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.idea/inspectionProfiles/Project_Default.xml

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.idea/misc.xml

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README.md

@@ -1,60 +0,0 @@
-### 1.任务说明
-
-​     对word格式（doc, docx）的高中数学试卷进行解析结构化
-
-  **主要支持3大类型**：1>>模板格式的教师类用卷（每道题目下面含答案和解析）
-
-​									 2>> 题文和答案分开的形式，即题文单独放一起，答案单独放一起
-
-​									 3>> 只含题文，或题文下只含答案或解析
-
-​    **要求**：
-
-​			1>>排版规范，每道题或其答案从前往后，从小到大排列，题号连续不重复；
-
-​			2>>与题文无关内容删除，特别是试卷中间和结尾的无用信息；
-
-​			3>>题型行尽量明确；
-
-​			4>>题文和答案分开的形式中，答案的标题要明显有“参考答案”类似字样，后面无用部分删除；
-
-​			5>>本文所述试卷仅包含题型行、题干、答案、解析、分析、点睛、点评等，像每个题后面插个变式训练类型的非正式试卷不支持！
-
-​	**结构化返回形式**：
-
-	{ "errcode": 0, "errmsg": "OK", "items": [{ "options": [ "", "", "", "" ], "option_rank": xx, "type": xx, "stem": xx, "analysis": xx, "key":xx, "score": xx, "is_optional": false, "is_multiple_choice": false },{},],"option_str": "不是选做题|4选2|2选1", "multiple_choice": "没有多选题|多选题" } 
-​	**解析流程**：
-
-​       ![image-20200805185530356](C:\Users\Administrator\AppData\Roaming\Typora\typora-user-images\image-20200805185530356.png)
-
-​    **解析报错类型**：
-
-​        第一种：大错误，需要按提示重新上传
-
-​			          1>>wordbin解析失败；
-
-​					  2>>题号出现无法自动纠正错误；
-
-​                      3>>题文和答案数目不一致；
-
-​		第二种：小错误，按小题报错信息进行修改
-
-​        			  1>>选择题选项格式不对；
-
-​					  2>>答案或解析缺失；
-
-​        第三种：显示问题，自行修改
-
-​					
-
-### 2.环境配置
-
-- 操作系统：Windows
-- 编程语言:python
-- 开发工具: pycharm
-- 代码托管平台: http://gitz.zhixinhuixue.net:18880/
-
-- 上线服务器: 182   和  185
-- 所需配套环境或服务：office word  、wordbin 、mathtype6
-
-### 

ans_structrue_old.py

@@ -1,447 +0,0 @@
-#!/usr/bin/env/python
-# -*- coding:utf-8 -*-
-
-import re
-from pprint import pprint
-from washutil import table_label_cleal, find_seq_num
-
-
-# 本文件包含以下函数
-# con_ans_split：将传进来的单道题（含答案或解析）按题干、答案、解析 拆分
-# ans_structure_total：针对答案部分解析结构化汇总
-# ans_structure： 拆分答案，并根据已拆分好的题目item_res 补上答案和解析
-# stem_ans_struc_combine: 题干结构化与答案结构化的合并
-# manyans_oneline_split(item_str,  one_type_num):对一行多个答案的情况进行拆分
-# only_parse_split:  拆分出答案和解析，主要针对答案页中的每个题的答案进行拆分
-# get_ans_from_parse:  从已知解析中 挑选 答案
-
-
-# def ans_structure_step1(anss, item_type_classify, item_res):
-#     """
-#     针对答案部分解析结构化汇总
-#     anss : 整个答案部分
-#     :return:  dd = {'parse': , 'key': }
-#     """
-#     anss = [k for k in anss if k.strip()]
-#     ans_label = [k for k, a in enumerate(anss) if re.match("【答案】", a.strip())]
-#     parse_label = [k for k, a in enumerate(anss) if re.match("【解析】", a.strip())]
-#     if len(ans_label) == 1 and len(parse_label) == 1:
-#         ans1 = anss[ans_label[0] + 1: parse_label[0]]
-#         parse1 = anss[parse_label[0]+1:]
-#         res_ans, flag1 = ans_structure_step2(ans1, item_type_classify, item_res,'group_ans')
-#         res_parse, flag2 = ans_structure_step2(parse1, item_type_classify, item_res, 'group_parse')
-#         if flag1 == flag2 == 1:
-#             for idx, item_r in enumerate(item_res):
-#                 if not res_ans[idx]['key']:
-#                     if not res_parse[idx]['key']:
-#                         item_res[idx]['key'] = "见解析"
-#                     else:
-#                         item_res[idx]['key'] = res_parse[idx]['key']
-#                 else:
-#                     item_res[idx]['key'] = res_ans[idx]['key']
-#
-#                 if not res_ans[idx]['parse']:
-#                     item_res[idx]['parse'] = res_parse[idx]['parse']
-#                 else:  # 解析中的parse肯定有
-#                     item_res[idx]['parse'] = res_ans[idx]['parse']+"<br/>【解析】"+res_parse[idx]['parse']
-#             return item_res
-#         elif flag1 == 2:
-#             return "【答案】组中题型数量与题目中不一致,请重点检查题目序号,重新手输题目序号"
-#         elif flag2 == 2:
-#             return "【解析】组中题型数量与题目中不一致,请重点检查题目序号,重新手输题目序号"
-#         else:
-#             return '【答案】组和【解析】组中题型数量与题目中均不一致,请重点检查题目序号,重新手输题目序号'
-#     else:
-#         res_ans, flag1 = ans_structure_step2(anss, item_type_classify, item_res)
-#         if flag1 == 1:
-#             for idx, item_r in enumerate(item_res):
-#                 item_res[idx]['key'] = res_ans[idx]['key']
-#                 item_res[idx]['parse'] = res_ans[idx]['parse']
-#         else:
-#             # return "答案中题目数量与题目中不一致,①请重点检查题目序号,重新手输题目序号;②将参考答案开头没用的信息去掉;" \
-#             #        "③是否有遗漏答案或答案格式不对；④答案中若存在一行多个答案时，保证每个题的答案间要留有多个空格！"
-#             return res_ans
-#         return item_res
-#
-#
-# def ans_structure_step2(anss, item_type_classify, item_res, *group):
-#     """
-#     拆分答案，并根据已拆分好的题目item_res 补上答案和解析
-#     有的答案放在表格里，如选择题、填空题、判断题，有的一行多个答案
-#     思路：1.先按一行没有多个题答案的情况取答案，数量与题干不同 时 >>>> 2.再按一行多个答案的情况取答案：
-#               1）先判断表格，拿到表格的答案；2）一行多个答案
-#     anss: 一组按所有不重复题号的答案
-#     item_type_classify: 题目中对各题型的统计
-#     :return: [{'parse': , 'key': },{},{}]
-#     """
-#     while not anss[0]:
-#         anss = anss[1:]
-#     if re.match(".+?省.+?试[卷题]|[^a-zA-Z]*?【专题】", anss[0]):
-#         anss = anss[1:]
-#
-#     # 预处理： 对答案部分的题号进行处理， 将(\d)类型的题号改为\d、类型
-#     sub_item_no = [int(no[0]+no[2]) for no in
-#                    re.findall(r'\n\s*([1-9]|[1-4][0-9])\s*[.．、､]|\n\s*([1-9]|[1-4][0-9])\s*[.．、､].+?\s+([1-9]|[1-4][0-9])\s*[.．、､].+?',
-#                               "\n" + "\n".join(anss))]
-#     if len(sub_item_no) <= 2:
-#         sub_item_no = [int(no[0]+no[2]) for no in re.findall(r'\n\s*\(([1-9]|[1-4][0-9])\)\s*[.．、､]?'
-#                                         r'|\n\s*\(([1-9]|[1-4][0-9])\)\s*[.．、､]?.+?\s+\(([1-9]|[1-4][0-9])\)\s*[.．、､]?.+?',
-#                                                              "\n" + "\n".join(anss))]
-#         if len(sub_item_no) > 3:
-#             anss = re.sub(r'\n\s*\(([1-9]|[1-4][0-9])\)\s*[.．、､]?', "\n" + r"【@\1､", "\n" + "\n".join(anss))
-#             anss = re.sub(r'(\n【@([1-9]|[1-4][0-9])､.+?\s+)\(([1-9]|[1-4][0-9])\)\s*[.．、､]?', r"\1【@\3､", anss)
-#             anss = anss.replace("【@", "").split("\n")[1:]
-#
-#     # --------- 一行多个答案的情况----存在一行中有选择题和填空题答案，填空题答案尽量每题占一行----------
-#     all_item_ans = []
-#     table_ans = []
-#     ans_no = []
-#     while anss and "table" in anss[0]:  # 答案以表格形式呈现, 表格应放在前两行位置，不要插在答案中间
-#         row_list = []                   # 要求表格形式为 横纵分明 ，不存在合并
-#         for tt in re.finditer('<tr>(((?!(</?tr>)).)*)</tr>', anss[0], re.S):  # 先划分每行
-#             tt_list = re.split(r'</p></td>|<td><p>|</td><td>|</td>|<td>', tt.group(1))  # 再划分每列
-#             # row_list.append([col for col in tt_list if col.strip()])  # 也有可能答案为空
-#             row_list.append(tt_list)
-#         if row_list:
-#             print("^^^^^^存在答案放在表格里的情况！^^^^^^^")
-#             if len(row_list) % 2 != 0:
-#                 print('表格形式呈现的答案不是偶数行')
-#             else:
-#                 # print("row_list:", row_list)
-#                 for k, v in enumerate(row_list):
-#                     # print('-----',v)
-#                     if (k + 1) % 2 == 1:  # 奇数行==》答案序号行
-#                         item_no = [int(i) if re.sub(r"[^\d]", "", i) else -1 for i in v]
-#                         item_no_st = [num for num, i in enumerate(item_no) if i != -1]   # 可能开头是-1
-#                         ans_no.extend([i for i in item_no if i != -1])  # 表格序号
-#                         table_ans.extend(row_list[k + 1][item_no_st[0]: item_no_st[-1] + 1])   # 表格答案
-#         anss = anss[1:]
-#     # 先按一行没有多个题答案的情况取答案
-#     anss_str = table_label_cleal("\n" + "\n".join(anss))
-#     if re.search("<table>.+?</table>", anss_str) is None:
-#         anss_str = anss_str.split("</table>")[-1].replace("</div>", "")
-#     anss_str = re.sub(r"([A-H])\s*[.．](\s*([1-4][0-9]|[1-9])\s*[.．、､])", r"\1  \2", anss_str)
-#     anss_str = re.sub(r"([；;])(\s*([1-4][0-9]|[1-9])\s*[．、､])", r"\1  \2", anss_str)
-#
-#     rest_item_split = re.split(r'\n+\s*[1-4][0-9]\s*[.．、､]|\n+\s*[1-9]\s*[.．、､]', anss_str)
-#     if not rest_item_split[0]:
-#         rest_item_split = rest_item_split[1:]
-#     all_item_ans.extend(table_ans)
-#     all_item_ans.extend(rest_item_split)
-#     print("表格答案：", table_ans)
-#     pprint(all_item_ans)
-#     # ------------先按没有一行多个答案的情况-------------------
-#     if item_type_classify and len(all_item_ans) == sum(list(item_type_classify.values())):
-#         res1 = []
-#         for num1, one_ans in enumerate(all_item_ans):
-#             parse = only_parse_split(one_ans, item_res[num1]["type"], item_res[num1]['stem'])
-#             res1.append(parse)
-#         return res1, 1
-#     elif not item_type_classify and len(all_item_ans) == len(item_res):
-#         res1 = []
-#         for num1, one_ans in enumerate(all_item_ans):
-#             parse = only_parse_split(one_ans, item_res[num1]["type"], item_res[num1]['stem'])
-#             res1.append(parse)
-#         return res1, 1
-#     else:  # 答案个数与题目不一致时,再按一行多个答案处理(题目个数正常，答案个数比题目少时)
-#         print('-----存在一行多个答案的情况-----')
-#         all_item_ans = []
-#         all_item_ans.extend(table_ans)
-#         # 再按一行多个答案的情况取答案
-#         manyans_oneline_split = re.split(r'\n\s*[1-4][0-9]\s*[.．、､]|\n\s*[1-9]\s*[.．、､]'
-#                                          r'|(?<![：:.．、､+\-*/=])\s[1-4][0-9]\s*[.．、､]|(?<![：:.．、､+\-*/=])\s[1-9]\s*[.．、､]'
-#                                          r'|\s{2,}[1-4][0-9]\s*[.．、､]|\s{2,}[1-9]\s*[.．、､]', anss_str)
-#
-#         temp_no = re.findall(r'\n\s*([1-4][0-9]|[1-9])\s*[.．、､]'
-#                                          r'|(?<![：:.．、､+\-*/=])\s([1-4][0-9]|[1-9])\s*[.．、､]|\s{2,}([1-4][0-9]|[1-9])\s*[.．、､]', anss_str)
-#         temp_no = [int("".join(i)) for i in temp_no]
-#         # print("temp_no:",temp_no)
-#         # print('manyans_oneline_split:', manyans_oneline_split, len(manyans_oneline_split))
-#         if not temp_no and not all_item_ans:  # 没有表格答案的情况，如1~10 ACBBD...
-#             row_ans = re.findall("[A-Z](?<!\))", manyans_oneline_split[0].strip())
-#             all_item_ans.extend(row_ans)
-#             temp_no = re.findall("(\d)-(\d{1,2})", manyans_oneline_split[0])
-#             for t in temp_no:
-#                 ans_no.extend(list(range(int(t[0]), int(t[1])+1)))
-#             if row_ans:
-#                 manyans_oneline_split = []
-#         elif temp_no and not manyans_oneline_split[0]:
-#             manyans_oneline_split = manyans_oneline_split[1:]
-#             ans_no.extend(temp_no)
-#         elif re.match("A-Z", manyans_oneline_split[1].strip()) is None and \
-#                 len(re.findall("[A-Z](?<!\))", manyans_oneline_split[0].strip())) == len(item_res) - (len(manyans_oneline_split)-1):
-#             print('第一行答案不是以题号形式一个个给出')
-#             row_ans = re.findall("[A-Z](?<!\))", manyans_oneline_split[0].strip())
-#             all_item_ans.extend(row_ans)
-#             manyans_oneline_split = manyans_oneline_split[1:]
-#             if temp_no and temp_no[0] > len(row_ans):
-#                 ans_no.extend(list(range(temp_no[0]-len(row_ans), temp_no[0])))
-#                 ans_no.extend(temp_no)
-#             else:
-#                 print("答案序号有问题！！")
-#                 ans_no.extend(['']*len(row_ans))
-#                 ans_no.extend(temp_no)
-#         # print("manyans_oneline_split:************")
-#         # pprint(manyans_oneline_split)
-#         print("ans_no:", ans_no)
-#         all_item_ans.extend(manyans_oneline_split)
-#         combine_res = stem_ans_struc_combine(item_type_classify, item_res, all_item_ans, ans_no, group)
-#         # if not combine_res:
-#         #     return '答案数量与题干数量不一致，请检查题干和答案中的题号,是否有遗漏答案或答案格式不对；' \
-#         #            '答案中若存在一行多个答案时，保证每个题的答案间要留有多个空格！', 2
-#
-#         return combine_res
-
-
-
-# def stem_ans_struc_combine(item_type_classify, item_res, all_item_ans, ans_no, group):
-#     """
-#     题干结构化与答案结构化的合并
-#     :return:
-#     """
-#     print("item_type_classify:", item_type_classify)
-#     print("题干中的题目数量：", len(item_res))
-#     print("答案中的题目数量：", len(all_item_ans))
-#     if item_type_classify and len(all_item_ans) == sum(list(item_type_classify.values())):
-#         res1 = []
-#         for num1, one_ans in enumerate(all_item_ans):
-#             parse = only_parse_split(one_ans, item_res[num1]["type"], item_res[num1]['stem'])
-#             res1.append(parse)
-#         return res1, 1
-#     elif not item_type_classify and len(all_item_ans) == len(item_res):
-#         res1 = []
-#         for num1, one_ans in enumerate(all_item_ans):
-#             parse = only_parse_split(one_ans, item_res[num1]["type"], item_res[num1]['stem'])
-#             res1.append(parse)
-#         return res1, 1
-#     else:
-#         print('答案数量与题干数量不一致，请检查题干和答案中的题号,是否有遗漏答案或答案格式不对；',
-#               '答案中若存在一行多个答案时，保证每个题的答案间要留有多个空格！', 2)
-#         print("试题个数：", len(item_res))
-#         print("答案中的题号：", ans_no)
-#         # ----------------------是否正确对上序号还需进一步验证！！！！！！！！！！-------------------------------
-#         res1 = []; simp_res = []
-#         err_n = 0  # 与题目id没对上号的个数， 默认答案一般也是从前往后排序
-#         for k, one_item in enumerate(item_res):  # 以题目为主
-#             search_range = ans_no
-#             if k+3-err_n <= len(ans_no):
-#                 search_range = ans_no[k-err_n:k+3-err_n]
-#             elif k-err_n < len(ans_no):
-#                 search_range = ans_no[k-err_n:]
-#             # print("答案的搜索范围search_range:",search_range)
-#             if one_item['item_id'] in search_range:  # 在对应位置前
-#                 ans_no_st = [k1+k-err_n for k1, v1 in enumerate(search_range) if v1 == one_item['item_id']]  # 默认取第一个作为对应答案
-#                 # print("答案的位置{0}：{1}, ----对应题目id:{2}".format(ans_no_st, all_item_ans[ans_no_st[0]],one_item['item_id']))
-#                 parse = only_parse_split(all_item_ans[ans_no_st[0]], one_item["type"], one_item['stem'])
-#                 one_item['key'] = parse['key']
-#                 one_item['parse'] = parse['parse']
-#                 res1.append(one_item)
-#                 if group == 'group_ans':
-#                     simp_res.append({'parse': "", 'key': parse['key'],'item_id':one_item['item_id']})
-#                 if group == 'group_parse':
-#                     simp_res.append({'parse': parse['parse'], 'key': parse['key'],'item_id':one_item['item_id']})
-#             else:
-#                 err_n += 1
-#                 one_item.update({'parse': "", 'key': ""})
-#                 res1.append(one_item)
-#                 if group:
-#                     simp_res.append({'parse': '', 'key': '', 'item_id': one_item['item_id']})
-#         if simp_res:
-#             return simp_res, 1
-#
-#         return res1, 2
-
-
-
-
-# def one2more_ans_split(item_list, item_type):
-#     """
-#     对一行多个答案的情况进行拆分
-#     :return:
-#     """
-#     manyans_oneline_split = []
-#     while item_list and \
-#             len(re.findall(r"(^|\s+)[1-9][0-9]?\s*[.．、､]\s*(【答案】|答案\s*[：:]?)?\s*[A-D]", item_list[0])) > 1:
-#         print('选择题存在一行多个答案的情况！！！')  # 主要以选择题的为主
-#
-#         # 处理 1.xxx    2.xxx    3.xxx
-#         ans_line1 = item_list[0]
-#         if not item_type or item_type.replace("题", "") in ["单选", "多选", "选择", "不定选择"]:
-#             ans_line1 = re.sub(r"[^A-D\d.．、､()]", "", item_list[0])
-#
-#         if re.match(r"[1-9][0-9]?[.．、､][A-D]", ans_line1):  # 第一个答案为选择题的情况
-#             one_ans_split = re.split(r'^\s*[1-9][0-9]?\s*[.．、､]|\s+[1-9][0-9]?\s*[.．、､]', item_list[0])
-#             if not one_ans_split[0]:
-#                 one_ans_split = one_ans_split[1:]
-#             manyans_oneline_split.extend(one_ans_split)
-#         else:  # 第一个答案为非选择题或没有序号的情况
-#             one_ans_split = re.split(r'^\s*[1-9][0-9]?\s*[.．、､]|\s+[1-9][0-9]?\s*[.．、､]', item_list[0])
-#             if not one_ans_split[0]:
-#                 one_ans_split = one_ans_split[1:]
-#             if manyans_oneline_split and not manyans_oneline_split[-1]:  # 序号和答案跨行的情况
-#                 manyans_oneline_split[-1] = one_ans_split[0]
-#                 manyans_oneline_split.extend(one_ans_split[1:])
-#             else:
-#                 manyans_oneline_split.extend(one_ans_split)
-#         item_list = item_list[1:]
-#         # if item_list:
-#         #     ans_line1 = re.sub(r"[^A-D\d.．、､]", "", item_list[0])
-#
-#     if manyans_oneline_split and not manyans_oneline_split[-1]:
-#         print('答案要求：题目序号不在行首时不要与该题答案跨行')
-#
-#     # 填空题答案也可能一行多个
-#     if item_type == '填空题':  # 在题干题型明确时
-#         one_type_ans_split = re.split(r'\n\s*[1-9][0-9]?\s*[.．、､]|(?<![：:])\s+[1-9][0-9]?\s*[.．、､](?!png)',
-#                                  table_label_cleal("\n"+"\n".join(item_list)))
-#         while not one_type_ans_split[0]:
-#             del one_type_ans_split[0]
-#         one_type_ans_split.extend(one_type_ans_split)
-#         return one_type_ans_split
-
-    # 对item_list剩余文本按题号继续拆分，包括一行多个答案的情况
-    # while re.match("\n\s*([1-9][0-9]?)\s*[.．、､].+?\s+([1-9][0-9]?)\s*[.．、､]", item_list[0]):
-        # item_no_seq = re.findall("[\n\s]\s*([1-9][0-9]?)\s*[.．、､]", "\n" + "\n".join(item_list))
-        # item_no_seq = [int(one) for one in item_no_seq]
-        # # print("item_no_seq:",find_seq_num(item_no_seq))
-        # if len(find_seq_num(item_no_seq)) == 1:
-        #     all_type_ans_split = re.split(r'\n\s*[1-9][0-9]?\s*[.．、､]|(?<![：:])\s+[1-9][0-9]?\s*[.．、､](?!png)',
-        #                                   table_label_cleal("\n" + "\n".join(item_list)))
-        #     while not all_type_ans_split[0].strip():
-        #         del all_type_ans_split[0]
-        #     manyans_oneline_split.extend(all_type_ans_split)
-
-    # return manyans_oneline_split
-
-
-
-
-
-# def get_ans_from_parse(item_parse, item_type, res_con):
-#     """
-#     从已知解析中 挑选 答案
-#     :param item_parse: 总解析
-#     :param item_type: 题型
-#     :return:
-#     """
-#     item_parse = re.split("【点评】|【点睛】", item_parse)[0].strip()
-#     # 将解析中末尾出现的图片去掉
-#     while re.search('\n\s*<imgsrc\d+\sw_h=(\d+\*\d{3})/>\s*$', item_parse):
-#         item_parse = re.sub('\n\s*<imgsrc\d+\sw_h=(\d+\*\d{3})/>\s*$', "", item_parse)
-#     item_ans = ""
-#     if item_type.replace("题", "") in ["单选", "多选", "选择", "不定选择"]:
-#         ans = re.search(r'故选\s*[：:]?\s*<imgsrc\d+\sdata-latex="\$?([A-Z;；和与、､\s]+)\$?"/>'
-#                         r'|故选\s*[：:]?\s*([A-Z;；和与、､\s]+)', item_parse.replace("$", ""))
-#         if ans:
-#             item_ans = ans.group(1) if ans.group(1) is not None else ans.group(2)
-#             item_ans = re.sub(r"[.;；．]\s*$", "", item_ans)
-#         elif not ans:
-#             item_ans = "见解析"
-#     elif item_type:
-#         ans0 = re.search(r'故选\s*[：:]?\s*([A-Z;；和与、､\s]+)[.．；;。]?$', item_parse)  # 试验题中可能还有选择题
-#         ans01 = re.search(r'故选\s*[：:]\s*<imgsrc\d+\sdata-latex="\$?([A-Z;；和与、､\s]+)\$?"/>', item_parse)  # 选择题的题型可能前面分错
-#         ans1 = re.search(r'(故|因[而此]|所以)\s*[：:]?\s*(答案分?别?[为是填]?|填)\s*[：:]?\s*(((?!(<img)).)+?)[.．]?\s*(\n|$)', item_parse)
-#         ans11 = re.search(r'((?<!解)答\s*[：:]|整理得\s*[：:]?)\s*(.+?)([.．；;]?\s*$|[.．]\s*\n)', item_parse)
-#         ans2 = re.search(r'(故|因[而此]|所以)\s*[：:]?\s*(答案分?别?[为是填]?|填)\s*[：:]?\s*(<imgsrc.+?/>)[.．]?\s*(\n|$)', item_parse, re.S)
-#         ans22 = re.search(r'(故|因[而此]|所以)\s*[：:]?\s*(答案分?别?[为是填]?|填)\s*[：:]?\s*([^∴∵因所故即【】]+?)([.．]\s*(\n|$)|$)', item_parse)
-#         ans21 = re.search(r'综上所述\s*[：:]\s*([^∴∵故因所即【】]+?)[.．；;]\s*$', item_parse)
-#         ans3 = re.search(r'(故|因[而此]|所以|∴)\s*[：:]?.+?[为是填]\s*[：:]?\s*([^∴∵故因所即【】]+?)([.．；;，,]\s*$|[.．]\s*\n)', item_parse)
