Basic goods
The first lecture on collection
The Meaning and Representation of 1. 1 Set
Basic relations and basic operations between 1.2 sets
1.3 simple logic
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The second lecture on functions
2. 1 function and function representation
2.2 Three elements of function
2.3 Functional image
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The third lecture on the properties of functions
3. Monotonicity of1function
3.2 Functional equivalence
3.3 inverse function
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Lecture 4 Elementary Function Model
4. 1 proportional function, inverse proportional function, linear function and quadratic function
4.2 Power function
4.3 Exponential function
4.4 Logarithmic function
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Comprehensive application article
Theoretical application of function
The Application of 1. Function in Equation
Second, the application of function in inequality
Practical application of function
First, the use of analytical formulas.
Secondly, choose the analysis formula.
Thirdly, the analytical formula is established.
Fourth, the design analytical formula
Comprehensive application training problem
-Solid geometry-
Basic goods
The first lecture on space geometry
1. 1 spatial geometry
1.2 orthographic projection and three views
1.3 surface area and volume of space geometry
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The second point is the relationship between points, lines and planes.
2. 1 The positional relationship among points, lines and surfaces in space
2.2 Parallelism-Determination and characteristics of parallelism of straight lines and planes
2.3 Vertical Relationship-Determination and Properties of Vertical Lines and Vertical Planes
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Comprehensive application article
Theoretical application of solid geometry
First, an example of constructing geometric proof inequality
Second, the maximum (minimum) value problem with geometry as the carrier.
Practical application of solid geometry
First, the application of area as a carrier
Second, the application of volume as a carrier
Third, the practical application of spatial straight lines and planes
Fourthly, the practical application of two planes in space.
Comprehensive application training problem
Analytic geometry
Basic goods
The first lecture on plane analytic geometry
1. 1 sum of straight lines (linear) equation
1.2 Circle sum equation
1.3 space rectangular coordinate system
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Lecture 2 Ellipse
2. 1 ellipse
2.2 The relationship between straight line and ellipse
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Lecture 3 Parabola
3. 1 parabola
3.2 The relationship between straight line and parabola
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Lecture 4 Hyperbola
4. 1 hyperbola
4.2 The relationship between straight line and hyperbola
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Comprehensive application article
Theoretical application of analytic geometry
First, the problem of assembly.
Second, the problem of equations and inequalities.
Third, the maximum (minimum) value and value range.
Fourth, the function problem.
Comprehensive test questions of theoretical application
Practical application of analytic geometry
First, the linear application problem
Second, the circular application problem
Third, elliptical application questions
Fourth, the application of parabola
Fifth, the application of hyperbola
Practical application of comprehensive examination questions
-Algorithm-
catalogue
Basic goods
The first lecture on primary algorithm
The concept of 1. 1 algorithm
1.2 program block diagram
1.3 basic algorithm statement
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The second lecture on algorithm cases
2. 1 phase division and polyphase subtraction, algorithm and sorting
2.2 decimal system
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Comprehensive application article
Theoretical application of algorithm
Practical application of binary algorithm
-Statistics and probability-
Basic goods
The first lecture of statistics
1. 1 random sampling
1.2 estimate the population with samples
Correlation between 1.3 variables
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Lecture 2 Probability
2. 1 Probability of random events
2.2 Classical probability
2.3 Geometric probability
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Comprehensive application article
Theoretical application of statistics and probability
Practical application of statistics and probability
-trigonometric function-
Basic goods
Lecture 1 trigonometric function
1. 1 arbitrary angle and arc system
1.2 trigonometric function at any angle
Basic relations of 1.3 equidistant trigonometric functions
The inductive formula of 1.4 trigonometric function
1.5 Find the angle with the known trigonometric function value.
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The second lecture on images and properties of trigonometric functions
2. Images and properties of1trigonometric function
2.2 image of function y = asin (ω χ+φ)
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The third lecture is the sum and difference formula of sine, cosine and tangent angles.
3. 1 sine, cosine and tangent sum difference formula
3.2 Double Angle Trigonometric Function
3.3 Review the problem-solving skills of trigonometric functions
3.4 Deflection Triangle
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Comprehensive application article
Theoretical application of trigonometric function
First, the application of trigonometric functions in algebra
Second, the application of trigonometric function in solid geometry
Third, the application of trigonometric function in analytic geometry
Practical application of trigonometric function
First, the problem of taking the right triangle as the model.
Second, the problem of taking right triangle and oblique triangle as models
Thirdly, the problem of taking the oblique triangle as the model.
Fourth, the problem with the function y = asin (Ω χ+φ) as the model.
Comprehensive application training problem
plane vector
The first basic article
The first lecture on vectors and their operations
1. 1 vector
Addition and subtraction of 1.2 vector
1.3 product of real number and vector
1.4 Arithmetic of Sum of Quantities of Plane Vector
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The second lecture on plane vector in coordinate form and its operation
2. Coordinate representation of1plane vector
2.2 Coordinate operation of plane vector
2.3 Boundary point of line segment
2.4 Translation
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The second comprehensive application article
Theoretical application of plane vector
Practical application of plane vector
Comprehensive application training problem
series
Basic goods
The first lecture series
The concept of 1. 1 sequence
The sum of the first n items of 1.2 series.
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The second lecture is about arithmetic progression.
2. 1 Basic concept of arithmetic progression
2.2 the basic nature of arithmetic progression
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The third lecture is about geometric series.
3. The basic concept of1geometric series
3.2 Basic Properties of Geometric Series
3.3 Examples of integrating arithmetic progression and geometric progression into one topic
3.4 Research topic: the application of sequence in installment payment.
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The fourth lecture is about the limit of sequence and the introduction of mathematical induction.
4. Limit of1sequence
4.2 Mathematical induction
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Comprehensive application article
Theoretical application of sequence
Arithmetic progression's application.
Application of geometric series
The combination of three sequences and other knowledge.
Practical application of sequence
Arithmetic progression's application.
Application of geometric series
Comprehensive application training problem
inequality
The first basic article
The first lecture on inequality and its properties
1. 1 inequality and its properties
The application of 1.2 comparison method in inequality
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The second lecture on the proof of inequality
2. 1 basic inequality
2.2 the proof method of inequality
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The third lecture on the solution of inequality
3. Solution of1rational inequality
3.2 Solutions to Unreasonable Inequality
3.3 Solving Exponential Inequalities and Logarithmic Inequalities
3.4 Inequalities with absolute values
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The second comprehensive application article
Theoretical application of inequality
First, the application of inequality solution
Secondly, some conclusions about the distribution of real roots of quadratic equations.
Third, use inequality to find the maximum (minimum) value of the function.
Practical application of inequality
I. use "a, b ∈ r+= >; A+b≥2√ab "solution inequality.
Second, use "a, b, c ∈ r+= >; A+b+c≥3 cubic √abc "solution inequality.
Third, use "ax +bx+c≤0 squared (a≠0)" to solve the inequality application problem.
Comprehensive application training problem
-Calculus-
Basic goods
Limit first lecture
Limit of 1. 1 sequence
The limit of 1.2 function
Continuity of 1.3 function
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The second lecture on derivatives
2. The concept of1derivative and its geometric significance
2.2 Calculation of derivative
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Lecture 3 Integration
3. 1 indefinite integral
3.2 The concept and calculation of definite integral
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Comprehensive application article
The fourth lecture on the application of derivatives
4. Application of1limit
4.2 Application of Derivatives
4.3 Application of Integral
4.4 Use derivatives to explain equations, inequalities and function problems.
4.5 Examples of using calculus to solve application problems