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1987年高考数学试题中的立几筒答题,由于题目出现差错引起了广泛的议论。无独有偶,某市1987年立几教改测试题中也出现了类似的差错.由于立几题目失误难以觉察使编题者甚感头痛,为预防“失误”,审题时应注意以下几点: 一、检查题目中有关的平面或空间图形中各元素的数量关系是否正常上述高考题可以看作是由部编教材习题九中的第9题改编而来.(原题为:正四棱台上下底面边长各为α、b,侧面积等于两底面积之和,它的高是多少?高考题为:一个正三棱台的上底和下底周长各为12cm和30cm,而侧面积等于两底面积之差,求斜高),由于题意的改变题中各“数”的变化范围已相应缩小,不再可以随意而定,因为由其中的元素所构成的三角形必须满足三角形任两边之和大于第三边等性质,而编题者恰恰忽略
In the 1987 mathematics test questions in the college entrance examination, several questions were answered. Due to errors in the subject, there was widespread discussion. Coincidentally, a city made similar mistakes in several reforms in 1987. Due to the fact that it was difficult to detect a few mistakes, the editors felt a headache. In order to prevent “mistakes”, the following points should be noted when examining a problem: Check whether the number of elements in the relevant plane or space graph is normal or not. The above college entrance examination questions can be regarded as an adaptation of the 9th question in Part 9 of the textbook review. (The original title is: The lengths are α, b, and the lateral area is equal to the sum of the area of the two bases. What is the height of the area? The college entrance examination title is: The circumference of the upper base and the lower base of a positive triangular table is 12cm and 30cm, respectively, and the side area is equal to two bases. The difference between the areas and the slope is high. Since the change range of each “number” in the title question has been reduced correspondingly, it can no longer be determined arbitrarily, because the triangle formed by the elements must satisfy the sum of any two sides of the triangle. Greater than the third edge, etc., and editors just ignore