Senior high school mathematics solid geometry problem-solving skills 1. Strategies to show the relationship between parallel position and vertical position;

(1) Judging from the nature of the known idea and the idea to prove it, that is, combining analytical method and comprehensive method to find the idea to prove the problem.

(2) Adding auxiliary lines (or faces) according to the nature of problem setting conditions is one of the commonly used methods.

(3) The three perpendicular theorem and its inverse theorem are used most frequently in the college entrance examination questions, so it should be given priority to prove that the straight line is vertical.

2. Calculation methods and skills of spatial angle:

Main steps: one post, two certificates and three calculations; If you use vectors, it is a proof and two calculations.

(1) Angle formed by two straight lines on different planes ① Translation method: ② Complement method: ③ Vector method:

(2) The angle formed by a straight line and a plane

(1) To calculate the angle between a straight line and a plane, the key is to make a vertical line, find a projection and convert it into the same triangle for calculation, or use a vector for calculation.

② Calculate by formula.

(3) dihedral angle

① Practice of plane angle: (1) Definition method; (2) Three vertical theorems and their inverse theorem methods; (3) Vertical plane method.

(2) Calculation method of plane angle:

(i) Find the plane angle, and then calculate it by triangle (solving triangle) or by vector; (ii) Projection area method; (3) Vector included angle formula.

3. Calculation methods and skills of spatial distance:

(1) Find the distance from a point to a straight line: the perpendicular of a point to a straight line is often determined by using the three perpendicular theorem, and then it is solved in the related triangle, or the distance from a point to a straight line is found by using the method of equal area.

(2) Find the distance between two straight lines on different planes: generally, find the common vertical line first, and then find the length of the segment of the common vertical line. If you can't do the common perpendicular directly, you can convert it into a line-plane distance solution (in this case, you don't need the college entrance examination).

(3) Find the distance from a point to a plane: generally, find (or make) a plane perpendicular to the known plane passing through the point, make a vertical line through the plane of the point by using the properties of the vertical plane, and then calculate; Can you use it too? Triangular pyramid volume method? Find the distance directly; Sometimes when it is difficult to find the distance from a known point to a plane directly, we can convert the distance from a point to a plane into the distance from a straight line to a plane, so? Transfer? Ask from another angle? Distance from point to plane? . Finding the distance from a straight line to a plane and the distance from a plane to a plane are generally converted into the distance from a point to a plane.

4. Memorize some commonly used small conclusions, such as: the volume formula of regular tetrahedron is; Area projection formula; ? Vertical and horizontal oblique relationship? ; Minimum angle theorem. Finding out that the projection of the apex of the pyramid at the bottom is the condition of the inner heart, outer heart and vertical center of the bottom, which may be the premise of answering some questions quickly.

5. Pay attention to the geometric elements before and after the folding of plane graphics and the expansion of three-dimensional graphics. Invariance? With what? The same? .

6. Questions related to the ball can only be applied? The old way? Find the radius of the ball.

7. Solid geometry reading questions:

(1) Find out what the geometric shape is, regular, irregular, combination, etc.

(2) Defining the structural features of geometry. What is the relationship between plane, straight line and line (parallel, vertical, equal)?

(3) Pay attention to what are vertical planes, vertical lines, parallel lines and parallel lines.

High school mathematics learning methods 1

Strengthen reflection after doing the questions, so as to achieve fragmentation of knowledge and stringing of problems. Over time, build a scientific network content and method system. As the saying goes:? Money is hard to buy. Look back? . Generally speaking, there are too few problems that can be said and done, and many problems that practice makes perfect are out of the question. Therefore, we should do more questions appropriately. However, exams are generally difficult to enter the sea of questions and pile up questions. Therefore, it is necessary to sort out the knowledge learned reasonably and systematically, sum up and reflect on it, so as to improve the mathematics level of senior high school.

High school mathematics learning methods II

Accumulate high school mathematics materials at any time, and pay attention to accumulating review materials. Arrange class notes, exercises, district unit tests and various papers in chronological order. Every time you read it, mark the key content of the next reading on it. In this way, the math review materials can be seen more accurately and clearly.

