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临近高考,盘点数学科目易错点总结【一】;
日期【2019-01-15 14:39】 共阅:【】次
临近高考,盘点数学科目易错点总结【一】;
 
 
 
1.集合中元素的特征认识不明
 
  元素具有确定性,无序性,互异性三种性质。要看清楚集合的描述对象,到底是数集,还是点集,是求x范围呢,还是求y的范围。
 
  2.遗忘空集
 
  A包含于B时求集合A,容易遗漏A可以为空集的情况。比如A为(x-1)的平方>0,x=1时A为空集,也属于B.求子集或真子集个数时容易漏掉空集。
 
  3.忽视集合中元素的互异性
 
  一般检验的时候要检查元素是否互异。
 
  4.充分必要条件颠倒致误
 
  必要不充分和充分不必要的区别——:比如p可以推出q,而q推不出p,就是充分不必要条件,p不可以推出q,而q却可以推出p,就是必要不充分。
 
  还容易错的是语序错误,例如,“p的充分条件是q”等价于“q是p的充分条件”,q推出p,很多学生一看到充分条件就“前推后”,导致错误,要注意题目的措辞。
 
  5.对含有量词的命题否定不当
 
  比如说“至少有一个”的否定是“一个都没有”,“至少有两个”的否定是“至多有一个”,“至多有三个”的否定是“至少有四个”。诸如此类。
 
  6.求函数定义域忽视细节致误
 
  根号内≥0,真数大于零,分母不为零,比较容易出错的是忽视分母。
 
  7.函数单调性的判断错误
 
  这个就得注意函数的符号,比如f(-x)的单调性与原函数相反。
 
  更多高考答题技巧信息查看:http://www.gaosan.com/datijiqiao/
 
  8.函数奇偶性判定中常见的两种错误
 
  判定主要注意:1,定义域必须关于原点对称,2,注意奇偶函数的判断定理,化简要小心负号。
 
  9.求解函数值域时忽视自变量的取值范围
 
  总之有关函数的题,不管是要你求什么,第一步先看定义域,这个是关键。如果用了换元法求函数值域,一定要先求出“新元”的范围。
 
  10.抽象函数中推理不严谨致误
 
  注意赋值法的运用,一般赋0,±1,-x,1/x等。
 
 
 
 
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.
 
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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.
 
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