<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">1.</span><span data-v-16cfdac0="" class="stem">计算<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image1.png" width="54px" height="26px" data-latex="$$">的结果等于（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image2.png" width="20px" height="17px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>2</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-32" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span><script type="math/tex" id="MathJax-Element-1">2</script></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image3.png" width="27px" height="17px" data-latex="$$"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>15</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.325ex" height="2.074ex" viewBox="0 -772.3 1001 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-31"></use><use xlink:href="#MJMAIN-35" x="500" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></span></span><script type="math/tex" id="MathJax-Element-2">15</script></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">C</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据有理数的乘法法则运算即可求解．<br>【详解】解：由题意可知：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image4.png" width="94px" height="26px" data-latex="$$">，<br>故选：C．<br>【点睛】本题考查了有理数的乘法法则，属于基础题，运算过程中注意符号即可．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">2.</span><span data-v-16cfdac0="" class="stem"><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image5.png" width="49px" height="18px" data-latex="$$">的值等于（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image6.png" width="27px" height="45px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image7.png" width="27px" height="45px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>1</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-31" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-3">1</script></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>2</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-32" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span><script type="math/tex" id="MathJax-Element-4">2</script></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">A</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据30°的正切值直接求解即可．<br>【详解】解：由题意可知，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image8.png" width="86px" height="45px" data-latex="$$">，<br>故选：A．<br>【点睛】本题考查30°的三角函数，属于基础题，熟记其正切值即可．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">3.</span><span data-v-16cfdac0="" class="stem">据2021年5月12日《天津日报》报道，第七次全国人口普查数据公布，普查结果显示，全国人口共141178万人．将141178用科学记数法表示应为（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image9.png" width="96px" height="21px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image10.png" width="86px" height="21px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image11.png" width="88px" height="21px" data-latex="$$"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image12.png" width="88px" height="21px" data-latex="$$"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">B</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】科学记数法的表示形式为a×10<sup>n</sup>的形式，其中1≤|a|＜10，n为整数．确定n的值时，要看把原数变成a时，小数点移动了多少位，n的绝对值与小数点移动的位数相同．<br>【详解】解：141178=1.41178×10<sup>5</sup>，<br>故选：B．<br>【点睛】此题考查科学记数法的表示方法，关键是确定a的值以及n的值．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">4.</span><span data-v-16cfdac0="" class="stem">在一些美术字中，有的汉字是轴对称图形．下面4个汉字中，可以看作是轴对称图形的是（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image13.png" width="78px" height="78px"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image14.png" width="80px" height="80px"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image15.png" width="75px" height="78px"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image16.png" width="70px" height="81px"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">A</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据轴对称图形的概念对各项分析判断即可得解．<br>【详解】A．是轴对称图形，故本选项符合题意；<br>B．不是轴对称图形，故本选项不符合题意；<br>C．不是轴对称图形，故本选项不符合题意；<br>D．不是轴对称图形，故本选项不符合题意．<br>故选A．<br>【点睛】本题考查判断轴对称图形，理解轴对称图形的概念是解答的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">5.</span><span data-v-16cfdac0="" class="stem">如图是一个由6个相同的正方体组成的立体图形，它的主视图是（ ）<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image17.png" width="136px" height="131px"></span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image18.png" width="116px" height="116px"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image19.png" width="136px" height="105px"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image20.png" width="128px" height="96px"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image21.png" width="123px" height="91px"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">D</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据三视图中的主视图定义，从前往后看，得到的平面图形即为主视图．<br>【详解】解：从正面看到的平面图形是3列小正方形，从左至右第1列有1个，第2列有2个，第3列有2个，<br>故选：D．<br>【点睛】本题主要考查了组合体的三视图，解题的关键是根据主视图的概念由立体图形得到相应的平面图形．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">6.</span><span data-v-16cfdac0="" class="stem">估算<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image22.png" width="32px" height="24px" data-latex="$$">的值在(  )</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0="">2和3之间</span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0="">3和4之间</span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0="">4和5之间</span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0="">5和6之间</span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">C</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】估算无理数的大小．<br>【详解】因为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image23.png" width="103px" height="25px" data-latex="$$">,所以<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image22.png" width="32px" height="24px" data-latex="$$">的值在4和5之间．<br>故选C．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">7.</span><span data-v-16cfdac0="" class="stem">方程组<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image24.png" width="75px" height="48px" data-latex="$$">的解是（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image25.png" width="47px" height="48px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image26.png" width="43px" height="48px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image27.png" width="55px" height="48px" data-latex="$$"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image28.png" width="55px" height="48px" data-latex="$$"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">B</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】直接利用加减消元法解该二元一次方程组即可．<br>【详解】<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image29.png" width="124px" height="50px" data-latex="$$">，<br>②-①得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image30.png" width="113px" height="21px" data-latex="$$">，即<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image31.png" width="45px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image32.png" width="35px" height="19px" data-latex="$$">．<br>将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image32.png" width="35px" height="19px" data-latex="$$">代入①得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image33.png" width="57px" height="22px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image34.png" width="35px" height="20px" data-latex="$$">．<br>故原二元一次方程组的解为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image26.png" width="43px" height="48px" data-latex="$$">．<br>故选B．<br>【点睛】本题考查解二元一次方程组．掌握解二元一次方程组的方法和步骤是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">8.</span><span data-v-16cfdac0="" class="stem">如图，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image35.png" width="58px" height="18px" data-latex="$$">的顶点A，B，C的坐标分别是<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image36.png" width="144px" height="26px" data-latex="$$">，则顶点D的坐标是（ ）<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image37.png" width="194px" height="128px"></span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image38.png" width="40px" height="22px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image39.png" width="48px" height="26px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image40.png" width="35px" height="26px" data-latex="$$"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image41.png" width="35px" height="27px" data-latex="$$"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">C</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据平行四边形性质以及点的平移性质计算即可．<br>【详解】解：∵四边形ABCD是平行四边形，<br>点B的坐标为(-2，-2)，点C的坐标为(2，-2)，<br>∴点B到点C为水平向右移动4个单位长度，<br>∴A到D也应向右移动4个单位长度，<br>∵点A的坐标为(0，1)，<br>则点D的坐标为(4，1)，<br>故选:C．<br>【点睛】本题主要考查平行四边形的性质，以及平移的相关知识点，熟知点的平移特点是解决本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">9.</span><span data-v-16cfdac0="" class="stem">计算<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image42.png" width="85px" height="41px" data-latex="$$">的结果是（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>3</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-33" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-5">3</script></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image43.png" width="48px" height="19px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>1</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-31" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-6">1</script></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image44.png" width="39px" height="41px" data-latex="$$"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">A</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】先根据分式的减法运算法则计算，再提取公因式3，最后约分化简即可．