I. Algebra sum equation:

Algebraic simplification: learn to simplify algebraic expressions by using the distribution law and the skill of merging similar items to reduce tedious calculations.

Factorization: master the factorization methods, especially the factorization of common factors, complete square formula, square of difference/sum and other common formulas.

Properties of quadratic function: Learn to draw and analyze functions quickly by using the open direction, vertex and axis symmetry of quadratic function.

Second, geometry:

Symmetry of figures: Understanding the symmetry of figures, such as the symmetry of squares, can be used to prove geometric theorems.

Similar triangles: Using the properties of similar triangles, we can solve the problems of equal proportion division and proportion.

Knowledge about the circle: It is very helpful to master the arc length, sector area, central angle and tangent of the circle.

Third, functions and images:

Function image analysis: learn to observe function images and understand the characteristics of function, such as increase and decrease, extreme value and inflection point.

Application of derivative: learn to use derivative to solve problems such as maximum, tangent and curve concavity.

Derivative law: master the basic derivative law, such as the derivative law of power function, trigonometric function and exponential function.

Fourth, probability statistics:

Permutation and combination skills: Learn to use the knowledge of permutation and combination to solve problems, such as counting the number of permutations and combinations.

Probability calculation: Understand the basic probability calculation methods such as conditional probability and Bayesian theorem, and apply them to practical problems.

V. Sequence and Series:

General formula of series: Learn to find the general formula of arithmetic progression and geometric progression, and make quick calculation and derivation.

Sum of series: master the sum formulas of commonly used series, such as geometric progression and arithmetic progression, so as to make quick sum.

Six, trigonometric function:

Trigonometric function transformation: understand the transformation rules of sine, cosine and tangent function images, such as translation and scaling.

Trigonometric function identity: master the basic identities of trigonometric functions, such as sum-difference product, angle-doubling formula, etc.

Seven, advanced mathematics:

Differential equation: Mastering the basic concepts and solutions of differential equations can solve some basic differential equation problems.

Integral calculation: understand the geometric meaning and basic properties of integral, and master the calculation methods of indefinite integral and definite integral.

Limit nature: Understand the definition and nature of function limit, and master the limit algorithm.

Eight, problem-solving skills:

Multi-angle thinking: Try different methods to solve a problem, and think from multiple angles, and you may get an answer faster.

Make connections: There are connections between different mathematical knowledge. Learning to connect different knowledge points is helpful for understanding and application.

Simplify complexity: When encountering complex problems, try to break them down into several simple steps and solve them step by step.

Problem solving skills: develop the habit of clearing your mind first and then calculating to avoid making mistakes due to carelessness.

Practice summary: often practice various topics, summarize the methods and skills of solving problems, and form your own ideas and routines for solving problems.

Nine, learning methods and attitudes:

Solid foundation: Mathematics is a step-by-step subject, so we should have a solid grasp of basic knowledge and lay a good foundation for subsequent knowledge.

Persist in reviewing: Mathematics needs to be constantly consolidated, and it needs to be reviewed properly every day to keep its knowledge active.

Autonomous learning: do more autonomous learning, try to solve the problems encountered and improve the ability to solve problems.

Positive thinking: don't give up when you encounter difficulties, and actively think about ways and ideas to solve problems.

Patience and perseverance: It takes patience and perseverance to learn mathematics, and it may take time and perseverance to solve problems.