数学（天津专用）-2025届新高三开学摸底考试卷.zip

2402_86598838数学（天津专用）-2025届新高三开学摸底考试卷.zip 1.48MB

资源文件列表:

数学（天津专用）-2025届新高三开学摸底考试卷.zip 大约有4个文件

数学（天津专用）-2025届新高三开学摸底考试卷/
数学（天津专用）-2025届新高三开学摸底考试卷/数学（天津专用）（答题卡）.docx 60.77KB
数学（天津专用）-2025届新高三开学摸底考试卷/数学（天津专用）（考试版）.docx 388.08KB
数学（天津专用）-2025届新高三开学摸底考试卷/数学（天津专用）（解析版）.docx 1.26MB

资源介绍:

数学（天津专用）-2025届新高三开学摸底考试卷.zip

<link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89649381/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89649381/bg1.jpg"/><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div></div><div class="c x2 y5 w2 h4"><div class="t m0 x0 h5 y6 ff2 fs1 fc1 sc0 ls0 ws0">1</div></div><div class="t m0 x3 h6 y7 ff2 fs2 fc1 sc0 ls0 ws0">2025</div><div class="t m0 x4 h7 y8 ff3 fs2 fc1 sc0 ls0 ws0">届新高三开学摸底考试卷（天津专用）</div><div class="t m0 x5 h7 y9 ff3 fs2 fc1 sc0 ls0 ws0">数学</div><div class="t m0 x6 h6 ya ff2 fs2 fc1 sc0 ls0 ws0">•</div><div class="t m0 x7 h7 y9 ff3 fs2 fc1 sc0 ls0 ws0">全解全析</div><div class="t m0 x8 h8 yb ff4 fs3 fc1 sc0 ls0 ws0">（考试时间：</div><div class="t m0 x9 h9 yc ff2 fs3 fc1 sc0 ls0 ws0">120</div><div class="t m0 xa h8 yb ff4 fs3 fc1 sc0 ls0 ws0">分钟</div><div class="t m0 xb h9 yc ff2 fs3 fc1 sc0 ls0 ws0"> </div><div class="t m0 xc h8 yb ff4 fs3 fc1 sc0 ls0 ws0">试卷满分：</div><div class="t m0 xd h9 yc ff2 fs3 fc1 sc0 ls0 ws0">150</div><div class="t m0 xe h8 yb ff4 fs3 fc1 sc0 ls0 ws0">分）</div><div class="t m0 x1 ha yd ff5 fs3 fc1 sc1 ls0 ws0">注意<span class="_ _0"></span>事项<span class="_ _0"></span>：</div><div class="t m0 xf h9 ye ff2 fs3 fc1 sc0 ls0 ws0">1</div><div class="t m0 x10 ha yf ff3 fs3 fc1 sc0 ls0 ws0">．答<span class="_ _0"></span>卷前<span class="_ _0"></span>，考生<span class="_ _0"></span>务必<span class="_ _0"></span>将自<span class="_ _0"></span>己的姓<span class="_ _0"></span>名、<span class="_ _0"></span>准考证<span class="_ _0"></span>号等<span class="_ _0"></span>填写<span class="_ _0"></span>在答题<span class="_ _0"></span>卡和<span class="_ _0"></span>试卷指<span class="_ _0"></span>定位<span class="_ _0"></span>置上。</div><div class="t m0 xf h9 y10 ff2 fs3 fc1 sc0 ls0 ws0">2</div><div class="t m0 x10 ha y11 ff3 fs3 fc1 sc0 ls0 ws0">．回<span class="_ _0"></span>答选<span class="_ _0"></span>择题<span class="_ _0"></span>时，<span class="_ _0"></span>选出<span class="_ _0"></span>每小<span class="_ _0"></span>题答<span class="_ _0"></span>案后，<span class="_ _0"></span>用铅<span class="_ _0"></span>笔把<span class="_ _0"></span>答题<span class="_ _0"></span>卡上<span class="_ _0"></span>对应<span class="_ _0"></span>题目<span class="_ _0"></span>的答案<span class="_ _0"></span>标号<span class="_ _0"></span>涂黑<span class="_ _0"></span>。如<span class="_ _0"></span>需改<span class="_ _0"></span>动，<span class="_ _0"></span>用</div><div class="t m0 xf ha y12 ff3 fs3 fc1 sc0 ls0 ws0">橡皮<span class="_ _0"></span>擦干<span class="_ _0"></span>净后，<span class="_ _0"></span>再选<span class="_ _0"></span>涂其<span class="_ _0"></span>他答案<span class="_ _0"></span>标号<span class="_ _0"></span>。回答<span class="_ _0"></span>非选<span class="_ _0"></span>择题<span class="_ _0"></span>时，将<span class="_ _0"></span>答案<span class="_ _0"></span>写在答<span class="_ _0"></span>卡上<span class="_ _0"></span>。写在<span class="_ _0"></span>本试<span class="_ _0"></span>卷上<span class="_ _0"></span>无效。</div><div class="t m0 xf h9 y13 ff2 fs3 fc1 sc0 ls0 ws0">3</div><div class="t m0 x10 ha y14 ff3 fs3 fc1 sc0 ls0 ws0">．