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Master the concepts, representations, and operations of sets.
1.1 Basic Concepts and Definitions of Sets
1.2 Representation Methods of Sets
1.3 Relationships and Operations of Sets
Deep dive into domains, ranges, monotonicity, parity, and elementary functions.
2.1 Concepts and Definitions of Functions
2.2 Representation Methods of Functions
2.3 Properties of Functions
2.5 Power and Exponential Functions
2.6 Logarithmic Functions
Master solving quadratic equations, inequalities, and fractional equations.
3.1 Solving Quadratic Equations
3.2 Solving Linear Inequalities
3.3 Solving Quadratic Inequalities
3.4 Solving Fractional Equations
Master trigonometric identities, graphs, and angle formulas.
4.1 Basic Concepts and Definitions
4.2 Angle Measurement and Radians
4.3 Graphs and Properties
4.4 Sum and Difference Formulas
4.5 Double Angle Formulas
4.7 Product-to-Sum and Sum-to-Product
Conquer formulas for general terms and sums of arithmetic and geometric sequences.
5.1 Basic Concepts and Simple Representations
5.2 Arithmetic Sequences and their Sums
5.3 Geometric Sequences and their Sums
Learn limits, differentiation rules, and applications in function analysis.
6.1 Concept of Derivatives
6.2 Operations and Chain Rule
6.3 Applications in Analyzing Functions
6.4 Derivatives of Implicit Functions
6.5 Derivatives of Parametric Functions
6.6 Higher-Order Derivatives
6.7 Limits of Sequences and Functions
Master coordinates, lines, circles, and plane vectors.
7.1 Rectangular Coordinate System
7.2 Inclination and Slope of Lines
7.5 Relationships Between Lines
7.6 Basic Concepts of Plane Vectors
7.7 Operations of Plane Vectors
7.8 Dot Product of Plane Vectors
Deep analysis of standard equations and geometric properties of conics.
Understand the concepts, geometric meaning, and operations of complex numbers.
9.1 Basic Concepts of Complex Numbers
9.2 Algebraic Operations of Complex Numbers
Master the 3D coordinate system and space vector operations.
10.1 Space Rectangular Coordinate System
10.2 Space Vectors and Operations
Use space vectors to solve positional and distance problems.
11.1 Equations of Planes in Space
11.2 Equations of Lines in Space
11.3 Relationships of Points, Lines, and Planes
11.4 Distance Between Parallel Planes
Master addition/multiplication principles, permutations, combinations, and the binomial theorem.
12.1 Addition and Multiplication Principles
12.2 Permutations and Combinations
From classical probability to normal distributions and data analysis.
13.1 Basic Concepts of Probability
13.2 Random Events and Probability
13.3 Classical Probability Model
13.4 Properties and Calculations
13.5 Discrete Random Variables
13.7 Introduction to Statistics
13.8 Data Description and Analysis