Extending in all directions, the river is full of water and the fish is shallow, which makes the unintelligent students smarter and the intelligent students smarter.
Sun Weigang
This book is the work of Sun Weigang, a famous math educator. Based on the analysis and mastery of basic knowledge, each chapter consists of two parts: study guidance and examples. After refining the concept, the laws, methods and thinking rules of the periphery of the concept are extended. The book points out that to learn mathematics well, we must look at problems from a systematic perspective and learn the learning methods of multiple solutions to one problem, multiple solutions to one problem (a conclusion) and multiple solutions to one problem (good at summarizing).
Directory:
First algebra
Chapter 65438 Basic knowledge of +0 algebra
First, study guidance
Second, examples
Chapter II Rational Numbers
First, study guidance
Second, examples
Chapter III Addition and Subtraction of Algebraic Expressions
First, study guidance
Second, examples
Chapter 4 One-dimensional Linear Equation
First, study guidance
Second, examples
Chapter V Binary Linear Equations
First, study guidance
Second, examples
Chapter VI One-dimensional Linear Inequalities and One-dimensional Linear Inequalities.
First, study guidance
Second, examples
Chapter VII Multiplication and Division of Algebraic Expressions
First, study guidance
Second, examples
Chapter VIII Factorization
First, study guidance
Second, examples
Chapter 9 Scores
First, study guidance
Second, examples
Chapter 65438 +00 root
First, study guidance
Second, examples
Chapter 1 1 quadratic radical
First, study guidance
Second, examples
Chapter 12 One-variable quadratic equation
First, study guidance
Second, examples
Chapter 13 Functions and Their Images
First, study guidance
Second, examples
Chapter 14 index
First, study guidance
Second, examples
Chapter 15 Common Logarithms
First, study guidance
Second, examples
Chapter 16 Solving Triangle
First, study guidance
Second, examples
Second plane geometry
Chapter 17 Line segments and angles
First, study guidance
Second, examples
Chapter 18 Intersecting lines and parallel lines
First, study guidance
Second, examples
Chapter 19 Triangle
First, study guidance
Second, examples
Chapter 20 Quadrilateral
First, study guidance
Second, examples
Chapter 265438 +0 area and Pythagorean theorem
First, study guidance
Second, examples
Chapter 22 Similarity
First, study guidance
Second, examples
Chapter 23 Circle
First, study guidance
Second, examples
Selected lectures on the third topic
Chapter 24 Propositions and Point Trajectories
Chapter 25 Reduction to absurdity and the same law
Chapter 26 Symmetry
Chapter 27 Solving Comprehensive Problems
Answers and tips
postscript
Video Course of Mathematics Tutoring Teaching in Junior Middle Schools in Sun Weigang;
Senior one, senior two and senior three complete mathematics teaching contents, * * 18 CD,18 class hours!
Speaker: Sun Weigang, special teacher.
Directory:
Mathematics for the first grade of junior high school (6 discs)
B0 19 junior algebra ①
0 1 1, learning methods
Second, the preliminary knowledge of algebraic expressions is the key to finding algebraic values.
Third, rational numbers.
04 1, numerical axis
05 2. Triple Meaning and Same Essence of "One"
06 3, understand the absolute value
07 4, rational number mixed operation
In May 2008, the initial chaos was quickly ended.
09 6. Don't skip digit recognition and reading.
B020 Junior One Algebra ②
0 1 1. Addition and subtraction of algebraic expressions
1, polynomials in descending order.
02 2. Parentheses are easy to make mistakes.
3. Example (4 solutions)
03 4. Simplification of addition and subtraction of algebraic expressions.
5. Example (4 solutions)
04 bivariate and unary linear equations
1, example of test equation (three solutions)
05 2, the steps to solve a linear equation.
3. Several equation solutions different from textbooks.
06 4. Divide the two sides of the equation step by step with the x coefficient.
07 5, denominator error analysis example 6.
B02 1 elementary algebra ③
0 1 (continued) one-dimensional linear equation
6. Homotopy equation
The principle of (1) simultaneous solution to equation Ⅰ
02 (2) Homosolution Principle of Equation Ⅱ
03 7, the principle of solving the equation process
04 8, the application of a linear equation.