考<span class="_ _0"></span>试结<span class="_ _0"></span>束后，<span class="_ _0"></span>将本<span class="_ _0"></span>试卷<span class="_ _0"></span>和答题<span class="_ _0"></span>卡一<span class="_ _0"></span>并交回<span class="_ _0"></span>。</div><div class="t m0 x11 hb y15 ff6 fs4 fc1 sc1 ls0 ws0">第一部分（选<span class="_ _0"></span>择题<span class="ff7 sc0"> <span class="_ _1"> </span></span>共<span class="_ _2"> </span><span class="ff7 sc0">45<span class="_"> </span></span>分）</div><div class="t m0 x1 ha y16 ff6 fs3 fc1 sc1 ls0 ws0">一、选择题<span class="_ _3"></span>：<span class="_ _3"></span>本题共</div><div class="t m0 x12 hc y17 ff7 fs3 fc1 sc0 ls0 ws0">9</div><div class="t m0 x13 ha y16 ff6 fs3 fc1 sc1 ls0 ws0">小题，每小题</div><div class="t m0 x14 hc y17 ff7 fs3 fc1 sc0 ls0 ws0">5</div><div class="t m0 x15 ha y16 ff6 fs3 fc1 sc1 ls0 ws0">分，共</div><div class="t m0 x16 hc y17 ff7 fs3 fc1 sc0 ls0 ws0">45</div><div class="t m0 x17 ha y16 ff6 fs3 fc1 sc1 ls0 ws0">分。在每小题给<span class="_ _0"></span>出的四个选项中，选出符<span class="_ _0"></span>合题目要求的一</div><div class="t m0 x1 ha y18 ff6 fs3 fc1 sc1 ls0 ws0">项。</div><div class="t m0 x1 ha y19 ff2 fs3 fc1 sc0 ls0 ws0">1<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）已知集合</span></div><div class="c x18 y1a w3 hd"><div class="t m1 x19 he y1b ff2 fs5 fc1 sc0 ls0 ws0">4</div><div class="t m1 x1a he y1c ff2 fs5 fc1 sc0 ls0 ws0">{<span class="_ _5"> </span>|<span class="_ _6"> </span>0<span class="_ _7"></span>}</div><div class="t m1 x19 he y1d ff2 fs5 fc1 sc0 ls0 ws0">1</div><div class="t m1 x1b he y1b ff9 fs5 fc1 sc0 ls0 ws0">x</div><div class="t m1 x1c he y1c ff9 fs5 fc1 sc0 ls0 ws0">A<span class="_ _8"> </span>x</div><div class="t m1 x1d he y1d ff9 fs5 fc1 sc0 ls0 ws0">x</div><div class="t m1 x1e hf y1b ffa fs5 fc1 sc0 ls0 ws0">-</div><div class="t m1 x1f hf y1c ffa fs5 fc1 sc0 ls0 ws0">=</div><div class="t m1 x20 hf y1d ffa fs5 fc1 sc0 ls0 ws0">+</div><div class="t m1 x21 h10 y1c ffb fs5 fc1 sc0 ls0 ws0">„</div></div><div class="t m0 x22 ha y19 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x23 y1e w4 h11"><div class="t m2 x1a h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">{<span class="_ _5"> </span>|<span class="_ _9"> </span>5<span class="_ _a"> </span>4<span class="_ _7"></span>}<span class="_ _b"></span><span class="ff9">B<span class="_ _c"> </span>x<span class="_ _d"> </span>x<span class="_ _e"></span><span class="ffa">=<span class="_ _f"> </span>-<span class="_ _5"> </span><<span class="_ _10"> </span><</span></span></div></div><div class="t m0 x24 ha y19 ff8 fs3 fc1 sc0 ls0 ws0">，则</div><div class="c x25 y20 w5 h13"><div class="t m3 x26 h14 y21 ff2 fs7 fc1 sc0 ls0 ws0">(<span class="_ _c"> </span>)<span class="_ _11"> </span>(</div><div class="t m3 x27 h15 y22 ff9 fs8 fc1 sc0 ls0 ws0">R</div><div class="t m3 x28 h16 y21 ff9 fs7 fc1 sc0 ls0 ws0">A<span class="_ _c"> </span>B<span class="_"> </span><span class="ffa">=</span></div><div class="t m3 x29 h17 y23 ffb fs9 fc1 sc0 ls0 ws0">I</div><div class="t m3 x2a h18 y21 ffb fs7 fc1 sc0 ls0 ws0">ð</div></div><div class="t m0 x2b ha y19 ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c x2c y1e w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha y24 ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．