Chapter 1 Set and Simple Logic
collection
1. 1 set
1.2 subset, complete set and complement set
1.3 intersection and union
1.4 Inequality solution with absolute value
1.5 One-dimensional linear inequality solution
Number of elements in the reading material collection
Second, simple logic.
1.6 logical connector
1.7 Four propositions
The necessary and sufficient condition of 1.8
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Chapter II Functions
A function
2. 1 function
2.2 Representation of functions
2.3 Monotonicity of Functions
2.4 inverse function
Two exponents and exponential functions
2.5 Index
2.6 exponential function
Triplogarithms and Logarithmic Functions
2.7 logarithm
The invention of reading material logarithm
2.8 logarithmic function
2.9 Application example of function
Mathematical model of free falling motion of reading materials
In practice, the functional model of practical problems is established.
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Chapter III Sequence of Numbers
3. 1 series
3.2 arithmetic progression
3.3 arithmetic progression's top n sums
Read about savings calculation.
3.4 geometric series
3.5 the first n sums of geometric series
Research study topic: the application of sequence in installment payment
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Chapter 4 trigonometric functions under the first volume
Trigonometric function of arbitrary angle
4. Generalization of the concept of10 angle
4.2 Arc system
4.3 trigonometric function at any angle
Trigonometric Function and Euler of Reading Materials
4.4 Basic formula of trigonometric function with the same angle
4.5 Inductive formula of sine and cosine
Trigonometric function of sum and difference of paired angles
4.6 Sine, cosine and tangent of sum and difference of two angles
4.7 Sine, Cosine and Tangent of Double Angle
Images and properties of trigonometric functions
4.8 Images and Properties of Sine and Cosine Functions
4.9 Image of function y=Asin(ωx+φ)
4. Properties of10 image and tangent function
4. 1 1 Find the angle with the known trigonometric function value.
Reading materials Tide and port water depth
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The fifth chapter plane vector
Vector and its operation
5. 1 vector
5.2 Addition and subtraction of vectors
5.3 Product of real number and vector
5.4 Coordinate Operation of Plane Vector
5.5 Fixed fractional points of line segments
5.6 Arithmetic of Sum of Quantities of Plane Vectors
5.7 Coordinate Representation of the Quantity Product of Plane Vector
5.8 Translation
Three types of reading material carriers
Binary declination triangle
5.9 sine theorem and cosine theorem
5. Application example of10 declination triangle
Application of Triangle in Practical Surveying Work
How did people measure radius of the earth in the early days?
Topic of inquiry learning: the application of vectors in physics
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In the second volume
Chapter VI Inequality
6. Properties of1inequality
6.2 Arithmetic Average and Geometric Average
6.3 Proof of Inequality
6.4 Examples of unequal solutions
6.5 Inequalities with absolute values
Arithmetic average and geometric average of n positive numbers in reading materials
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Chapter VII Equations of Lines and Circles
7. 1 Angle and slope of straight line
7.2 linear equation
7.3 positional relationship between two straight lines
Reading material vectors and straight lines
7.4 Simple linear programming
Research-based learning projects and practical assignments: the practical application of linear programming
7.5 Curves and Equations
Reading materials Descartes and Fermat
7.6 Equation of Circle
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Chapter VIII Conic Curve Equation
8. 1 ellipse and its standard equation
8.2 Simple Geometric Properties of Ellipse
8.3 hyperbola and its standard equation
8.4 Simple geometric properties of hyperbola
8.5 parabola and its standard equation
8.6 Simple Geometric Properties of Parabola
Optical characteristics of conic curve of reading material and its application
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Book two, the next A
Chapter 9 Lines, Planes and Simple Geometry
9. 1 plane
9.2 Spatial straight line
9.3 Determination and properties of parallel lines and planes
9.4 Determination and properties of straight lines perpendicular to the plane
9.5 Determination and characteristics of two parallel planes
9.6 Determination and properties of verticality of two planes
9.7 prism
9.8 pyramids
Cylindrical and conical volumes of reading materials
The theme of inquiry learning: the discovery of polyhedral euler theorem
Reading materials Euler formula and types of regular polyhedron
9.9 ball
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Chapter 10 permutation, combination and binomial theorem
10. 1 classification counting principle and step counting principle
10.2 arrangement
10.3 combination
On the arrangement and combination of reading materials from the perspective of collection
10.4 binomial theorem
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Chapter 11 Probability
1 1. 1 probability of random events
1 1.2 mutually exclusive events has the probability of occurrence.