-#         ans31 = re.search(r'(故|因[而此]|所以|∴)\s*([^当为是填∴∵故因所即则【】]+?)[.．；;]\s*$', item_parse)
-#         ans32 = re.search(r'(故|因[而此]|所以)\s*[：:]?[^当为是填∴∵故因所即【】]+?[为是填]\s*[：:]?\s*(<imgsrc.+?/>)[.．]?\s*(\n|$)',
-#                           item_parse, re.S)
-#         ans4 = re.search(r'\n\s*[＝=]([^＝\n]+?)[.．]?\s*$', item_parse)
-#         ans42 = re.search(r'[＝=](?!")(((?!([故＝∴即]|原式|因[而此]|所以|\n|=[^"])).)+?)[.．]?\s*$', item_parse)
-#         ans41 = re.search(r'原式\s*[＝=].+?[＝=](?!")(((?!(＝|=[^"])).)+?|\s*<imgsrc.+?/>)([.．]?\s*$|[.．]\s*\n)', item_parse)
-#         if not (item_type == '填空题' and len(re.findall(r"_{2,}|_+([^_]*?)_+", res_con)) == 1) and \
-#                 len(re.findall(r"[（(]\d[)）]|[\n:：;；。】]([（(](i{1,3}|[ⅰⅱⅲⅳⅠⅡⅢIV①②③④])[)）]|[①②③④]\s*(?![+-]))",
-#                                item_parse.replace(" ", ""))) > 1 or "证明" in item_parse:
-#             item_ans = "见解析"
-#         elif ans0:
-#             item_ans = ans0.group(1)
-#         elif ans01:
-#             item_ans = ans01.group(1)
-#         elif ans1 or ans11:
-#             item_ans = ans1.group(3) if ans1 else ans11.group(2)
-#         elif ans2:
-#             item_ans = ans2.group(3)
-#         elif ans22:
-#             item_ans = ans22.group(3)
-#         elif ans21:
-#             item_ans = ans21.group(1)
-#         elif (ans3 or ans31 or ans32) and '证明' not in item_parse:
-#             if ans3:
-#                 item_ans = ans3.group(2)
-#             if ans31:
-#                 item_ans = ans31.group(2)
-#             if ans32:
-#                 item_ans = ans32.group(2)
-#         elif (ans4 or ans41 or ans42) and '证明' not in item_parse:
-#             if ans4:
-#                 item_ans = ans4.group(1)
-#             if ans41:
-#                 item_ans = ans41.group(1)
-#             if ans42:
-#                 item_ans = ans42.group(1)
-#         else:
-#             item_ans = "见解析"
-#     return item_ans
-
-# def con_ans_split(one_item_list, item_topic_name, topic_no):
-#     """
-#     将传进来的单道题（含答案或解析）按题干、答案、解析 拆分
-#     :param one_item_list: [str,str,str] 每个元素为一行数据, ocr一行行识别, 保留每行数据;如果是word,直接用wordbin拿到html格式进行解析
-#     :param item_topic_name:题型
-#     :param topic_no:题号
-#     :return: one_item:{"stem":xxxx,"key":xxx,"parse":xxx}
-#     """
-#     pattern1 = re.compile(r"【(.*?)\s+(.*?)】|【(.*?)<imgsrc.+?/>(.*?)】")
-#     con0 = re.sub(r"】[:：]", "】", "#&#".join(one_item_list))  # 是否换行后面再考虑
-#     con0 = re.sub(r"\[来源.*?\]", "", con0).replace("\xa0", " ").replace("\u3000", " ")
-#     while re.search(pattern1, con0):
-#         con0 = re.sub(pattern1, r"【\1\2】", con0)  # 去掉 【】 中的图片和空格
-#
-#     big_struc_dict = {"type": item_topic_name, "topic_no": topic_no}
-#     if re.search("【(答案|[解分][析答]|详解)】", con0):
-#         label = re.findall("【(答案|[解分][析答]|详解|点[评睛])】", con0)
-#         label_split = re.split(r"【答案】|【[解分][析答]】|【详解】|【点[评睛]】", con0)
-#         big_struc_dict1 = dict(zip(label, label_split[1:]))
-#         big_struc_dict1['con'] = label_split[0]
-#         # 将键值为空的键删掉
-#         big_struc_dict.update({k: v for k, v in big_struc_dict1.items() if v.replace("#&#", "").strip() != ""})
-#     else:
-#         big_struc_dict['con'] = con0
-#
-#     return big_struc_dict
-
-
-if __name__ == '__main__':
-    # oneitem = {'stem': '7．化简<img src="files/image7.jpeg" style="width: 28.8pt; height: '
-    #            '28.8pt" width="38" height="38" />÷<img src="files/image8.jpeg" '
-    #            'style="width: 47.95pt; height: 30.7pt" width="64" height="41" '
-    #            '/>的结果是（\u3000\u3000）\n'
-    #            'A．<img src="files/image9.jpeg" style="width: 21.6pt; height: '
-    #            '28.8pt" width="29" height="38" />B．<img src="files/image10.jpeg" '
-    #            'style="width: 21.7pt; height: 26.2pt" width="29" height="35" '
-    #            '/>C．<img src="files/image11.jpeg" style="width: 21.6pt; height: '
-    #            '28.8pt" width="29" height="38" />D．<img src="files/image12.jpeg" '
-    #            'style="width: 21.7pt; height: 26.2pt" width="29" height="35" />\n'}
-    # res = one_item_parse(oneitem, '单选题')
-    # oneitem = ["1．下列说法正确的是（　　）","A．射线是高速运动的电子流","B．氢原子可通过吸收光子实现从低能级向高能级跃迁",
-    #             "C．太阳辐射能量的主要来源是太阳内部发生的重核裂变","D．的半衰期是3.8天，1克经过7.6天后全部发生衰变",
-    #             "【答案】B","【解析】","【分析】","【详解】","A．γ射线是电磁波，故A错误；","B．按照波尔理论，氢原子吸收光子后，将从低能级向高能级跃迁，故B正确;",
-    #             "C．太阳辐射能量的主要来源是太阳中发生的轻核聚变，故C错误；","D．的半衰期是3.8天，7.6天是2个半衰期，根据可知，有发生衰",
-    #             "变，还剩下克没有衰变，故D错误。","故选B。"]
-    # num = 1
-    # item_type = '选择题'
-    # res = con_ans_split(oneitem, item_type, num)
-    # pprint(res)
-
-    one_ans = '故答案为：3．\n'
-    parse = only_parse_split(one_ans, "填空题")
-    print(parse)
-
-    # a = dict(zip(["2","2","3"], [2,4,6]))
-    # print(a)
-    con = '【分析】 首先根据分式值为零的条件，可得<img src="999image136.png" style="width: 77.35pt; height: 33.85pt" width="103" height="45" />；然后根据因式分解法解一元二次方程的步骤，求出x的值为多少即可．\n【解答】 解：∵分式<img src="999image137.png" style="width: 57.5pt; height: 31.7pt" width="77" height="42" />的值为0，\n<p>∴<img src="999image138.png" style="width: 77.35pt; height: 33.85pt" width="103" height="45" />\n<p>解得x=3，\n<p>即x的值为3．\n<p>故答案为：3．\n【点评】 （1）此题主要考查了分式值为零的条件'
-    con = re.search(r'(故|因[而此]|所以)\s*[：:]?\s*(答案分?别?[为是填]?|填)\s*[：:]?\s*(((?!(<img)).)+?)[.．]?\s*(\n|$)', con)
-    print(':',con.group(3))

app_test.py

@@ -1,87 +0,0 @@
-#!/usr/bin/env/python
-# -*- coding:utf-8 -*-
-import pickle
-
-from gevent import monkey
-
-monkey.patch_all()  # 打上猴子补丁
-from flask import Flask, render_template, send_from_directory
-from flask import request, redirect, Response
-from flask_cors import *
-from multiprocessing import Process, Queue
-from gevent import pywsgi
-import configs
-from structure.danti_structure import single_parse
-from structure.structure_main import WordParseStructure
-import os, datetime, hashlib
-import time, json, random
-import pprint
-
-from utils.ruku_opera import Ruku
-from pprint import pprint
-
-logger = configs.myLog(__name__, log_cate="reparse_ruku_log").getlog()
-
-app = Flask(__name__)
-app.debug = True
-CORS(app, supports_credentials=True)
-
-
-@app.route('/danti_structure', methods=["GET", "POST"])
-def danti_structure():
-    """
-    单题再解析、结构化
-    :return:
-    """
-    word_id = request.json.get("paper_id", 0)
-    one_item = request.json.get("single_item_data", "")
-    item_type = request.json.get("item_type", "")
-    logger.info("【单题解析】==request.POST.dict==>word_id:{}, item_type:{}".format(word_id, item_type))
-    # logger.info("【单题解析】==request.POST.single_item_data==>\n{}\n".format(one_item))
-    print(word_id, item_type)
-
-    res = {"errcode": 0, "errmsgs":"", "data": {}}
-    if item_type:
-        one_res = single_parse(one_item, item_type, word_id)
-        if type(one_res) == str:
-            res["errcode"] = 1
-            res["errmsgs"] = one_res
-        else:
-            res["data"] = one_res
-
-    else:
-        res["errcode"] = 1
-        res["errmsgs"] = "没有选定题型"
-
-    return json.dumps(res, ensure_ascii=False)
-
-
-@app.route('/ser_static/<path:file_path>', methods=["GET"])
-def ser_static(file_path):  # endpoint的位置是函数接口名，不能用static，与flask内部变量重名
-    """
-    :param file_path: 图片的本地绝对路径
-    :return:
-    """
-    return send_from_directory(configs.IMG_FOLDER, file_path)
-
-
-
-def start_new_server(port):
-    server = pywsgi.WSGIServer(('',port),app)
-    server.start_accepting()
-
-
-if __name__ == "__main__":
-    # app.run(host=configs.server_ip, port=configs.server_port, processes=True, debug=True)  # threaded=True
-    # app.run(processes=4)  # 多进程或多线程只能选择一个，不能同时开启
-    # 5fc64a0a4994183dda7e74b9
-
-    from multiprocessing import cpu_count, Process
-
-    # app.debug = True
-    # server = pywsgi.WSGIServer((configs.server_ip, configs.server_port), app)
-    # server.serve_forever()
-    for i in range(cpu_count()):
-        p = Process(target=start_new_server)
-        p.start()
-

data/5fca003e84ac587a71dd202e.html

@@ -1,232 +0,0 @@
-<html><head><meta charset="utf-8" /></head><body>
-<p>湖北省黄冈市浠水县实验高级中学2019-2020学年高一数学上学期12月训练试题（含解析）</p>
-<p>一、选择题（本大题共12小题，共60.0分）</p>
-<p>1.设集合<img src="files/image1.png" width="151px" height="24px" data-latex="$$" />，<img src="files/image2.png" width="121px" height="21px" data-latex="$$" />，则<img src="files/image3.png" width="54px" height="20px" data-latex="$$" />（    ）</p>
-<p>A. <img src="files/image4.png" width="60px" height="41px" data-latex="$$" />B. <img src="files/image5.png" width="48px" height="41px" data-latex="$$" />C. <img src="files/image6.png" width="37px" height="41px" data-latex="$$" />D. <img src="files/image7.png" width="41px" height="41px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>试题分析：集合<img src="files/image8.png" width="265px" height="29px" data-latex="$$" />，集合<img src="files/image9.png" width="96px" height="33.75pt" />，所以<img src="files/image10.png" width="151px" height="45px" data-latex="$$" />,故选D.</p>
-<p>考点：1、一元二次不等式；2、集合的运算.</p>
-<p> </p>
-<p> </p>
-<p>2.已知偶函数<img src="files/image11.png" width="39px" height="27px" data-latex="$$" />在区间<img src="files/image12.png" width="51px" height="27px" data-latex="$$" />上单调递增，则满足<img src="files/image13.png" width="117px" height="45px" data-latex="$$" />的<img src="files/image14.png" width="13px" height="15px" data-latex="$$" />的取值范围为（）</p>
-<p>A. <img src="files/image15.png" width="44px" height="41px" data-latex="$$" />B. <img src="files/image16.png" width="43px" height="41px" data-latex="$$" />C. <img src="files/image17.png" width="44px" height="41px" data-latex="$$" />D. <img src="files/image18.png" width="44px" height="42px" data-latex="$$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据单调性，将函数值的大小关系转变为自变量间的大小关系，注意偶函数对应的函数的对称情况.</p>
-<p>【详解】因为偶函数<img src="files/image11.png" width="39px" height="27px" data-latex="$$" />是在<img src="files/image12.png" width="51px" height="27px" data-latex="$$" />上递增，则<img src="files/image11.png" width="39px" height="27px" data-latex="$$" />在<img src="files/image19.png" width="51px" height="27px" data-latex="$$" />递减，且<img src="files/image20.png" width="103px" height="45px" data-latex="$$" />；又因为<img src="files/image13.png" width="117px" height="45px" data-latex="$$" />，根据单调性和奇偶性有：<img src="files/image21.png" width="101px" height="41px" data-latex="$$" />，解得：<img src="files/image22.png" width="72px" height="45px" data-latex="$$" />,</p>
-<p>故选A.</p>
-<p>【点睛】本题考查利用函数单调性、奇偶性求解参数范围问题，难度一般.对于这种奇偶性和单调性的综合问题，除了可以直接分析问题，还可以借助图象来分析，也可以高效解决问题.</p>
-<p> </p>
-<p> </p>
-<p>3. 若a＞b＞0，0＜c＜1，则</p>
-<p>A. log<sub>a</sub>c＜log<sub>b</sub>cB. log<sub>c</sub>a＜log<sub>c</sub>bC. a<sup>c</sup>＜b<sup>c </sup>D. c<sup>a</sup>＞c<sup>b</sup></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>试题分析：对于选项A，<img src="files/image23.png" width="167px" height="44px" data-latex="$$" />，<img src="files/image24.png" width="69px" height="19px" data-latex="$$" />，<img src="files/image25.png" width="63px" height="21px" data-latex="$$" />，而<img src="files/image26.png" width="61px" height="19px" data-latex="$$" />，所以<img src="files/image27.png" width="67px" height="21px" data-latex="$$" />，但不能确定<img src="files/image28.png" width="57px" height="21px" data-latex="$$" />的正负，所以它们的大小不能确定;对于选项B，<img src="files/image29.png" width="169px" height="44px" data-latex="$$" />,<img src="files/image27.png" width="67px" height="21px" data-latex="$$" />，两边同乘以一个负数<img src="files/image30.png" width="29px" height="44px" data-latex="$$" />改变不等号方向，所以选项B正确;对于选项C，利用<img src="files/image31.png" width="44px" height="24px" data-latex="$$" />在第一象限内是增函数即可得到<img src="files/image32.png" width="48px" height="21px" data-latex="$$" />，所以C错误;对于选项D，利用<img src="files/image33.png" width="43px" height="24px" data-latex="$$" />在<img src="files/image34.png" width="16px" height="18px" data-latex="$$" />上为减函数易得<img src="files/image35.png" width="48px" height="21px" data-latex="$$" />，所以D错误.所以本题选B.</p>
-<p>【考点】指数函数与对数函数的性质</p>
-<p>【名师点睛】比较幂或对数值的大小,若幂的底数相同或对数的底数相同,通常利用指数函数或对数函数的单调性进行比较；若底数不同,可考虑利用中间量进行比较.</p>
-<p> </p>
-<p> </p>
-<p>4.若<img src="files/image14.png" width="13px" height="15px" data-latex="$$" />，<img src="files/image36.png" width="47px" height="24px" data-latex="$$" />，且<img src="files/image37.png" width="83px" height="21px" data-latex="$$" />，则<img src="files/image38.png" width="52px" height="21px" data-latex="$$" />的最小值是（   ）</p>
-<p>A. <img src="files/image39.png" width="12px" height="19px" data-latex="$$" />B. <img src="files/image40.png" width="24px" height="41px" data-latex="$$" />C. <img src="files/image41.png" width="35px" height="45px" data-latex="$$" />D. <img src="files/image42.png" width="21px" height="41px" data-latex="$$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>从题设可得<img src="files/image43.png" width="77px" height="48px" data-latex="$$" />，则<img src="files/image44.png" width="416px" height="44px" data-latex="$$" />，应选答案A．</p>
-<p>5.设p：实数x，y满足x＞1且y＞1，q：实数x，y满足x＋y＞2，则p是q的(　　)</p>
-<p>A. 充分不必要条件</p>
-<p>B. 必要不充分条件</p>
-<p>C. 充要条件</p>
-<p>D. 既不充分也不必要条件</p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【详解】“若<img src="files/image45.png" width="35px" height="19px" data-latex="$$" />且<img src="files/image46.png" width="32px" height="20px" data-latex="$$" />则<img src="files/image47.png" width="62px" height="21px" data-latex="$$" />”是真命题，其逆命题是假命题，故<img src="files/image48.png" width="15px" height="16px" data-latex="$$" />是<img src="files/image49.png" width="12px" height="19px" data-latex="$$" />的充分不必要条件,故选A.</p>
-<p>6.下列叙述正确的是(　　)</p>
-<p>A. 若<img src="files/image50.png" width="52px" height="21px" data-latex="$$" />，则<img src="files/image51.png" width="37px" height="19px" data-latex="$$" /></p>
-<p>B. 若<img src="files/image52.png" width="52px" height="22px" data-latex="$$" />，则<img src="files/image53.png" width="33px" height="17px" data-latex="$$" /></p>
-<p>C. 若<img src="files/image54.png" width="37px" height="19px" data-latex="$$" />，则<img src="files/image55.png" width="52px" height="22px" data-latex="$$" /></p>
-<p>D. 若<img src="files/image50.png" width="52px" height="21px" data-latex="$$" />|，则<img src="files/image56.png" width="47px" height="19px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>A. 令a=2，b=−2，此时<img src="files/image57.png" width="48px" height="27px" data-latex="$$" />，而a≠b，故本选项错误；</p>
-<p>B. 令a=−3，b=2，此时<img src="files/image58.png" width="48px" height="27px" data-latex="$$" />，而a&lt;b，故本选项错误；</p>
-<p>C. 令a=−3，b=2，此时<img src="files/image59.png" width="37px" height="19px" data-latex="$$" />，而<img src="files/image58.png" width="48px" height="27px" data-latex="$$" />，故本选项错误；</p>
-<p>D. 若<img src="files/image57.png" width="48px" height="27px" data-latex="$$" />，则<img src="files/image60.png" width="47px" height="19px" data-latex="$$" />，故本选项正确．</p>
-<p>故选D.</p>
-<p>7.设函数<img src="files/image61.png" width="151px" height="51px" data-latex="$$" />，则满足<img src="files/image62.png" width="60px" height="27px" data-latex="$$" />的x的取值范围是<img src="files/image63.png" width="11px" height="21px" data-latex="$$" />　　<img src="files/image64.png" width="11px" height="21px" data-latex="$$" /></p>
-<p>A. <img src="files/image65.png" width="44px" height="27px" data-latex="$$" />B. <img src="files/image66.png" width="36px" height="27px" data-latex="$$" />C. <img src="files/image67.png" width="48px" height="27px" data-latex="$$" />D. <img src="files/image68.png" width="51px" height="27px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>分类讨论：<img src="files/image69.png" width="21px" height="21px" data-latex="$$" />当<img src="files/image70.png" width="35px" height="17px" data-latex="$$" />时；<img src="files/image71.png" width="21px" height="21px" data-latex="$$" />当<img src="files/image72.png" width="35px" height="17px" data-latex="$$" />时，再按照指数不等式和对数不等式求解，最后求出它们的并集即可．</p>
-<p>【详解】当<img src="files/image70.png" width="35px" height="17px" data-latex="$$" />时，<img src="files/image73.png" width="53px" height="20px" data-latex="$$" />的可变形为<img src="files/image74.png" width="53px" height="17px" data-latex="$$" />，<img src="files/image75.png" width="37px" height="19px" data-latex="$$" />，<img src="files/image76.png" width="71px" height="19px" data-latex="$$" />．</p>
-<p>当<img src="files/image72.png" width="35px" height="17px" data-latex="$$" />时，<img src="files/image77.png" width="83px" height="24px" data-latex="$$" />的可变形为<img src="files/image78.png" width="40px" height="41px" data-latex="$$" />，<img src="files/image79.png" width="48px" height="17px" data-latex="$$" />，故答案为<img src="files/image68.png" width="51px" height="27px" data-latex="$$" />．</p>
-<p>故选D．</p>
-<p>【点睛】本题主要考查不等式的转化与求解，应该转化特定的不等式类型求解．</p>
-<p><img src="files/image80.png" width="10px" height="18px" data-latex="$$" />此处有视频，请去附件查看】</p>
-<p> </p>
-<p>8.当<img src="files/image81.png" width="42px" height="19px" data-latex="$$" />时，不等式<img src="files/image82.png" width="97px" height="21px" data-latex="$$" />恒成立，则k的取值范围是（  ）</p>
-<p>A. <img src="files/image83.png" width="49px" height="21px" data-latex="$$" />B. <img src="files/image12.png" width="51px" height="27px" data-latex="$$" />C. <img src="files/image84.png" width="37px" height="27px" data-latex="$$" />D. （0，4）</p>
-<p>【答案】C</p>
-<p>【解析】</p>
-<p>当<img src="files/image85.png" width="37px" height="19px" data-latex="$$" />时，不等式<img src="files/image86.png" width="97px" height="21px" data-latex="$$" />可化为<img src="files/image87.png" width="33px" height="19px" data-latex="$$" />，显然恒成立；当<img src="files/image88.png" width="37px" height="19px" data-latex="$$" />时，若不等式<img src="files/image86.png" width="97px" height="21px" data-latex="$$" />恒成立，则对应函数的图象开口朝上且与<img src="files/image14.png" width="13px" height="15px" data-latex="$$" />轴无交点，则<img src="files/image89.png" width="105px" height="48px" data-latex="$$" />解得：<img src="files/image90.png" width="62px" height="19px" data-latex="$$" />，综上<img src="files/image91.png" width="13px" height="19px" data-latex="$$" />的取值范围是<img src="files/image92.png" width="37px" height="27px" data-latex="$$" />，故选C.</p>
-<p>9.函数<img src="files/image93.png" width="148px" height="47px" data-latex="$$" />的定义域为<img src="files/image34.png" width="16px" height="18px" data-latex="$$" />，则实数<img src="files/image94.png" width="17px" height="15px" data-latex="$$" />的取值范围是（　　）</p>
-<p>A. <img src="files/image95.png" width="39px" height="27px" data-latex="$$" />B. <img src="files/image84.png" width="37px" height="27px" data-latex="$$" />C. <img src="files/image96.png" width="37px" height="27px" data-latex="$$" />D. <img src="files/image97.png" width="37px" height="27px" data-latex="$$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>【详解】试题分析：由题意可知<img src="files/image98.png" width="107px" height="21px" data-latex="$$" />恒成立，当<img src="files/image99.png" width="40px" height="19px" data-latex="$$" />时<img src="files/image100.png" width="33px" height="19px" data-latex="$$" />恒成立；当<img src="files/image101.png" width="41px" height="19px" data-latex="$$" />时需满足<img src="files/image102.png" width="49px" height="48px" data-latex="$$" />，代入解不等式可得<img src="files/image103.png" width="64px" height="19px" data-latex="$$" />，综上可知实数<img src="files/image94.png" width="17px" height="15px" data-latex="$$" />的取值范围是<img src="files/image84.png" width="37px" height="27px" data-latex="$$" /></p>
-<p>考点：函数定义域</p>