<br>【详解】原式<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image45.png" width="65px" height="40px" data-latex="$$">，<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image46.png" width="68px" height="40px" data-latex="$$"><br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image47.png" width="22px" height="17px" data-latex="$$">．<br>故选A．<br>【点睛】本题考查分式的减法．掌握分式的减法运算法则是解答本题你的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">10.</span><span data-v-16cfdac0="" class="stem">若点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image48.png" width="184px" height="26px" data-latex="$$">都在反比例函数<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image49.png" width="52px" height="40px" data-latex="$$">的图象上，则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image50.png" width="58px" height="24px" data-latex="$$">的大小关系是（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image51.png" width="78px" height="24px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image52.png" width="80px" height="24px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image53.png" width="78px" height="24px" data-latex="$$"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image54.png" width="78px" height="25px" data-latex="$$"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">B</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】将A、B、C三点坐标代入反比例函数解析式，即求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image55.png" width="70px" height="25px" data-latex="$$">的值，即可比较得出答案．<br>【详解】分别将A、B、C三点坐标代入反比例函数解析式得：<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image56.png" width="85px" height="40px" data-latex="$$">、<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image57.png" width="88px" height="40px" data-latex="$$">、<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image58.png" width="88px" height="40px" data-latex="$$">．<br>则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image52.png" width="80px" height="24px" data-latex="$$">．<br>故选B．<br>【点睛】本题考查比较反比例函数值．掌握反比例函数图象上的点的坐标满足其解析式是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">11.</span><span data-v-16cfdac0="" class="stem">如图，在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image59.png" width="50px" height="18px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image60.png" width="93px" height="18px" data-latex="$$">，将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image59.png" width="50px" height="18px" data-latex="$$">绕点C逆时针旋转得到<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image61.png" width="46px" height="18px" data-latex="$$">，点A，B的对应点分别为D，E，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image62.png" width="27px" height="17px" data-latex="$$">．当点A，D，E在同一条直线上时，下列结论一定正确的是（ ）<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image63.png" width="164px" height="144px"></span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image64.png" width="109px" height="18px" data-latex="$$"></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image65.png" width="63px" height="19px" data-latex="$$"></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image66.png" width="105px" height="18px" data-latex="$$"></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image67.png" width="68px" height="19px" data-latex="$$"></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">D</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】由旋转可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image68.png" width="153px" height="19px" data-latex="$$">，即可求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image69.png" width="88px" height="18px" data-latex="$$">，由于<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image70.png" width="85px" height="19px" data-latex="$$">，则可判断<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image71.png" width="108px" height="19px" data-latex="$$">，即A选项错误；由旋转可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image72.png" width="63px" height="19px" data-latex="$$">，由于<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image73.png" width="64px" height="18px" data-latex="$$">，即推出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image74.png" width="64px" height="18px" data-latex="$$">，即B选项错误；由三角形三边关系可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image75.png" width="103px" height="18px" data-latex="$$">，即可推出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image76.png" width="103px" height="18px" data-latex="$$">，即C选项错误；由旋转可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image77.png" width="67px" height="19px" data-latex="$$">，再由<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image69.png" width="88px" height="18px" data-latex="$$">，即可证明<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image78.png" width="48px" height="18px" data-latex="$$">为等边三角形，即推出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image79.png" width="88px" height="19px" data-latex="$$">．即可求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image80.png" width="151px" height="19px" data-latex="$$">，即证明<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image81.png" width="65px" height="19px" data-latex="$$">，即D选项正确；<br>【详解】由旋转可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image68.png" width="153px" height="19px" data-latex="$$">，<br>∵点A，D，E在同一条直线上，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image82.png" width="192px" height="13.95pt" data-latex="$$">，<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image70.png" width="85px" height="19px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image71.png" width="108px" height="19px" data-latex="$$">，故A选项错误，不符合题意；<br>由旋转可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image72.png" width="63px" height="19px" data-latex="$$">，<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image83.png" width="96px" height="14.5pt" data-latex="$$">为钝角，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image73.png" width="64px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image74.png" width="64px" height="18px" data-latex="$$">，故B选项错误，不符合题意；<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image75.png" width="103px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image76.png" width="103px" height="18px" data-latex="$$">，故C选项错误，不符合题意；<br>由旋转可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image77.png" width="67px" height="19px" data-latex="$$">，<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image69.png" width="88px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image78.png" width="48px" height="18px" data-latex="$$">为等边三角形，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image79.png" width="88px" height="19px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image80.png" width="151px" height="19px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image81.png" width="65px" height="19px" data-latex="$$">，故D选项正确，符合题意；<br>故选D．<br>【点睛】本题考查旋转的性质，三角形三边关系，等边三角形的判定和性质以及平行线的判定．利用数形结合的思想是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">12.</span><span data-v-16cfdac0="" class="stem">已知抛物线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image84.png" width="102px" height="24px" data-latex="$$">（<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image85.png" width="40px" height="20px" data-latex="$$">是常数，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image86.png" width="37px" height="19px" data-latex="$$">）经过点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image87.png" width="89px" height="21px" data-latex="$$">，当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image88.png" width="45px" height="19px" data-latex="$$">时，与其对应的函数值<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image89.png" width="32px" height="20px" data-latex="$$">．有下列结论：①<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image90.png" width="52px" height="19px" data-latex="$$">；②关于x的方程<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image91.png" width="124px" height="20px" data-latex="$$">有两个不等的实数根；③<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image92.png" width="82px" height="18px" data-latex="$$">．其中，正确结论的个数是（ ）</span></div><ul data-v-16cfdac0="" class="stem-options"><li data-v-16cfdac0="">A：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>0</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-30" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-7">0</script></span></li><li data-v-16cfdac0="">B：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>1</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-31" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-8">1</script></span></li><li data-v-16cfdac0="">C：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>2</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-32" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span><script type="math/tex" id="MathJax-Element-9">2</script></span></li><li data-v-16cfdac0="">D：<span data-v-16cfdac0=""><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mn>3</mn></math>" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.162ex" height="2.074ex" viewBox="0 -772.3 500.5 892.8" role="img" focusable="false" style="vertical-align: -0.28ex;" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-33" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-10">3</script></span></li></ul><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">D</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据函数与点的关系,一元二次方程根的判别式,不等式的性质，逐一计算判断即可<br>【详解】∵抛物线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image84.png" width="102px" height="24px" data-latex="$$">（<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image85.png" width="40px" height="20px" data-latex="$$">是常数，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image86.png" width="37px" height="19px" data-latex="$$">）经过点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image87.png" width="89px" height="21px" data-latex="$$">，当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image88.png" width="45px" height="19px" data-latex="$$">时，与其对应的函数值<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image89.png" width="32px" height="20px" data-latex="$$">．