of simple triangle is transformed into the simplest solution set;
Three. 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.
Fourth, "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, but it is skillful to eliminate dislocation and transform.
Learn from each other's strong points and calculate the sum formula of split terms. Inductive thinking is very good, just do a program to think about it:
Counting two and seeing three associations, guessing proves indispensable. There is also mathematical induction to prove that the steps are programmed:
First verify and then assume, from k to k plus 1, the reasoning process must be detailed and affirmed by the principle of induction.
Verb (abbreviation of verb) plural
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.
Solve with equations and pay attention to the whole substitution. On the geometric operation diagram, the addition parallelogram,
Subtractive triangle rule judgment; Multiplication and division operations, reverse and forward rotation, expansion and contraction of annual module length.
In triangular operation, it is necessary to distinguish between radiation angle and mode. It is very convenient to take a square and make a square by using Demofo formula.
The radial angle operation is very strange, and the product quotient is used to sum the difference. These four properties are inseparable, such as equality module and yoke,
Two will not be real numbers, and the comparison size is not allowed. Complex numbers are very close to real numbers, so we should pay attention to the essential differences.
Six, "permutation, combination and binomial theorem"
The two principles of addition and multiplication are the laws that run through. What has nothing to do with order is combination, but what needs order is arrangement.
Two formulas, two properties, two ideas and methods. Arrange and combine the summary, and the application questions must be transformed.
It is common sense to arrange and combine together and choose the back row first. Special elements and positions should be considered first.
Don't worry too much, and don't miss too much. Punching is a skill. Arrange combinatorial identities and define proof modeling tests.
On binomial theorem, China Yang Hui Triangle. Two properties, two formulas, function assignment transformation.
Seven. solid geometry
The trinity of point, line and surface is represented by cone billiards. All distances start from points, and all angles are made of lines.
Vertical parallelism is the key point, and the concept must be clear in the proof. Line, line, plane, plane, triple cycle.
When the whole idea of the equation is solved, it becomes consciousness. Before calculation, it is necessary to prove and draw the removed figure.
Auxiliary lines of solid geometry, usually vertical lines and planes. The concept of projection is very important and the key to solving problems.
The dihedral angle and volume projection formulas of lines with different planes are vivid. Axioms are naturally three vertical lines, which solve many problems.
Eight, "plane analytic geometry"
Directed line segments, straight circles, elliptic hyperbolic parabolas, polar coordinates of parametric equations and the combination of numbers and shapes are called normal forms.
Descartes' viewpoint pairs, points and ordered real number pairs correspond to each other, which opens up a new way of geometry.
The two ideas reflect each other and turn into ideas to fight the front line; The undetermined coefficient method is actually the idea of equations.
Summarize three types, draw a curve to solve the equation, and give the curve of the equation and the relationship between the curves.
Four tools are magic weapons with good coordinate parameters; Plane geometry can not be lost, find the complex number of rotation transformation.
Analytic geometry is geometry, and you can't get carried away. Graphics are intuitive and detailed, and mathematics is mathematics.
High school mathematics learning methods
1. Prepare notebooks and drafts.
Notebooks are not for you to remember formulas and concepts. Those things are all in the book. There is no need to copy them into the notebook again. The notebook mainly records the examples given by the teacher. After all, the teacher is very experienced, and the examples given must be very representative. If necessary, you can recite the problem-solving methods of examples and understand the ideas. The draft is just some unimportant questions. If the teacher asks you to draw inferences, you don't need to write it down in your notes, but you must do it accordingly. It's definitely better to write two strokes on paper and work it out than just think about it.
2. Be sure to concentrate in class.
You must have some interaction with the teacher. After a long time, the teacher is watching your lecture 90% of the time. If you don't nod, she won't go on . After all, a class lasts for 40 minutes, and a teacher gives each student less than one minute on average, so being selfish means buying yourself time. If you have questions after class, you'd better not ask your classmates, especially those who think they are smart, so they are good at math. Don't ask such people. It's not that people don't want to tell you. It's exam-oriented education. Those clever students don't necessarily listen carefully in class. Some people just do the problems according to their own ideas. Those problem-solving methods may be suitable for them but not for you, so you must find a teacher who will give you a set of problem-solving methods that are most suitable for the exam.
3. There are only some mathematical formulas. Don't do the problem if you can't recite the formula.
It's true, but there's really no need to recite it like ancient Chinese. There is no point, and I don't know how to use it by memorizing it. If the teacher takes the deduction formula in class, he must draw it on draft paper. Needless to say, you can push it yourself. The most important thing is to understand it. Just add the following feelings. It is good to do this kind of thing more. In addition, the most important thing is that the homework left by the teacher must be carefully completed. If you listen in class, it is impossible not to do your homework. In the process of writing your homework, you are consolidating what you have learned today, that is, helping you recite formulas and understand usage. Also, review is absolutely necessary. It's no use listening carefully in class without reviewing. Doing homework is one thing, and it happened that night. Take out the examples from the previous day's notes two minutes before class the next day, and you will probably remember them. Combined with what I learned the next day, there is no big problem ~ the formula is understood and almost memorized. If you are not at ease, just take a piece of paper and write down the formula. Read it before every big exam, and there will be no big problem if you don't make any noise.