-<p>10.若函数<img src="files/image104.png" width="160px" height="42px" data-latex="$$" />有两个不同的极值点，则实数<img src="files/image105.png" width="13px" height="14px" data-latex="$$" />的取值范围是（　　）</p>
-<p>A. <img src="files/image106.png" width="31px" height="17px" data-latex="$$" />B. <img src="files/image107.png" width="68px" height="19px" data-latex="$$" />C. <img src="files/image108.png" width="35px" height="19px" data-latex="$$" />D. <img src="files/image109.png" width="57px" height="19px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>求出函数的导数，结合二次函数的性质得到关于a的不等式组，解出即可．</p>
-<p>【详解】<img src="files/image11.png" width="39px" height="27px" data-latex="$$" />的定义域是（0，+∞），</p>
-<p><img src="files/image110.png" width="200px" height="44px" data-latex="$$" />，</p>
-<p>若函数<img src="files/image11.png" width="39px" height="27px" data-latex="$$" />有两个不同的极值点，</p>
-<p>则<img src="files/image111.png" width="122px" height="27px" data-latex="$$" />在（0，+∞）由2个不同的实数根，</p>
-<p>故<img src="files/image112.png" width="141px" height="72px" data-latex="$$" />，解得：<img src="files/image109.png" width="57px" height="19px" data-latex="$$" />，</p>
-<p>故选D．</p>
-<p>【点睛】本题考查了函数的极值问题，考查导数的应用以及二次函数的性质，是一道中档题．</p>
-<p>11.若<img src="files/image113.png" width="80px" height="41px" data-latex="$$" />，且<img src="files/image114.png" width="16px" height="15px" data-latex="$$" />为第四象限角，则<img src="files/image115.png" width="39px" height="17px" data-latex="$$" />的值等于（ ）</p>
-<p>A. <img src="files/image116.png" width="21px" height="41px" data-latex="$$" />B. <img src="files/image117.png" width="33px" height="41px" data-latex="$$" />C. <img src="files/image118.png" width="21px" height="41px" data-latex="$$" />D. <img src="files/image119.png" width="33px" height="41px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>∵sina=<img src="files/image120.png" width="32px" height="41px" data-latex="$$" />,且a为第四象限角,</p>
-<p>∴<img src="files/image121.png" width="148px" height="41px" data-latex="$$" />，</p>
-<p>则<img src="files/image122.png" width="125px" height="41px" data-latex="$$" />，</p>
-<p>故选D.</p>
-<p> </p>
-<p> </p>
-<p>12.已知函数<img src="files/image123.png" width="185px" height="48px" data-latex="$$" />，若函数<img src="files/image124.png" width="93px" height="29px" data-latex="$$" />有三个零点，则实数<img src="files/image91.png" width="13px" height="19px" data-latex="$$" />的取值范围是（    ）</p>
-<p>A. <img src="files/image125.png" width="47px" height="19px" data-latex="$$" />B. <img src="files/image126.png" width="68px" height="19px" data-latex="$$" />C. <img src="files/image127.png" width="79px" height="19px" data-latex="$$" />D. <img src="files/image128.png" width="45px" height="19px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>【详解】由<img src="files/image129.png" width="89px" height="27px" data-latex="$$" />=0得|f（x）|=－k≥0，</p>
-<p>所以k≤0，作出函数y=|f（x）|的图象，</p>
-<p><img src="files/image130.png" width="231px" height="144px" /></p>
-<p>由图象可知：要使y=－k与函数y=|f（x）|有三个交点，</p>
-<p>则有－k≥2，即k≤－2，</p>
-<p>故选D．</p>
-<p>二、填空题（本大题共4小题，共20.0分）</p>
-<p>13.已知角α的终边经过点P（3，<img src="files/image131.png" width="24px" height="24px" />），则与α终边相同的角的集合是______．</p>
-<p>【答案】<img src="files/image132.png" width="157px" height="45px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>试题分析：由三角函数定义可知<img src="files/image133.png" width="173px" height="45px" data-latex="$$" />，与其终边相同的角为<img src="files/image132.png" width="157px" height="45px" data-latex="$$" /></p>
-<p>考点：三角函数定义及角的推广</p>
-<p>14.若一扇形的圆心角为2，圆心角所对的弦长为2，则此扇形的面积为______．</p>
-<p>【答案】<img src="files/image134.png" width="39px" height="41px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>先计算出扇形的半径,再用面积公式可得面积.</p>
-<p>【详解】依题意可得扇形的半径为<img src="files/image135.png" width="33px" height="41px" data-latex="$$" />,</p>
-<p>所以此扇形的面积为<img src="files/image136.png" width="147px" height="41px" data-latex="$$" />.</p>
-<p>故答案为: <img src="files/image134.png" width="39px" height="41px" data-latex="$$" />.</p>
-<p>【点睛】本题考查了扇形的面积公式,属于基础题.</p>
-<p>15.已知命题p：∀x∈[1,2]，x<sup>2</sup>－a≥0，命题q：∃x∈R，x<sup>2</sup>＋2ax＋2－a＝0，若命题p且q是真命题，则实数a的取值范围是__________．</p>
-<p>【答案】<img src="files/image137.png" width="120px" height="23px" data-latex="$$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>命题<img src="files/image138.png" width="156px" height="27px" data-latex="$$" />,可得<img src="files/image139.png" width="72px" height="31px" data-latex="$$" />，命题<img src="files/image140.png" width="204px" height="25px" data-latex="$$" />，可得<img src="files/image141.png" width="39px" height="19px" data-latex="$$" /> , 结合<img src="files/image48.png" width="15px" height="16px" data-latex="$$" />与<img src="files/image49.png" width="12px" height="19px" data-latex="$$" />为真命题求交集可得结果.</p>
-<p><img src="files/image80.png" width="10px" height="18px" data-latex="$$" />详解】命题<img src="files/image138.png" width="156px" height="27px" data-latex="$$" />,<img src="files/image142.png" width="107px" height="31px" data-latex="$$" />，</p>
-<p>命题<img src="files/image140.png" width="204px" height="25px" data-latex="$$" />，</p>
-<p> <img src="files/image143.png" width="157px" height="27px" data-latex="$$" /> , </p>
-<p>解得<img src="files/image144.png" width="35px" height="19px" data-latex="$$" />或<img src="files/image145.png" width="45px" height="19px" data-latex="$$" />，</p>
-<p>又<img src="files/image48.png" width="15px" height="16px" data-latex="$$" />，<img src="files/image49.png" width="12px" height="19px" data-latex="$$" />为真命题，<img src="files/image146.png" width="103px" height="48px" data-latex="$$" />，解得<img src="files/image145.png" width="45px" height="19px" data-latex="$$" />或<img src="files/image147.png" width="35px" height="19px" data-latex="$$" />，</p>
-<p>故<img src="files/image105.png" width="13px" height="14px" data-latex="$$" />的取值范国是<img src="files/image145.png" width="45px" height="19px" data-latex="$$" />或<img src="files/image147.png" width="35px" height="19px" data-latex="$$" />，故答案为<img src="files/image145.png" width="45px" height="19px" data-latex="$$" />或<img src="files/image147.png" width="35px" height="19px" data-latex="$$" />.</p>
-<p>【点睛】本题考查了不等式恒成立问题、不等式的解法、逻辑联接词的应用，考查了推理能力,特称命题与全称命题，意在考查转化与化归思想以及综合应用所学知识解答问题的能力，属于中档题.</p>
-<p>16.如果关于<img src="files/image14.png" width="13px" height="15px" data-latex="$$" />的不等式<img src="files/image148.png" width="107px" height="22px" data-latex="$$" />的解集为<img src="files/image149.png" width="17px" height="19px" data-latex="$$" />，则实数<img src="files/image94.png" width="17px" height="15px" data-latex="$$" />的取值范围是___.</p>
-<p>【答案】<img src="files/image150.png" width="46px" height="22px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>当<img src="files/image99.png" width="40px" height="19px" data-latex="$$" />时，原命题成立，</p>
-<p>否则应有：<img src="files/image151.png" width="187px" height="53px" data-latex="$$" />，解得：<img src="files/image152.png" width="74px" height="19px" data-latex="$$" />，</p>
-<p>综上可得：实数<img src="files/image94.png" width="17px" height="15px" data-latex="$$" />的取值范围是<img src="files/image153.png" width="47px" height="27px" data-latex="$$" />.</p>
-<p>点睛：不等式ax<sup>2</sup>＋bx＋c＞0的解是全体实数(或恒成立)的条件是当a＝0时，b＝0，c＞0；当a≠0时，<img src="files/image154.png" width="44px" height="45px" data-latex="$$" />不等式ax<sup>2</sup>＋bx＋c＜0的解是全体实数(或恒成立)的条件是当a＝0时，b＝0，c＜0；当a≠0时，<img src="files/image155.png" width="44px" height="45px" data-latex="$$" />.</p>
-<p>三、解答题（本大题共6小题，共72.0分）</p>
-<p>17.已知全集为<img src="files/image34.png" width="16px" height="18px" data-latex="$$" />，函数<img src="files/image156.png" width="96px" height="35.25pt" data-latex="$$" />的定义域为集合<img src="files/image157.png" width="16px" height="18px" data-latex="$$" />，集合<img src="files/image158.png" width="135px" height="29px" data-latex="$$" />.</p>
-<p>（1）求<img src="files/image159.png" width="41px" height="20px" data-latex="$$" />； </p>
-<p>（2）若<img src="files/image160.png" width="221px" height="27px" data-latex="$$" />，求实数<img src="files/image94.png" width="17px" height="15px" data-latex="$$" />的取值范围.</p>
-<p>【答案】（1） <img src="files/image161.png" width="123px" height="27px" data-latex="$$" /> ；（2）<img src="files/image162.png" width="52px" height="27px" data-latex="$$" /> </p>
-<p>【解析】</p>
-<p>试题分析：（1）通过解不等式求得集合<img src="files/image163.png" width="35px" height="21px" data-latex="$$" />再求交集<img src="files/image164.png" width="117px" height="29px" data-latex="$$" />；（2）根据集合的子集关系求参数的范围.注意讨论空集的情况.</p>
-<p>试题解析：（1）由<img src="files/image165.png" width="56px" height="19px" data-latex="$$" />  得， 函数<img src="files/image166.png" width="39px" height="27px" data-latex="$$" /> 的定义域<img src="files/image167.png" width="91px" height="21px" data-latex="$$" />,又<img src="files/image168.png" width="88px" height="21px" data-latex="$$" />， 得<img src="files/image169.png" width="149px" height="27px" data-latex="$$" />，<img src="files/image170.png" width="136px" height="27px" data-latex="$$" />.</p>
-<p>（2）<img src="files/image171.png" width="141px" height="21px" data-latex="$$" />,①当<img src="files/image172.png" width="45px" height="19px" data-latex="$$" />  时，满足要求， 此时<img src="files/image173.png" width="63px" height="19px" data-latex="$$" />， 得<img src="files/image174.png" width="43px" height="41px" data-latex="$$" />;②当<img src="files/image175.png" width="45px" height="19px" data-latex="$$" /> 时，要<img src="files/image176.png" width="128px" height="21px" data-latex="$$" />，则<img src="files/image177.png" width="75px" height="75px" data-latex="$$" />，解得<img src="files/image178.png" width="67px" height="41px" data-latex="$$" />，由①② 得，<img src="files/image179.png" width="40px" height="19px" data-latex="$$" />，<img src="files/image180.png" width="15px" height="13px" data-latex="$$" />实数<img src="files/image94.png" width="17px" height="15px" data-latex="$$" /> 的取值范围<img src="files/image162.png" width="52px" height="27px" data-latex="$$" />.</p>
-<p>点睛：(1)认清元素的属性，解决集合问题时，认清集合中元素的属性(是点集、数集或其他情形)和化简集合是正确求解的两个先决条件.</p>
-<p>(2)注意元素的互异性.在解决含参数的集合问题时，要注意检验集合中元素的互异性，否则很可能会因为不满足“互异性”而导致解题错误.</p>
-<p>(3)防范空集.在解决有关<img src="files/image181.png" width="119px" height="21px" data-latex="$$" />等集合问题时，往往忽略空集的情况，一定先考虑<img src="files/image149.png" width="17px" height="19px" data-latex="$$" />是否成立，以防漏解.</p>
-<p>18.（1）计算：<img src="files/image182.png" width="145px" height="44px" data-latex="$$" />；</p>
-<p>（2）计算：<img src="files/image183.png" width="171px" height="42px" data-latex="$$" /></p>
-<p>【答案】（1）<img src="files/image184.png" width="21px" height="41px" data-latex="$$" />（2）3</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）根据指数幂的运算性质计算即可，</p>
-<p>（2）根据对数的运算性质计算即可．</p>
-<p>【详解】（1）原式=<img src="files/image185.png" width="29px" height="31px" data-latex="$$" />+<img src="files/image186.png" width="59px" height="47px" data-latex="$$" />-1=4+<img src="files/image187.png" width="24px" height="42px" data-latex="$$" />-1=<img src="files/image188.png" width="21px" height="41px" data-latex="$$" />;</p>
-<p>（2）原式=<img src="files/image189.png" width="360px" height="24px" data-latex="$$" /></p>
-<p>【点睛】本题考查了指数幂的运算性质和对数的运算性质，属于基础题．</p>
-<p>19.已知命题<img src="files/image190.png" width="91px" height="45px" data-latex="$$" />，命题<img src="files/image191.png" width="165px" height="21px" data-latex="$$" />，若<img src="files/image192.png" width="25px" height="17px" data-latex="$$" />是<img src="files/image193.png" width="25px" height="17px" data-latex="$$" />的必要不充分条件，求实数<img src="files/image194.png" width="17px" height="15px" />的取值范围．</p>
-<p>【答案】<img src="files/image195.png" width="74px" height="26px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>化简命题p：－2≤x≤10，若￢p是￢q<img src="files/image196.png" width="14px" height="19px" data-latex="$$" />必要不充分条件等价于q是p的必要不充分条件，从而可列出不等式组，求解即可.</p>
-<p>【详解】由题意得p：－2≤x≤10.  </p>
-<p> ∵￢p是￢q的必要不充分条件，</p>
-<p>∴q是p的必要不充分条件．     </p>
-<p>∴p⇒q，q<img src="files/image197.png" width="20px" height="16px" data-latex="$$" />p.</p>
-<p>∴<img src="files/image198.png" width="76px" height="48px" data-latex="$$" />∴<img src="files/image199.png" width="48px" height="48px" data-latex="$$" />∴m≥9.  </p>
-<p> 所以实数m的取值范围为{m|m≥9}．</p>
-<p>【点睛】本题主要考查了必要不充分条件，逆否命题，属于中档题.</p>
-<p>20.已知角<img src="files/image200.png" width="16px" height="15px" data-latex="$$" />终边上有一点<img src="files/image201.png" width="59px" height="27px" data-latex="$$" />，求下列各式的值．</p>
-<p>（1）<img src="files/image202.png" width="39px" height="17px" data-latex="$$" />；    </p>
-<p>（2）<img src="files/image203.png" width="88px" height="41px" data-latex="$$" /></p>
-<p>【答案】（1）<img src="files/image204.png" width="96px" height="30.75pt" data-latex="$$" />；（2）<img src="files/image205.png" width="25px" height="41px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p><img src="files/image80.png" width="10px" height="18px" data-latex="$$" />分析】</p>
-<p>（1）根据三角函数的定义，可知<img src="files/image206.png" width="65px" height="41px" data-latex="$$" />；</p>
-<p>（2）原式上下同时除以<img src="files/image207.png" width="39px" height="15px" data-latex="$$" />，变为<img src="files/image202.png" width="39px" height="17px" data-latex="$$" />表示的式子，即可求得结果.</p>
-<p>【详解】（1）<img src="files/image208.png" width="133px" height="41px" data-latex="$$" /> </p>
-<p>（2）<img src="files/image209.png" width="84px" height="19px" data-latex="$$" />，<img src="files/image210.png" width="76px" height="19px" data-latex="$$" /> </p>
-<p>原式上下同时除以<img src="files/image207.png" width="39px" height="15px" data-latex="$$" /> </p>
-<p><img src="files/image211.png" width="261px" height="47px" data-latex="$$" />.</p>
-<p>【点睛】本题考查了三角函数的定义，属于基础题型.</p>
-<p>21.已知函数<img src="files/image212.png" width="147px" height="29px" data-latex="$$" />是指数函数．</p>
-<p>(1)求<img src="files/image213.png" width="33px" height="20px" data-latex="$$" />的表达式；</p>
-<p>(2)判断<img src="files/image214.png" width="137px" height="21px" data-latex="$$" /><img src="files/image196.png" width="14px" height="19px" data-latex="$$" />奇偶性，并加以证明<img src="files/image215.png" width="4px" height="19px" /> </p>
-<p>(3)解不等式：<img src="files/image216.png" width="156px" height="24px" data-latex="$$" />．</p>
-<p>【答案】（1）<img src="files/image217.png" width="57px" height="23px" data-latex="$$" />（2）见证明；（3）<img src="files/image218.png" width="112px" height="41px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>(1)根据指数函数定义得到，<img src="files/image219.png" width="92px" height="21px" data-latex="$$" />检验得到答案.</p>
-<p>(2) <img src="files/image220.png" width="100px" height="24px" data-latex="$$" />，判断<img src="files/image221.png" width="83px" height="21px" data-latex="$$" />关系得到答案.</p>
-<p>(3)利用函数的单调性得到答案.</p>
-<p>【详解】解：（1）∵函数<img src="files/image212.png" width="147px" height="29px" data-latex="$$" />是指数函数，<img src="files/image222.png" width="37px" height="19px" data-latex="$$" />且<img src="files/image223.png" width="35px" height="19px" data-latex="$$" />，</p>
-<p>∴<img src="files/image219.png" width="92px" height="21px" data-latex="$$" />，可得<img src="files/image224.png" width="37px" height="19px" data-latex="$$" />或<img src="files/image225.png" width="31px" height="17px" data-latex="$$" />（舍去），∴<img src="files/image217.png" width="57px" height="23px" data-latex="$$" />；</p>
-<p>（2）由（1）得<img src="files/image220.png" width="100px" height="24px" data-latex="$$" />，</p>
-<p>∴<img src="files/image226.png" width="109px" height="24px" data-latex="$$" />，∴<img src="files/image227.png" width="103px" height="21px" data-latex="$$" />，∴<img src="files/image228.png" width="36px" height="21px" data-latex="$$" />是奇函数；</p>
-<p>（3）不等式：<img src="files/image229.png" width="156px" height="24px" data-latex="$$" />，以2为底单调递增，</p>
-<p>即<img src="files/image230.png" width="103px" height="19px" data-latex="$$" />，</p>
-<p>∴<img src="files/image231.png" width="83px" height="41px" data-latex="$$" />，解集为<img src="files/image218.png" width="112px" height="41px" data-latex="$$" />．</p>
-<p>【点睛】本题考查了函数的定义，函数的奇偶性，解不等式，意在考查学生的计算能力.</p>
-<p>22.设<img src="files/image232.png" width="40px" height="19px" data-latex="$$" />是常数，函数<img src="files/image233.png" width="115px" height="41px" data-latex="$$" />.</p>
-<p>(1)用定义证明函数<img src="files/image11.png" width="39px" height="26px" data-latex="$$" />是增函数；</p>
-<p>(2)试确定<img src="files/image105.png" width="13px" height="14px" data-latex="$$" />的值，使<img src="files/image11.png" width="39px" height="26px" data-latex="$$" />是奇函数；</p>
-<p>(3)当<img src="files/image11.png" width="39px" height="26px" data-latex="$$" />是奇函数时，求<img src="files/image11.png" width="39px" height="26px" data-latex="$$" />的值域.</p>
-<p>【答案】(1) 详见解析(2) <img src="files/image234.png" width="44px" height="27px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>试题分析：（1）证明函数单调性可根据函数单调性定义取值，作差变形，定号从而写结论（2）因为函数是奇函数所以<img src="files/image235.png" width="260px" height="41px" data-latex="$$" />（3）由<img src="files/image236.png" width="111px" height="41px" data-latex="$$" />.故<img src="files/image237.png" width="109px" height="41px" data-latex="$$" />，∴<img src="files/image238.png" width="35px" height="21px" data-latex="$$" /></p>
-<p>试题解析：</p>
-<p>(1)设<img src="files/image239.png" width="120px" height="24px" data-latex="$$" />，</p>
-<p>则<img src="files/image240.png" width="328px" height="53px" data-latex="$$" />.<img src="files/image241.png" width="24px" height="27px" data-latex="$$" /></p>
-<p>∵函数<img src="files/image242.png" width="44px" height="24px" data-latex="$$" />是增函数，又<img src="files/image243.png" width="45px" height="24px" data-latex="$$" />，∴<img src="files/image244.png" width="80px" height="21px" data-latex="$$" />，</p>
-<p>而<img src="files/image245.png" width="65px" height="21px" data-latex="$$" />，<img src="files/image246.png" width="67px" height="21px" data-latex="$$" />，∴<img src="files/image241.png" width="24px" height="27px" data-latex="$$" />式<img src="files/image247.png" width="25px" height="19px" data-latex="$$" />.</p>
-<p>∴<img src="files/image248.png" width="99px" height="27px" data-latex="$$" />，即<img src="files/image166.png" width="39px" height="27px" data-latex="$$" />是<img src="files/image34.png" width="16px" height="18px" data-latex="$$" />上的增函数.</p>
-<p>(2)∵<img src="files/image235.png" width="260px" height="41px" data-latex="$$" />对<img src="files/image249.png" width="39px" height="19px" data-latex="$$" />恒成立，</p>
-<p>∴<img src="files/image147.png" width="35px" height="19px" data-latex="$$" />.</p>
-<p>(3)当<img src="files/image147.png" width="35px" height="19px" data-latex="$$" />时，<img src="files/image250.png" width="136px" height="41px" data-latex="$$" />.</p>
-<p>∴<img src="files/image237.png" width="109px" height="41px" data-latex="$$" />，∴<img src="files/image238.png" width="35px" height="21px" data-latex="$$" />，</p>
-<p>继续解得<img src="files/image251.png" width="91px" height="44px" data-latex="$$" />，</p>
-<p>∴<img src="files/image252.png" width="67px" height="21px" data-latex="$$" />，因此，函数<img src="files/image166.png" width="39px" height="27px" data-latex="$$" />的值域是<img src="files/image253.png" width="44px" height="27px" data-latex="$$" />.</p>
-<p>点睛：本题考差了函数单调性，奇偶性的概念及其判断、证明，函数的值域求法，对于定义来证明单调性要注意做差后的式子的化简.</p>
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-<p>湖南省常德市2019-2020学年高一数学上学期第一次月考试题（含解析）</p>
-<p>一、选择题（本大题12小题，每小题5分，共60分）</p>
-<p>1. 若sinα＞0，且cosα＜0，则角α是（ ）</p>
-<p>A. 第一象限角B. 第二象限角C. 第三象限角D. 第四象限角</p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>试题分析：直接由三角函数的象限符号取交集得答案．</p>
-<p>解：由sinα＞0，可得α为第一、第二及y轴正半轴上的角；</p>