05 (1) Find out the principle
06 (2) List process
07 (3) Seek the best choice
08 a. Deformation of graphics or objects
09 b. Find two or more unknowns.
10 c, tripping problem
1 1 d, work problem
12 e, problems related to solution concentration
13 (4) Without it, the original religion will never change.
B022 Junior One Algebra ④
0 1 linear and binary linear equations
1, a binary linear equation always has countless solutions.
02 2. Solutions of binary linear equations: one set of solutions, countless sets of solutions, and no solution.
03 3, addition and subtraction and "addition" elimination method
04 4, the goal should be "consistent"
05 5, the application of linear equations
06 II. Unary Linear Inequalities and Unary Linear Inequalities Group
1, the properties of inequality and the principle of difference between inequality and solution.
07 2, the solution of one-dimensional linear inequality should be focused.
08 3, the method of testing the linear inequality of one variable
Third, multiplication and division of algebraic expressions.
1, coefficient and exponent operations are confused.
10 2,8 multiplication formula
1 1 3. Calculate by multiplication formula.
12 4. It is easy to make mistakes and form a habit.
B023 First Geometry ①
0 1 1, the purpose and method of learning geometry
02. Points and lines
1, defined and undefined nouns
03 2. Two straight lines cannot have two or more things in common.
The distance between the line segments connecting two points is different.
05 4. Expression of midpoint
06 Third, the expression of angular bisector
07 Four, the essence of unit conversion
Five, an important way to learn geometry.
09 1, grasp the essence of the concept
10 2, get into the habit of understanding concepts with graphics.
1 1 3. Cultivate the ability of drawing.
12 4, pay attention to the narrative
13 six. A valuable picture
14 seven. Strengthen the practice of high-taste questions (Example 5)
B024 First Geometry ②
0 1 I. Summary
02 1, laying a good foundation for learning geometry.
03 2, master logical reasoning and argumentation.
04 3. Organization of Geometry Learning
05 4, there are not many topics, but they are wonderful.
Second, intersecting lines and parallel lines.
07 1, pendulum model and the idea of using motion
08 2. It has nothing to do with whether the complementary angle is parallel to two straight lines.
09 3. Attach importance to the proof of parallel axiomatic reasoning.
10 4, in the same plane.
1 1 III. Expression of reasoning proof
12 1, each step of reasoning has a corresponding causal relationship.
13 2, to prevent the confusion between nature and judgment
14 3. The basis cannot be specious.
15 4. Beginners should never skip too much.
Mathematics in the second day of junior high school (6 discs)
B025 Junior Two Algebra ①
0 1 First of all, accurately understand the significance and operational requirements of factorization.
Second, establish reasonable decomposition steps.
03 1, extracting the common factor (Example 3)
04 2, look at a few items
(1) binomial formula (Example 4)
Trinomial formula
I. Example 4
B, about the cross multiplication
06 (3) Quadrupole (Example 5)
07 (4) Six Items (Example 4)
B026 Junior Two Algebra ②
01i. (continued) factorization
1, add project examples (5 solutions)
02 2, alternative method
03 3, double cross multiplication
04 4, undetermined coefficient method
05 seconds, fraction
1, Problems in Understanding the Concept of Fraction
06 2. "You can change two of the three symbols at will" and "negative sign"
07 3, two common mistakes
08 4. Addition and subtraction of fractions with different denominators
09 5. Two Methods of Simplifying Complex Fractions (Example 3)
10 6, test the fractional equation
1 1 7, master some skills
B027 Junior Two Algebra ③
0 1 one, the root of a number
1, key point: negative numbers have no square root and the arithmetic square root of real numbers is nonnegative.
Integer and fraction cannot be infinite cyclic decimals.
Quadratic and quadratic roots
1, negative numbers have no square root (Example 2)
04 2. The arithmetic square root of real numbers is nonnegative (Example 3)
05 3, add a formula.
06 4. Pay attention to flexibility (Example 2)
5. Classify topics with rational denominator (Example 3)
B028 second grade geometry ①
0 1 1. Line segments of straight lines and triangles
02 Second, the proof of the theorem of triangle interior angle sum
03 three. Nature, Judgment and Definition
4. Edge, edge and angle cannot be judged as congruences of triangles.
5. Equality of certificates.
06 1, Symmetry, Rotation and Translation Graphics
07 2, Example 2
08 3. The figure is asymmetrical, rotated or translated.