1 1.3 Probability of simultaneous occurrence of mutually independent events
Is it fair for individuals to draw lots first and then choose reading materials?
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Volume II B Chapter 9 Lines, Planes and Simple Geometry
9. Basic properties of1plane
9.2 Parallel straight lines and non-planar straight lines in space
9.3 The straight line is parallel to the plane, and the plane is parallel to the plane.
9.4 The straight line is perpendicular to the plane
9.5 Space Vector and Its Operation
9.6 Coordinate operation of space vector
9.7 Angle and dihedral angle formed by straight line and plane
9.8 distance
Popularization and application of the concept of reading material vector
9.9 Prisms and pyramids
The theme of inquiry learning: the discovery of polyhedral euler theorem
Reading materials Euler formula and types of regular polyhedron
9. 10 ball
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Chapter 10 permutation, combination and binomial theorem
10. 1 classification counting principle and distribution counting principle
10.2 arrangement
10.3 combination
On the arrangement and combination of reading materials from the perspective of collection
10.4 binomial theorem
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Chapter 11 Probability
1 1. 1 probability of random events
1 1.2 mutually exclusive events has the probability of occurrence.
1 1.3 Probability of simultaneous occurrence of mutually independent events
Is it fair to draw lots first and then choose reading materials?
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Book III (Science) Chapter I Probability and Statistics
1. 1 Distribution table of discrete random variables
1.2 expectation and variance of discrete random variables
1.3 sampling method
The estimated population distribution is 1.4.
Cumulative percentage distribution of reading materials
1.5 normal distribution
1.6 linear regression
Derivation of linear regression equation of reading materials
Practical assignments study practical problems through sampling surveys.
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Chapter II Limits
2. 1 Mathematical induction and its application examples
Incomplete induction and complete induction of reading materials
Research learning theme: Yang Hui Triangle
2.2 sequence restrictions
2.3 Functional limitations
2.4 Four operations of limit
The sum of infinite geometric series of reading materials.
2.5 Functional continuity
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Chapter III Derivatives
3. The concept of1derivative
3.2 Derivatives of Several Common Functions
Examples of the rate of change of reading materials
3.3 Derivative of sum, difference, product and quotient of functions
3.4 Derivative of Compound Function
3.5 Derivatives of Logarithmic and Exponential Functions
Approximate calculation of reading materials
3.6 Monotonicity of Functions
3.7 Extreme value of function
3.8 Maximum and Minimum Values of Functions
3.9 Background and historical significance of calculus establishment
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Chapter IV Extension of Number System-Complex Number
4. The concept of1complex number
4.2 Operation of Complex Numbers
4.3 the expansion of the number system
Topic of research study: the relationship between complex number and plane vector and trigonometric function
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Appendix I Comparison Table of Chinese and English Vocabulary
Appendix II Derivative Formula Table
Book III (Liberal Arts) Chapter I Statistics
1. 1 sampling method
The estimated population distribution is 1.2.
1.3 Estimation of Overall Expectation and Variance
Practical assignments study practical problems through sampling surveys.
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Appendix random number table
Chapter II Derivatives
2. Background of1derivative
2.2 the concept of derivative
2.3 Derivatives of Polynomial Functions
2.4 Monotonicity and Extremum of Functions
2.5 Maximum and Minimum Values of Functions
2.6 the background and historical significance of calculus.
Research learning theme: Yang Hui Triangle
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Appendix part Chinese and English vocabulary comparison table