-<p>由cosα＜0，可得α为第二、第三及x轴负半轴上的角．</p>
-<p>∴取交集可得，α是第二象限角．</p>
-<p>故选B．</p>
-<p>考点：三角函数值的符号．</p>
-<p>2.函数<img src="files/image1.png" width="147px" height="45px" data-latex="$$" /><img src="files/image2.png" width="14px" height="19px" data-latex="$$" />最小正周期为（ 　  ）</p>
-<p>A. <img src="files/image3.png" width="16px" height="42px" data-latex="$$" />B. <img src="files/image4.png" width="17px" height="41px" data-latex="$$" />C. <img src="files/image5.png" width="15px" height="15px" data-latex="$$" />D. <img src="files/image6.png" width="24px" height="19px" data-latex="$$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据正切函数的周期公式<img src="files/image7.png" width="44px" height="41px" data-latex="$$" />进行计算即可.</p>
-<p>【详解】函数<img src="files/image1.png" width="147px" height="45px" data-latex="$$" />的最小正周期为：<img src="files/image8.png" width="72px" height="41px" data-latex="$$" />，</p>
-<p>故选：B.</p>
-<p>【点睛】本题考查正切函数的最小正周期，熟记公式是解题的关键，属于基础题.</p>
-<p>3.已知A={第一象限角}，B={锐角}，C={小于90°的角}，那么A、B、C关系是(   )</p>
-<p>A. B=A∩CB. B∪C=CC. A<img src="files/image9.png" width="17px" height="19px" data-latex="$$" />CD. A=B=C</p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>由集合A，B，C，求出B与C的并集，判断A与C的包含关系，以及A，B，C三者之间的关系即可．</p>
-<p>【详解】由题B<img src="files/image10.png" width="16px" height="16px" data-latex="$$" />A，</p>
-<p>∵A＝{第一象限角}，B＝{锐角}，C＝{小于90°的角}，</p>
-<p>∴B∪C＝{小于90°的角}＝C，即B<img src="files/image10.png" width="16px" height="16px" data-latex="$$" />C，</p>
-<p>则B不一定等于A∩C，A不一定是C的真子集，三集合不一定相等，</p>
-<p>故选B．</p>
-<p>【点睛】此题考查了集合间的基本关系及运算，熟练掌握象限角，锐角，以及小于90°的角表示的意义是解本题的关键，是易错题</p>
-<p>4.化简：<img src="files/image11.png" width="109px" height="23px" data-latex="$$" />（  　 ）</p>
-<p>A. <img src="files/image12.png" width="14px" height="23px" data-latex="$$" />B. <img src="files/image13.png" width="25px" height="22px" data-latex="$$" />C. <img src="files/image14.png" width="35px" height="21px" data-latex="$$" />D. <img src="files/image15.png" width="43px" height="21px" data-latex="$$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据平面向量减法法则和相反向量的意义计算即可.</p>
-<p>【详解】<img src="files/image16.png" width="309px" height="25px" data-latex="$$" />，</p>
-<p>故选：A.</p>
-<p>【点睛】本题主要考查平面向量减法的三角形法则，属于基础题.</p>
-<p>5.在ΔABC中,若<img src="files/image17.png" width="199px" height="32px" data-latex="$$" /> ,则<img src="files/image18.png" width="55px" height="24px" data-latex="$$" />=（   ）</p>
-<p>A. 6B. 4C. -6D. -4</p>
-<p>【答案】C</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>向量的点乘，<img src="files/image19.png" width="233px" height="32px" data-latex="$$" /></p>
-<p>【详解】<img src="files/image20.png" width="399px" height="41px" data-latex="$$" />,选C.</p>
-<p>【点睛】向量的点乘，需要注意后面乘的是两向量的夹角的余弦值，本题如果直接计算的话，<img src="files/image21.png" width="61px" height="24px" data-latex="$$" />的夹角为∠BAC的补角</p>
-<p>6.已知向量<img src="files/image22.png" width="61px" height="27px" data-latex="$$" />，向量<img src="files/image23.png" width="72px" height="28px" data-latex="$$" />，则向量<img src="files/image24.png" width="13px" height="19px" data-latex="$$" />在向量<img src="files/image25.png" width="15px" height="23px" data-latex="$$" />方向上的投影为（   ）</p>
-<p>A. <img src="files/image26.png" width="20px" height="16px" data-latex="$$" />B. <img src="files/image27.png" width="20px" height="17px" data-latex="$$" />C. <img src="files/image28.png" width="12px" height="17px" data-latex="$$" />D. <img src="files/image29.png" width="13px" height="17px" data-latex="$$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>由题意可得：<img src="files/image30.png" width="303px" height="36px" data-latex="$$" /> ，</p>
-<p>则：向量<img src="files/image24.png" width="13px" height="19px" data-latex="$$" />在向量<img src="files/image25.png" width="15px" height="23px" data-latex="$$" />方向上<img src="files/image2.png" width="14px" height="19px" data-latex="$$" />投影为<img src="files/image31.png" width="189px" height="55px" data-latex="$$" /> .</p>
-<p>本题选择B选项.</p>
-<p>点睛：在向量数量积的几何意义中，投影是一个数量，不是向量．设向量a，b的夹角为θ，当θ为锐角时，投影为正值；当θ为钝角时，投影为负值；当θ为直角时，投影为0；</p>
-<p>7.已知<img src="files/image32.png" width="40px" height="32px" data-latex="$$" />，<img src="files/image33.png" width="41px" height="32px" data-latex="$$" />，且<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />夹角为<img src="files/image36.png" width="27px" height="19px" data-latex="$$" />，则<img src="files/image37.png" width="63px" height="32px" data-latex="$$" />等于（  　 ）</p>
-<p>A. 1B. 3C. <img src="files/image38.png" width="47px" height="24px" data-latex="$$" />D. <img src="files/image39.png" width="47px" height="24px" data-latex="$$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>先根据平面向量的运算法则对式子展开，然后根据平面向量的数量积公式计算即可.</p>
-<p>【详解】因为<img src="files/image32.png" width="40px" height="32px" data-latex="$$" />，<img src="files/image33.png" width="41px" height="32px" data-latex="$$" />，且<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />夹角为<img src="files/image36.png" width="27px" height="19px" data-latex="$$" />，</p>
-<p>所以<img src="files/image40.png" width="383px" height="35px" data-latex="$$" />.</p>
-<p>故选：B.</p>
-<p>【点睛】本题主要考查平面向量的数量积的计算，属于基础题.</p>
-<p>8.函数<img src="files/image41.png" width="112px" height="45px" data-latex="$$" />的图象 （ ）</p>
-<p>A. 关于点<img src="files/image42.png" width="48px" height="45px" data-latex="$$" />对称B. 关于直线<img src="files/image43.png" width="42px" height="42px" data-latex="$$" />对称</p>
-<p>C. 关于点<img src="files/image44.png" width="48px" height="45px" data-latex="$$" />对称D. 关于直线<img src="files/image45.png" width="41px" height="41px" data-latex="$$" />对称</p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>分别求出函数<img src="files/image41.png" width="112px" height="45px" data-latex="$$" />的对称中心坐标和对称轴方程，然后对<img src="files/image46.png" width="13px" height="19px" data-latex="$$" />赋整数值得出结果.</p>
-<p>【详解】对于函数<img src="files/image41.png" width="112px" height="45px" data-latex="$$" />，令<img src="files/image47.png" width="133px" height="41px" data-latex="$$" />，得<img src="files/image48.png" width="77px" height="41px" data-latex="$$" />，<img src="files/image49.png" width="38px" height="19px" data-latex="$$" />，</p>
-<p>令<img src="files/image50.png" width="160px" height="41px" data-latex="$$" />，得<img src="files/image51.png" width="81px" height="41px" data-latex="$$" />，<img src="files/image49.png" width="38px" height="19px" data-latex="$$" />，</p>
-<p>所以，函数<img src="files/image41.png" width="112px" height="45px" data-latex="$$" />的图象的对称中心坐标为<img src="files/image52.png" width="135px" height="45px" data-latex="$$" />，对称轴为直线<img src="files/image53.png" width="132px" height="41px" data-latex="$$" />，</p>
-<p>令<img src="files/image54.png" width="35px" height="19px" data-latex="$$" />，可知函数<img src="files/image41.png" width="112px" height="45px" data-latex="$$" />图象的一个对称中心坐标为<img src="files/image42.png" width="48px" height="45px" data-latex="$$" />，故选A.</p>
-<p>【点睛】本题考查三角函数的对称中心和对称轴方程，一般先求出对称中心坐标和对称轴方程通式，然后通过赋值法得到，考查计算能力，属于基础题.</p>
-<p>9.函数<img src="files/image55.png" width="120px" height="45px" data-latex="$$" /><img src="files/image2.png" width="14px" height="19px" data-latex="$$" />单调递增区间是(    )</p>
-<p>A. <img src="files/image56.png" width="179px" height="45px" data-latex="$$" />B. <img src="files/image57.png" width="188px" height="45px" data-latex="$$" /></p>
-<p>C. <img src="files/image58.png" width="167px" height="45px" data-latex="$$" />D. <img src="files/image59.png" width="169px" height="45px" data-latex="$$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p><img src="files/image60.png" width="224px" height="45px" data-latex="$$" />.</p>
-<p>则<img src="files/image61.png" width="119px" height="45px" data-latex="$$" />的单调减区间即为函数<img src="files/image62.png" width="119px" height="45px" data-latex="$$" />的单调递增区间.</p>
-<p>即<img src="files/image63.png" width="233px" height="41px" data-latex="$$" />.</p>
-<p>解得<img src="files/image64.png" width="188px" height="45px" data-latex="$$" /></p>
-<p>故选B.</p>
-<p>10.要得到函数<img src="files/image65.png" width="102px" height="41px" data-latex="$$" />的图象，只需将<img src="files/image66.png" width="102px" height="42px" data-latex="$$" />图象上的所有点（   ）</p>
-<p>A. 向左平行移动<img src="files/image67.png" width="15px" height="37px" data-latex="$$" />个单位长度B. 向右平行移动<img src="files/image67.png" width="15px" height="37px" data-latex="$$" />个单位长度</p>
-<p>C<img src="files/image68.png" width="3px" height="9px" data-latex="$$" /> 向左平行移动<img src="files/image69.png" width="20px" height="37px" data-latex="$$" />个单位长度D. 向右平行移动<img src="files/image69.png" width="20px" height="37px" data-latex="$$" />个单位长度</p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>试题分析：<img src="files/image70.png" width="479px" height="48px" data-latex="$$" />，向右平移<img src="files/image69.png" width="20px" height="37px" data-latex="$$" />个单位得<img src="files/image71.png" width="111px" height="45px" data-latex="$$" />.选D.</p>
-<p>考点：三角函数图像变换</p>
-<p>【思路点睛】三角函数的图象变换，提倡“先平移，后伸缩”，但“先伸缩，后平移”也常出现在题目中，所以也必须熟练掌握.无论是哪种变形，切记每一个变换总是对字母x而言. 函数y＝Asin(ωx＋φ)，x∈R是奇函数⇔φ＝kπ(k∈Z)；函数y＝Asin(ωx＋φ)，x∈R是偶函数⇔φ＝kπ＋(k∈Z)；函数y＝Acos(ωx＋φ)，x∈R是奇函数⇔φ＝kπ＋(k∈Z)；函数y＝Acos(ωx＋φ)，x∈R是偶函数⇔φ＝kπ(k∈Z).</p>
-<p>11.已知函数<img src="files/image72.png" width="93px" height="41px" data-latex="$$" />的定义域为<img src="files/image73.png" width="36px" height="22px" data-latex="$$" />，值域为<img src="files/image74.png" width="44px" height="21px" data-latex="$$" />，则<img src="files/image75.png" width="35px" height="19px" data-latex="$$" />的值不可能是（ ）</p>
-<p>A. <img src="files/image76.png" width="27px" height="41px" data-latex="$$" />B. <img src="files/image6.png" width="24px" height="19px" data-latex="$$" />C. <img src="files/image77.png" width="25px" height="41px" data-latex="$$" />D. <img src="files/image78.png" width="32px" height="41px" data-latex="$$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>【详解】<img src="files/image72.png" width="93px" height="41px" data-latex="$$" />的周期为<img src="files/image79.png" width="21px" height="17px" data-latex="$$" />，<img src="files/image75.png" width="35px" height="19px" data-latex="$$" />不可能超过一个周期，如果超过一个周期值域为<img src="files/image80.png" width="46px" height="21px" data-latex="$$" />， <img src="files/image81.png" width="68px" height="42px" data-latex="$$" />，所以<img src="files/image75.png" width="35px" height="19px" data-latex="$$" />的值不可能是<img src="files/image78.png" width="32px" height="41px" data-latex="$$" /></p>
-<p>12.函数y=Asin(ωx+φ)(A＞0,ω＞0)的部分图象如图所示,则f(1)+f(2)+f(3)+<img src="files/image82.png" width="19px" height="10px" data-latex="$$" />+f(11)的值等于</p>
-<p><img src="files/image83.png" width="155px" height="102px" /></p>
-<p>A. 2B. <img src="files/image84.png" width="48px" height="23px" data-latex="$$" />C. <img src="files/image85.png" width="56px" height="23px" data-latex="$$" />D. <img src="files/image86.png" width="64px" height="23px" data-latex="$$" /></p>
-<p>【答案】C</p>
-<p>【解析】</p>
-<p>由图可知，<img src="files/image87.png" width="40px" height="17px" data-latex="$$" />，函数的周期为<img src="files/image88.png" width="79px" height="41px" data-latex="$$" />所以<img src="files/image89.png" width="44px" height="41px" data-latex="$$" />.φ=<img src="files/image28.png" width="12px" height="17px" data-latex="$$" />.所以<img src="files/image90.png" width="105px" height="41px" data-latex="$$" />.所<img src="files/image91.png" width="36px" height="27px" data-latex="$$" />=<img src="files/image92.png" width="231px" height="28px" data-latex="$$" />=<img src="files/image93.png" width="119px" height="28px" data-latex="$$" />=<img src="files/image94.png" width="51px" height="27px" data-latex="$$" />=<img src="files/image95.png" width="73px" height="28px" data-latex="$$" />=<img src="files/image96.png" width="21px" height="17px" data-latex="$$" /></p>
-<p><img src="files/image97.png" width="44px" height="27px" data-latex="$$" />=<img src="files/image98.png" width="72px" height="28px" data-latex="$$" />=<img src="files/image28.png" width="12px" height="17px" data-latex="$$" />.所以<img src="files/image99.png" width="277px" height="28px" data-latex="$$" />.故选C.</p>
-<p>二、填空题（本大题4小题，每小题5分，共20分）</p>
-<p>13.已知<img src="files/image100.png" width="59px" height="19px" data-latex="$$" />，则<img src="files/image101.png" width="112px" height="29px" data-latex="$$" />_______</p>
-<p>【答案】<img src="files/image102.png" width="14px" height="42px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>将<img src="files/image103.png" width="99px" height="29px" data-latex="$$" />展开，然后分子分母同时除以<img src="files/image104.png" width="45px" height="21px" data-latex="$$" />，得到一个关于<img src="files/image105.png" width="39px" height="17px" data-latex="$$" />的式子，代值计算即可.</p>
-<p>【详解】<img src="files/image103.png" width="99px" height="29px" data-latex="$$" /></p>
-<p><img src="files/image106.png" width="203px" height="21px" data-latex="$$" /> </p>
-<p><img src="files/image107.png" width="137px" height="44px" data-latex="$$" /> </p>
-<p><img src="files/image108.png" width="69px" height="41px" data-latex="$$" /> </p>
-<p><img src="files/image109.png" width="26px" height="42px" data-latex="$$" /> .</p>
-<p>故答案为：<img src="files/image102.png" width="14px" height="42px" data-latex="$$" /> .</p>
-<p>【点睛】本题考查同角三角函数的基本关系以及“弦化切”的应用，属于常考题.</p>
-<p>14.函数<img src="files/image110.png" width="143px" height="27px" data-latex="$$" />，若<img src="files/image111.png" width="61px" height="27px" data-latex="$$" />，则<img src="files/image112.png" width="60px" height="27px" data-latex="$$" />____</p>
-<p>【答案】<img src="files/image113.png" width="21px" height="19px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>试题分析：<img src="files/image114.png" width="297px" height="27px" data-latex="$$" />，<img src="files/image115.png" width="244px" height="27px" data-latex="$$" /></p>
-<p>考点：函数求值</p>
-<p>15.已知一个扇形周长为4，面积为1，则其中心角等于         (弧度).</p>
-<p>【答案】2</p>
-<p>【解析】</p>
-<p>试题分析：由周长为4，可得<img src="files/image116.png" width="64px" height="19px" data-latex="$$" />，又由面积为1，可得<img src="files/image117.png" width="49px" height="41px" data-latex="$$" />，解得<img src="files/image118.png" width="68px" height="21px" data-latex="$$" />，∴<img src="files/image119.png" width="65px" height="41px" data-latex="$$" />.</p>
-<p>考点：弧度制下的扇形的相关公式.</p>
-<p>16.已知向量<img src="files/image120.png" width="109px" height="28px" data-latex="$$" />，<img src="files/image121.png" width="69px" height="25px" data-latex="$$" />，则<img src="files/image122.png" width="40px" height="35px" data-latex="$$" />的最大值为_________</p>
-<p>【答案】3</p>
-<p>【解析】</p>
-<p><img src="files/image123.png" width="10px" height="18px" data-latex="$$" />分析】</p>
-<p>对<img src="files/image122.png" width="40px" height="35px" data-latex="$$" />先平方再开方，然后利用辅助角公式及三角函数的有界性计算即可.</p>
-<p>【详解】<img src="files/image124.png" width="15px" height="13px" data-latex="$$" /><img src="files/image125.png" width="45px" height="37px" data-latex="$$" /><img src="files/image126.png" width="64px" height="25px" data-latex="$$" /><img src="files/image127.png" width="107px" height="25px" data-latex="$$" /><img src="files/image128.png" width="156px" height="25px" data-latex="$$" /><img src="files/image129.png" width="115px" height="41px" data-latex="$$" />，</p>
-<p>又<img src="files/image130.png" width="123px" height="41px" data-latex="$$" />，</p>
-<p><img src="files/image131.png" width="15px" height="13px" data-latex="$$" /><img src="files/image132.png" width="91px" height="37px" data-latex="$$" />，</p>
-<p><img src="files/image131.png" width="15px" height="13px" data-latex="$$" /><img src="files/image133.png" width="84px" height="35px" data-latex="$$" />.</p>
-<p>所以<img src="files/image122.png" width="40px" height="35px" data-latex="$$" />的最大值为<img src="files/image134.png" width="12px" height="19px" data-latex="$$" />.</p>
-<p>故答案为：<img src="files/image134.png" width="12px" height="19px" data-latex="$$" />.</p>
-<p>【点睛】本题主要考查平面向量的坐标运算、三角函数的性质以及辅助角公式，属于常考题.</p>
-<p>三、计算题（本大题6小题，共70分。解答应写出文字说明、证明过程或演算步骤）</p>
-<p>17.已知向量<img src="files/image135.png" width="72px" height="28px" data-latex="$$" />，<img src="files/image136.png" width="71px" height="32px" data-latex="$$" />，求<img src="files/image137.png" width="29px" height="23px" data-latex="$$" />及向量<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角<img src="files/image138.png" width="13px" height="19px" data-latex="$$" />.</p>
-<p>【答案】<img src="files/image139.png" width="61px" height="23px" data-latex="$$" />；<img src="files/image140.png" width="51px" height="41px" data-latex="$$" /></p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据平面向量数量积坐标计算公式直接计算即可.</p>
-<p>【详解】解：<img src="files/image124.png" width="15px" height="13px" data-latex="$$" />向量<img src="files/image135.png" width="72px" height="28px" data-latex="$$" />，<img src="files/image136.png" width="71px" height="32px" data-latex="$$" />,</p>
-<p> <img src="files/image131.png" width="15px" height="13px" data-latex="$$" /><img src="files/image141.png" width="165px" height="24px" data-latex="$$" />，<img src="files/image142.png" width="43px" height="32px" data-latex="$$" />，<img src="files/image33.png" width="41px" height="32px" data-latex="$$" />，</p>
-<p><img src="files/image131.png" width="15px" height="13px" data-latex="$$" /><img src="files/image143.png" width="121px" height="56px" data-latex="$$" />， </p>
-<p>又<img src="files/image144.png" width="64px" height="19px" data-latex="$$" />，</p>
-<p><img src="files/image131.png" width="15px" height="13px" data-latex="$$" /><img src="files/image140.png" width="51px" height="41px" data-latex="$$" />.</p>
-<p>【点睛】本题考查平面向量的坐标运算及夹角公式，熟记公式是解题的关键，属于常考题.</p>
-<p>18.（1）求值<img src="files/image145.png" width="368px" height="27px" data-latex="$$" /></p>
-<p>（2）化简<img src="files/image146.png" width="284px" height="69px" data-latex="$$" /></p>
-<p>【答案】（1）<img src="files/image147.png" width="16px" height="42px" data-latex="$$" />；（2）<img src="files/image148.png" width="100px" height="27px" data-latex="$$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）先利用诱导公式化简成特殊角的三角函数，然后根据特殊角的三角函数值进行计算；</p>
-<p>（2）直接用诱导公式化简即可.</p>
-<p>【详解】（1）<img src="files/image145.png" width="368px" height="27px" data-latex="$$" /></p>
-<p><img src="files/image149.png" width="247px" height="24px" data-latex="$$" /> </p>
-<p><img src="files/image150.png" width="135px" height="45px" data-latex="$$" /> </p>
-<p><img src="files/image151.png" width="29px" height="38px" data-latex="$$" />；</p>
-<p>（2）<img src="files/image146.png" width="284px" height="69px" data-latex="$$" /></p>
-<p><img src="files/image152.png" width="208px" height="67px" data-latex="$$" /> </p>
-<p><img src="files/image153.png" width="160px" height="44px" data-latex="$$" /></p>
-<p><img src="files/image154.png" width="63px" height="15px" data-latex="$$" /></p>
-<p>【点睛】本题考查三角函数式的化简，熟练运用诱导公式进行计算是关键，诱导公式口诀“奇变偶不变，符号看象限”，属于常考题.</p>
-<p>19.平面内给定三个向量<img src="files/image155.png" width="63px" height="28px" data-latex="$$" />，<img src="files/image156.png" width="70px" height="30px" data-latex="$$" />，<img src="files/image157.png" width="60px" height="28px" data-latex="$$" /></p>
-<p>（1）求<img src="files/image158.png" width="85px" height="32px" data-latex="$$" />；</p>
-<p>（2）若<img src="files/image159.png" width="120px" height="32px" data-latex="$$" />，求实数<img src="files/image46.png" width="13px" height="19px" data-latex="$$" />的值.</p>