When the bisector of the angle and the corresponding parallel line appear at the same time, grasp the isosceles triangle.
10 seven. Angle dividing line
1, four ideas
1 1 2, example 2
B029 second grade geometry ②
0 1 1, the solution of the sum of polygons' internal angles
Second, the outer angle of a polygon is different from that in polygons and formulas.
Third, the evolution of quadrilateral graphics.
04 1, subordinate inclusion relation
05 2, the nature of quadrilateral
06 3, decision theorem
The stronger the conclusion of the property theorem, the better, and the weaker the premise of judging the theorem.
08 Five, the law of solving problems
1, edge and corner methods, for example, 1
09 2. Diagonal Method, Example 2
10 six. Summarize the thinking law of solving problems in practice.
1, involving trapezoidal questions, generally add four kinds of auxiliary lines.
1 1 2. The problem of proving that a quantity is the sum of two quantities
12 3, involving intermediate points.
B030 second grade geometry ③
0 1 1. (Continued) Thinking Law of Solving Problems
4. For the two intermediate problems,
Second, similar shapes.
1, the nature and foresight of proportion
03 2, the general law of similarity and consistency
04 3, two ways to think easily
05 4, the law of similar accumulation
06 5. Prove the thinking law of the proportion of four line segments.
07 (1) Example 1( 10 solutions)
08 (2) Example 2(3 solutions)
Mathematics in Grade Three (6 CDs)
B03 1 third grade algebra ①
0 1 unary quadratic equation should be learned skillfully and solidly.
02 Second, the way of thinking to solve the quadratic equation of one variable
03 1, convert the coefficient into an integer.
04 2, reduce the common factor
05 3. Turn the negative value of quadratic coefficient into positive value.
Third, sort out the application programs of several methods.
Fourth, remember ax? +bx+c=0 requires a ≠0.
V. How to choose "tools"
09 1, make good use of discriminant
10 2. Make good use of the relation theorem between roots and coefficients.
1 1 six. Basic theme types
12 cases 1
13 cases 2
B032 Grade 3 Algebra ②
0 1 (continued) One-variable quadratic equation
First of all, we should test the solution of irrational number equation.
02 case 1
03 cases 2
How to deal with two or more root numbers
Second, the overall idea of substitution method.
Example 1
Example 2(3 solutions)
B033 third grade algebra ③
0 1 function and its image
1, coordinate system knowledge points
Constants are relative in application.
03 3. Functional essence: correspondence.
04 4, independent variable value range
05 5. Combination of numbers and shapes
06 6, the method of finding the quadratic resolution function.
07 7, the thinking method of solving the maximum (minimum) value of application problems
B034 Grade 3 Algebra Geometry ④
0 1 1. Thinking method for solving the maximum (minimum) value of application problems (continued)
Second, solve comprehensive problems.
03 three. geometry
1, solving right triangle
04 (1) The changing principle of sine, cosine, tangent and cotangent of special angle.
05 (2) The height of the bottom object cannot be measured.
06 2, circle
07 (1) Grasp the essence of the circle
08 (2) Seek the connection with circle related knowledge.
09 (3) System Memory Theorem
10 (4) Summarize the thinking law of solving problems.
1 1 (5) lays a good foundation for reduction to absurdity.
B035 Grade 3 Mathematics General Review ⑤
0 1 1. Strengthen the understanding of the concept essence, sort out the knowledge system, and summarize the thinking method of solving problems.
Second, a comprehensive example.
3. Examples of thinking methods to solve problems
1, right triangle
04 2, solve the problem of area
05 3. Solve the problem about the circle.
06 4, reduction to absurdity
B036 Grade 3 Mathematics General Review ⑥
0 1 First of all, use the law of thinking to solve problems.
02 1, moderately difficult problem (5 solutions)
03 2. Difficult questions
Example 1
04 cases 2
05 case 3
06 cases 4
07 case 5
Second, talk about examples of reduction to absurdity.