<br>∴c=1＞0，a-b+c= -1<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image93.png" width="5px" height="9px" data-latex="$$">4a-2b+c＞1，<br>∴a-b= -2<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image93.png" width="5px" height="9px" data-latex="$$">2a-b＞0，<br>∴2a-a-2＞0，<br>∴a＞2＞0，<br>∴b=a+2＞0，<br>∴abc＞0，<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image91.png" width="124px" height="20px" data-latex="$$">,<br>∴△=<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image94.png" width="88px" height="24px" data-latex="$$">=<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image95.png" width="48px" height="20px" data-latex="$$">＞0,<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image91.png" width="124px" height="20px" data-latex="$$">有两个不等的实数根；<br>∵b=a+2，a＞2，c=1，<br>∴a+b+c=a+a+2+1=2a+3，<br>∵a＞2，<br>∴2a＞4，<br>∴2a+3＞4+3＞7，<br>故选D．<br>【点睛】本题考查了二次函数的性质，一元二次方程根的判别式，不等式的基本性质，熟练掌握二次函数的性质，灵活使用根的判别式，准确掌握不等式的基本性质是解题的关键．</span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">13.</span><span data-v-16cfdac0="" class="stem">计算<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image96.png" width="77px" height="18px" data-latex="$$">的结果等于_____．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image97.png" width="20px" height="19px" data-latex="$$"></span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据合并同类项的性质计算，即可得到答案．<br>【详解】<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image98.png" width="194px" height="26px" data-latex="$$"><br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image97.png" width="20px" height="19px" data-latex="$$">．<br>【点睛】本题考查了整式加减的知识；解题的关键是熟练掌握合并同类项的性质，从而完成求解．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">14.</span><span data-v-16cfdac0="" class="stem">计算<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image99.png" width="117px" height="25px" data-latex="$$">的结果等于_____．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">9</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据二次根式的混合运算法则结合平方差公式计算即可．<br>【详解】<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image100.png" width="219px" height="25px" data-latex="$$">．<br>故答案为9．<br>【点睛】本题考查二次根式的混合运算．掌握二次根式的混合运算法则是解答本题你的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">15.</span><span data-v-16cfdac0="" class="stem">不透明袋子中装有7个球，其中有3个红球，4个黄球，这些球除颜色外无其他差别，从袋子中随机取出1个球，则它是红球的概率是_____．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image101.png" width="15px" height="40px" data-latex="$$"></span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据概率的求法，找准两点：①全部情况的总数；②符合条件的情况数目；二者的比值就是其发生的概率．<br>【详解】解：∵袋子中共有7个球，其中红球有3个，<br>∴从袋子中随机取出1个球，它是红球的概率是<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image101.png" width="15px" height="40px" data-latex="$$">，<br>故答案为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image101.png" width="15px" height="40px" data-latex="$$">．<br>【点睛】本题考查概率的求法：如果一个事件有n种可能，而且这些事件的可能性相同，其中事件A出现m种结果，那么事件A的概率P(A)=<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image102.png" width="20px" height="40px" data-latex="$$"> ．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">16.</span><span data-v-16cfdac0="" class="stem">将直线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image103.png" width="55px" height="20px" data-latex="$$">向下平移2个单位长度，平移后直线的解析式为_____．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image104.png" width="76px" height="20px" data-latex="$$"></span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】直接根据“上加下减，左加右减”的平移规律求解即可．<br>【详解】将直线y=-6x向下平移2个单位长度，所得直线的解析式为y=-6x-2．<br>故答案为y=-6x-2．<br>【点睛】本题考查一次函数图象的平移变换．掌握其规律 “左加右减，上加下减”是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">17.</span><span data-v-16cfdac0="" class="stem">如图，正方形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image105.png" width="48px" height="18px" data-latex="$$">的边长为4，对角线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image106.png" width="55px" height="21px" data-latex="$$">相交于点O，点E，F分别在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image107.png" width="55px" height="20px" data-latex="$$">的延长线上，且<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image108.png" width="101px" height="20px" data-latex="$$">，G为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image109.png" width="25px" height="17px" data-latex="$$">的中点，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image110.png" width="27px" height="18px" data-latex="$$">，交<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image111.png" width="28px" height="19px" data-latex="$$">于点H，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image112.png" width="28px" height="19px" data-latex="$$">，则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image112.png" width="28px" height="19px" data-latex="$$">的长为________．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image113.png" width="167.1pt" height="192px"></span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image114.png" width="32px" height="45px" data-latex="$$"></span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】先作辅助线构造直角三角形，求出CH和MG的长，再求出MH的长，最后利用勾股定理求解即可．<br>【详解】解:如图,作OK⊥BC，垂足为点K，<br>∵正方形边长为4，<br>∴OK=2，KC=2，<br>∴KC=CE，<br>∴CH是△OKE<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image115.png" width="14px" height="18px" data-latex="$$">中位线<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image116.png" width="101px" height="40px" data-latex="$$">，<br>作GM⊥CD，垂足为点M，<br>∵G点为EF中点，<br>∴GM是△FCE的中位线，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image117.png" width="103px" height="40px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image118.png" width="287px" height="40px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image119.png" width="184px" height="40px" data-latex="$$">，<br>在Rt△MHG中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image120.png" width="270px" height="53px" data-latex="$$">，<br>故答案<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image121.png" width="16px" height="20px" data-latex="$$">：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image122.png" width="32px" height="45px" data-latex="$$">．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image123.png" width="168.2pt" height="192px"><br>【点睛】本题综合考查了正方形的性质、三角形中位线定理、勾股定理等内容，解决本题的关键是能作出辅助线构造直角三角形，得到三角形的中位线，利用三角形中位线定理求出相应线段的长，利用勾股定理解直角三角形等．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">18.</span><span data-v-16cfdac0="" class="stem">如图，在每个小正方形的边长为1的网格中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image59.png" width="50px" height="18px" data-latex="$$">的顶点A，C均落在格点上，点B在网格线上．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image124.png" width="303px" height="255px"><br>(Ⅰ)线段<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image125.png" width="28px" height="18px" data-latex="$$">的长等于_____；<br>(Ⅱ)以<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image126.png" width="27px" height="17px" data-latex="$$">为直径的半圆的圆心为O，在线段<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image126.png" width="27px" height="17px" data-latex="$$">上有一点P，满足<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image127.png" width="65px" height="18px" data-latex="$$">，请用无刻度的直尺，在如图所示的网格中，画出点P，并简要说明点P的位置是如何找到的（不要求证明）_____．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">①. <img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image128.png" width="24px" height="24px" data-latex="$$"> ②. 见解析</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】(Ⅰ)根据勾股定理计算即可；<br>(Ⅱ)现将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image129.png" width="45px" height="18px" data-latex="$$">补成等腰三角形，然后构建全等三角形即可．<br>【详解】解：(Ⅰ)∵每个小正方形的边长为1，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image130.png" width="131px" height="26px" data-latex="$$">，<br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image128.png" width="24px" height="24px" data-latex="$$">；<br>(Ⅱ)如图，取<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image131.png" width="27px" height="18px" data-latex="$$">与网格线的交点D，则点D为BC中点，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image132.png" width="27px" height="19px" data-latex="$$">并延长，与半圆相交于点E，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image133.png" width="24px" height="15px" data-latex="$$">并延长，与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image125.png" width="28px" height="18px" data-latex="$$">的延长线相交于点F，则OE为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image134.png" width="45px" height="17px" data-latex="$$">中位线，且<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image135.png" width="65px" height="17px" data-latex="$$">，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image136.png" width="26px" height="16px" data-latex="$$">交<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image131.png" width="27px" height="18px" data-latex="$$">于点G，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image137.png" width="25px" height="17px" data-latex="$$">并延长，与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image126.png" width="27px" height="17px" data-latex="$$">相交于点P，因为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image138.png" width="96px" height="19px" data-latex="$$">，则点P即为所求．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image139.png" width="293px" height="249px"><br>【点睛】本题主要考查复杂作图能力，勾股定理，中位线定理，全等三角形的判定和性质，等腰三角形的性质，平行线的性质等知识点，掌握以上知识点并与已知图形结合是解决本题关键．