Function error-prone knowledge point
1: the meaning of each undetermined coefficient.
2. Mastering the solutions of various analytic functions skillfully, several undetermined coefficients need several point values.
3. Use the image to find the solution set of inequality and the solution of equation (group), and use the image properties to determine the increase or decrease.
4. Two variables use function models to solve practical problems, and pay attention to the differences between equation, function and inequality models to solve problems in different fields.
5. Using function image classification (parallelogram, similarity, right triangle, isosceles triangle) and the solution of classification.
Equations (groups) and inequalities (groups)
1: The solution of various equations (groups) should be mastered skillfully. An equation (group) has no solution, which means that the conditions for the equation to be established cannot be found.
2. When using the properties of the equation, we should pay attention to the situation that both sides are divided by a number, and also pay attention to solving the equation and the basic idea of the equation. The main trap of eliminating reduction is to eliminate a time backtracking test of x common factor!
3. When using the property of inequality 3, it is easy to forget to change the direction of the invariant sign, which leads to the wrong result.
4. The topic of the range of the quadratic equation in one variable is easily ignored, and the coefficient of the quadratic term is not 0.
5. The equality of one-dimensional linear inequalities with and without solutions is easily ignored.
6. When solving the fractional equation, the first step is to remove the denominator, and the fractional phase is equivalent to brackets, so it is easy to forget the root test and lead to errors in the operation results.
7. To solve the inequality (group) problem, we must first determine the solution set, and the method of determining the solution set uses the number axis.
8. Using function images to find inequality solution sets and equation solutions.
6. You must find the coordinates of the intersection with the coordinate axis. The solution of maximum area, minimum distance sum and maximum distance difference.
7. The application of the thinking method of combining numbers and shapes should also pay attention to solving problems by combining the essence of images. The combination of function images and graphics can learn the method of decomposing complex graphics into simple graphics, and graphics provide data for images or images provide data for graphics.
8. The range of independent variables is: the square root of the quadratic root is non-negative, the denominator of the fraction is not 0, the exponential base of 0 is not 0, and all others are real numbers.
Law of mathematics learning in grade three
Study hard, study textbooks, study exams, grasp teaching requirements, understand the key points in teaching and the difficulties in students' learning, and improve professional quality. In addition, we should study teaching methods according to the requirements of current education reform and students' reality, so as to improve teaching efficiency.
We should pay attention to the process of the development of knowledge, understand the basic concepts comprehensively and accurately, and avoid taking things as they are, and then "understand" and "master" the concepts through a lot of practice. This can only get twice the result with half the effort, not only can't "remember" a lot of mathematical concepts, but also can't solve problems flexibly.
When learning examples at ordinary times, we should pay attention to analyzing and solving problems, and correct the wrong learning method that does not study the learning process but only pursues the results; We should pay attention to the infiltration of mathematical thinking methods and abandon rote learning methods. Mathematical thinking method is the soul and essence of mathematics and the source of cultivating students' innovative consciousness and practical ability, so it is also the focus of senior high school entrance examination. In junior middle school, we should pay attention to mathematical thinking methods such as equation thinking, function thinking, divisible thinking, reduction thinking, combination of numbers and shapes, classified discussion thinking, method of substitution, collocation method and undetermined coefficient method, so as to improve students' ability to analyze and solve problems.