费费数学宝典详解版(二十).

1、y=x^2+2qx+r，X轴上有几个交点？

（1）q^2>r；

（2）r^2>q；

【答案】A

【思路】AX^2+BX+C=0这个方程， IF B^2-4AC>0，方程有两个不相等的实根；IF B^2-4AC=0，方程有两个相等的实根；IF B^2-4AC<0，方程无解。

2、一个班有18个男生，全班有26人选修生物课，问全班人数？

（1）男生中选修生物课的有15人；

（2）女生人数是没有选修生物课的人数的2倍；

【答案】B

【思路】设全班人数为X，则女生人数为X-18，没选修的人数为X-26，只有条件二可解X。

3、There are 100 students in the class. Each student must choose at least one course of English, French, and German. But no student can choose all the three class. There are 30 students learn E, and 60 students learn French, and 15 students learning German also learn English. How many students learn German? (students learning E do not learn French and F not G)

【答案】25

【思路】100-30-60+15=25，学E不学F，也就是E与F的交集为0，同理F与G的交集也为0，那么只有E与G有交集为15，则学E学G的人为60+30-15，现在要求F只要把学E学G的减掉即可。

4、Every internal angle in a polygon is less than 180. How much is the average internal angle for a polygon:

（1）there are two right internal angles;

（2）there are five vertices;

【答案】B

【思路】五个顶点就表示有五个角，那么这个图形就是无边形，内角和为（N-2）*180=3*180=540，其平均数为540/5=108。而条件一无法确定到底有几个角。

5、There are two set A and B which only includes positive integer. A and B have the same number of positive integers. Is the median of A greater than the average of B?

（1）the items in A are even, the items in B is odd;

（2）the sum of A is equal to sum of B;

【答案】E

【思路】举反例：A{-2，2} B{-1，1} OR A{2，4，6，8} B{1，3，5，11}