目前部分同学在解题运算中存在不少问题,主要表现在: (1)不顾目标,盲目计算。例如解“把直径为10的一个金属球熔化后,不计损失能做成多少个直径为5的小球?”不少人先算出大、小球的体积,然后作除法,而不会直接利用直径的立方比。又如,“设|a|≤1,求arccosa+arccos(-a)的值”。多数人先求出此两角和的余弦值,从而判定其值为π。其实,根据余弦函数线及反余弦函数的主值区间,画个草图便可得出结果来。甚至,由a是常量,取a=0代入即可(此为85年高考题。要求直接写出结果)。再如,“用1、2、3、4、5这五个数字可以组成比20000大,并且百位数不是数字3的没有重复数字的五位数共有(A)96个;(B)78个;(C)72个;(D)64个(85年高考选择题)”。仔细审题不难看出这种数的个数多 At present, some students have many problems in solving problems, mainly in: (1) Blindly calculating without regard to goals. For example, “How many balls with a diameter of 5 can be made after melting a metal ball with a diameter of 10 after melting it?” Many people first calculate the volume of large and small balls, and then divide them, instead of using them directly. The cubic ratio of the diameter. For another example, “set|a|≤1, find the value of arccosa+arccos(-a)”. Most people first find the cosine of the two-cornered sum to determine its value as π. In fact, according to the main value range of the cosine function line and the inverse cosine function, a sketch can be drawn. Even from a is a constant, take a = 0 can be replaced (this is the 85 college entrance exam questions. Requirements directly write the results). Another example is, "With five numbers 1, 2, 3, 4, and 5, you can make up to 20,000, and there is no repeat number in the 100-digit number. There are 96 non-repetitive numbers (A); (B) 78 (C) 72; (D) 64 (85 college entrance examination multiple-choice questions). It is not difficult to see the number of such numbers