High school mathematics learning methods 3

It is a common problem that freshmen's learning initiative is too poor to cooperate with teachers' active learning. Students often have a good time after finishing their homework. Junior high school students are basically the same, and obedient children can learn well. High school is not like this. Although there is a lot of homework, it is definitely not enough. The teacher also said a lot, but the teacher didn't specify who should do what. Therefore, freshmen must improve their initiative in learning mathematics. Prepare for the transition to the future college students' learning style.

High school mathematics learning method 4

Reasonable planning step by step, high school study is very tense. Every student should devote almost all his energy. If you want to make rapid progress, you must make a long-term and practical goal and plan for your mathematics study, such as reaching the average grade at the end of the first semester and reaching the first third of the grade in the first school year. In addition, we should make a study plan for ourselves, arrange our spare time in detail, and make reasonable minor adjustments in time.

Summary of senior high school mathematics learning methods 1. Strengthen reflection after doing the problem.

2. Take the initiative to review, summarize and improve

3. Pay attention to correcting mistakes and not repeating them.

4. Accumulate information and organize it at any time.

5. Cooperate with teachers to learn actively

6. Reasonable planning and gradual progress.

Induction of Main Test Sites of Mathematics in Senior High School

One: Assembly

Basic operation of test center 1:set

Test site 2: the relationship between sets

Second: Function

Test Center 3: Functions and Their Representation

Test Site 4: Basic Properties of Functions

Test site 5: linear function and quadratic function.

Test Site 6: Exponent and Exponential Function

Test site 7: Logarithms and Logarithmic Functions

Test site 8: power function

Test center 9: function image

Test location 10: functional range and maximum value

Test center 1 1: Application of function

Third, the preliminary study of solid geometry

Test center 12: structure, three views and straight views of space geometry

Test center 13: surface area and volume of space geometry.

Test center 14: the positional relationship between points, lines and surfaces.

Test center 15: the nature and judgment of parallel lines and planes

Test Center 16: Measurement and characteristics of vertical lines and planes.

Test center 17: space corner

Test center 18: space vector

Four: straight lines and circles

Test center 19: the relationship between straight line equation and two straight lines

Test site 20: Equation of circle

Test site 2 1: the positional relationship between straight lines and circles, and between circles.

V: Preliminary block diagram of the algorithm

Test Center 22: Algorithm Preliminary and Block Diagram

Six: trigonometric functions

Test site 23: trigonometric function, isomorphic function, inductive formula from any angle

Test site 24: images and properties of trigonometric functions

Test site 25: the maximum value of trigonometric function and its comprehensive application

Test site 26: trigonometric identity transformation

Test site 27: Solving Triangle

Seven: plane vector

Test site 28: the concept and operation of plane vector

Test Site 29: Use of Carrier

Eight: sequence

Test center 30: the concept of sequence and its representation

Test center 3 1: arithmetic progression.

Test site 32: geometric series

Test Site 33: Comprehensive Application of Sequences

Nine: Inequality

Test site 34: inequality and inequality

Test site 35: solution of inequality

Test site 36: linear programming

Test site 37: comprehensive application of inequality

X: Counting principle

Test site 38: permutation and combination

Test site 39: binomial theorem

XI: probability and statistics

Test Center 40: Classical Probability and Geometric Probability

Test site 4 1: probability

Test Center 42: Statistics and Statistical Cases

XII: Common logical terms

Test site 43: simple logic

Test center 44: sufficient conditions and necessary conditions

XIII: Conic curve

Test site 45: ellipse

Test site 46: hyperbola

Test site 47: parabola

Test site 48: positional relationship between straight line and conic curve

Test site 49: conic equation

Test site 50: Synthesis of conic curves

Fourteen: Derivative and Its Application

Test site 5 1: derivatives and integrals

Test Site 52: Application of Derivatives

Fifteenth: Reasoning and Proof

Test site 53: perceptual reasoning and deductive reasoning

Test center 54: direct proof and indirect proof

Test site 55: mathematical induction

Sixteen: the expansion of number system and the introduction of complex numbers

Test site 56: the expansion of number system and the introduction of complex numbers

Seventeen: the content of the exam.

Test site 57: Selected lectures on geometric proof

Test Site 58: Coordinate System and Parameter Equation