</span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">19.</span><span data-v-16cfdac0="" class="stem">解不等式组<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image140.png" width="103px" height="50px" data-latex="$$"><br>请结合题意填空，完成本题的解答．<br>(Ⅰ)解不等式①，得_______________；<br>(Ⅱ)解不等式②，得_______________；<br>(Ⅲ)把不等式①和②的解集在数轴上表示出来：<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image141.png" width="356px" height="72px"><br>(Ⅳ)原不等式组的解集为___________．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">(Ⅰ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image142.png" width="43px" height="19px" data-latex="$$">；(Ⅱ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image143.png" width="35px" height="18px" data-latex="$$">；(Ⅲ)把不等式①和②的解集在数轴上表示见解析；(Ⅳ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image144.png" width="67px" height="19px" data-latex="$$">．</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】根据解一元一次不等式组的步骤和不等式组的解集在数轴上的表示方法即可解答．<br>【详解】(Ⅰ)解不等式<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image145.png" width="58px" height="19px" data-latex="$$">，得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image142.png" width="43px" height="19px" data-latex="$$">．<br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image142.png" width="43px" height="19px" data-latex="$$">；<br>(Ⅱ)解不等式<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image146.png" width="73px" height="18px" data-latex="$$">，得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image143.png" width="35px" height="18px" data-latex="$$">．<br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image143.png" width="35px" height="18px" data-latex="$$">；<br>(Ⅲ)在数轴上表示为：<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image147.png" width="348px" height="105px"> ；<br>(Ⅳ)原不等式的解集为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image144.png" width="67px" height="19px" data-latex="$$">．<br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image144.png" width="67px" height="19px" data-latex="$$">．<br>【点睛】本题考查解一元一次不等式组和在数轴上表示不等式组的解集．掌握解一元一次不等式组的步骤是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">20.</span><span data-v-16cfdac0="" class="stem">某社区为了增强居民节约用水的意识，随机调查了部分家庭一年的月均用水量（单位：t）．<br>根据调查结果，绘制出如下的统计图①和图②．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image148.png" width="535px" height="255px"><br>请根据相关信息，解答下列问题：<br>(Ⅰ)本次接受调查的家庭个数为________，图①中m的值为_______；<br>(Ⅱ)求统计的这组月均用水量数据的平均数、众数和中位数．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">(Ⅰ)50，20；(Ⅱ)这组数据的平均数是5.9；众数为6；中位数为6．</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】(Ⅰ)利用用水量为5t的家庭个数除以其所占百分比即可求出本次接受调查的家庭个数；利用用水量为6.5t的家庭个数除以本次接受调查的家庭个数即得出其所占百分比，即得出m的值．<br>(Ⅱ)根据加权平均数的公式，中位数，众数的定义即可求出结果．<br>【详解】(Ⅰ)本次接受调查的家庭个数=<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image149.png" width="67px" height="40px" data-latex="$$">，<br>由题意可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image150.png" width="112px" height="40px" data-latex="$$"> ，<br>解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image151.png" width="49px" height="18px" data-latex="$$">．<br>故答案为50，20．<br>(Ⅱ)观察条形统计图，<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image152.png" width="308px" height="40px" data-latex="$$">，<br>∴这组数据的平均数是5.9．<br>∵在这组数据中，6出现了16次，出现的次数最多，<br>∴这组数据的众数为6．<br>∵将这组数据按从小到大的顺序排列，其中处于中间的两个数都是6，<br>即有<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image153.png" width="60px" height="40px" data-latex="$$">，<br>∴这组数据的中位数为6．<br>【点睛】本题考查条形统计图与扇形统计图相关联，加权平均数，中位数以及众数．从条形统计图与扇形统计图中找到必要的数据和信息是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">21.</span><span data-v-16cfdac0="" class="stem">已知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image59.png" width="50px" height="18px" data-latex="$$">内接于<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image154.png" width="183px" height="20px" data-latex="$$">，点D是<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image155.png" width="29px" height="20px" data-latex="$$">上一点．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image156.png" width="378px" height="199px"><br>(Ⅰ)如图①，若<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image157.png" width="27px" height="17px" data-latex="$$">为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image155.png" width="29px" height="20px" data-latex="$$">的直径，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image111.png" width="28px" height="19px" data-latex="$$">，求<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image158.png" width="48px" height="19px" data-latex="$$">和<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image159.png" width="49px" height="18px" data-latex="$$">的大小；<br>(Ⅱ)如图②，若<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image111.png" width="28px" height="19px" data-latex="$$">//<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image160.png" width="25px" height="17px" data-latex="$$">，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image62.png" width="27px" height="17px" data-latex="$$">，过点D作<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image155.png" width="29px" height="20px" data-latex="$$">的切线，与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image161.png" width="27px" height="19px" data-latex="$$">的延长线交于点E，求<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image162.png" width="27px" height="17px" data-latex="$$">的大小．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">(Ⅰ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image163.png" width="88px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image164.png" width="88px" height="18px" data-latex="$$">；(Ⅱ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image165.png" width="65px" height="18px" data-latex="$$">．</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】(Ⅰ)由圆周角定理的推论可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image166.png" width="86px" height="19px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image167.png" width="148px" height="18px" data-latex="$$">，即可推出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image168.png" width="187px" height="18px" data-latex="$$">；由等腰三角形的性质结合三角形内角和定理可求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image169.png" width="145px" height="18px" data-latex="$$">，从而求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image170.png" width="206px" height="18px" data-latex="$$">．<br>(Ⅱ)连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image132.png" width="27px" height="19px" data-latex="$$">，由平行线的性质可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image171.png" width="148px" height="18px" data-latex="$$">．由圆内接四边形的性质可求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image172.png" width="198px" height="18px" data-latex="$$">．再由三角形内角和定理可求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image173.png" width="88px" height="18px" data-latex="$$">．从而由圆周角定理求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image174.png" width="159px" height="18px" data-latex="$$">．由切线的性质可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image175.png" width="88px" height="18px" data-latex="$$">．即可求出<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image176.png" width="165px" height="18px" data-latex="$$">．<br>【详解】(Ⅰ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image157.png" width="27px" height="17px" data-latex="$$">为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image155.png" width="29px" height="20px" data-latex="$$">的直径，<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image177.png" width="172px" height="181px"><br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image166.png" width="86px" height="19px" data-latex="$$">．<br>∵在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image155.png" width="29px" height="20px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image167.png" width="148px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image168.png" width="187px" height="18px" data-latex="$$">；<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image178.png" width="161px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image179.png" width="272px" height="41px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image170.png" width="206px" height="18px" data-latex="$$">．<br>(Ⅱ)如图，连接<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image132.png" width="27px" height="19px" data-latex="$$">．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image180.png" width="217px" height="202px"><br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image181.png" width="63px" height="21px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image171.png" width="148px" height="18px" data-latex="$$">．<br>∵四边形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image105.png" width="48px" height="18px" data-latex="$$">是圆内接四边形，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image182.png" width="87px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image172.png" width="198px" height="18px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image183.png" width="252px" height="18px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image174.png" width="159px" height="18px" data-latex="$$">．<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image184.png" width="27px" height="17px" data-latex="$$">是<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image155.png" width="29px" height="20px" data-latex="$$">的切线，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image185.png" width="68px" height="19px" data-latex="$$">，即<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image175.png" width="88px" height="18px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image176.png" width="165px" height="18px" data-latex="$$">．