1. Function and equation: Students often confuse the definition domain, value domain and image of a function, as well as the concept of the solution of an equation. They may ignore the limitations of the field, leading to the wrong answer.
2. Trigonometric function: Students may make mistakes when calculating the value of trigonometric function, especially when dealing with special angles (such as 30, 45, 60). They may forget to use proper trigonometric functions or the properties of the unit circle.
3. Derivatives and integrals: Students may make calculation mistakes in the process of derivatives and integrals, especially when dealing with complex function expressions. They may forget to use the basic derivative and integral rules, or sign errors appear in the calculation process.
4. Probability and statistics: Students may make mistakes when dealing with probability and statistics. They may confuse the probability of events with the probability of sample space, or make mistakes in calculating the number of combinations.
5. Solid geometry: Students may make mistakes in calculating volume and surface area. They may forget to use the appropriate formula, or make a sign error in the calculation process.
6. Analytic geometry: Students may make mistakes when solving analytic geometry problems. They may forget to use the nature of the coordinate system, or there may be symbol errors in the calculation process.
7. Inequality and linear programming: Students may make mistakes when solving inequality and linear programming problems. They may forget to use proper inequality properties, or make sign mistakes in the process of solving.