Outline of compulsory mathematics content in senior high school
The positional relationship between two planes:
(1) The definition that two planes are parallel to each other: there is no common point between two planes in space.
(2) the positional relationship between two planes:
The two planes are parallel-have nothing in common; Two planes intersect-there is a straight line.
First, parallel
Theorem for determining the parallelism of two planes: If two intersecting lines in one plane are parallel to the other plane, then the two planes are parallel.
Parallel theorem of two planes: if two parallel planes intersect with the third plane at the same time, the intersection lines are parallel.
B, crossroads
dihedral angle
(1) Half-plane: A straight line in a plane divides this plane into two parts, and each part is called a half-plane.
(2) dihedral angle: The figure composed of two half planes starting from a straight line is called dihedral angle. The range of dihedral angle is [0, 180].
(3) The edge of dihedral angle: This straight line is called the edge of dihedral angle.
(4) Dihedral facet: These two half planes are called dihedral facets.
(5) Plane angle of dihedral angle: Take any point on the edge of dihedral angle as the endpoint, and make two rays perpendicular to the edge in two planes respectively. The angle formed by these two rays is called the plane angle of dihedral angle.
(6) Straight dihedral angle: A dihedral angle whose plane angle is a right angle is called a straight dihedral angle.
Esp。 The two planes are perpendicular.
Definition of two planes perpendicular: two planes intersect, and if the angle formed is a straight dihedral angle, the two planes are said to be perpendicular to each other. Write it down as X.
A theorem to determine the perpendicularity of two planes: If one plane passes through the perpendicular of the other plane, then the two planes are perpendicular to each other.
Verticality theorem of two planes: If two planes are perpendicular to each other, a straight line perpendicular to the intersection in one plane is perpendicular to the other plane.
Formula 1:
Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
Equation 2:
Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;
Sine (π+α) =-Sine α
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
Formula 3:
The relationship between arbitrary angle α and the value of-α trigonometric function;
Sine (-α) =-Sine α
cos(-α)=cosα
tan(-α)=-tanα
Kurt (-α) =-Kurt α
Equation 4:
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:
Sine (π-α) = Sine α
cos(π-α)=-cosα
tan(π-α)=-tanα
cot(π-α)=-coα
Formula 5:
The relationship between 2π-α and the trigonometric function value of α can be obtained by formula 1 and formula 3:
Sine (2π-α)=- Sine α
cos(2π-α)=cosα
tan(2π-α)=-tanα
Kurt (2π-α)=- Kurt α
Equation 6:
The relationship between π/2 α and 3 π/2 α and the trigonometric function value of α;
sin(π/2+α)=cosα
cos(π/2+α)=-sinα
tan(π/2+α)=-cotα
cot(π/2+α)=-tanα
sin(π/2-α)=cosα
cos(π/2-α)=sinα
tan(π/2-α)=cotα
cot(π/2-α)=tanα
sin(3π/2+α)=-cosα
cos(3π/2+α)=sinα
tan(3π/2+α)=-cotα
cot(3π/2+α)=-tanα
sin(3π/2-α)=-cosα
cos(3π/2-α)=-sinα
tan(3π/2-α)=cotα
cot(3π/2-α)=tanα
What are the ways to learn math well?
First, interest.
Nowadays, families and schools have high expectations for their children, and girls are generally quiet and psychologically fragile. In addition, mathematics is more difficult, which easily leads to the decrease of girls' interest in mathematics.
Therefore, as a teacher, we should pay more attention to their learning situation, exchange subjects with them and understand their ideas. Only by understanding their thoughts can we effectively make corresponding study plans and dispel their nervousness, so as to achieve a good study state. At the same time, parents should pay more attention to their children's situation and don't reprimand them as soon as they see their poor grades, which will have a certain impact on their psychology and may even weaken their interest in mathematics. We should take a positive attitude towards children's study. Girls' emotions are different from boys'. They are generally more patient to overcome difficulties and achieve goals for interested people.
Second, confidence.
Girls' thinking ability in images is generally worse than that of boys, and so is their logical thinking ability, which easily leads to the phenomenon of lack of self-confidence. In fact, girls' accuracy is very high and standardized, so we can see that girls' math answers are mostly neat, which is actually an advantage.
Everyone has advantages and disadvantages. We should not underestimate ourselves because of our shortcomings. On the contrary, we should strive to overcome our shortcomings and enhance our self-confidence. It is necessary to know more about general problem-solving methods, some commonly used mathematical formulas, problem-solving skills and problem-solving speed. Many girls can't solve math problems quickly, and even some girls haven't done several big problems by then, so it's a pity to lose points.
Third, learning methods.
Many girls like to learn mathematics step by step and pay attention to the basics, but rarely do difficult problems, which leads to weak problem-solving ability. Girls are very serious in class. When reviewing, they like to read notes and books, but they ignore the cultivation of their own abilities, which leads to poor adaptability.
Therefore, girls should start from these points and work harder. We should not be afraid of difficult problems, but we should not do them blindly. Proper training will greatly improve our math ability. In addition, when studying mathematics, girls should learn more from boys, learn some of their excellent skills, and then transform them into their own learning skills, and combine them with problem-solving and more training, which is believed to be of great help to their mathematics level.
Fourth, preview before class.
As the saying goes, "stupid birds fly first", you can have a general understanding of the new content in advance after previewing, so that you can be targeted when listening to the class, and pay attention to the knowledge you don't know, which is likely to have a miraculous effect. Moreover, previewing in advance can also give a hint to girls' psychology, which is also of great benefit to improving girls' confidence.
What are the methods and skills to learn math well?
The simplest learning method is "enlightenment", that is, thinking hard and learning a mathematical concept. In addition to understanding what this concept means, you should do exercises to deepen your practice. Many people don't reflect after problems, that is, they don't think about why they are wrong. What caused this mistake, how to avoid this problem next time, and how to summarize it.
Grasp the classroom. Science study focuses on weekdays and is not suitable for surprise review. The most important thing to study on weekdays is to attend class for 45 minutes. Listen attentively and keep your thoughts close to the teacher. Finish homework with high quality. When writing homework, I sometimes repeat the same type of questions. At this time, we should consciously check the speed and accuracy, and we can have a deeper thinking on such problems every time we finish.
For the wrong questions that can't be done: understand each step and think about why; If this happens frequently, it is necessary to change the calculation methods and habits, such as learning to check the calculation twice to improve the accuracy. The point is to think! The deeper you think, the more thoroughly you learn, and you can get high grades with a small number of questions. But this idea is not out of thin air, but based on the wrong question. Learn from your mistakes and make up for your own shortcomings, and you will make fewer and fewer mistakes next time.
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