<br>【点睛】本题为圆的综合题．考查圆周角定理及其推论，等腰三角形的性质，三角形内角和定理，平行线的性质，圆的内接四边形的性质以及切线的性质．利用数形结合的思想以及连接常用的辅助线是解答本题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">22.</span><span data-v-16cfdac0="" class="stem">如图，一艘货船在灯塔C的正南方向，距离灯塔257海里的A处遇险，发出求救信号．一艘救生船位于灯塔C的南偏东<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image186.png" width="26px" height="18px" data-latex="$$">方向上，同时位于A处的北偏东<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image187.png" width="26px" height="19px" data-latex="$$">方向上的B处，救生船接到求救信号后，立即前往救援．求<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image126.png" width="27px" height="17px" data-latex="$$">的长（结果取整数）．参考数据：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image188.png" width="93px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image189.png" width="24px" height="24px" data-latex="$$">取1.73．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image190.png" width="212px" height="298px"></span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0=""><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image126.png" width="27px" height="17px" data-latex="$$">的长约为168海里．</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】如图，过点B作BH⊥CA，垂足为H,解直角三角形即可<br>【详解】如图，过点B作BH⊥CA，垂足为H．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image191.png" width="189px" height="279px"><br>根据题意，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image192.png" width="237px" height="20px" data-latex="$$">．<br>∵在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image193.png" width="69px" height="19px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image194.png" width="116px" height="40px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image195.png" width="118px" height="40px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image196.png" width="322px" height="41px" data-latex="$$">．<br>∵在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image197.png" width="63px" height="19px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image198.png" width="116px" height="40px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image199.png" width="156px" height="45px" data-latex="$$">．<br>又<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image200.png" width="103px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image201.png" width="131px" height="45px" data-latex="$$">．<br>可得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image202.png" width="130px" height="43px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image203.png" width="293px" height="43px" data-latex="$$">．<br>答：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image126.png" width="27px" height="17px" data-latex="$$">的长约为168海里．<br>【点睛】本题考查了解直角三角形的应用，构造高线构造出直角三角形，并灵活解之是解题的关键．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">23.</span><span data-v-16cfdac0="" class="stem">在“看图说故事”活动中，某学习小组结合图象设计了一个问题情境．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image204.png" width="406px" height="164px"><br>已知学校、书店、陈列馆依次在同一条直线上，书店离学校<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image205.png" width="40px" height="18px" data-latex="$$">，陈列馆离学校<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image206.png" width="40px" height="19px" data-latex="$$">．李华从学校出发，匀速骑行<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image207.png" width="32px" height="19px" data-latex="$$">到达书店；在书店停留<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image208.png" width="32px" height="18px" data-latex="$$">后，匀速骑行<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image209.png" width="33px" height="18px" data-latex="$$">到达陈列馆；在陈列馆参观学习一段时间，然后回学校；回学校途中，匀速骑行<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image209.png" width="33px" height="18px" data-latex="$$">后减速，继续匀速骑行回到学校．给出的图象反映了这个过程中李华离学校的距离<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image210.png" width="30px" height="20px" data-latex="$$">与离开学校的时间<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image211.png" width="21px" height="18px" data-latex="$$">之间的对应关系．<br>请根据相关信息，解答下列问题：<br>(Ⅰ)填表<br><table><tbody><tr><td>离开学校的时间/<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image212.png" width="12px" height="17px" data-latex="$$"></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image213.png" width="24px" height="19px" data-latex="$$"></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image214.png" width="24px" height="19px" data-latex="$$"></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image215.png" width="24px" height="19px" data-latex="$$"></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image216.png" width="9px" height="17px" data-latex="$$"></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image217.png" width="12px" height="18px" data-latex="$$"></td></tr><tr><td>离学校的距离/<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image218.png" width="25px" height="17px" data-latex="$$"></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image219.png" width="12px" height="17px" data-latex="$$"></td><td></td><td></td><td><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image220.png" width="19px" height="17px" data-latex="$$"></td><td></td></tr></tbody></table><br>(Ⅱ)填空：<br>①书店到陈列馆的距离为________<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image218.png" width="25px" height="17px" data-latex="$$">；<br>②李华在陈列馆参观学的时间为_______h；<br>③李华从陈列馆回学校途中，减速前的骑行速度为______<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image221.png" width="38px" height="18px" data-latex="$$">；<br>④当李华离学校的距离为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image222.png" width="33px" height="17px" data-latex="$$">时，他离开学校的时间为_______h．<br>(Ⅲ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image223.png" width="70px" height="19px" data-latex="$$">时，请直接写出y关于x的函数解析式．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">(Ⅰ)10，12，20；(Ⅱ)①8；②3；③28；④<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image224.png" width="14px" height="41px" data-latex="$$">或<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image225.png" width="22px" height="41px" data-latex="$$">；(Ⅲ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image227.png" width="54px" height="20px" data-latex="$$">；当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image228.png" width="70px" height="18px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image229.png" width="43px" height="22px" data-latex="$$">；当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image230.png" width="60px" height="17px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image231.png" width="75px" height="20px" data-latex="$$">．</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】(Ⅰ)根据函数图象，利用待定系数法，分段写出函数解析式，根据表格中x，代入相应的解析式，得到y；<br>(Ⅱ)①根据图象进行分析即可；<br>②根据图象进行分析即可；<br>③根据<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image232.png" width="72px" height="19px" data-latex="$$">时的函数解析式可求；<br>④分<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">和<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image233.png" width="70px" height="19px" data-latex="$$">两种情况讨论，将距离为4km代入相应的解析式求出时间x；<br>(Ⅲ)根据函数图象，利用待定系数法，分段写出函数解析式即可．<br>【详解】对函数图象进行分析：<br>①当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image234.png" width="40px" height="20px" data-latex="$$">，由图象可知，当x=0.6时，y=12，<br>则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image235.png" width="57px" height="19px" data-latex="$$">，解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image236.png" width="45px" height="18px" data-latex="$$"><br>∴当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image227.png" width="54px" height="20px" data-latex="$$"><br>②由图象可知，当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image228.png" width="70px" height="18px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image229.png" width="43px" height="22px" data-latex="$$"><br>③当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image230.png" width="60px" height="17px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image237.png" width="60px" height="20px" data-latex="$$">，由图象可知，当x=1时，y=12；当x=1.5时，y=20，<br>则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image238.png" width="95px" height="48px" data-latex="$$"> ，解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image239.png" width="53px" height="48px" data-latex="$$"><br>∴当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image230.png" width="60px" height="17px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image231.png" width="75px" height="20px" data-latex="$$"><br>④由图象可知，当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image240.png" width="83px" height="19px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image241.png" width="47px" height="20px" data-latex="$$"><br>⑤当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image232.png" width="72px" height="19px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image237.png" width="60px" height="20px" data-latex="$$">，由图象可知，当x=4.5时，y=20；当x=5时，y=6，<br>则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image242.png" width="96px" height="36pt" data-latex="$$">，解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image243.png" width="63px" height="48px" data-latex="$$"><br>∴当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image232.png" width="72px" height="19px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image244.png" width="100px" height="20px" data-latex="$$"><br>⑥当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image233.png" width="70px" height="19px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image237.png" width="60px" height="20px" data-latex="$$">，由图象可知，当x=5时，y=6；当x=5.5时，y=0，<br>则<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image245.png" width="86px" height="48px" data-latex="$$">，解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image246.png" width="63px" height="48px" data-latex="$$"><br>∴当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image233.png" width="70px" height="19px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image247.png" width="93px" height="20px" data-latex="$$"><br>(Ⅰ)∵当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">时，函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image227.png" width="54px" height="20px" data-latex="$$"><br>∴当x=0.5时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image248.png" width="108px" height="20px" data-latex="$$">．