Multiplication and Factorization of Mathematical Formulas in Senior One A2-B2 = (A+B) (A-B) A3+B3 = (A+B) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2)-Complete Mathematics Formulas in Senior High School.
Trigonometric inequality |a+b|? |a|+|b| |a-b|？ |a|+|b| |a|？ B<=>- b? Answer? b
|a-b|？ |a|-|b| -|a|？ Answer? |a|
Solution of quadratic equation in one variable-B+? (b2-4ac)/2a -b-？ (b2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
Discriminant _ High School Mathematical Formula
B2-4ac=0 Note: This equation has two equal real roots.
B2-4ac >0 Note: The equation has two unequal real roots.
B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.
formulas of trigonometric functions
Two-angle sum formula
sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
Half-angle formula _ high school mathematics formula
sin(A/2)=？ (( 1-cosA)/2) sin(A/2)=-？ (( 1-cosA)/2)
cos(A/2)=？ (( 1+cosA)/2) cos(A/2)=-？ (( 1+cosA)/2)
tan(A/2)=？ (( 1-cosA)/(( 1+cosA))tan(A/2)=-？ (( 1-cosA)/(( 1+cosA))
ctg(A/2)=？ (( 1+cosA)/(( 1-cosA))ctg(A/2)=-？ (( 1+cosA)/(( 1-cosA))
On the formula of circle
Volume = 4/3(π)(R3)
Area =(π)(R2)
Circumference = 2(π)r
The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0
(A) ellipse circumference calculation formula
Ellipse circumference formula: L=2? b+4(a-b)
Ellipse circumference's theorem: the circumference of an ellipse is equal to the length of the short semi-axis and the radius is (2? B) Increase the difference between the major axis length (a) and the minor axis length (b) of the ellipse by four times.
(2) Elliptic area calculation formula-high school mathematics formula.
Elliptic area formula: S=? abdominal muscle
Ellipse area theorem: the area of an ellipse is equal to π (? Multiply the product of the major axis length (a) and the minor axis length (b) of an ellipse.
When solving inequality with parameters, improper classification discussion leads to errors.
The solution is as follows: AX2+BX+C > The coefficients of 0 and x2 should be discussed separately. When a=0, this inequality is linear, and B and C should be further classified and discussed when solving. When a. 0 and? & gt0, the inequality can be changed into (x-x 1)(x-x2)>0, where x 1, x2(x 10, the solution set of the inequality is (-? ，x 1)？ (x2，+？ ) if a
Error-prone point 2 inequality always holds, which leads to errors due to improper handling.
The conventional method to solve the problem of inequality constancy is the monotonicity of the corresponding function, among which the main methods are the combination of numbers and shapes, the separation of variables and the principal component method. The conclusion is produced by the maximum value. Pay attention to the difference between constancy and existence of inequality, such as for any x? [a, b] all have f(x)? G(x) holds, that is, f(x)-g(x)? 0, but for x? [a, b], make f(x)? If g(x) holds, it is an existential problem, that is, f(x)min? G(x)max, pay special attention to the relationship between the maximum value and the minimum value in the two functions.
Error-prone point 3 ignores the solid line and dotted line in the three views and leads to errors.
Three views are drawn according to the principle of orthographic projection, in strict accordance with? Long alignment, high alignment, equal width? If the surfaces of two adjacent objects intersect, the intersection line of the surfaces is their original dividing line. Both the dividing line and the visible contour line are drawn with solid lines, and the invisible contour line is drawn with dotted lines, which is easy to be ignored.
The calculation and transformation of the area and volume of error-prone point 4 are not flexible, which leads to errors.
The calculation of area and volume not only requires students to have solid basic knowledge, but also needs to use some important thinking methods. It is an important question in the college entrance examination. So we should master the following common ways of thinking. (1) Back to the pyramid idea: This is a common thinking method when dealing with pyramid bodies. (2) Digging and filling method: it is commonly used in calculating irregular figure area or geometric volume. (3) Equal product transformation method: make full use of the characteristics of any side of the triangular pyramid as the bottom surface, and flexibly solve the volume of the triangular pyramid. (4)
Listen carefully in class and review in time after class.
The acceptance of new knowledge and the cultivation of mathematical ability are mainly carried out in the classroom, so we should pay attention to the learning efficiency in the classroom and seek correct learning methods. In class, you should keep up with the teacher's ideas, actively explore thinking, predict the next steps, and compare your own problem-solving ideas with what the teacher said. In particular, we should do a good job in learning basic knowledge and skills, and review them in time after class, leaving no doubt. First of all, we should recall the knowledge points the teacher said before doing various exercises, and correctly master the reasoning process of various formulas. If we are not clear, we should try our best to recall them instead of turning to the book immediately. In a sense, you should not create a learning way of asking questions if you don't understand. For some problems, because of their unclear thinking, it is difficult to solve them at the moment. Let yourself calm down and analyze the problems carefully and try to solve them by yourself. At every learning stage, we should sort out and summarize, and combine the points, lines and surfaces of knowledge into a knowledge network and bring it into our own knowledge system.
Do more questions appropriately and develop good problem-solving habits.
If you want to learn math well, it is inevitable to do more problems, and you should be familiar with the problem-solving ideas of various questions. At the beginning, we should start with the basic problems, take the exercises in the textbook as the standard, lay a good foundation repeatedly, and then find some extracurricular exercises to help broaden our thinking, improve our ability to analyze and solve problems, and master the general rules of solving problems. For some error-prone topics, you can prepare a set of wrong questions, write your own problem-solving ideas and correct problem-solving processes, and compare them to find out your own mistakes so as to correct them in time. We should develop good problem-solving habits at ordinary times. Let your energy be highly concentrated, make your brain excited, think quickly, enter the best state, and use it freely in the exam. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it is often exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.
Adjust the mentality and treat the exam correctly.
First of all, we should focus on basic knowledge, basic skills and basic methods, because most of the exams are basic topics. For those difficult and comprehensive topics, we should seriously think about them, try our best to sort them out, and then summarize them after finishing the questions. Adjust your mentality, let yourself calm down at any time, think in an orderly way, and overcome impetuous emotions. In particular, we should have confidence in ourselves and always encourage ourselves. No one can beat me except yourself. If you don't beat yourself, no one can beat my pride.