Method 1: Basic concept test Basic concepts, laws and formulas are the most easily overlooked by students when reviewing, so conceptual errors are easy to occur when solving problems. Therefore, concept testing is a method to suit the remedy to the case. For example, how many of the following functions are power functions?

( 1)y = 2 x2(2)y = x3+2(3)y = x-2(4)y =(x- 1)-3

A: There are three. Wrong, let's recall the definition of power function first: all functions with the shape y=xa(a∈R) are called power functions. Compared with the defined form, only (3) is a power function, so there is only one.

Method 2: Symmetry principle test method Symmetry conditions will inevitably lead to the symmetry of the conclusion (this conclusion is usually called the law of insufficient reasons), and the answer can be tested quickly by using this symmetry principle.

For example, factorization (xy+1) (x+1) (y+1)+xy = (xy-y+1) (xy+x+1) is obviously wrong. The left end is symmetrical about X and Y, so the right end should be symmetrical about X and Y. The correct answer should be: (xy+1) (x+1) (y+1)+xy = (xy+y+1) (xy+x+650)

Method 3: the special case test method is often easier to solve than the general situation, so it is a very quick method to test the answer through special values, special situations or extreme States, because the universality of contradictions lies in particularity.

Method 4: There are some wrong answers in the dimension requirement testing method, which can be quickly detected from the dimension. For example, if the base area of a regular pyramid is S and lateral area is Q, then the volume is S(Q-S).

This answer is obviously wrong, because the dimensions of S and Q are both area units, so the dimension of S (S(S-Q) is the square of area unit instead of unit of volume.

The correct answer is 16S(Q2-S2). ..

Dimension test is more widely used in physics and chemistry, and also has some applications in memorizing formulas and testing wrong questions, which should be paid enough attention to.

Method 5: Invariant test method Some mathematical problems remain unchanged during the process of change and deformation, such as the shape and size of the figure and the basic amount of translation, rotation and folding of the figure. Using the invariants in this changing process, we can directly verify the correctness of some answers.

Method 6: Equivalence relation test method Equivalence relation is not only widely used in equivalence transformation when solving problems, but also can get twice the result with half the effort when testing answers.

Method 7: Grasping the whole thinking test method can not only cultivate our whole concept and develop good thinking habits, but also get a surprise effect by echoing each other and being harmonious as a whole when testing answers.

Method 8: The correctness of the answer of logical reasoning test method is not only reflected in the harmony and unity with conditions, but also reflects the regularity and mathematical beauty. This provides us with another new way to test the answer.

Method 9: Number-shape combination test method Number is an abstract generalization of shape, shape is an intuitive expression of number, and the combination of number and shape complements each other. If the problem solved by algebraic method can be related to the geometric background, it may be verified intuitively by geometric method; The answers obtained by geometric methods can also be accurately tested by algebraic methods.

Method 10: One-question multi-solution test method Multi-solution is more reassuring than one solution, and it is easier to find problems. When a problem is solved and reconsidered, good ideas often come up and good methods are obtained. After solving it in a novel way, mistakes must be corrected, and double insurance is formed without mistakes.

Method 11: Direct Test Method The direct test method is to check, check and test the problem-solving process and related conclusions around the original problem-solving method. In order to cooperate with the inspection, we must first use the draft paper correctly. I suggest you fold the draft paper out of the mark, calculate it in order, and mark it with the title number to facilitate inspection and comparison.

If it helps you, please adopt it! ! !