故第一空为10．<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image228.png" width="70px" height="18px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image229.png" width="43px" height="22px" data-latex="$$">．故第二空为12．<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image249.png" width="83px" height="19px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image241.png" width="47px" height="20px" data-latex="$$">．故第二空为20．<br>(Ⅱ)①李华从学校出发，匀速骑行<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image207.png" width="32px" height="19px" data-latex="$$">到达书店；在书店停留<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image208.png" width="32px" height="18px" data-latex="$$">后，匀速骑行<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image209.png" width="33px" height="18px" data-latex="$$">到达陈列馆．由图象可知书店到陈列馆的距离<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image250.png" width="67px" height="19px" data-latex="$$">；<br>②李华在陈列馆参观学习一段时间，然后回学校．由图象可知李华在陈列馆参观学的时间<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image251.png" width="80px" height="19px" data-latex="$$">；<br>③当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image232.png" width="72px" height="19px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image244.png" width="100px" height="20px" data-latex="$$">，所以李华从陈列馆回学校途中，减速前的骑行速度为28；<br>④当李华离学校的距离为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image222.png" width="33px" height="17px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">或<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image233.png" width="70px" height="19px" data-latex="$$"><br>由上对图象的分析可知：<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image227.png" width="54px" height="20px" data-latex="$$"><br>令<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image252.png" width="38px" height="22px" data-latex="$$">，解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image253.png" width="38px" height="40px" data-latex="$$"><br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image233.png" width="70px" height="19px" data-latex="$$">时，设函数关系式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image247.png" width="93px" height="20px" data-latex="$$"><br>令<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image252.png" width="38px" height="22px" data-latex="$$">，解得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image254.png" width="47px" height="42px" data-latex="$$"><br>∴当李华离学校的距离为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image222.png" width="33px" height="17px" data-latex="$$">时，他离开学校的时间为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image224.png" width="14px" height="41px" data-latex="$$">或<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image225.png" width="22px" height="41px" data-latex="$$">．<br>(Ⅲ)由上对图象的分析可知：<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image226.png" width="73px" height="18px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image227.png" width="54px" height="20px" data-latex="$$">；<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image228.png" width="70px" height="18px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image229.png" width="43px" height="22px" data-latex="$$">；<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image230.png" width="60px" height="17px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image231.png" width="75px" height="20px" data-latex="$$">．<br>【点睛】本题考查函数的图象与实际问题．解题的关键在于读懂函数的图象，分段进行分析．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">24.</span><span data-v-16cfdac0="" class="stem">在平面直角坐标系中，O为原点，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">是等腰直角三角形，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image256.png" width="150px" height="20px" data-latex="$$">，顶点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image257.png" width="52px" height="27px" data-latex="$$">，点B在第一象限，矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image258.png" width="49px" height="18px" data-latex="$$">的顶点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image259.png" width="70px" height="45px" data-latex="$$">，点C在y轴的正半轴上，点D在第二象限，射线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image260.png" width="28px" height="19px" data-latex="$$">经过点B．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image261.png" width="712px" height="217px"><br>(Ⅰ)如图①，求点B的坐标；<br>(Ⅱ)将矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image258.png" width="49px" height="18px" data-latex="$$">沿x轴向右平移，得到矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">，点O，C，D，E的对应点分别为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image263.png" width="20px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image264.png" width="20px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image265.png" width="20px" height="15px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image266.png" width="20px" height="17px" data-latex="$$">，设<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image267.png" width="53px" height="17px" data-latex="$$">，矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">重叠部分的面积为S．<br>①如图②，当点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image266.png" width="20px" height="17px" data-latex="$$">在x轴正半轴上，且矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">重叠部分为四边形时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image268.png" width="35px" height="16px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image269.png" width="27px" height="19px" data-latex="$$">相交于点F，试用含有t的式子表示S，并直接写出t的取值范围；<br>②当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image270.png" width="62px" height="41px" data-latex="$$">时，求S的取值范围（直接写出结果即可）．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">(Ⅰ)点B的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image271.png" width="39px" height="26px" data-latex="$$">；(Ⅱ)①<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image272.png" width="130px" height="41px" data-latex="$$">， t的取值范围是<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image273.png" width="66px" height="41px" data-latex="$$">；②<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image274.png" width="81px" height="41px" data-latex="$$">．</span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】(I)过点B作<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image275.png" width="67px" height="19px" data-latex="$$">，垂足为H，由等腰三角形的“三线合一”性质得到<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image276.png" width="102px" height="41px" data-latex="$$">，再由∠BOH=45°得到△OBH为等腰直角三角形，进而<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image277.png" width="93px" height="18px" data-latex="$$">，由此求得B点坐标；<br>(II)①由平移知，四边形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">是矩形，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image278.png" width="197px" height="41px" data-latex="$$">，进而得到<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image279.png" width="117px" height="41px" data-latex="$$">，再由重叠部分面积<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image280.png" width="114px" height="24px" data-latex="$$">即可求解；<br>②画出不同情况下重叠部分的图形，分<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image281.png" width="62px" height="41px" data-latex="$$">和<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image282.png" width="62px" height="41px" data-latex="$$">两种情况，将重叠部分的面积表示成关于t的二次函数，再结合二次函数的最值问题求解．<br>【详解】解：(I)如图，过点B作<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image275.png" width="67px" height="19px" data-latex="$$">，垂足为H．<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image283.png" width="381px" height="181px"><br>由点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image257.png" width="52px" height="27px" data-latex="$$">，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image284.png" width="48px" height="19px" data-latex="$$">．<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image285.png" width="150px" height="20px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image276.png" width="102px" height="41px" data-latex="$$">．<br>又∠BOH=45°，<br>∴△OBH为等腰直角三角形，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image277.png" width="93px" height="18px" data-latex="$$">．<br>∴点B的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image271.png" width="39px" height="26px" data-latex="$$">．<br>(II)①由点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image259.png" width="70px" height="45px" data-latex="$$">，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image286.png" width="53px" height="41px" data-latex="$$">．由平移知，四边形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">是矩形，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image278.png" width="197px" height="41px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image287.png" width="162px" height="41px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image288.png" width="90px" height="18px" data-latex="$$">．