-<p>【答案】（1）<img src="files/image160.png" width="32px" height="24px" data-latex="$$" />；（2）<img src="files/image161.png" width="36px" height="19px" data-latex="$$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）先根据平面向量的坐标计算<img src="files/image162.png" width="80px" height="23px" data-latex="$$" />，再根据平面向量的模长计算公式进行计算；</p>
-<p>（2）根据向量平行的条件即可得出.</p>
-<p>【详解】解：（1）∵<img src="files/image163.png" width="291px" height="28px" data-latex="$$" /></p>
-<p>∴<img src="files/image164.png" width="129px" height="32px" data-latex="$$" />；</p>
-<p>（2）∵<img src="files/image165.png" width="253px" height="28px" data-latex="$$" />，<img src="files/image166.png" width="93px" height="28px" data-latex="$$" />，</p>
-<p>且<img src="files/image159.png" width="120px" height="32px" data-latex="$$" />  </p>
-<p>∴<img src="files/image167.png" width="209px" height="27px" data-latex="$$" />.</p>
-<p>【点睛】本题考查平面向量平行的坐标表示以及模长计算，熟记公式是解题的关键，属于基础题.</p>
-<p>20.已知<img src="files/image32.png" width="40px" height="32px" data-latex="$$" />，<img src="files/image168.png" width="53px" height="32px" data-latex="$$" />.</p>
-<p>（1）若<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角为<img src="files/image36.png" width="27px" height="19px" data-latex="$$" />，求<img src="files/image169.png" width="40px" height="32px" data-latex="$$" />;</p>
-<p>（2）若<img src="files/image170.png" width="32px" height="21px" data-latex="$$" />与<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />垂直，求<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角.</p>
-<p>【答案】（1）<img src="files/image171.png" width="59px" height="28px" data-latex="$$" />；（2）<img src="files/image172.png" width="27px" height="19px" data-latex="$$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）先计算出<img src="files/image173.png" width="68px" height="45px" data-latex="$$" />，再根据<img src="files/image174.png" width="237px" height="40px" data-latex="$$" />代值进行计算；</p>
-<p>（2）设<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角为<img src="files/image138.png" width="13px" height="19px" data-latex="$$" />，若<img src="files/image170.png" width="32px" height="21px" data-latex="$$" />与<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />垂直，则有<img src="files/image175.png" width="88px" height="32px" data-latex="$$" />，由此求得<img src="files/image176.png" width="37px" height="19px" data-latex="$$" />的值，然后得出<img src="files/image138.png" width="13px" height="19px" data-latex="$$" />的值.</p>
-<p>【详解】解：（1）∵<img src="files/image32.png" width="40px" height="32px" data-latex="$$" />，<img src="files/image168.png" width="53px" height="32px" data-latex="$$" />，<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角为<img src="files/image36.png" width="27px" height="19px" data-latex="$$" />，</p>
-<p>∴<img src="files/image177.png" width="271px" height="45px" data-latex="$$" />，</p>
-<p>∴<img src="files/image178.png" width="437px" height="49px" data-latex="$$" />；</p>
-<p>（2）设<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角为<img src="files/image138.png" width="13px" height="19px" data-latex="$$" />，</p>
-<p>∵<img src="files/image179.png" width="73px" height="32px" data-latex="$$" />，</p>
-<p>∴<img src="files/image175.png" width="88px" height="32px" data-latex="$$" />即<img src="files/image180.png" width="83px" height="25px" data-latex="$$" />，</p>
-<p>∴<img src="files/image181.png" width="137px" height="23px" data-latex="$$" /> ，</p>
-<p>∴<img src="files/image182.png" width="76px" height="45px" data-latex="$$" />，</p>
-<p>又∵<img src="files/image183.png" width="75px" height="16px" data-latex="$$" />，</p>
-<p>∴<img src="files/image184.png" width="52px" height="19px" data-latex="$$" />，</p>
-<p>即<img src="files/image34.png" width="13px" height="23px" data-latex="$$" />与<img src="files/image35.png" width="13px" height="23px" data-latex="$$" />的夹角为<img src="files/image172.png" width="27px" height="19px" data-latex="$$" />.</p>
-<p>【点睛】本题考查向量的模的计算、向量垂直的条件以及向量夹角的计算，应正确理解并熟练运用公式进行计算，属于常考题.</p>
-<p>21.已知A、B、C是△ABC的三个内角，向量m＝(－1，<img src="files/image185.png" width="24px" height="24px" data-latex="$$" />)，n＝(cosA，sinA)，且m·n＝1.</p>
-<p>(1)求角A；</p>
-<p>(2)若<img src="files/image186.png" width="101px" height="41px" data-latex="$$" />＝－3，求tanC．</p>
-<p>【答案】(1) <img src="files/image187.png" width="16px" height="37px" data-latex="$$" />;(2) <img src="files/image188.png" width="56px" height="46px" data-latex="$$" />.</p>
-<p>【解析】</p>
-<p>试题分析:(1)由m·n＝1，代入坐标用两角和与差的正弦公式化简,即可求出角A;(2)将已知条件用完全平方公式和平方差公式化简,可得<img src="files/image189.png" width="81px" height="41px" data-latex="$$" />＝－3,分式上下同除以<img src="files/image190.png" width="39px" height="19px" data-latex="$$" />,解出<img src="files/image191.png" width="39px" height="19px" data-latex="$$" />,又tanC＝tan[π－(A＋B)],利用诱导公式和两角和与差的正切公式化简,把<img src="files/image192.png" width="39px" height="19px" data-latex="$$" />和<img src="files/image191.png" width="39px" height="19px" data-latex="$$" />的值代入即可.</p>
-<p>试题解析:</p>
-<p> (1)∵m·n＝1，</p>
-<p>∴<img src="files/image193.png" width="24px" height="24px" data-latex="$$" />sinA－cosA＝1,2(sinA·<img src="files/image194.png" width="27px" height="45px" data-latex="$$" />－cosA·<img src="files/image195.png" width="16px" height="41px" data-latex="$$" />)＝1，</p>
-<p>sin(A－<img src="files/image196.png" width="17px" height="41px" data-latex="$$" />)＝<img src="files/image195.png" width="16px" height="41px" data-latex="$$" />，</p>
-<p>∵0&lt;A&lt;π，－<img src="files/image196.png" width="17px" height="41px" data-latex="$$" />&lt;A－<img src="files/image196.png" width="17px" height="41px" data-latex="$$" />&lt;<img src="files/image197.png" width="25px" height="41px" data-latex="$$" />，</p>
-<p>∴A－<img src="files/image196.png" width="17px" height="41px" data-latex="$$" />＝<img src="files/image196.png" width="17px" height="41px" data-latex="$$" />.∴A＝<img src="files/image198.png" width="17px" height="41px" data-latex="$$" />.</p>
-<p>(2)由题知<img src="files/image199.png" width="95px" height="41px" data-latex="$$" />＝－3，</p>
-<p>∴<img src="files/image200.png" width="181px" height="53px" data-latex="$$" />＝－3</p>
-<p>∴<img src="files/image189.png" width="81px" height="41px" data-latex="$$" />＝－3</p>
-<p>∴<img src="files/image201.png" width="57px" height="41px" data-latex="$$" />＝－3，∴tanB＝2.</p>
-<p>∴tanC＝tan[π－(A＋B)]</p>
-<p>＝－tan(A＋B)＝－<img src="files/image202.png" width="85px" height="41px" data-latex="$$" />＝<img src="files/image203.png" width="56px" height="45px" data-latex="$$" />.</p>
-<p>点睛:本题考查平面向量数量积的坐标运算,同角三角函数的基本关系和两角和与差的正切公式. 平面向量的数量积计算问题，往往有两种形式，一是利用数量积的定义式，二是利用数量积的坐标运算公式，涉及几何图形的问题，先建立适当的平面直角坐标系，可起到化繁为简的妙用. 利用向量夹角公式、模公式及向量垂直的充要条件，可将有关角度问题、线段长问题及垂直问题转化为向量的数量积来解决．列出方程组求解未知数.</p>
-<p>22.已知函数<img src="files/image204.png" width="333px" height="45px" data-latex="$$" />的最大值为<img src="files/image134.png" width="12px" height="19px" data-latex="$$" />，<img src="files/image205.png" width="39px" height="27px" data-latex="$$" /></p>
-<p>的图像的相邻两对称轴间的距离为<img src="files/image29.png" width="13px" height="17px" data-latex="$$" />，与<img src="files/image206.png" width="14px" height="18px" data-latex="$$" />轴的交点坐标为<img src="files/image207.png" width="37px" height="21px" data-latex="$$" />.</p>
-<p>（1）求函数<img src="files/image205.png" width="39px" height="27px" data-latex="$$" />的解析式；</p>
-<p>（2）设数列<img src="files/image208.png" width="69px" height="27px" data-latex="$$" />，<img src="files/image209.png" width="19px" height="24px" data-latex="$$" />为其前<img src="files/image210.png" width="13px" height="15px" data-latex="$$" />项和，求<img src="files/image211.png" width="27px" height="24px" data-latex="$$" />.</p>
-<p>【答案】（1）<img src="files/image212.png" width="137px" height="45px" data-latex="$$" />（2）<img src="files/image213.png" width="68px" height="24px" data-latex="$$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）根据题中条件，先求出<img src="files/image214.png" width="36px" height="16px" data-latex="$$" />，再由对称轴距离得到<img src="files/image215.png" width="41px" height="41px" data-latex="$$" />，求出<img src="files/image216.png" width="45px" height="41px" data-latex="$$" />，进而可求出结果；</p>
-<p>（2）先由（1）得到<img src="files/image217.png" width="167px" height="45px" data-latex="$$" />，分别讨论<img src="files/image210.png" width="13px" height="15px" data-latex="$$" />为偶数与<img src="files/image210.png" width="13px" height="15px" data-latex="$$" />为奇数，即可求出结果.</p>
-<p>【详解】（1）∵<img src="files/image218.png" width="212px" height="41px" data-latex="$$" />，依题意：<img src="files/image219.png" width="88px" height="41px" data-latex="$$" />，∴<img src="files/image214.png" width="36px" height="16px" data-latex="$$" />.</p>
-<p>又<img src="files/image215.png" width="41px" height="41px" data-latex="$$" />，∴<img src="files/image220.png" width="51px" height="41px" data-latex="$$" />，得<img src="files/image216.png" width="45px" height="41px" data-latex="$$" />.∴<img src="files/image221.png" width="172px" height="45px" data-latex="$$" />. 令<img src="files/image222.png" width="37px" height="19px" data-latex="$$" />得：<img src="files/image223.png" width="91px" height="21px" data-latex="$$" />，又<img src="files/image224.png" width="67px" height="41px" data-latex="$$" />，∴<img src="files/image225.png" width="53px" height="41px" data-latex="$$" />.</p>
-<p>故函数<img src="files/image205.png" width="39px" height="27px" data-latex="$$" />的解析式为：<img src="files/image212.png" width="137px" height="45px" data-latex="$$" /></p>
-<p>（2）由<img src="files/image212.png" width="137px" height="45px" data-latex="$$" />知：<img src="files/image217.png" width="167px" height="45px" data-latex="$$" />.</p>
-<p>当<img src="files/image210.png" width="13px" height="15px" data-latex="$$" />为偶数时，<img src="files/image226.png" width="63px" height="27px" data-latex="$$" />;</p>
-<p>当<img src="files/image210.png" width="13px" height="15px" data-latex="$$" />为奇数时，<img src="files/image227.png" width="344px" height="27px" data-latex="$$" />.</p>
-<p>∴<img src="files/image228.png" width="171px" height="24px" data-latex="$$" />.</p>
-<p>【点睛】本题主要考查三角函数的性质，熟记相关知识点即可，属于常考题型.</p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
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-<p>湖南省长郡中学2019-2020学年高一数学上学期模块检测试题（含解析）</p>
-<p>一、选择题(共12小题，每小题3分，共36分)</p>
-<p>1.已知全集U＝R，集合<img src="files/image1.png" width="232px" height="29px" data-latex="$A=\left\{ x\left| 0\le x\le 2 \right. \right\},B=\{x\left| {{x}^{2}} \right.-x>0\}$" />，则图中的阴影部分表示的集合为(　　)</p>
-<p><img src="files/image2.png" width="119px" height="69px" /></p>
-<p>A. <img src="files/image3.png" width="109px" height="21px" data-latex="$$" />B. <img src="files/image4.png" width="96px" height="15.75pt" data-latex="$$" />C. <img src="files/image5.png" width="34px" height="22px" data-latex="$$" />D. <img src="files/image6.png" width="32px" height="21px" data-latex="$$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>B={x|x<sup>2</sup>﹣x＞0}={x|x＞1或x＜0}，</p>
-<p>由题意可知阴影部分对应的集合为∁<sub>U</sub>（A∩B）∩（A∪B），</p>
-<p>∴A∩B={x|1＜x≤2}，A∪B=R，</p>
-<p>即∁<sub>U</sub>（A∩B）={x|x≤1或x＞2}，</p>
-<p>∴∁<sub>U</sub>（A∩B）∩（A∪B）={x|x≤1或x＞2}，</p>
-<p>即（﹣∞，1]U（2，+∞）</p>
-<p>故选A</p>
-<p>2.下列各组函数中，<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />与<img src="files/image8.png" width="37px" height="27px" data-latex="$g\left( x \right)$" />相等的是(    )</p>
-<p>A. <img src="files/image9.png" width="85px" height="27px" data-latex="$f\left( x \right)=2-x$" />，<img src="files/image10.png" width="90px" height="27px" data-latex="$g\left( x \right)=2-\left| x \right|$" />B. <img src="files/image11.png" width="81px" height="31px" data-latex="$f\left( x \right)=\sqrt{{{x}^{2}}}$" />，<img src="files/image12.png" width="91px" height="36px" data-latex="$g\left( x \right)={{\left( \sqrt[3]{x} \right)}^{3}}$" /></p>
-<p>C. <img src="files/image13.png" width="95px" height="44px" data-latex="$f\left( x \right)=\frac{{{x}^{2}}}{x}+2$" />，<img src="files/image14.png" width="84px" height="27px" data-latex="$g\left( x \right)=2+x$" />D. <img src="files/image15.png" width="95px" height="44px" data-latex="$f\left( x \right)=\frac{{{x}^{2}}-x}{x}$" />，<img src="files/image16.png" width="91px" height="44px" data-latex="$g\left( x \right)=\frac{{{x}^{2}}}{x}-1$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据两个函数的定义域相同，解析式也相同，即可判断它们是相等函数．</p>
-<p>【详解】对于A，f（x）＝2﹣x，与g（x）＝2﹣|x|的解析式不同，不是相等函数；</p>
-<p>对于B，<img src="files/image17.png" width="111px" height="31px" data-latex="$f\left( x \right)=\sqrt{{{x}^{2}}}=\left| x \right|$" />，与g（x）<img src="files/image18.png" width="69px" height="36px" data-latex="$={{\left( \sqrt[3]{x} \right)}^{3}}=$" />x的解析式不同，不是相等函数；</p>
-<p>对于C，f（x）<img src="files/image19.png" width="47px" height="44px" data-latex="$=\frac{{{x}^{2}}}{x}+$" />2＝x+2（x≠0），与g（x）＝2+x（x∈R）的定义域不同，不是相等函数；</p>
-<p>对于D，f（x）<img src="files/image20.png" width="69px" height="44px" data-latex="$=\frac{{{x}^{2}}-x}{x}=$" />x﹣1（x≠0），与g（x）<img src="files/image21.png" width="47px" height="44px" data-latex="$=\frac{{{x}^{2}}}{x}-$" />1＝x﹣1（x≠0）的定义域相同，对应关系也相同，是相等函数．</p>
-<p>故选：D．</p>
-<p><img src="files/image22.png" width="10px" height="18px" data-latex="$$" />点睛】本题考查了判断两个函数是否为相等函数的应用问题，是基础题．</p>
-<p>3.在定义域内既是奇函数又是减函数的是（　   ）</p>
-<p>A. <img src="files/image23.png" width="63px" height="41px" data-latex="$f(x)=\frac{1}{x}$" />B. <img src="files/image24.png" width="95px" height="41px" data-latex="$f(x)=-x+\frac{1}{x}$" /></p>
-<p>C. <img src="files/image25.png" width="92px" height="21px" data-latex="$f(x)=-x|x|$" />D. <img src="files/image26.png" width="171px" height="48px" data-latex="$f(x)=\left\{ \begin{array}{*{35}{l}}   -x+1,x\in (0,+\infty )  \\   -x-1,x\in (-\infty ,0]  \\\end{array} \right.$" /></p>
-<p>【答案】C</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据奇偶性与单调性判断选择.</p>
-<p>【详解】<img src="files/image27.png" width="65px" height="41px" data-latex="$f\left( x \right)=\frac{1}{x}$" />在定义域<img src="files/image28.png" width="63px" height="21px" data-latex="$(-\infty ,0)\bigcup $" /> <img src="files/image29.png" width="49px" height="21px" data-latex="$(0,+\infty )$" />内是奇函数,但不是减函数，在区间<img src="files/image30.png" width="49px" height="21px" data-latex="$(-\infty ,0)$" />和<img src="files/image29.png" width="49px" height="21px" data-latex="$(0,+\infty )$" />上都是减函数</p>
-<p><img src="files/image31.png" width="97px" height="41px" data-latex="$f\left( x \right)=-x+\frac{1}{x}$" />在定义域<img src="files/image28.png" width="63px" height="21px" data-latex="$(-\infty ,0)\bigcup $" /> <img src="files/image29.png" width="49px" height="21px" data-latex="$(0,+\infty )$" />内是奇函数,但不是减函数，在区间<img src="files/image30.png" width="49px" height="21px" data-latex="$(-\infty ,0)$" />和<img src="files/image29.png" width="49px" height="21px" data-latex="$(0,+\infty )$" />上都是减函数</p>
-<p><img src="files/image32.png" width="217px" height="53px" data-latex="$f\left( x \right)=-x\left| x \right|=\left\{ \begin{matrix}   -{{x}^{2}},x\in \left( 0,+\infty  \right),  \\   {{x}^{2}},x\in \left( -\infty ,0 \right]  \\\end{matrix} \right.$" />在定义域<img src="files/image33.png" width="62px" height="21px" data-latex="$(-\infty ,+\infty )$" />内既是奇函数又是减函数</p>
-<p><img src="files/image34.png" width="180px" height="53px" data-latex="$f\left( x \right)=\left\{ \begin{matrix}   -x+1,x\in \left( 0,+\infty  \right),  \\   -x-1,x\in \left( -\infty ,0 \right]  \\\end{matrix} \right.$" />在定义域<img src="files/image33.png" width="62px" height="21px" data-latex="$(-\infty ,+\infty )$" />内不是奇函数（因为<img src="files/image35.png" width="93px" height="27px" data-latex="$f\left( 0 \right)=-1\ne 0$" />），</p>
-<p>综上选C.</p>
-<p>【点睛】本题考查函数奇偶性与单调性，考查基本分析判断能力，属基础题.</p>
-<p>4.已知<img src="files/image36.png" width="61px" height="24px" data-latex="$a=\sqrt{0.3}$" />，<img src="files/image37.png" width="111px" height="24px" data-latex="$b={{2}^{0.3}},c={{0.3}^{0.2}}$" />则<img src="files/image38.png" width="40px" height="21px" data-latex="$a,b,c$" />三者的大小关系是(    )</p>
-<p>A. <img src="files/image39.png" width="60px" height="19px" data-latex="$b>c>a$" />B. <img src="files/image40.png" width="60px" height="19px" data-latex="$b>a>c$" />C. <img src="files/image41.png" width="53px" height="17px" data-latex="$a>b>c$" />D. <img src="files/image42.png" width="60px" height="19px" data-latex="$c>b>a$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>因为<img src="files/image43.png" width="193px" height="27px" data-latex="$\text{a}\in \left( 0,1 \right),\text{b}>1,\text{c}\in \left( 0,1 \right),{{0.3}^{0.5}}$" />&lt;<img src="files/image44.png" width="36px" height="21px" data-latex="${{0.3}^{0.2}}$" />，所以<img src="files/image45.png" width="60px" height="19px" data-latex="$\text{a}<\text{c}<\text{b}$" />,选A.</p>
-<p>5.已知集合<img src="files/image46.png" width="235px" height="32px" data-latex="$A=\left\{ \left( x,y \right)\left| {{x}^{2}}+{{y}^{2}}\le 2,x\in Z,y\in Z \right. \right\}$" />，则<img src="files/image47.png" width="16px" height="18px" data-latex="$A$" />中元素的个数为(    )</p>
-<p>A. <img src="files/image48.png" width="13px" height="17px" data-latex="$4$" />B. <img src="files/image49.png" width="12px" height="19px" data-latex="$5$" />C. <img src="files/image50.png" width="12px" height="19px" data-latex="$8$" />D. <img src="files/image51.png" width="12px" height="19px" data-latex="$9$" /></p>
-<p>【答案】D</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>集合A的元素代表圆周及其内部的点，即可得到结论</p>
-<p>【详解】根据题意：A＝{（x，y）|x<sup>2</sup>+y<sup>2</sup>≤2，x，y∈Z}＝{（﹣1，﹣1），（﹣1，0），（﹣1，1），（0，﹣1），（0，0）（0，1），（1，﹣1），（1，0），（1，1）}共9个元素，是平面直角坐标系中9个点．</p>
-<p>故选：D．</p>
-<p>【点睛】本题考查集合的表示以及点与圆的位置关系，解题时需注意集合A的元素为两坐标均为整数的点，本题属于基础题．</p>
-<p>6.设定义在<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />上的函数<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />对任意实数<img src="files/image54.png" width="28px" height="17px" data-latex="$x,y$" />满足<img src="files/image55.png" width="152px" height="21px" data-latex="$f(x)+f(y)=f(x+y)$" />，且<img src="files/image56.png" width="60px" height="21px" data-latex="$f(2)=4$" />，则<img src="files/image57.png" width="89px" height="21px" data-latex="$f(0)+f(-2)$" />的值为（ ）</p>
-<p>A. －2B. <img src="files/image58.png" width="24px" height="21px" data-latex="$-\,4$" />C. 0D. 4</p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>试题分析：令<img src="files/image59.png" width="62px" height="21px" data-latex="$x=y=0$" />，则有<img src="files/image60.png" width="125px" height="21px" data-latex="$f(0)+f(0)=f(0)$" />，故得<img src="files/image61.png" width="59px" height="21px" data-latex="$f(0)=0$" />，</p>
-<p>令<img src="files/image62.png" width="45px" height="19px" data-latex="$x=-2$" />，<img src="files/image63.png" width="39px" height="21px" data-latex="$y=2$" />，则有<img src="files/image64.png" width="159px" height="21px" data-latex="$f(-2)+f(2)=f(0)=0$" />，</p>
-<p>又<img src="files/image56.png" width="60px" height="21px" data-latex="$f(2)=4$" />,<img src="files/image65.png" width="89px" height="21px" data-latex="$\therefore f(-2)=-4$" /><img src="files/image66.png" width="135px" height="21px" data-latex="$\therefore f(0)+f(-2)=-4$" />故选<img src="files/image67.png" width="15px" height="16px" data-latex="$B$" />.</p>
-<p>考点：函数的值.</p>
-<p>7.已知集合<img src="files/image68.png" width="125px" height="32px" data-latex="$$" />，<img src="files/image69.png" width="145px" height="29px" data-latex="$$" />，若<img src="files/image70.png" width="67px" height="27px" data-latex="$A\bigcap \left( {{\complement }_{\text{R}}}B \right)$" />中恰好含有<img src="files/image71.png" width="13px" height="17px" data-latex="$2$" />个整数，则实数<img src="files/image72.png" width="13px" height="14px" data-latex="$a$" />的取值范围是(    )</p>
