上海市重点：七宝中学高三(上)学期月考英语试题及参考答案(2020.10)

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5．若，则方程的解为＿＿＿＿． 6．已知正方形的四个顶点分别为，，，，点 分别在线段上运动，且，设与交于点，则点 的轨迹方程是＿＿＿． 7．年龄在60岁（含60岁）以上的人称为老龄人，某小区的老龄人有350人，他们的健康状况如下表： 其中健康指数的含义是：2代表“健康”，1代表“基本健康”，0代表“不健康，但生活能够自理”，-1代表“生活不能自理”.按健康指数大于0和不大于0进行分层抽样，从该小区的老龄人中抽取5位，并随机地访问其中的3位.则被访问的3位老龄人中恰有1位老龄人的健康指数不大于0的概率是_____（用分数作答）. 8．已知数列{}的通项公式为，则 +++的最简表达式为_____.

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【解析】【解答】对于A选项，，f（x）的定义域为R，g（x）的定义域为[0，+∞），∴不是同一函数； 对于B选项的定义域为 的定义域为∴不是同一函数；对于C选项，f（0）=-1，g（0）=1，f（0）≠g（0），∴不是同一函数． 对于B选项，f（x）的定义域为，g（x）的定义域为，且且两函数解析式化简后为同一解析式，∴是同一函数. 故答案为：D. 【分析】判断两个函数是否表示同一个，看定义域和对应关系是否相同即可. 3.已知，则“ ”是“ ”的（） A. 充分非必要条件 B. 必要非充分条 件 C. 充要条件 D. 既非充分又非必要条件 【答案】A 【考点】必要条件、充分条件与充要条件的判断 【解析】【解答】由题意可知：a，b∈R+，若“a2+b2＜1” 则a2+2ab+b2＜1+2ab+a2?b2， ∴（a+b）2＜（1+ab）2 ∴ab+1＞a+b． 若ab+1＞a+b，当a=b=2时，ab+1＞a+b成立，但a2+b2＜1不成立． 综上可知：“a2+b2＜1”是“ab+1＞a+b”的充分不必要条件． 故答案为：A． 【分析】根据不等式的性质，结合充分、必要条件的概念进行判断即可. 4.汽车的“燃油效率”是指汽车每消耗1升汽油行使的里程，下图描述了甲、乙、丙三辆汽车在不同速度下得燃油效率情况，下列叙述中正确的是（）