<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image289.png" width="55px" height="17px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image290.png" width="85px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image291.png" width="146px" height="18px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image292.png" width="187px" height="18px" data-latex="$$"><br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image293.png" width="116px" height="18px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image279.png" width="117px" height="41px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image294.png" width="207px" height="48px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image295.png" width="265px" height="48px" data-latex="$$">．<br>整理后得到：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image272.png" width="130px" height="41px" data-latex="$$">．<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image296.png" width="19px" height="20px" data-latex="$$">与A重合时，矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">重叠部分刚开始为四边形，如下图(1)所示：此时<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image297.png" width="75px" height="18px" data-latex="$$">，<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image298.png" width="383px" height="212px"><br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image299.png" width="20px" height="20px" data-latex="$$">与B重合时，矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">重叠部分为三角形，接下来往右平移时重叠部分一直为三角形直到<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image300.png" width="18px" height="20px" data-latex="$$">与A点重合，如下图(2)所示：<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image301.png" width="437px" height="199px"><br>此时<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image302.png" width="177px" height="41px" data-latex="$$">，<br>∴t的取值范围是<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image273.png" width="66px" height="41px" data-latex="$$">，<br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image272.png" width="130px" height="41px" data-latex="$$">，其中：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image273.png" width="66px" height="41px" data-latex="$$">；<br>②当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image281.png" width="62px" height="41px" data-latex="$$">时，矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">重叠部分的面积如下图3所示：<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image303.png" width="396px" height="207px"><br>此时<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image304.png" width="75px" height="18px" data-latex="$$">，∠BAO=45°，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image305.png" width="54px" height="18px" data-latex="$$">为等腰直角三角形，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image306.png" width="116px" height="18px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image307.png" width="292px" height="41px" data-latex="$$">，<br>∴重叠部分面积<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image308.png" width="337px" height="41px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image309.png" width="12px" height="17px" data-latex="$$">是关于<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image310.png" width="9px" height="15px" data-latex="$$">的二次函数，且对称轴为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image311.png" width="33px" height="19px" data-latex="$$">，且开口向下，<br>故自变量离对称轴越远，其对应的函数值越小，<br>故将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image312.png" width="32px" height="37px" data-latex="$$">代入，<br>得到最大值<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image313.png" width="192px" height="31.15pt" data-latex="$$">，<br>将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image314.png" width="35px" height="40px" data-latex="$$">代入，<br>得到最小值<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image315.png" width="192px" height="31.15pt" data-latex="$$">，<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image282.png" width="62px" height="41px" data-latex="$$">时，矩形<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image262.png" width="63px" height="19px" data-latex="$$">与<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image255.png" width="43px" height="18px" data-latex="$$">重叠部分的面积如下图4所示：<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image316.png" width="378px" height="216px"><br>此时<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image317.png" width="197px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image318.png" width="198px" height="41px" data-latex="$$"><br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image305.png" width="54px" height="18px" data-latex="$$">和<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image319.png" width="57px" height="18px" data-latex="$$">均为等腰直角三角形，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image307.png" width="292px" height="41px" data-latex="$$">，<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image320.png" width="312px" height="41px" data-latex="$$">，<br>∴重叠部分面积<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image321.png" width="510px" height="41px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image309.png" width="12px" height="17px" data-latex="$$">是关于<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image310.png" width="9px" height="15px" data-latex="$$">的二次函数，且对称轴为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image322.png" width="42px" height="41px" data-latex="$$">，且开口向下，<br>故自变量离对称轴越远，其对应的函数值越小，故将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image322.png" width="42px" height="41px" data-latex="$$">代入，得到最大值<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image323.png" width="196px" height="41px" data-latex="$$">，<br>将<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image324.png" width="35px" height="41px" data-latex="$$">代入，<br>得到最小值<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image325.png" width="185px" height="41px" data-latex="$$">，<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image326.png" width="55px" height="41px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image327.png" width="54px" height="41px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image309.png" width="12px" height="17px" data-latex="$$">的最小值为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image328.png" width="22px" height="40px" data-latex="$$">，最大值为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image329.png" width="22px" height="40px" data-latex="$$">，<br>故答案为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image330.png" width="82px" height="41px" data-latex="$$">．<br>【点睛】本题考查了矩形的性质、坐标与图形性质、平移的性质、直角三角形的性质、二次函数的最值等问题，属于综合题，需要画出动点不同状态下的图形求解，本题难度较大，需要分类讨论．<br></span></li></ul></div></div><!----><div data-v-16cfdac0="" class="handle-stem" style="display: none;"><div data-v-16cfdac0="" class="divider" style="width: 100%; height: 1px; background-color: rgb(220, 223, 230); margin: 5px 0px;"></div><div data-v-16cfdac0="" class="btns" style="display: flex; justify-content: flex-end;"><button data-v-16cfdac0="" type="button" class="el-button el-button--primary el-button--mini" style="margin-left: 10px;"><!----><i class="el-icon-edit"></i><span>编辑</span></button><button data-v-16cfdac0="" type="button" class="el-button el-button--danger el-button--mini"><!----><i class="el-icon-delete"></i><span>删除</span></button></div></div>

<div data-v-16cfdac0=""><div data-v-16cfdac0="" class="stem-wraper"><span data-v-16cfdac0="" class="topic-number">25.</span><span data-v-16cfdac0="" class="stem">已知抛物线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image331.png" width="111px" height="24px" data-latex="$$">（a，c为常数，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image86.png" width="37px" height="19px" data-latex="$$">）经过点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image332.png" width="60px" height="27px" data-latex="$$">，顶点为D．<br>(Ⅰ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image333.png" width="30px" height="17px" data-latex="$$">时，求该抛物线的顶点坐标；<br>(Ⅱ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image334.png" width="37px" height="18px" data-latex="$$">时，点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image335.png" width="73px" height="26px" data-latex="$$">，若<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image336.png" width="96px" height="16.65pt" data-latex="$$">，求该抛物线的解析式；<br>(Ⅲ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image337.png" width="40px" height="17px" data-latex="$$">时，点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image338.png" width="73px" height="26px" data-latex="$$">，过点C作直线l平行于x轴，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image339.png" width="61px" height="27px" data-latex="$$">是x轴上的动点，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image340.png" width="88px" height="26px" data-latex="$$">是直线l上的动点．当a为何值时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image341.png" width="70px" height="17px" data-latex="$$">的最小值为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image342.png" width="40px" height="24px" data-latex="$$">，并求此时点M，N的坐标．</span></div><!