-<p>A. <img src="files/image73.png" width="60px" height="19px" data-latex="$3<a<4$" />B. <img src="files/image74.png" width="60px" height="19px" data-latex="$3\le a<4$" />C. <img src="files/image75.png" width="60px" height="19px" data-latex="$3<a\le 4$" />D. <img src="files/image76.png" width="60px" height="19px" data-latex="$3\le a\le 4$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>可根据题意得出∁<sub>R</sub>B＝{x|﹣4＜x≤a}，根据条件得出A∩（∁<sub>R</sub>B）＝{x|﹣4＜x＜﹣3或1＜x≤a}，从而可得出a的取值范围．</p>
-<p>【详解】根据题意，a＞﹣4，则∁<sub>R</sub>B＝{x|﹣4＜x≤a}，</p>
-<p>又A＝{x|x＜﹣3或x＞1}，A∩（∁<sub>R</sub>B）中恰好含有2个整数，</p>
-<p>∴A∩（∁<sub>R</sub>B）＝{x|﹣4＜x＜﹣3或1＜x≤a}，</p>
-<p>∴3≤a＜4．</p>
-<p>故选：B．</p>
-<p>【点睛】本题考查描述法的定义，以及交集、补集的运算，注意数轴法的应用及端点值问题，是易错题</p>
-<p>8.已知函数<img src="files/image77.png" width="88px" height="42px" data-latex="$f\left( x \right)=\frac{x+2}{x-1}$" /><img src="files/image78.png" width="5px" height="9px" data-latex="$$" />记<img src="files/image79.png" width="245px" height="27px" data-latex="$f\left( 2 \right)+f\left( 3 \right)+f\left( 4 \right)+\cdots +f\left( 10 \right)=m,$" /><img src="files/image80.png" width="263px" height="45px" data-latex="$f\left( \frac{1}{2} \right)+f\left( \frac{1}{3} \right)+f\left( \frac{1}{4} \right)+\cdots +f\left( \frac{1}{10} \right)=n$" />,则<img src="files/image81.png" width="52px" height="16px" data-latex="$m+n=$" /></p>
-<p>A. <img src="files/image82.png" width="21px" height="19px" data-latex="$-9$" />B. 9C. <img src="files/image83.png" width="19px" height="19px" data-latex="$10$" />D. <img src="files/image84.png" width="30px" height="18px" data-latex="$-10$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>推导出<img src="files/image85.png" width="117px" height="45px" data-latex="$f\left( x \right)+f\left( \frac{1}{x} \right)=-$" />1，再由f（2）+f（3）+f（4）+…+f（10）＝m，<img src="files/image86.png" width="263px" height="45px" data-latex="$f\left( \frac{1}{2} \right)+f\left( \frac{1}{3} \right)+f\left( \frac{1}{4} \right)+\cdots +f\left( \frac{1}{10} \right)=n$" />，能求出m+n的值．</p>
-<p>【详解】解：∵函数<img src="files/image87.png" width="88px" height="41px" data-latex="$f\left( x \right)=\frac{x+2}{x-1}$" />，</p>
-<p>∴<img src="files/image88.png" width="217px" height="80px" data-latex="$f\left( x \right)+f\left( \frac{1}{x} \right)=\frac{x+2}{x-1}+\frac{\frac{1}{x}+2}{\frac{1}{x}-1}=-$" />1，</p>
-<p>∵f（2）+f（3）+f（4）+…+f（10）＝m，<img src="files/image86.png" width="263px" height="45px" data-latex="$f\left( \frac{1}{2} \right)+f\left( \frac{1}{3} \right)+f\left( \frac{1}{4} \right)+\cdots +f\left( \frac{1}{10} \right)=n$" />，</p>
-<p>∴m+n＝9×（﹣1）＝﹣9．</p>
-<p>故选A．</p>
-<p>【点睛】本题考查函数值的求法，考查函数性质等基础知识，考查运算求解能力，是基础题．</p>
-<p>9.已知函数<img src="files/image89.png" width="133px" height="22px" data-latex="$f(x)=(x-a)(x-b)$" />（其中<img src="files/image90.png" width="33px" height="17px" data-latex="$a>b$" />），若<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />的图像如右图所示，则函数<img src="files/image91.png" width="88px" height="24px" data-latex="$g(x)={{a}^{x}}+b$" />的图像大致为（ ）</p>
-<p><img src="files/image92.png" width="168px" height="126px" /></p>
-<p>A. <img src="files/image93.png" width="118px" height="120px" />B. <img src="files/image94.png" width="118px" height="117px" />C. <img src="files/image95.png" width="116px" height="114px" />D. <img src="files/image96.png" width="111px" height="118px" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />的图像，得到<img src="files/image97.png" width="57px" height="19px" data-latex="$0<a<1$" />，<img src="files/image98.png" width="44px" height="19px" data-latex="$b<-1$" />，进而可得出结果.</p>
-<p>【详解】由<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />的图像可知，<img src="files/image97.png" width="57px" height="19px" data-latex="$0<a<1$" />，<img src="files/image98.png" width="44px" height="19px" data-latex="$b<-1$" />，观察图像可知，答案选A．</p>
-<p>【点睛】本题主要考查二次函数图像，指数函数图像，熟记函数性质即可，属于常考题型.</p>
-<p>10.若不等式<img src="files/image99.png" width="103px" height="21px" data-latex="$a{{x}^{2}}+bx+4>0$" />的解集为<img src="files/image100.png" width="92px" height="29px" data-latex="$\left\{ x\left| -2<x<1 \right. \right\}$" />，则二次函数<img src="files/image101.png" width="105px" height="24px" data-latex="$y=b{{x}^{2}}+4x+a$" />在区间<img src="files/image102.png" width="36px" height="27px" data-latex="$\left[ 0,3 \right]$" />上的最大值、最小值分别为（    ）.</p>
-<p>A. <img src="files/image103.png" width="35px" height="21px" data-latex="$0,-8$" />B. <img src="files/image104.png" width="35px" height="21px" data-latex="$0,-4$" /></p>
-<p>C. <img src="files/image105.png" width="27px" height="21px" data-latex="$4,0$" />D. <img src="files/image106.png" width="25px" height="21px" data-latex="$8,0$" /></p>
-<p>【答案】A</p>
-<p>【解析】</p>
-<p>【详解】由题意知<img src="files/image107.png" width="37px" height="19px" data-latex="$a<0$" />且二次方程<img src="files/image108.png" width="103px" height="21px" data-latex="$a{{x}^{2}}+bx+4=0$" /><img src="files/image109.png" width="14px" height="19px" data-latex="$$" />两个根分别为<img src="files/image110.png" width="21px" height="17px" data-latex="$-2$" />和1.则有<img src="files/image111.png" width="59px" height="41px" data-latex="$-\frac{b}{a}=-1$" />，<img src="files/image112.png" width="49px" height="41px" data-latex="$\frac{4}{a}=-2$" />.故<img src="files/image113.png" width="47px" height="19px" data-latex="$a=-2$" />，<img src="files/image114.png" width="45px" height="19px" data-latex="$b=-2$" />.所以，二次函数<img src="files/image115.png" width="105px" height="24px" data-latex="$y=b{{x}^{2}}+4x+a$" />在区间<img src="files/image116.png" width="36px" height="27px" data-latex="$\left[ 0,3 \right]$" />上的最大值是0，最小值是<img src="files/image117.png" width="21px" height="19px" data-latex="$-8$" />. 选A.</p>
-<p>11.高斯是德国著名的数学家，近代数学奠基者之一，享有数学王子的美誉，他和阿基米德，牛顿并列为世界三大数学家，用其名字命名的“高斯函数”为：设<img src="files/image118.png" width="42px" height="19px" data-latex="$x\in R$" />，用<img src="files/image119.png" width="24px" height="27px" data-latex="$\left[ x \right]$" />表示不超过<img src="files/image120.png" width="13px" height="15px" data-latex="$x$" />的最大整数，则<img src="files/image121.png" width="48px" height="27px" data-latex="$y=\left[ x \right]$" />称为高斯函数，例如<img src="files/image122.png" width="67px" height="20px" data-latex="$$" />，<img src="files/image123.png" width="57px" height="27px" data-latex="$\left[ 2.1 \right]=2$" />.已知函数<img src="files/image124.png" width="116px" height="44px" data-latex="$f\left( x \right)=\frac{{{2}^{x}}}{{{2}^{x}}+1}-\frac{1}{2}$" />，则函数<img src="files/image125.png" width="79px" height="29px" data-latex="$y=\left[ f\left( x \right) \right]$" />的值域为(    )</p>
-<p>A. <img src="files/image126.png" width="36px" height="27px" data-latex="$\left\{ 0,1 \right\}$" />B. <img src="files/image127.png" width="25px" height="27px" data-latex="$\left\{ 0 \right\}$" />C. <img src="files/image128.png" width="47px" height="27px" data-latex="$$" />D. <img src="files/image129.png" width="57px" height="27px" data-latex="$\left\{ -1,0,1 \right\}$" /></p>
-<p>【答案】C</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p><img src="files/image130.png" width="291px" height="44px" data-latex="$f\left( x \right)=\frac{{{2}^{x}}}{{{2}^{x}}+1}-\frac{1}{2}=\frac{{{2}^{x}}+1-1}{{{2}^{x}}+1}-\frac{1}{2}=\frac{1}{2}-\frac{1}{{{2}^{x}}+1}$" />，得函数f（x）为R上的增函数，所以f（x）∈（<img src="files/image131.png" width="27px" height="41px" data-latex="$-\frac{1}{2}$" />，<img src="files/image132.png" width="16px" height="41px" data-latex="$\frac{1}{2}$" />），进而可以得到y＝[f（x）]的值域．</p>
-<p>【详解】依题意，<img src="files/image130.png" width="291px" height="44px" data-latex="$f\left( x \right)=\frac{{{2}^{x}}}{{{2}^{x}}+1}-\frac{1}{2}=\frac{{{2}^{x}}+1-1}{{{2}^{x}}+1}-\frac{1}{2}=\frac{1}{2}-\frac{1}{{{2}^{x}}+1}$" />，</p>
-<p>因为y＝2<sup>x</sup>+1为R上的增函数，所以函数f（x）为R上的增函数，</p>
-<p>所以f（x）∈（<img src="files/image131.png" width="27px" height="41px" data-latex="$-\frac{1}{2}$" />，<img src="files/image132.png" width="16px" height="41px" data-latex="$\frac{1}{2}$" />），</p>
-<p>所以y＝[f（x）]的值域为{﹣1，0}，</p>
-<p>故选：C．</p>
-<p>【点睛】本题考查了新定义高斯函数，考查了函数的值域，函数的单调性，属于基础题．</p>
-<p>12.设集合<img src="files/image133.png" width="121px" height="27px" data-latex="$M=\left\{ 1,2,3,4,5,6 \right\}$" />，<img src="files/image134.png" width="80px" height="24px" data-latex="${{S}_{1}},{{S}_{2}},\cdots ,{{S}_{k}}$" />都是<img src="files/image135.png" width="22px" height="18px" data-latex="$M$" />的含两个元素的子集，且满足：对任意的<img src="files/image136.png" width="76px" height="27px" data-latex="${{S}_{i}}=\left\{ {{a}_{i}},{{b}_{i}} \right\}$" />，<img src="files/image137.png" width="83px" height="29px" data-latex="${{S}_{j}}=\left\{ {{a}_{j}},{{b}_{j}} \right\}$" />(<img src="files/image138.png" width="157px" height="27px" data-latex="$$" />)，都有<img src="files/image139.png" width="193px" height="54px" data-latex="$\max \left\{ \frac{{{a}_{i}}}{{{b}_{i}}},\frac{{{b}_{i}}}{{{a}_{i}}} \right\}\ne \max \left\{ \frac{{{a}_{j}}}{{{b}_{j}}},\frac{{{b}_{j}}}{{{a}_{j}}} \right\}$" />(<img src="files/image140.png" width="71px" height="27px" data-latex="$\max \left\{ x,y \right\}$" />表示两个数<img src="files/image120.png" width="13px" height="15px" data-latex="$x$" />，<img src="files/image141.png" width="14px" height="18px" data-latex="$y$" />中的较大者)，则<img src="files/image142.png" width="13px" height="19px" data-latex="$k$" />的最大值是(    )</p>
-<p>A. <img src="files/image83.png" width="19px" height="19px" data-latex="$10$" />B. <img src="files/image143.png" width="17px" height="17px" data-latex="$11$" />C. <img src="files/image144.png" width="19px" height="17px" data-latex="$12$" />D. <img src="files/image145.png" width="19px" height="19px" data-latex="$13$" /></p>
-<p>【答案】B</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>根据题意，首先分析出M的所有含2个元素的子集数目，进而对其特殊的子集分析排除，注意对min<img src="files/image146.png" width="72px" height="51px" data-latex="$$" />min<img src="files/image147.png" width="64px" height="53px" data-latex="$$" />（min{x，y}表示两个数x、y中的较小者）的把握，即可得答案．</p>
-<p>【详解】根据题意，对于M，含2个元素的子集有15个，</p>
-<p>但{1，2}、{2，4}、{3，6}只能取一个；</p>
-<p>{1，3}、{2，6}只能取一个；</p>
-<p>{2，3}、{4，6}只能取一个，</p>
-<p>故满足条件的两个元素的集合有11个；</p>
-<p>故选：B．</p>
-<p>【点睛】本题考查学生对集合及其子集、元素的把握、运用，注意对题意的分析．</p>
-<p>二、填空题(本大题共4个小题，每小题4分，共16分)</p>
-<p>13.已知集合<img src="files/image148.png" width="149px" height="29px" data-latex="$A=\left\{ 0,m,{{m}^{2}}-3m+2 \right\}$" />，且<img src="files/image149.png" width="38px" height="18px" data-latex="$2\in A$" />，求实数<img src="files/image150.png" width="17px" height="15px" data-latex="$m$" />的值______．</p>
-<p>【答案】3</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>由题意结合集合元素的互异性分类讨论求解实数m的值即可.</p>
-<p>【详解】由题意分类讨论：</p>
-<p>若<img src="files/image151.png" width="42px" height="18px" data-latex="$m=2$" />，则<img src="files/image152.png" width="103px" height="21px" data-latex="${{m}^{2}}-3m+2=0$" />，不满足集合元素的互异性，舍去；</p>
-<p>若<img src="files/image153.png" width="103px" height="22px" data-latex="${{m}^{2}}-3m+2=2$" />，解得：<img src="files/image154.png" width="40px" height="19px" data-latex="$m=3$" />或<img src="files/image155.png" width="40px" height="19px" data-latex="$m=0$" />，</p>
-<p>其中<img src="files/image155.png" width="40px" height="19px" data-latex="$m=0$" />不满足集合元素的互异性，舍去，</p>
-<p>综上可得，<img src="files/image154.png" width="40px" height="19px" data-latex="$m=3$" />.</p>
-<p>【点睛】本题主要考查集合与元素的关系，集合元素的互异性等知识，意在考查学生的转化能力和计算求解能力.</p>
-<p>14.定义在<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />上的奇函数<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />满足：当<img src="files/image156.png" width="142px" height="24px" data-latex="$x\ge 0,f\left( x \right)={{x}^{2}}-2x+a$" />，则<img src="files/image157.png" width="59px" height="27px" data-latex="$f\left( -3 \right)=$" />__________．</p>
-<p>【答案】<img src="files/image158.png" width="21px" height="19px" data-latex="$-3$" /></p>
-<p>【解析】</p>
-<p><img src="files/image159.png" width="52px" height="27px" data-latex="$\because f\left( x \right)$" />为<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />上的奇函数，<img src="files/image160.png" width="331px" height="29px" data-latex="$\therefore f\left( 0 \right)=a=0,f\left( -3 \right)=-f\left( 3 \right)=-\left( {{3}^{2}}-2\times 3 \right)=-3$" />，</p>
-<p>故答案为<img src="files/image158.png" width="21px" height="19px" data-latex="$-3$" />.</p>
-<p>15.已知函数<img src="files/image161.png" width="157px" height="45px" data-latex="$f\left( x \right)=\frac{mx-1}{\sqrt{m{{x}^{2}}+4mx+3}}$" />的定义域为<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />，则实数<img src="files/image150.png" width="17px" height="15px" data-latex="$m$" />的取值范围是__________.</p>
-<p>【答案】.<img src="files/image162.png" width="44px" height="45px" data-latex="$\left[ 0,\frac{3}{4} \right)$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>由题意可得，对任意实数x，mx<sup>2</sup>+4mx+3＞0恒成立，然后分m＝0和m≠0分类求解m的范围，取并集得答案．</p>
-<p>【详解】函数f（x）<img src="files/image163.png" width="121px" height="47px" data-latex="$=\frac{mx-1}{\sqrt{m{{x}^{2}}+4mx+3}}$" />的定义域为R，</p>
-<p>则对任意实数x，mx<sup>2</sup>+4mx+3＞0恒成立，</p>
-<p>当m＝0时，不等式3＞0恒成立；</p>
-<p>当m≠0时，要使mx<sup>2</sup>+4mx+3＞0恒成立，则<img src="files/image164.png" width="112px" height="48px" data-latex="$$" />，解得：0<img src="files/image165.png" width="57px" height="41px" data-latex="$$" />．</p>
-<p>综上，实数m的取值范围是[0，<img src="files/image166.png" width="16px" height="41px" data-latex="$\frac{3}{4}$" />）．</p>
-<p>故答案为：[0，<img src="files/image166.png" width="16px" height="41px" data-latex="$\frac{3}{4}$" />）．</p>
-<p>【点睛】本题考查函数的定义域及其求法，考查数学转化思想方法和分类讨论的数学思想方法，是中档题．</p>
-<p>16.关于函数<img src="files/image167.png" width="114px" height="52px" data-latex="$f\left( x \right)=\frac{\sqrt{{{x}^{2}}-{{x}^{4}}}}{\left| x-1 \right|-1}$" />的性质描述，正确的是__________.①<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />的定义域为<img src="files/image168.png" width="91px" height="27px" data-latex="$\left[ -1,0 \right)\bigcup \left( 0,1 \right]$" />；②<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />的值域为<img src="files/image169.png" width="39px" height="22px" data-latex="$\left( -1,1 \right)$" />；③<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />的图象关于原点对称；④<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />在定义域上是增函数.</p>
-<p>【答案】①②③</p>
-<p>【解析】</p>
-<p><img src="files/image22.png" width="10px" height="18px" data-latex="$$" />分析】</p>
-<p>由被开方式非负和分母不为0，解不等式可得f（x）的定义域，可判断①；化简f（x），讨论0＜x≤1，﹣1≤x＜0，分别求得f（x）的范围，求并集可得f（x）的值域，可判断②；由f（﹣1）＝f（1）＝0，f(x)不是增函数，可判断④；由奇偶性的定义得f（x）为奇函数，可判断③．</p>
-<p>【详解】①，由<img src="files/image170.png" width="89px" height="53px" data-latex="$\left\{ \begin{array}{*{35}{l}}   {{x}^{2}}-{{x}^{4}}\ge 0  \\   \left| x-1 \right|-1\ne 0  \\\end{array} \right.$" />，解得﹣1≤x≤1且x≠0，</p>
-<p>可得函数<img src="files/image167.png" width="114px" height="52px" data-latex="$f\left( x \right)=\frac{\sqrt{{{x}^{2}}-{{x}^{4}}}}{\left| x-1 \right|-1}$" />的定义域为[﹣1，0）∪（0，1]，故①正确；</p>
-<p>②，由①可得f（x）＝<img src="files/image171.png" width="64px" height="47px" data-latex="$\frac{\sqrt{{{x}^{2}}-{{x}^{4}}}}{-x}$" />，即f（x）＝﹣<img src="files/image172.png" width="76px" height="47px" data-latex="$\frac{|x|\sqrt{1-{{x}^{2}}}}{x}$" />，</p>
-<p>当0＜x≤1可得f（x）＝﹣<img src="files/image173.png" width="51px" height="27px" data-latex="$\sqrt{1-{{x}^{2}}}$" />∈（﹣1，0]；当﹣1≤x＜0可得f（x）＝<img src="files/image173.png" width="51px" height="27px" data-latex="$\sqrt{1-{{x}^{2}}}$" />∈[0，1）．</p>
-<p>可得f（x）的值域为（﹣1，1），故②正确；</p>
-<p>③，由f（x）＝﹣<img src="files/image172.png" width="76px" height="47px" data-latex="$\frac{|x|\sqrt{1-{{x}^{2}}}}{x}$" />的定义域为[﹣1，0）∪（0，1]，关于原点对称，</p>
-<p>f（﹣x）＝<img src="files/image172.png" width="76px" height="47px" data-latex="$\frac{|x|\sqrt{1-{{x}^{2}}}}{x}$" />＝﹣f（x），则f（x）为奇函数，即有f（x）的图象关于原点对称，故③正确．</p>
-<p>④，由f（﹣1）＝f（1）＝0，则f（x）在定义域上不是增函数，故④错误；</p>
-<p>故答案为：①②③</p>
-<p>【点睛】本题考查函数的性质和应用，主要是定义域和值域的求法、单调性的判断和图象的特征，考查定义法和分类讨论思想，以及化简运算能力和推理能力，属于中档题．</p>
-<p>三、解答题(本大题共6个小题，共48分)</p>
-<p>17.(1)计算：<img src="files/image174.png" width="196px" height="49px" data-latex="${{0.064}^{-\frac{1}{3}}}-{{\left( -\frac{1}{8} \right)}^{0}}+{{16}^{\frac{3}{4}}}+{{0.25}^{\frac{1}{2}}}$" />；</p>
-<p>(2)已知<img src="files/image175.png" width="69px" height="21px" data-latex="$x+{{x}^{-1}}=3$" />，求<img src="files/image176.png" width="54px" height="21px" data-latex="${{x}^{4}}-{{x}^{-4}}$" />的值.</p>
-<p>【答案】(1)10；(2) <img src="files/image177.png" width="41px" height="24px" data-latex="$\pm 3\sqrt{5}$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）利用指数运算性质即可得出．</p>
-<p>（2）由<img src="files/image175.png" width="69px" height="21px" data-latex="$x+{{x}^{-1}}=3$" />平方得<img src="files/image178.png" width="79px" height="21px" data-latex="${{x}^{2}}+{{x}^{-2}}=7$" />，进而得<img src="files/image179.png" width="87px" height="21px" data-latex="${{x}^{4}}+{{x}^{-4}}=47$" />，再利用<img src="files/image180.png" width="192px" height="24pt" data-latex="${{\left( {{x}^{2}}-{{x}^{-2}} \right)}^{2}}={{x}^{4}}-2+{{x}^{-4}}=45$" />即可得出．</p>
-<p>【详解】(1)原式<img src="files/image181.png" width="309px" height="44px" data-latex="$=\frac{1}{\sqrt[3]{0.064}}-1+\sqrt[4]{{{16}^{3}}}+\sqrt{0.25}=\frac{5}{2}-1+8+\frac{1}{2}=10$" /></p>
-<p>(2)由<img src="files/image175.png" width="69px" height="21px" data-latex="$x+{{x}^{-1}}=3$" /></p>
-<p>得<img src="files/image178.png" width="79px" height="21px" data-latex="${{x}^{2}}+{{x}^{-2}}=7$" /></p>
-<p>∴<img src="files/image179.png" width="87px" height="21px" data-latex="${{x}^{4}}+{{x}^{-4}}=47$" /></p>
-<p>∴<img src="files/image180.png" width="192px" height="24pt" data-latex="${{\left( {{x}^{2}}-{{x}^{-2}} \right)}^{2}}={{x}^{4}}-2+{{x}^{-4}}=45$" /></p>
-<p>即<img src="files/image182.png" width="105px" height="24px" data-latex="${{x}^{2}}-{{x}^{-2}}=\pm 3\sqrt{5}$" /></p>
-<p>【点睛】本题考查了指数运算性质、乘法公式及其变形，考查了推理能力与计算能力，属于基础题．</p>
-<p>18.已知函数<img src="files/image183.png" width="92px" height="41px" data-latex="$$" />．</p>
-<p>（1）判断<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />的奇偶性；</p>
-<p>（2）写出<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />的单调递增区间，并用定义证明．</p>
-<p>【答案】（1）奇函数；（2）<img src="files/image53.png" width="33px" height="20px" data-latex="$$" />在<img src="files/image184.png" width="64px" height="41px" data-latex="$(-\infty ,-\frac{1}{2})$" />上为增函数，证明见解析.</p>
-<p>【解析】</p>
-<p>试题分析：（1）由<img src="files/image185.png" width="101px" height="21px" />可得函数<img src="files/image186.png" width="36px" height="21px" />为奇函数；（2）证明如下.</p>
-<p>试题解析：（1）<img src="files/image186.png" width="36px" height="21px" />的定义域为<img src="files/image187.png" width="67px" height="27px" data-latex="$\left\{ x|x\ne 0 \right\}$" />．</p>
-<p>又<img src="files/image188.png" width="179px" height="41px" data-latex="$f(-x)=-(4x+\frac{1}{x})=-f(x)$" />，</p>
-<p>∴<img src="files/image186.png" width="36px" height="21px" />为奇函数．</p>
-<p>（2）<img src="files/image186.png" width="36px" height="21px" />的单调递增区间为<img src="files/image184.png" width="64px" height="41px" data-latex="$(-\infty ,-\frac{1}{2})$" />，<img src="files/image189.png" width="55px" height="41px" data-latex="$(\frac{1}{2},+\infty )$" />．</p>
-<p>证明：设<img src="files/image190.png" width="72px" height="41px" data-latex="$\frac{1}{2}<{{x}_{1}}<{{x}_{2}}$" />，<img src="files/image191.png" width="224px" height="45px" data-latex="$f({{x}_{1}})-f({{x}_{2}})=4{{x}_{1}}+\frac{1}{{{x}_{1}}}-4{{x}_{2}}-\frac{1}{{{x}_{2}}}$" /><img src="files/image192.png" width="136px" height="45px" data-latex="$=\frac{({{x}_{1}}-{{x}_{2}})(4{{x}_{1}}{{x}_{2}}-1)}{{{x}_{1}}{{x}_{2}}}$" />，</p>
