1. Unknown features of elements in a set
Elements have three properties: certainty, disorder and mutual heterogeneity. To see clearly the description object of a set, whether it is a set or a point set, whether it is to find the range of X or y.
2. Forget empty sets
When A is included in B, it is easy to omit that A can be an empty set. For example, when A is the square of (x-1) > 0, and when x = 1, A is an empty set, which also belongs to B. It is easy to omit the empty set when calculating the number of subsets or true subsets.
3. Ignoring the mutual heterogeneity of elements in a set
Generally, when checking, we should check whether the elements are different from each other.
4. Faults caused by reversal of necessary and sufficient conditions
Necessity is not sufficient and sufficient and unnecessary difference - for example, P can deduce q, while Q can not deduce P is sufficient and unnecessary condition, P can not deduce q, but Q can deduce p, which is necessary and inadequate.
It is also easy to make mistakes in word order. For example, "the sufficient condition of P is q" is equivalent to "the sufficient condition of Q is p". When Q introduces p, many students "push forward and backward" when they see the sufficient condition, which leads to errors. We should pay attention to the wording of the topic.
5. Inappropriate negation of propositions containing quantifiers
For example, "at least one" negation is "none", "at least two" negation is "at most one", "at most three" negation is "at least four". And so on.
6. Mistakes caused by neglecting details in finding function domain
In the root number (> 0), the true number is greater than zero, and the denominator is not zero. It is easy to make mistakes by neglecting the denominator.
7. Misjudgement of Monotonicity of Functions
This requires attention to the symbols of functions, such as the monotonicity of F (-x), which is opposite to the original function.
For more information on college entrance examination skills: http://www.gaosan.com/datijiqiao/
8. Two common errors in judging parity of functions
The main points of judgment are as follows: 1. The definition field must be symmetrical about the origin; 2. Attention should be paid to the judgment theorem of even and odd functions, and the minus sign should be simplified carefully.
9. Neglecting the range of independent variables when solving function range
In a word, no matter what you ask about functions, the first step is to look at the domain, which is the key. If we use the method of substitution to find the range of function, we must first find the range of "new element".
10. Imperfect reasoning in abstract functions
Attention should be paid to the application of the assignment method, which generally assigns 0, +1, -x, 1/x, etc.