----><div data-v-16cfdac0="" class="topic-analysis"><ul data-v-16cfdac0="" class="topic-analysis-items"><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【答案】</span><span data-v-16cfdac0="">(Ⅰ)抛物线的顶点坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image343.png" width="43px" height="21px" data-latex="$$">；(Ⅱ)<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image344.png" width="98px" height="42px" data-latex="$$">或<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image345.png" width="109px" height="41px" data-latex="$$">；(Ⅲ)点M的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image346.png" width="56px" height="45px" data-latex="$$">，点N的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image347.png" width="60px" height="45px" data-latex="$$"></span></li><li data-v-16cfdac0="" class="topic-analysis-content"><span data-v-16cfdac0="" class="analysis-prefix">【解析】</span><span data-v-16cfdac0="">【分析】(Ⅰ)结合题意，通过列一元一次方程并求解，即可得到抛物线的解析式，将解析式化为顶点式，即可得到答案<br>(Ⅱ)根据题意，得抛物线的解析式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image348.png" width="108px" height="24px" data-latex="$$">；根据抛物线对称轴的性质，计算得点D的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image349.png" width="63px" height="20px" data-latex="$$">；过点D作<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image350.png" width="55px" height="20px" data-latex="$$">轴于点G，根据勾股定理和一元二次方程的性质，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image351.png" width="43px" height="41px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image352.png" width="45px" height="41px" data-latex="$$">，从而得到答案；<br>(Ⅲ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image337.png" width="40px" height="17px" data-latex="$$">时，将点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image353.png" width="78px" height="21px" data-latex="$$">向左平移3个单位长度，向上平移1个单位长度得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image354.png" width="73px" height="21px" data-latex="$$">；作点F关于x轴的对称点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image355.png" width="20px" height="19px" data-latex="$$">，当满足条件的点M落在线段<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image356.png" width="32px" height="17px" data-latex="$$">上时，根据两点之间线段最短的性质，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image341.png" width="70px" height="17px" data-latex="$$">最小，结合题意，根据勾股定理和一元二次方程性质，得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image357.png" width="55px" height="40px" data-latex="$$">，从而得直线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image356.png" width="32px" height="17px" data-latex="$$">的解析式，通过计算即可得到答案．<br>【详解】(Ⅰ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image333.png" width="30px" height="17px" data-latex="$$">时，抛物线的解析式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image358.png" width="97px" height="24px" data-latex="$$">．<br>∵抛物线经过点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image359.png" width="55px" height="20px" data-latex="$$"><br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image360.png" width="89px" height="18px" data-latex="$$"><br>解得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image361.png" width="43px" height="19px" data-latex="$$"><br>∴抛物线的解析式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image362.png" width="96px" height="22.05pt" data-latex="$$"><br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image363.png" width="176px" height="24px" data-latex="$$"><br>∴抛物线的顶点坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image343.png" width="43px" height="21px" data-latex="$$">；<br>(Ⅱ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image334.png" width="37px" height="18px" data-latex="$$">时，由抛物线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image331.png" width="111px" height="24px" data-latex="$$">经过点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image359.png" width="55px" height="20px" data-latex="$$">，可知<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image361.png" width="43px" height="19px" data-latex="$$"><br>∴抛物线的解析式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image348.png" width="108px" height="24px" data-latex="$$"><br>∴抛物线的对称轴为：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image32.png" width="35px" height="19px" data-latex="$$"><br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image32.png" width="35px" height="19px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image364.png" width="66px" height="21px" data-latex="$$"><br>∴抛物线的顶点D的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image349.png" width="63px" height="20px" data-latex="$$">；<br>过点D作<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image350.png" width="55px" height="20px" data-latex="$$">轴于点G<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image365.png" width="364px" height="313px"><br>在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image366.png" width="69px" height="18px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image367.png" width="50px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image368.png" width="192px" height="21px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image369.png" width="218px" height="25px" data-latex="$$"><br>在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image370.png" width="63px" height="18px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image367.png" width="50px" height="18px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image371.png" width="148px" height="21px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image372.png" width="176px" height="21px" data-latex="$$">．<br>∵<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image336.png" width="96px" height="16.65pt" data-latex="$$">，即<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image373.png" width="87px" height="21px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image374.png" width="156px" height="29px" data-latex="$$"><br>解得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image351.png" width="43px" height="41px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image352.png" width="45px" height="41px" data-latex="$$"><br>∴抛物线的解析式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image344.png" width="98px" height="42px" data-latex="$$">或<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image345.png" width="109px" height="41px" data-latex="$$">．<br>(Ⅲ)当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image337.png" width="40px" height="17px" data-latex="$$">时，将点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image353.png" width="78px" height="21px" data-latex="$$">向左平移3个单位长度，向上平移1个单位长度得<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image354.png" width="73px" height="21px" data-latex="$$">．<br>作点F关于x轴的对称点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image355.png" width="20px" height="19px" data-latex="$$">，得点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image355.png" width="20px" height="19px" data-latex="$$">的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image375.png" width="57px" height="21px" data-latex="$$"><br>当满足条件的点M落在线段<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image356.png" width="32px" height="17px" data-latex="$$">上时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image341.png" width="70px" height="17px" data-latex="$$">最小，<br>此时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image376.png" width="166px" height="25px" data-latex="$$">．<br>过点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image265.png" width="20px" height="15px" data-latex="$$">作<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image377.png" width="55px" height="21px" data-latex="$$">轴于点H<br><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image378.png" width="320px" height="255px"><br>在<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image379.png" width="68px" height="18px" data-latex="$$">中，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image380.png" width="58px" height="17px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image381.png" width="174px" height="21px" data-latex="$$">，<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image382.png" width="240px" height="25px" data-latex="$$">．<br>又<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image383.png" width="73px" height="21px" data-latex="$$">，即<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image384.png" width="114px" height="25px" data-latex="$$">．<br>解得：<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image357.png" width="55px" height="40px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image385.png" width="45px" height="41px" data-latex="$$">（舍）<br>∴点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image355.png" width="20px" height="19px" data-latex="$$"><img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image115.png" width="14px" height="18px" data-latex="$$">坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image386.png" width="55px" height="45px" data-latex="$$">，点<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image265.png" width="20px" height="15px" data-latex="$$">的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image387.png" width="53px" height="45px" data-latex="$$">．<br>∴直线<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image356.png" width="32px" height="17px" data-latex="$$">的解析式为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image388.png" width="80px" height="41px" data-latex="$$">．<br>当<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image389.png" width="35px" height="20px" data-latex="$$">时，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image390.png" width="50px" height="40px" data-latex="$$">．<br>∴<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image391.png" width="54px" height="41px" data-latex="$$">，<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image392.png" width="69px" height="41px" data-latex="$$"><br>∴点M的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image346.png" width="56px" height="45px" data-latex="$$">，点N的坐标为<img src="http://zxhx-1302712961.cos.ap-shanghai.myqcloud.com/zyk/uploadfiles/wording/6180d27ea5c2e2943b92acdd/image347.png" width="60px" height="45px" data-latex="$$">．<br>【点睛】本题考查了二次函数、一元一次方程、勾股定理、一元二次方程、平移、两点之间线段最短的知识；解题的关键是熟练掌握二次函数、勾股定理、一元二次方程、平移的性质，从而完成求解．</span></li></ul></div></div><!----><div 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