-<p>∵<img src="files/image190.png" width="72px" height="41px" data-latex="$\frac{1}{2}<{{x}_{1}}<{{x}_{2}}$" />，∴<img src="files/image193.png" width="69px" height="24px" data-latex="${{x}_{1}}-{{x}_{2}}<0$" />，<img src="files/image194.png" width="81px" height="24px" data-latex="$4{{x}_{1}}{{x}_{2}}-1>0$" />，<img src="files/image195.png" width="55px" height="24px" data-latex="${{x}_{1}}{{x}_{2}}>0$" />，</p>
-<p>∴<img src="files/image196.png" width="115px" height="24px" data-latex="$f({{x}_{1}})-f({{x}_{2}})<0$" />，即<img src="files/image197.png" width="92px" height="24px" data-latex="$f({{x}_{1}})<f({{x}_{2}})$" />，</p>
-<p>∴<img src="files/image186.png" width="36px" height="21px" />在<img src="files/image189.png" width="55px" height="41px" data-latex="$(\frac{1}{2},+\infty )$" />上为增函数．</p>
-<p>同理，<img src="files/image186.png" width="36px" height="21px" />在<img src="files/image184.png" width="64px" height="41px" data-latex="$(-\infty ,-\frac{1}{2})$" />上为增函数．</p>
-<p>考点：函数的性质．</p>
-<p>19.已知全集<img src="files/image198.png" width="45px" height="19px" data-latex="$U=R$" />，集合<img src="files/image199.png" width="236px" height="29px" data-latex="$A=\left\{ \left. x \right|-3<x<2 \right\},B=\left\{ \left. x \right|1\le x\le 6 \right\}$" />，<img src="files/image200.png" width="161px" height="29px" data-latex="$C=\left\{ \left. x \right|a-1\le x\le 2a+1 \right\}$" />.</p>
-<p>（1）求<img src="files/image201.png" width="73px" height="27px" data-latex="$A\cap \left( {{C}_{U}}B \right)$" />；</p>
-<p>（2）若<img src="files/image202.png" width="73px" height="20px" data-latex="$C\subseteq A\cup B$" />，求实数<img src="files/image72.png" width="13px" height="14px" data-latex="$a$" />的取值范围.</p>
-<p>【答案】（1）<img src="files/image203.png" width="167px" height="29px" data-latex="$A\cap {{C}_{U}}B=\left\{ \left. x \right|-3<x<1 \right\}$" />;（2）<img src="files/image72.png" width="13px" height="14px" data-latex="$a$" />的取值范围是<img src="files/image204.png" width="125px" height="45px" data-latex="$\left( -\infty ,-2 \right)\cup \left( -2,\frac{5}{2} \right]$" /></p>
-<p>【解析】</p>
-<p>试题分析：（1）先求出<img src="files/image205.png" width="99px" height="29px" data-latex="${{C}_{U}}B=\left\{ \left. x \right| \right.x<1$" />或<img src="files/image206.png" width="43px" height="27px" data-latex="$\left. x>6 \right\}$" />，再根据交集的定义直接求出<img src="files/image207.png" width="73px" height="27px" data-latex="$A\cap \left( {{C}_{U}}B \right)$" />即可；（2）先求得<img src="files/image208.png" width="152px" height="29px" data-latex="$A\cup B=\left\{ \left. x \right|-3<x\le 6 \right\}$" />，在由<img src="files/image209.png" width="73px" height="20px" data-latex="$C\subseteq A\cup B$" />，考虑<img src="files/image210.png" width="45px" height="19px" data-latex="$C=\varnothing $" />后，根据子集的定义列不等式，即可求出<img src="files/image72.png" width="13px" height="14px" data-latex="$a$" />的取值范围.</p>
-<p>试题解析：（1）∵<img src="files/image205.png" width="99px" height="29px" data-latex="${{C}_{U}}B=\left\{ \left. x \right| \right.x<1$" />或<img src="files/image206.png" width="43px" height="27px" data-latex="$\left. x>6 \right\}$" />，<img src="files/image211.png" width="124px" height="29px" data-latex="$A=\left\{ \left. x \right|-3<x<2 \right\}$" />，</p>
-<p>∴<img src="files/image212.png" width="167px" height="29px" data-latex="$A\cap {{C}_{U}}B=\left\{ \left. x \right|-3<x<1 \right\}$" />.</p>
-<p>（2）<img src="files/image208.png" width="152px" height="29px" data-latex="$A\cup B=\left\{ \left. x \right|-3<x\le 6 \right\}$" />，</p>
-<p>①当<img src="files/image213.png" width="84px" height="19px" data-latex="$2a+1<a-1$" />即<img src="files/image214.png" width="45px" height="19px" data-latex="$a<-2$" />时，<img src="files/image215.png" width="103px" height="20px" data-latex="$C=\varnothing \subseteq A\cup B$" />；</p>
-<p>②当<img src="files/image216.png" width="84px" height="19px" data-latex="$2a+1\ge a-1$" />即<img src="files/image217.png" width="45px" height="19px" data-latex="$a\ge -2$" />时，要使<img src="files/image218.png" width="83px" height="20px" data-latex="$C=\subseteq A\cup B$" />，有<img src="files/image219.png" width="77px" height="48px" data-latex="$\left\{ \begin{matrix}   a-1>-3,  \\   2a+1\le 6,  \\\end{matrix} \right.$" /> ∴<img src="files/image220.png" width="59px" height="69px" data-latex="$\left\{ \begin{matrix}   a>-2,  \\   a\le \frac{5}{2}.  \\\end{matrix} \right.$" /> </p>
-<p>又<img src="files/image217.png" width="45px" height="19px" data-latex="$a\ge -2$" />，∴<img src="files/image221.png" width="72px" height="41px" data-latex="$-2<a\le \frac{5}{2}$" />，∴<img src="files/image72.png" width="13px" height="14px" data-latex="$a$" />的取值范围是<img src="files/image204.png" width="125px" height="45px" data-latex="$\left( -\infty ,-2 \right)\cup \left( -2,\frac{5}{2} \right]$" />.</p>
-<p>20.某公司共有60位员工，为提高员工的业务技术水平，公司拟聘请专业培训机构进行培训．培训的总费用由两部分组成：一部分是给每位参加员工支付400元的培训材料费；另一部分是给培训机构缴纳的培训费．若参加培训的员工人数不超过30人，则每人收取培训费1000元；若参加培训的员工人数超过30人，则每超过1人，人均培训费减少20元．设公司参加培训的员工人数为x人，此次培训的总费用为y元．</p>
-<p>（1）求出y与x之间的函数关系式；</p>
-<p>（2）请你预算：公司此次培训的总费用最多需要多少元？</p>
-<p>【答案】(1) <img src="files/image222.png" width="256px" height="45px" data-latex="$y=\{\begin{array}{*{35}{l}}   1400x,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 30,x\in N  \\   -20{{x}^{2}}+2000x,\,\,\,30<x\le 60,x\in N  \\\end{array}$" /> (2)50000</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）依据参加培训的员工人数分段计算培训总费用．</p>
-<p>（2）依据（1）求出函数的最大值即可．</p>
-<p>【详解】（1）当<img src="files/image223.png" width="111px" height="21px" data-latex="$0\le x\le 30,x\in N$" />时，<img src="files/image224.png" width="171px" height="21px" data-latex="$y=400x+1000x=1400x$" />； </p>
-<p>当<img src="files/image225.png" width="119px" height="21px" data-latex="$30<x\le 60,x\in N$" />时，<img src="files/image226.png" width="211px" height="21px" data-latex="$y=400x+[1000-20(x-30)]\cdot x$" /></p>
-<p><img src="files/image227.png" width="112px" height="21px" data-latex="$=-20{{x}^{2}}+2000x$" />， </p>
-<p>故<img src="files/image228.png" width="259px" height="48px" data-latex="$y=\left\{ \begin{array}{*{35}{l}}   1400x,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 30,x\in N  \\   -20{{x}^{2}}+2000x,\,\,\,30<x\le 60,x\in N  \\\end{array} \right.$" /> </p>
-<p>（2）当<img src="files/image223.png" width="111px" height="21px" data-latex="$0\le x\le 30,x\in N$" />时，</p>
-<p><img src="files/image229.png" width="144px" height="21px" data-latex="$y\le 1400\times 30=42000$" />元，此时x＝30；</p>
-<p>当<img src="files/image225.png" width="119px" height="21px" data-latex="$30<x\le 60,x\in N$" />时，</p>
-<p><img src="files/image230.png" width="219px" height="24px" data-latex="$y\le -20\times {{50}^{2}}+2000\times 50=50000$" />元，此时<img src="files/image231.png" width="45px" height="19px" data-latex="$x=50$" />． </p>
-<p>综上所述，公司此次培训的总费用最多需要<img src="files/image232.png" width="44px" height="19px" data-latex="$50000$" />元．</p>
-<p>【点睛】本题考察函数的应用，要求依据实际问题构建分段函数的数学模型并依据数学模型求实际问题的最大值，注意建模时理顺各数据间的关系．</p>
-<p>21.已知指数函数<img src="files/image233.png" width="62px" height="27px" data-latex="$y=g\left( x \right)$" />满足<img src="files/image234.png" width="68px" height="27px" data-latex="$g\left( 3 \right)=27$" />，定义域为<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />的函数<img src="files/image235.png" width="123px" height="49px" data-latex="$f\left( x \right)=\frac{n-g\left( x \right)}{m+3g\left( x \right)}$" />是奇函数.</p>
-<p>(1)求函数<img src="files/image233.png" width="62px" height="27px" data-latex="$y=g\left( x \right)$" />，<img src="files/image236.png" width="64px" height="27px" data-latex="$y=f\left( x \right)$" />的解析式；</p>
-<p>(2)若对任意的<img src="files/image237.png" width="49px" height="23px" data-latex="$t\in \left( 1,4 \right)$" />，不等式<img src="files/image238.png" width="156px" height="27px" data-latex="$f\left( 2t-3 \right)+f\left( t-k \right)>0$" />恒成立，求实数<img src="files/image142.png" width="13px" height="19px" data-latex="$k$" />的取值范围.</p>
-<p>【答案】(1) <img src="files/image239.png" width="101px" height="44px" data-latex="$f\left( x \right)=\frac{1-{{3}^{x}}}{3+{{3}^{x+1}}}$" />；(2) <img src="files/image240.png" width="49px" height="27px" data-latex="$\left[ 9,+\infty  \right)$" />.</p>
-<p>【解析】</p>
-<p>【分析】</p>
-<p>（1）设g（x）＝a<sup>x</sup>（a＞0且a≠1），根据g（3）＝27，得g（x）,利用定义域为R的函数f（x）<img src="files/image241.png" width="85px" height="49px" data-latex="$=\frac{n-g\left( x \right)}{m+3g\left( x \right)}$" />是奇函数即可解出；</p>
-<p>（2）对任意的t∈R不等式<img src="files/image238.png" width="156px" height="27px" data-latex="$f\left( 2t-3 \right)+f\left( t-k \right)>0$" />恒成立，则<img src="files/image242.png" width="212px" height="27px" data-latex="$f\left( 2t-3 \right)>-f\left( t-k \right)=f\left( k-t \right)$" />化为<img src="files/image243.png" width="62px" height="19px" data-latex="$3t-3<k$" />在<img src="files/image237.png" width="49px" height="23px" data-latex="$t\in \left( 1,4 \right)$" />上恒成立，求一次函数最值即可得出</p>
-<p>【详解】(1)设<img src="files/image244.png" width="158px" height="27px" data-latex="$$" />，则<img src="files/image245.png" width="52px" height="21px" data-latex="${{a}^{3}}=27$" /></p>
-<p>∴<img src="files/image246.png" width="36px" height="19px" data-latex="$a=3$" /></p>
-<p>∴<img src="files/image247.png" width="65px" height="27px" data-latex="$g\left( x \right)={{3}^{x}}$" /></p>
-<p>∴<img src="files/image248.png" width="107px" height="44px" data-latex="$f\left( x \right)=\frac{n-{{3}^{x}}}{m+{{3}^{x+1}}}$" /></p>
-<p>∵<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />是奇函数</p>
-<p>∴<img src="files/image249.png" width="61px" height="27px" data-latex="$f\left( 0 \right)=0$" />，即<img src="files/image250.png" width="116px" height="41px" data-latex="$\frac{n-1}{3+m}=0\Rightarrow n=1$" /></p>
-<p>∴<img src="files/image251.png" width="107px" height="44px" data-latex="$f\left( x \right)=\frac{1-{{3}^{x}}}{{{3}^{x+1}}+m}$" /></p>
-<p>又<img src="files/image252.png" width="101px" height="27px" data-latex="$f\left( -1 \right)=-f\left( 1 \right)$" /></p>
-<p>∴<img src="files/image253.png" width="158px" height="60px" data-latex="$\frac{1-\frac{1}{3}}{m+1}=-\frac{1-3}{9+m}\Rightarrow m=3$" /></p>
-<p>∴<img src="files/image239.png" width="101px" height="44px" data-latex="$f\left( x \right)=\frac{1-{{3}^{x}}}{3+{{3}^{x+1}}}$" />，经检验<img src="files/image254.png" width="97px" height="27px" data-latex="$f\left( -x \right)=f\left( x \right)$" />成立</p>
-<p>(2)由(1)知<img src="files/image255.png" width="285px" height="44px" data-latex="$f\left( x \right)=\frac{1-{{3}^{x}}}{3+{{3}^{x+1}}}=-\frac{1}{3}\cdot \frac{{{3}^{x}}-1}{{{3}^{x}}+1}=-\frac{1}{3}+\frac{2}{3}\cdot \frac{1}{{{3}^{x}}+1}$" /></p>
-<p>∴<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />在<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />上为减函数</p>
-<p>又∵<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />是奇函数</p>
-<p><img src="files/image238.png" width="156px" height="27px" data-latex="$f\left( 2t-3 \right)+f\left( t-k \right)>0$" /></p>
-<p>∴<img src="files/image242.png" width="212px" height="27px" data-latex="$f\left( 2t-3 \right)>-f\left( t-k \right)=f\left( k-t \right)$" /></p>
-<p>∵<img src="files/image7.png" width="39px" height="27px" data-latex="$f\left( x \right)$" />是减函数，由上式得：<img src="files/image256.png" width="83px" height="19px" data-latex="$2t-3<k-t$" /></p>
-<p>即对任意的<img src="files/image237.png" width="49px" height="23px" data-latex="$t\in \left( 1,4 \right)$" />，有<img src="files/image243.png" width="62px" height="19px" data-latex="$3t-3<k$" />恒成立</p>
-<p>令<img src="files/image257.png" width="81px" height="27px" data-latex="$h\left( t \right)=3t-3$" />，<img src="files/image237.png" width="49px" height="23px" data-latex="$t\in \left( 1,4 \right)$" />，易知<img src="files/image258.png" width="32px" height="27px" data-latex="$h\left( t \right)$" />在<img src="files/image237.png" width="49px" height="23px" data-latex="$t\in \left( 1,4 \right)$" />上递增</p>
-<p>所以<img src="files/image259.png" width="163px" height="27px" data-latex="$h\left( t \right)<h(3)=3\times 4-3=9$" /></p>
-<p>∴<img src="files/image260.png" width="37px" height="19px" data-latex="$k\ge 9$" />，即实数<img src="files/image142.png" width="13px" height="19px" data-latex="$k$" />的取值范围为<img src="files/image240.png" width="49px" height="27px" data-latex="$\left[ 9,+\infty  \right)$" /></p>
-<p><img src="files/image22.png" width="10px" height="18px" data-latex="$$" />点睛】本题综合考查了指数函数的定义及其性质、函数的奇偶性、单调性、恒成立问题的等价转化、一次函数的单调性等基础知识与基本技能方法，属于难题</p>
-<p>22.定义对于函数<img src="files/image7.png" width="39px" height="26px" data-latex="$f\left( x \right)$" />， 若在定义域内存在实数<img src="files/image120.png" width="13px" height="15px" data-latex="$x$" />， 满足<img src="files/image261.png" width="107px" height="27px" data-latex="$f\left( -x \right)=-f\left( x \right)$" />，则称<img src="files/image7.png" width="39px" height="26px" data-latex="$f\left( x \right)$" />为“局部奇函数”.</p>
-<p>（1）已知二次函数<img src="files/image262.png" width="225px" height="27px" data-latex="$f\left( x \right)=a{{x}^{2}}+2x-4a\left( a\in R,a\ne 0 \right)$" />,试判断<img src="files/image7.png" width="39px" height="26px" data-latex="$f\left( x \right)$" />是否为定义域<img src="files/image52.png" width="16px" height="18px" data-latex="$R$" />上的“局部奇函数”若是，求出满足<img src="files/image261.png" width="107px" height="27px" data-latex="$f\left( -x \right)=-f\left( x \right)$" />的<img src="files/image120.png" width="13px" height="15px" data-latex="$x$" />的值； 若不是， 请说明理由；</p>
-<p>（2）若<img src="files/image263.png" width="96px" height="20.25pt" />是定义在区间<img src="files/image264.png" width="41px" height="27px" data-latex="$\left[ -1,1 \right]$" />上的“局部奇函数”，求实数<img src="files/image150.png" width="17px" height="15px" data-latex="$m$" />的取值范围.</p>
-<p>【答案】（1）<img src="files/image265.png" width="45px" height="19px" data-latex="$x=\pm 2$" />，<img src="files/image7.png" width="39px" height="26px" data-latex="$f\left( x \right)$" />为“局部奇函数；（2）<img src="files/image266.png" width="91px" height="45px" data-latex="$m\in \left[ -\frac{5}{4},-1 \right]$" />.</p>
-<p>【解析】</p>
-<p>试题分析：（1）若<img src="files/image267.png" width="35px" height="22px" />为“局部奇函数”，则根据定义验证条件是否成立即可；（2）利用局部奇函数的定义，求出使方程<img src="files/image268.png" width="100px" height="22px" />有解的实数<img src="files/image269.png" width="17px" height="15px" />的取值范围，可得答案.</p>
-<p>试题解析：（1） 当<img src="files/image270.png" width="187px" height="27px" data-latex="$f\left( x \right)=a{{x}^{2}}+2x-4a\left( a\in R \right)$" />，方程<img src="files/image271.png" width="120px" height="27px" data-latex="$f\left( x \right)+f\left( -x \right)=0$" />即<img src="files/image272.png" width="97px" height="29px" data-latex="$2a\left( {{x}^{2}}-4 \right)=0$" />，有解<img src="files/image265.png" width="45px" height="19px" data-latex="$x=\pm 2$" />，所以<img src="files/image7.png" width="39px" height="26px" data-latex="$f\left( x \right)$" />为 “局部奇函数”.</p>
-<p>（2）当<img src="files/image263.png" width="96px" height="20.25pt" />时，<img src="files/image271.png" width="120px" height="27px" data-latex="$f\left( x \right)+f\left( -x \right)=0$" />可化为<img src="files/image273.png" width="113px" height="21px" data-latex="${{2}^{x}}+{{2}^{-x}}+2m=0$" />，因为<img src="files/image7.png" width="39px" height="26px" data-latex="$f\left( x \right)$" />的定义域为<img src="files/image264.png" width="41px" height="27px" data-latex="$\left[ -1,1 \right]$" />，所以方程<img src="files/image273.png" width="113px" height="21px" data-latex="${{2}^{x}}+{{2}^{-x}}+2m=0$" />在<img src="files/image264.png" width="41px" height="27px" data-latex="$\left[ -1,1 \right]$" />上有解.令<img src="files/image274.png" width="96px" height="33.75pt" />,则<img src="files/image275.png" width="76px" height="41px" data-latex="$-2m=t+\frac{1}{t}$" />，设<img src="files/image276.png" width="77px" height="41px" data-latex="$g\left( t \right)=t+\frac{1}{t}$" />，则</p>
-<p><img src="files/image276.png" width="77px" height="41px" data-latex="$g\left( t \right)=t+\frac{1}{t}$" />在<img src="files/image277.png" width="55px" height="27px" data-latex="$t\in \left( 0,1 \right]$" />上为减函数，在<img src="files/image278.png" width="68px" height="27px" data-latex="$t\in \left[ 1,+\infty  \right)$" />上为增函数，（要证明），所以当<img src="files/image279.png" width="65px" height="45px" data-latex="$t\in \left[ \frac{1}{2},2 \right]$" />时，<img src="files/image280.png" width="88px" height="45px" data-latex="$g\left( t \right)\in \left[ 2,\frac{5}{2} \right]$" />，所以<img src="files/image281.png" width="88px" height="45px" data-latex="$-2m\in \left[ 2,\frac{5}{2} \right]$" />，即<img src="files/image266.png" width="91px" height="45px" data-latex="$m\in \left[ -\frac{5}{4},-1 \right]$" />.</p>
-<p>考点：二次函数的性质.</p>
-<p>【方法点睛】本题主要考查新定义的应用，利用新定义，建立方程关系，然后利用函数性质进行求解是解决本题的关键，考查学生的运算能力.在该种题型中主要考查两个方面一是新定义判定的考查；二是新定义性质的考查，理解局部奇函数的定义，对<img src="files/image270.png" width="187px" height="27px" data-latex="$f\left( x \right)=a{{x}^{2}}+2x-4a\left( a\in R \right)$" />按定义验证即可；在（2）中考查了局部奇函数的性质，将题意转化为<img src="files/image273.png" width="113px" height="21px" data-latex="${{2}^{x}}+{{2}^{-x}}+2m=0$" />在<img src="files/image264.png" width="41px" height="27px" data-latex="$\left[ -1,1 \right]$" />上有解的问题.</p>
-<p> </p>
-<p> </p>
-<p> </p>
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-<html><head><meta charset="utf-8" /></head><body>
-<p>四校联考2017—2018学年度第一学期期中考试</p>
-<p>高一物理试卷</p>
-<p>考试时间： 60分钟  总分： 100分   </p>
-<p>一．单项选择题（本大题共20小题，每小题3分，共60分）</p>
-<p>请阅读下列材料，回答1 – 3 小题</p>
-<p>在冬季的时候，由于路面结冰，极易造成交通事故。一辆质量为3t的汽车，以40km/h的速度沿平直公路行驶，已知橡胶轮胎与普通路面的动摩擦因数为μ<sub>1 </sub>= 0.6，与结冰地面的动摩擦因数为μ<sub>2 </sub>= 0.2（g = 10m/s<sup>2</sup>）</p>
-<p>1．汽车的重力为</p>
-<p>A．3×10<sup>2</sup>N    B．3×10<sup>3</sup>N    C．3×10<sup>4</sup>N     D．3×10<sup>5</sup>N</p>
-<p>2．在汽车正常行驶时，以汽车为参考系</p>
-<p>A．路边的树是静止的</p>
-<p>B．路边的树向后运动</p>
-<p>C．汽车里的乘客是运动的</p>
-<p>D．前方的汽车一定是运动的</p>
-<p>3．甲、乙两辆相同的汽车分别在普通路面和结冰地面上，刹车滑行做匀减速直线运动。下图中x表示位移、v表示速度，能正确描述该过程的图像是</p>
-<p><img src="files/image1.png" width="378pt" height="85.95pt" data-latex="$$" /></p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p>4．在考察下列运动员的比赛成绩时，可视为质点的是 </p>
-<p>    A．马拉松             B．跳水            C．击剑            D．体操</p>
-<p>5．在运动会上，甲、乙两位同学进行百米赛跑，假如起跑加速的时间忽略，把他<img src="files/image2.png" width="1.6pt" height="1.05pt" />们的运动近似当作匀速直线运动来处理．他们同时从起跑线起跑，经过一段时间后他们的位置如图所示，分别作出在这段时间内两人运动的位移x、速度v与时间t的关系图象如下，其中能正确反映他们运动的是</p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p>6．下列物理量属于标量的是</p>
-<p>A．速度      　  B．位移       C．加速度        D．质量</p>
-<p>7．以下的计时数据指时间的是 </p>
-<p>A. 天津开往德州的625次列车于13点35分从天津发车   [来源:学。科。网Z。X。X。K]</p>
-<p>B. 某人用15s跑完l00m         </p>
-<p>C. 中央电视台新闻联播节目19点开播    </p>
-<p>D. 1997年7月1日零时中国对香港恢复行使主权[来源:Z#xx#k.Com]</p>
-<p>8．下列几种速度，不是瞬时速度的是</p>
-<p>A．子弹以600m/s的速度射出枪口</p>
-<p>B．高速公路路标上标有“120km/h，注意车速”</p>
-<p>C．高速火车以260km/h的速度经过“哈尔滨到长春”这一路段</p>
-<p>D．足球以12m/s的速度射入球门</p>
-<p>9．从高为5m处以某一初速度竖直向下抛出一个小球，在与地面相碰后弹起，上升到2m高处被接住，则这段过程中</p>
-<p>A．小球的位移为3m，方向竖直向下，路程为3m</p>
-<p>B．小球的位移为7m，方向竖直向上，路程为7m </p>
-<p>C．小球的位移为3m，方向竖直向下，路程为7m</p>
-<p>D．小球的位移为7m，方向竖直向上，路程为3m</p>
-<p><img src="files/image3.png" width="108pt" height="79.85pt" />10．一质点沿一条直线运动的位移—时间图象如图所示，则</p>
-<p>A．质点在t<sub>1</sub>时刻的速度比t<sub>2</sub>时刻的速度大</p>
-<p>B．从t＝0时刻<img src="files/image4.png" width="1.6pt" height="1.6pt" />到t<sub>1</sub>时刻，<img src="files/image4.png" width=".55pt" height="1.05pt" />质点位移是x<sub>0</sub></p>
-<p>C．t＝0时刻，质点在坐标原点</p>
-<p>  D．从t<sub>1</sub><img src="files/image5.png" width="1.6pt" height="1.6pt" />时刻到t<sub>2</sub><img src="files/image5.png" width="1.6pt" height="1.6pt" />时刻<img src="files/image5.png" width="1.6pt" height="1.6pt" /><img src="files/image4.png" width="1.6pt" height="1.05pt" />，质点位移大小等于路程</p>
-<p> </p>
-<p>11．一列火车匀减速进站，停靠一段时间后又匀加速(同方向)出站。在下列所示的四幅v-t图像中，正确描述了火车运动情况的是</p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p>    A                B                  C                   D</p>
-<p>12．某航母跑道长200 m，飞机在航母上滑行的最大加速度为6 m/s<sup>2</sup>，起飞需要的最低速度为[来源:学*科*网]50 m/s．那么，飞机在滑行前，需要借助弹射系统获得的初速度至少为</p>
-<p>A．5 m/s        B．20 m/s      C．15 m/s       D．10 m/s</p>
-<p>13．如图所示，一个小球用细绳拴在天花板上并且静止在光滑斜面上，下列说法中的正确是</p>
-<p>  A．细绳对小球无弹力作用    </p>
-<p>B．斜面对小球的弹力方向垂直于水平面向上</p>
-<p>C．小球对斜面弹力方向垂直于斜面向下</p>
-<p>D．小球所受的重力方向垂直于斜面向下[来源:学|科|网]</p>
-<p>14．汽车以12m/s的速度开始刹车，刹车过程中加速度大小为4m/s<sup>2</sup>，关于汽车的运动情况，下列说法正确的是</p>
-<p>A．刹车后2s末的速度是20m/s      B．刹车后4s末的速度是-4m/s</p>
-<p>C．刹车后4s内的位移为18m       D．刹车后4s内的位移为16m</p>
-<p>15．一个木块置于粗糙程度处处相同的水平地面上，在一水平拉力的作用下沿地面向前滑行，当水平拉力增大时，木块受到的摩擦力大小将</p>
-<p>A．增大          B．不变         C．减小         D．无法确定</p>
-<p>16．书放在水平桌面上，桌面会受到书对桌面的压力，产生这个压力的直接原因是</p>
-<p>A．书的形变   　　　　　　　B.桌面的形变  </p>
-<p>C．书和桌面的形变   　　　　D.书受到的重力</p>
-<p>17．如图所示,一木块在两水平力F<sub>1</sub>、F<sub>2</sub>作用下静止在水平地面上, 两水平力大小分别是F<sub>1</sub>=18N,F<sub>2</sub>=10N,该木块与地面之间的最大静摩擦力及滑动摩擦力大小分别是15N和12N。若单独撤去F<sub>1</sub>或单独撤去F<sub>2</sub>的两种情况下,木块受摩擦力大小分别是</p>
-<p>A．10N    18N     B．12N    15N</p>
-<p>C．10N    12N     D．10N    15N</p>
-<p>18．甲乙两物体分别从高10m处和高20m处同时由静止自由下落，不计空气阻力，下面几种说法中不正确的是</p>
-<p>A．乙落地速度是甲落地速度的<img src="files/image6.png" width="15.6pt" height="14.5pt" data-latex="$$" />倍     </p>
-<p>B．从开始运动到落地所用的时间乙是甲的2倍</p>
-<p>C．下落1s时甲的速度与乙的速度相同  </p>
-<p>  D．甲、乙两物体在各自下落1m距离时速度相同</p>
-<p>19．一个小石块从空中a点自由落下，先后经过b点和c点，不计空气阻力．已知它经过b点时的速度为v，经过c点时的速度为3v.则ab段与bc段位移之比为</p>
-<p>A．1∶3         B．1∶5          C．1∶8        D．1∶9</p>
-<p>20．甲乙丙三辆汽车以相同的速度同时经过某一个路标，从此刻开始甲车一直匀速运动，乙车先加速后减速，丙车先减速后加速，它们经过下一个路标时速度又相等，则</p>
-<p>A. 甲车先通过下一个路标    B. 乙车先通过下一个路标<br />    C. 丙车先通过下一个路标    D. 条件不足，无法确定</p>
-<p>二、填空题（每空2分，共10分）</p>
-<p>21．在“练习使用打点计时器”实验中，</p>
-<p>（1）电火花计时器使用的电源是    ▲       （填序号）</p>
-<p>A．220V的交流电            B．220V的直流电</p>
-<p>    C．16V以下的直流电          D．6V以下的直流电</p>
-<p>（2）实验过程中，下列做法中正确的   ▲     （填序号）</p>
-<p>A．先使纸带运动，再接通电源           </p>
-<p>B．先接通电源，再使纸带运动</p>
-<p>C．打点结束时，先取下纸带，再关闭电源          </p>
-<p>D．打点结束时，先关闭电源，再取下纸带</p>
-<p> </p>
-<p>（3）如图所示是实验中得到的一条纸带，该纸带做的是匀加速直线运动，自A点起，相邻两计数点间的距离分别为10.0mm、16.0mm、22.0mm、28.0mm，相邻的两个计数点之间还有4个点没有画出，交流电的频率为50 Hz。则相邻的计数点的时间间隔为    ▲      s，B到E过程的平均速度是   ▲   m/s，纸带运动的加速度大小是   ▲      m/s<sup>2</sup>。</p>
-<p><img src="files/image7.png" width="250.2pt" height="40.8pt" /></p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p>三、解答题（本大题共3小题，共30分）</p>
-<p>22．（9分）一根原长为8cm的轻质弹簧，受4N的拉力作用时，伸长量为2cm，求解下列几个问题(g取10m/s<sup>2</sup>)</p>
-<p>（1）该弹簧的劲度系数k；</p>
-<p>（2如图所示，将一质量为1kg的木块放在水平地面上，木块与水平地面间的动摩擦因数μ=0.3，用该弹簧水平匀速拉动木块，求此时弹簧的长度。</p>
-<p> </p>
-<p> </p>
-<p>23．（9分）一辆小型汽车从静止开始以a=2m/s<sup>2</sup>的加速度做匀加速直线运动，前进25m后又匀速运动了5s后立即关闭发动机，做匀减速直线运动，又经过10s停下来。试求：</p>
-<p>(1)汽车做匀加速运动的时间；</p>
-<p>(2)汽车关闭发动机后的加速度；</p>
-<p>(3)从开始运动到停下来全过程的平均速度。</p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p>24．(12分)一个从离地高为80m处由静止开始做自由落体运动的小球，砸坏并穿过一水平放置在空中的玻璃板，砸穿玻璃板后小球经3s落到地面,在砸穿玻璃板过程中小球失去<img src="files/image8.png" width="11.8pt" height="31.15pt" data-latex="$$" />的速度，求 (g取10m/s<sup>2</sup>，不计空气阻力，玻璃板的厚度忽略不计)</p>
-<p> (1)小球从开始运动到下落至玻璃板处所用的时间；</p>
-<p> (2)玻璃板离地面的高度；</p>
-<p> (3)小球落地时的速度。</p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
-<p> </p>
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-<p>2017级高一下学期周考Ⅲ物理试题</p>
-<p> </p>
-<p> </p>
-<p>一、选择题（共16小题，每小题3分，共计48分，选对但不全的得1分，不选或错选得0分）</p>
-<p>1.关于万有引力定律，下列说法正确的是(　　)</p>
-<p>A．牛顿提出了万有引力定律，并测定了引力常量的数值</p>
-<p>B．万有引力定律只适用于天体之间</p>
-<p>C．万有引力的发现，揭示了自然界一种基本相互作用的规律</p>
-<p>D．地球绕太阳在椭圆轨道上运行，在近日点和远日点受到太阳的万有引力大小是相同的</p>
-<p>2.(多选)对做平抛运动的物体，在已知重力加速度g的条件下，给出下列4组条件，其中能求出平抛的初速度大小的是(　　)</p>
-<p>A．下落高度和水平位移</p>
-<p>B．水平位移和落地时的速度大小和方向</p>
-<p>C．位移大小和方向及水平位移</p>
-<p>D．位移大小及落地时的速度大小</p>
-<p><img src="files/image1.png" width="79pt" height="51.75pt" />3.如图所示，在同一平台上的O点水平抛出的三个物体，分别落到a、b、c三点，则三个物体运动的初速度<img src="files/image2.png" width="13.95pt" height="18.25pt" data-latex="$$" />、<img src="files/image3.png" width="13.95pt" height="18.25pt" data-latex="$$" />、<img src="files/image4.png" width="12.9pt" height="18.25pt" data-latex="$$" />和运动的时间<img src="files/image5.png" width="10.75pt" height="18.25pt" data-latex="$$" />、<img src="files/image6.png" width="10.75pt" height="18.25pt" data-latex="$$" />、<img src="files/image7.png" width="10.75pt" height="18.25pt" data-latex="$$" />的关系分别是(　　)</p>
-<p>A．<img src="files/image2.png" width="13.95pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image3.png" width="13.95pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image4.png" width="12.9pt" height="18.25pt" data-latex="$$" /> <img src="files/image5.png" width="10.75pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image6.png" width="10.75pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image7.png" width="10.75pt" height="18.25pt" data-latex="$$" />　　B．<img src="files/image2.png" width="13.95pt" height="18.25pt" data-latex="$$" />&lt;<img src="files/image3.png" width="13.95pt" height="18.25pt" data-latex="$$" />&lt;<img src="files/image4.png" width="12.9pt" height="18.25pt" data-latex="$$" />　<img src="files/image5.png" width="10.75pt" height="18.25pt" data-latex="$$" />＝<img src="files/image6.png" width="10.75pt" height="18.25pt" data-latex="$$" />＝<img src="files/image7.png" width="10.75pt" height="18.25pt" data-latex="$$" /></p>
-<p>C．<img src="files/image2.png" width="13.95pt" height="18.25pt" data-latex="$$" />&lt;<img src="files/image3.png" width="13.95pt" height="18.25pt" data-latex="$$" />&lt;<img src="files/image4.png" width="12.9pt" height="18.25pt" data-latex="$$" />　<img src="files/image5.png" width="10.75pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image6.png" width="10.75pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image7.png" width="10.75pt" height="18.25pt" data-latex="$$" /> D．<img src="files/image2.png" width="13.95pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image3.png" width="13.95pt" height="18.25pt" data-latex="$$" />&gt;<img src="files/image4.png" width="12.9pt" height="18.25pt" data-latex="$$" />　<img src="files/image5.png" width="10.75pt" height="18.25pt" data-latex="$$" />&lt;<img src="files/image6.png" width="10.75pt" height="18.25pt" data-latex="$$" />&lt;<img src="files/image7.png" width="10.75pt" height="18.25pt" data-latex="$$" /></p>
-<p><img src="files/image8.png" width="63pt" height="64.5pt" />4.如图所示，由于地球的自转，地球表面上P、Q两物体均绕地球自转轴做匀速圆周运动，对于P、Q两物体的运动，下列说法正确的是(　　)</p>
-<p>A．P、Q两物体的角速度大小相等</p>
-<p>B．P、Q两物体的线速度大小相等</p>
-<p>C．P物体的线速度比Q物体的线速度大</p>
-<p>D．P、Q两物体均受重力和支持力两个力作用</p>
-<p><img src="files/image9.png" width="87.75pt" height="49.5pt" />5.如图所示，物体A、B经无摩擦的定滑轮用细线连在一起，A物体受水平向右的力F的作用，此时B匀速下降，A水平向左运动，可知(　　)</p>
-<p>A．物体A做匀速运动</p>
-<p>B．物体A做加速运动</p>
-<p>C．物体A所受摩擦力逐渐增大</p>
-<p>D．物体A所受摩擦力不变</p>
-<p><img src="files/image10.png" width="76.5pt" height="47.25pt" />6.在斜面顶端的A点以速度v平抛一小球，经t<sub>1</sub>时间落到斜面上B点处，若在A点将此小球以速度0.5v水平抛出，经t<sub>2</sub>时间落到斜面上的C点处，以下判断正确的是(　　)</p>
-<p>A．AB∶AC＝2∶1  B.AB∶AC＝4∶1</p>
-<p>C．t<sub>1</sub>∶t<sub>2</sub>＝4∶1  D．t<sub>1</sub>∶t<sub>2</sub>＝【域公式】$eq \\r(2)$∶1</p>
-<p><img src="files/image11.png" width="72.75pt" height="81.75pt" />7.如图所示，在水平放置的半径为R的圆柱体的正上方的P点将一个小球以水平速度v<sub>0</sub>沿垂直于圆柱体的轴线方向抛出，小球飞行一段时间后恰好从圆柱体的Q点沿切线飞过，测得O、Q连线与竖直方向的夹角为θ，那么小球完成这段飞行的时间是(　　)</p>
-<p>A．t＝【域公式】$eq \\f(v<sub>0</sub>,gtan θ)$  B.t＝【域公式】$eq \\f(gtan θ,v<sub>0</sub>)$</p>
-<p>C．t＝【域公式】$eq \\f(Rsin θ,v<sub>0</sub>)$  D．t＝【域公式】$eq \\f(Rcos θ,v<sub>0</sub>)$</p>
-<p><img src="files/image12.png" width="94.5pt" height="57.75pt" />8.如图所示，甲、乙两水平圆盘紧靠在一块，甲圆盘为主动轮，乙靠摩擦随甲转动且无滑动。甲圆盘与乙圆盘的半径之比为r<sub>甲</sub>：r<sub>乙</sub>＝3∶1，两圆盘和小物体m<sub>1</sub>、m<sub>2</sub>之间的动摩擦因数相同，m<sub>1</sub>距O点为2r，m<sub>2</sub>距O′点为r，当甲缓慢转动起来且转速慢慢增加时(　　)</p>
-<p>A．m<sub>1</sub>与m<sub>2</sub>滑动前的角速度之比ω<sub>1</sub>∶ω<sub>2</sub>＝3∶1</p>
-<p>B．m<sub>1</sub>与m<sub>2</sub>滑动前的向心加速度之比a<sub>1</sub>∶a<sub>2</sub>＝1∶3</p>
-<p>C．随转速慢慢增加，m<sub>1</sub>先开始滑动</p>
-<p>D．随转速慢慢增加，m<sub>2</sub>先开始滑动</p>
-<p>9. 海王星有13颗已知的天然卫星．现认为“海卫二”绕海王星沿圆轨道匀速运转，已知海卫二质量2.0×10<sup>19</sup> kg，轨道半径5.5×10<sup>6</sup> km，运行的周期360天，万有引力常量G＝6.67×10<sup>－</sup><sup>11</sup>N·m<sup>2</sup>/kg<sup>2</sup>.则海王星的质量大约为(　　)</p>
-<p>A．1.0×10<sup>17</sup> kg　  B．1.0×10<sup>26</sup> kg     C．2.0×10<sup>11</sup> kg D．2.0×10<sup>19</sup> kg</p>
-<p>10.据报道，天文学家新发现了太阳系外的一颗行星。这颗行星的体积是地球的<img src="files/image13.png" width="10.2pt" height="10.75pt" data-latex="$$" />倍，质量是地球的<img src="files/image14.png" width="10.2pt" height="13.95pt" data-latex="$$" />倍。已知近地卫星绕地球运动的周期约为<img src="files/image15.png" width="10.75pt" height="12.9pt" data-latex="$$" />，引力常量为<img src="files/image16.png" width="12.9pt" height="13.95pt" data-latex="$$" />。则该行星的平均密度为(　　)</p>
-<p>A.  <img src="files/image17.png" width="27.95pt" height="31.15pt" data-latex="$$" />  B. <img src="files/image18.png" width="24.7pt" height="31.15pt" data-latex="$$" />     C. <img src="files/image19.png" width="34.95pt" height="31.15pt" data-latex="$$" /> D. <img src="files/image20.png" width="33.85pt" height="31.15pt" data-latex="$$" /></p>
-<p>11.如图所示，斜面ABC放在水平面上，斜边BC长为l，倾角为30°，在斜面的上端B点沿水平方向抛出一小球，结果小球刚好落在斜面下端C点，重力加速度为g，则小球初速度v<sub>0</sub>的值为(　　)</p>
-<p><img src="files/image21.png" width="76pt" height="45.75pt" />A.【域公式】$eq \\f(1,2)$【域公式】$eq \\r(gl)$  B.【域公式】$eq \\f(1,2)$【域公式】$eq \\r(2gl)$</p>
-<p>C.【域公式】$eq \\f(1,2)$【域公式】$eq \\r(3gl)$  D.【域公式】$eq \\f(1,2)$【域公式】$eq \\r(5gl)$</p>
-<p>12.（多选）在光滑水平面上，钉有两个钉子A、B，一根长细绳一端系一个小球，另一端固定在钉子A上，开始时小球与钉子A、B均在一条直线上（图示位置），且细绳的一大部分沿俯视顺时针方向缠绕在两钉子上，现使小球以初速度v<sub>0</sub>在水平面上沿俯视逆时针方向做匀速圆周运动，使两钉子之间缠绕的绳子逐渐释放，在绳子完全被释放后与释放前相比，下列说法正确的是 （   ）</p>
-<p><img src="files/image23.jpeg" width="119.25pt" height="28.5pt" />A．小球的速度变大<br />B．小球的角速度变大 <br />C．小球的加速度变小<br />D．细绳对小球的拉力变小</p>
-<p>13.（多选）两个质量相同的小球，在同一水平面内做匀速圆周运动，悬点相同，如图所示，A运动的半径比B的大，则（　　）</p>
-<p>A．A受到的向心力比B的大   B．B受到的向心力比A的大</p>
-<p>C．A、B的周期相同        D．A、B的角速度相同</p>
-<p>14.在一个光滑水平面内建立平面直角坐标系xOy，质量为1 kg 的物体原来静止在坐标原点O(0,0)，t＝0时受到如图所示随时间变化的外力作用，图甲中F<sub>x</sub>表示沿x轴方向的外力，图乙中F<sub>y</sub>表示沿y轴方向的外力，下列描述正确的是(　　)</p>
-<p><img src="files/image24.png" width="183.2pt" height="1in" /></p>
-<p>A．0～4 s内物体的运动轨迹是一条直线</p>
-<p>B．0～4 s内物体的运动轨迹是一条抛物线</p>
-<p>C．前2 s内物体做匀加速直线运动，后2 s内物体做匀加速曲线运动</p>
-<p>D．前2 s内物体做匀加速直线运动，后2 s内物体做匀速圆周运动</p>
-<p>15. 山城重庆的轻轨交通颇有山城特色，由于地域限制，弯道半径很小，在某些弯道上行驶时列车的车身严重倾斜。每到这样的弯道乘客都有一种坐过山车的感觉，很是惊险刺激。假设某弯道铁轨是圆弧的一部分，转弯半径为R，重力加速度为g，列车转弯过程中倾角(车厢地面与水平面夹角)为θ，则列车在这样的轨道上转弯行驶的安全速度(轨道不受侧向挤压)为(　　)</p>
-<p>A. <img src="files/image25.png" width="51.05pt" height="19.9pt" data-latex="$$" />   B. <img src="files/image26.png" width="53.2pt" height="19.9pt" data-latex="$$" />  C. <img src="files/image27.png" width="52.1pt" height="19.9pt" data-latex="$$" />   D. <img src="files/image28.png" width="55.9pt" height="19.9pt" data-latex="$$" /></p>
-<p>16.如图所示，两个用相同材料制成的靠摩擦传动的轮A和B水平放置，两轮半径R<sub>A</sub>=3R<sub>B</sub>．当主动轮A匀速转动时，在A轮边缘上放置的小木块恰能相对静止在A轮边缘上．若将小木块放在B轮上，欲使木块相对B轮也静止，则木块距B轮转轴的最大距离为（　　）<img src="files/image29.png" width="89.25pt" height="71.25pt" /></p>
-<p>A．<img src="files/image30.png" width="17.2pt" height="17.2pt" data-latex="$$" />    B.<img src="files/image31.png" width="19.9pt" height="31.7pt" data-latex="$$" />       C.<img src="files/image32.png" width="19.9pt" height="31.7pt" data-latex="$$" />       D. <img src="files/image33.png" width="19.9pt" height="31.7pt" data-latex="$$" /></p>
-<p>二、实验题 (每空3分，共计18分)</p>
-<p><img src="files/image34.png" width="118.5pt" height="90pt" />17.某同学在做平抛运动实验时得到了如图所示的物体运动轨迹，a、b、c三点的位置在运动轨迹上已标出．则：<br />（1）小球平抛的初速度为______ m/s．（g取10m/s<sup>2</sup>）<br />（2）小球开始做平抛运动的位置坐标为x=______cm，y=______cm．<br />（3）小球运动到b点的速度为______m/s．</p>
-<p>18在“探究加速度与质量的关系”的实验中。</p>
-<p>（1）备有器材：A.带有定滑轮的长木板；B.电磁打点计时器、低压交流电源、纸带；C.细绳、小车、砝码；D.装有细砂的砂桶；E.垫片；F.毫米刻度尺. 还缺少的一件器材是_________。</p>
-<p>（2）同学甲根据实验数据画出如图所示a－【域公式】$eq \\f(1,m)$图线，从图线可得砂和砂桶的总质量为____________kg。(g取10 m/s<sup>2</sup>)</p>
-<p> INCLUDEPICTURE "E:\\\\17-15\\\\高一下\\\\新建文件夹\\\\Z302.tif" \\* MERGEFORMAT  INCLUDEPICTURE "E:\\\\17-15\\\\高一下\\\\新建文件夹\\\\Z302.tif" \\* MERGEFORMAT <img src="files/image35.png" width="147.75pt" height="130.55pt" />$$</p>
-<p>三．计算题（共3小题，共34分，要求写出必要的文字说明、方程式和重要的演算步骤，只写出最后答案的不能得分）</p>
-<p><img src="files/image36.png" width="97.5pt" height="57.75pt" />19. （10分）如图所示，在距地面为H=45m处，有一小球A以初速度v<sub>0</sub>=10m/s水平抛出，与此同时，在A的正下方有一物块B也以相同的初速度v<sub>0</sub>同方向滑出，B与地面间的动摩擦因数为μ=0.5，A、B均可看做质点，空气阻力不计，重力加速度g取10m/s<sup>2</sup>，求：</p>
-<p>（1）A球从抛出到落地的时间和这段时间内的水平位移；</p>
-<p>（2）A球落地时，A、B之间的距离．</p>
-<p> </p>
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-<p><img src="files/image37.jpeg" width="84.75pt" height="129.75pt" />20. （12分）如图所示，小球Q在竖直平面内做匀速圆周运动，半径为r，当球Q运动到与O在同一水平线上时，有另一小球P在距圆周最高点为h处开始自由下落．要使两球在圆周最高点处相碰，Q球的角速度ω应满足什么条件？</p>
-<p> </p>
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-<p><img src="files/image38.png" width="73.5pt" height="78.75pt" />21. （12分）如图所示，用一根长为l＝1 m的细线，一端系一质量为m＝1 kg的小球(可视为质点)，另一端固定在一光滑锥体顶端，锥面与竖直方向的夹角θ＝37°，当小球在水平面内绕锥体的轴做匀速圆周运动的角速度为ω时，细线的张力为F<sub>T</sub>.(g取10 m/s<sup>2</sup>，结果可用根式表示)求：</p>
-<p> (1)若要小球刚好离开锥面，则小球的角速度ω<sub>0</sub>至少为多大？</p>
-<p>(2)若细线与竖直方向的夹角为60°，则小球的角速度ω′为多大？</p>
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-<p>          高一物理周考试卷答题页</p>
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-<p>17.（1）          m/s   （2） x=____   __cm，y=____   __cm．  （3）___ _  __m/s．</p>
-<p> </p>
-<p>18．（1）                （2）             kg</p>
-<p>19．（10分）</p>
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-<p>20．（12分）</p>
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-<p>21．（12分）</p>
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-<p>参考答案1C 2ABC 3C 4A 5B 6B 7C 8D 9B 10C 11C 12CD 13ACD 14C 15C 16D</p>
-<p>1解析：选C　牛顿提出了万有引力定律，卡文迪许测定了引力常量的数值，万有引力定律适用于任何物体之间，万有引力的发现，揭示了自然界一种基本相互作用的规律，选项A、B错误，C正确；地球绕太阳在椭圆轨道上运行，在近日点和远日点受到太阳的万有引力大小是不相同的，选项D错误。</p>
-<p>2解析：选ABC　由h＝【域公式】$eq \\f(1,2)$gt<sup>2</sup>，x＝v<sub>0</sub>t得v<sub>0</sub>＝x 【域公式】$eq \\r(\\f(g,2h))$，可知知道下落高度和水平位移，可以确定初速度，故A正确；已知落地时的速度大小和方向，根据平行四边形定则可以求出初速度。故B正确；已知位移大小和方向及水平位移，能求出下落的高度，结合A项分析知能求出初速度，故C正确；已知位移大小，不能求出水平位移和下落的高度，已知落地时的速度大小，方向未知，不能求出初速度，故D错误。</p>
-<p>3解析：选C　三个物体落地的高度h<sub>a</sub>&gt;h<sub>b</sub>&gt;h<sub>c</sub>，根据h＝【域公式】$eq \\f(1,2)$gt<sup>2</sup>，知t<sub>a</sub>&gt;t<sub>b</sub>&gt;t<sub>c</sub>，根据x<sub>a</sub>&lt;x<sub>b</sub>&lt;x<sub>c</sub>，x＝vt知，a的水平位移最短，时间最长，则速度最小；c的水平位移最长，时间最短，则速度最大，所以有v<sub>a</sub>&lt;v<sub>b</sub>&lt;v<sub>c</sub>。故C正确，A、B、D错误。</p>
-<p>4解析：选A　P、Q两物体都是绕地轴做匀速圆周运动，角速度相等，即ω<sub>P</sub>＝ω<sub>Q</sub>，选项A对；根据圆周运动线速度v＝ωR，P、Q两物体做匀速圆周运动的半径不等，即P、Q两物体做圆周运动的线速度大小不等，选项B错；Q物体到地轴的距离远，圆周运动半径大，线速度大，选项C错；P、Q两物体均受到万有引力和支持力作用，重力只是万有引力的一个分力，选项D错。</p>
-<p>5解析：选B　设系在A上的细线与水平方向夹角为θ，物体B的速度为v<sub>B</sub>，大小不变，细线的拉力为F<sub>T</sub>，则物体A的速度v<sub>A</sub>＝【域公式】$eq \\f(v<sub>B</sub>,cos θ)$，F<sub>f</sub><sub>A</sub>＝μ(mg－F<sub>T</sub>sin θ), 因物体B下降，θ增大，故v<sub>A</sub>增大，物体A做加速运动，A错误，B正确；物体B匀速下降，F<sub>T</sub>不变，故随θ增大，F<sub>f</sub><sub>A</sub>减小，C、D均错误。</p>
-<p>6解析：选B　平抛运动竖直方向上的位移和水平方向上的位移关系为tan θ＝【域公式】$eq \\f(y,x)$＝【域公式】$eq \\f(\\f(1,2)gt<sup>2</sup>,v<sub>0</sub>t)$＝【域公式】$eq \\f(gt,2v<sub>0</sub>)$，则t＝【域公式】$eq \\f(2v<sub>0</sub>tan θ,g)$，可知运动的时间与初速度成正比，所以t<sub>1</sub>∶t<sub>2</sub>＝2∶1。竖直方向上下落的高度h＝【域公式】$eq \\f(1,2)$gt<sup>2</sup>，可得竖直方向上的位移之比为4∶1。斜面上的距离s＝【域公式】$eq \\f(h,sin θ)$，知AB∶AC＝4∶1。故选B。</p>
-<p>7解析：选C　小球做平抛运动，tan θ＝【域公式】$eq \\f(v<sub>y</sub>,v<sub>0</sub>)$＝【域公式】$eq \\f(gt,v<sub>0</sub>)$，则时间t＝【域公式】$eq \\f(v<sub>0</sub>tan θ,g)$，选项A、B错误；在水平方向上有Rsin θ＝v<sub>0</sub>t，则t＝【域公式】$eq \\f(Rsin θ,v<sub>0</sub>)$，选项C正确，D错误。</p>
-<p> </p>
-<p>8解析：选D　甲、乙两圆盘边缘上的各点线速度大小相等，有：ω<sub>1</sub>·3r＝ω<sub>2</sub>·r，则得ω<sub>1</sub>∶ω<sub>2</sub>＝1∶3，所以小物体相对盘开始滑动前，m<sub>1</sub>与m<sub>2</sub>的角速度之比为1∶3，故A错误；小物体相对盘开始滑动前，根据a＝ω<sup>2</sup>r得：m<sub>1</sub>与m<sub>2</sub>的向心加速度之比为a<sub>1</sub>∶a<sub>2</sub>＝(ω<sub>1</sub><sup>2</sup>·2r)∶(ω<sub>2</sub><sup>2</sup>r)＝2∶9，故B错误；根据μmg＝mrω<sup>2</sup>＝ma知，因a<sub>1</sub>∶a<sub>2</sub>＝2∶9，圆盘和小物体的动摩擦因数相同，可知当转速增加时，m<sub>2</sub>先达到临界角速度，所以m<sub>2</sub>先开始滑动。故D正确，C错误。</p>
-<p>9解析：选B.万有引力提供向心力，因已知周期，且F<sub>万</sub>＝F<sub>向</sub>，故可知【域公式】$eq \\f(GMm,r<sup>2</sup>)$＝m【域公式】$eq \\f(4π<sup>2</sup>,T<sup>2</sup>)$r，解得M＝【域公式】$eq \\f(4π<sup>2</sup>r<sup>3</sup>,GT<sup>2</sup>)$，代入数据得M＝1.0×10<sup>26</sup> kg，B正确．</p>
-<p>10解析：选C　万有引力提供近地卫星绕地球运动的向心力G【域公式】$eq \\f(M<sub>地</sub>m,R<sup>2</sup>)$＝m【域公式】$eq \\f(4π<sup>2</sup>R,T<sup>2</sup>)$，且ρ<sub>地</sub>＝【域公式】$eq \\f(3M<sub>地</sub>,4πR<sup>3</sup>)$，由以上两式得ρ<sub>地</sub>＝【域公式】$eq \\f(3π,GT<sup>2</sup>)$。而【域公式】$eq \\f(ρ<sub>星</sub>,ρ<sub>地</sub>)$＝【域公式】$eq \\f(M<sub>星</sub>V<sub>地</sub>,V<sub>星</sub>M<sub>地</sub>)$＝【域公式】$eq \\f(b,a)$，因而ρ<sub>星</sub>＝【域公式】$eq \\f(3πb,aGT<sup>2</sup>)$，C正确。</p>
-<p><img src="files/image39.png" width="76.5pt" height="75pt" />11解析：选C　平抛运动的水平位移x＝lcos θ＝v<sub>0</sub>t，竖直方向的位移y＝lsin θ＝【域公式】$eq \\f(1,2)$gt<sup>2</sup>，联立可得v<sub>0</sub>＝【域公式】$eq \\f(1,2)$【域公式】$eq \\r(3gl)$，C正确。</p>
-<p>12CD</p>
-<p>13. 解析：ACD 对其中一个小球受力分析，如图，受重力、绳子的拉力，由于小球做匀速圆周运动，故由合力提供向心力；将重力与拉力合成，合力指向圆心，由几何关系得，向心力为：F=mgtanθ…①<br />则知A受到的向心力比B的大，故A正确，B错误．<br /><a href="https://www.baidu.com/s?wd=CD&amp;tn=44039180_cpr&amp;fenlei=mv6quAkxTZn0IZRqIHckPjm4nH00T1dBnjubPWDYrADvnhR3mH9B0ZwV5Hcvrjm3rH6sPfKWUMw85HfYnjn4nH6sgvPsT6KdThsqpZwYTjCEQLGCpyw9Uz4Bmy-bIi4WUvYETgN-TLwGUv3EnH6vnHn3rHfLnHn4nHR1nHTsPs">CD</a>、由向心力公式得到，F=mω<sup>2</sup>r…②；<br />设球与悬挂点间的高度差为h，由几何关系，得：r=htanθ…③；<br />由①②③解得：ω=<img src="files/image40.png" width="22.05pt" height="34.95pt" data-latex="$$" />与绳子的长度和转动半径无关，即角速度、周期大小相同；故C、D正确．</p>
-<p>14解析：选C　0～2 s内物体沿x轴方向做初速度为零的匀加速直线运动，2 s时受沿y轴方向的恒力作用，与速度方向垂直，故2～4 s内物体做类平抛运动，C项正确。</p>
-<p>15解析：选C　轨道不受侧向挤压时，轨道对列车的作用力就只有弹力，重力和弹力的合力提供向心力，根据向心力公式mgtan θ＝m【域公式】$eq \\f(v<sup>2</sup>,R)$，得v＝【域公式】$eq \\r(gRtan θ)$，C正确。</p>
-<p>16.D</p>
-<p>17.  (1)2；(2) （-10，-1.25）；(3)2.5</p>
-<p>18.根据牛顿第二定律可知，a＝【域公式】$eq \\f(F,m)$，则F即为a－【域公式】$eq \\f(1,m)$图象的斜率，所以砂和砂桶的总重力m′g＝F＝【域公式】$eq \\f(2.4,12)$ N＝0.20 N，解得m′＝0.020 kg。(0.018～0.022均正确)</p>
-<p>19(1)30m (2)10m解析：（1）由平抛运动可知：<img src="files/image41.png" width="115pt" height="52.1pt" data-latex="$$" /></p>
-<p>（2）对B物块，由牛二定律：<img src="files/image42.png" width="145.05pt" height="18.25pt" data-latex="$$" /></p>
-<p>减速至停止所需时间<img src="files/image43.png" width="80.05pt" height="31.15pt" data-latex="$$" /></p>
-<p>所以在A落地之前B已停止运动.B的总位移为<img src="files/image44.png" width="75.2pt" height="32.8pt" data-latex="$$" /></p>
-<p>所以AB间距离为<img src="files/image45.png" width="83.8pt" height="18.25pt" data-latex="$$" /> </p>
-<p>20．</p>
-<p><img src="files/image46.jpeg" width="422.85pt" height="155.3pt" /></p>
-<p>21解析：(1)若要小球刚好离开锥面，则小球只受到重力和细线的拉力，受力分析如图所示．小球做匀速圆周运动的轨迹圆在水平面上，故向心力水平，在水平方向运用牛顿第二定律及向心力公式得：</p>
-<p><img src="files/image47.png" width="45.65pt" height="82.2pt" /></p>
-<p>mgtan θ＝mω【域公式】$eq \\o\\al(<sup>2</sup>,<sub>0</sub>)$lsin θ</p>
-<p>解得ω【域公式】$eq \\o\\al(<sup>2</sup>,<sub>0</sub>)$＝【域公式】$eq \\f(g,lcos θ)$</p>
-<p>即ω<sub>0</sub>＝ 【域公式】$eq \\r(\\f(g,lcos θ))$＝【域公式】$eq \\f(5,2)$【域公式】$eq \\r(2)$ rad/s.</p>
-<p>(2)同理，当细线与竖直方向成60°角时，由牛顿第二定律及向心力公式得：</p>
-<p>mgtan α＝mω′<sup>2</sup>lsin α</p>
-<p>解得：ω′<sup>2</sup>＝【域公式】$eq \\f(g,lcos α)$，即ω′＝ 【域公式】$eq \\r(\\f(g,lcos α))$＝2【域公式】$eq \\r(5)$ rad/s.</p>
-<p>答案：(1)【域公式】$eq \\f(5,2)$【域公式】$eq \\r(2)$ rad/s　(2)2【域公式】$eq \\r(5)$ rad/s</p>
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