</span></div><div class="c x2e y25 w7 h11"><div class="t m0 x26 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _0"></span><span class="ffa">-<span class="_ _3"></span>¥</span></div></div><div class="t m0 x2f ha y24 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x30 y26 w8 h13"><div class="t m5 x31 h16 y21 ff2 fs7 fc1 sc0 ls0 ws0">1<span class="_ _3"></span>]<span class="_ _12"> </span>(<span class="_ _0"></span>4<span class="_ _13"></span>,<span class="_ _8"> </span>)<span class="_ _14"></span><span class="ffa">-<span class="_ _15"> </span>+¥</span></div><div class="t m5 x28 h17 y23 ffb fs9 fc1 sc0 ls0 ws0">U</div></div><div class="t m0 x32 ha y24 ff2 fs3 fc1 sc0 ls0 ws0">B<span class="ff8">．</span></div><div class="c x33 y25 w7 h11"><div class="t m0 x26 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _0"></span><span class="ffa">-<span class="_ _3"></span>¥</span></div></div><div class="t m0 x34 ha y24 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x35 y25 w9 h11"><div class="t m0 x31 h1a y1f ff2 fs6 fc1 sc0 ls0 ws0">1<span class="_ _3"></span>)<span class="_ _16"> </span>(<span class="_ _0"></span>4<span class="_ _17"></span><span class="ffa">-<span class="_ _18"> </span><span class="fsa">È</span></span></div></div><div class="t m0 x36 ha y24 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x37 y25 w7 h11"><div class="t m0 x38 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">)<span class="_ _19"></span><span class="ffa">+¥</span></div></div><div class="t m0 x2d ha y27 ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．</span></div><div class="c x2e y28 wa h11"><div class="t m0 x26 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _1a"> </span>5<span class="_ _13"></span>,<span class="_ _1b"> </span>1<span class="_ _3"></span>)<span class="_ _1c"></span><span class="ffa">-<span class="_ _1d"> </span>-</span></div></div><div class="t m0 x32 ha y27 ff2 fs3 fc1 sc0 ls0 ws0">D<span class="ff8">．</span></div><div class="c x33 y28 wb h11"><div class="t m0 x26 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _1a"> </span>5<span class="_ _1e"></span><span class="ffa">-</span></div></div><div class="t m0 x39 ha y27 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x3a y28 wc h11"><div class="t m6 x31 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">1<span class="_ _3"></span>]<span class="_ _1f"></span><span class="ffa">-</span></div></div><div class="t m0 x1 ha y29 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b y2a wd h1b"><div class="t m0 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">D</div></div><div class="t m0 x1 ha y2c ff1 fs3 fc2 sc0 ls0 ws0">【分析】先解分式不等式求出集合</div><div class="c x3c y2d we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x14 ha y2c ff1 fs3 fc2 sc0 ls0 ws0">，再根据集合的基本运算即可求解．</div><div class="t m0 x1 ha y2e ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：</div><div class="c x30 y2f wf hd"><div class="t m8 x3d he y1b ff2 fs5 fc1 sc0 ls0 ws0">4</div><div class="t m8 x3e he y1c ff2 fs5 fc1 sc0 ls0 ws0">{<span class="_ _5"> </span>|<span class="_ _6"> </span>0<span class="_ _7"></span>}<span class="_ _18"> </span>{<span class="_ _5"> </span>|<span class="_ _20"> </span>1<span class="_ _21"> </span>4<span class="_ _7"></span>}</div><div class="t m8 x3d he y1d ff2 fs5 fc1 sc0 ls0 ws0">1</div><div class="t m8 x3f he y1b ff9 fs5 fc1 sc0 ls0 ws0">x</div><div class="t m8 x1f he y1c ff9 fs5 fc1 sc0 ls0 ws0">A<span class="_ _8"> </span>x<span class="_ _22"> </span>x<span class="_ _23"> </span>x</div><div class="t m8 x40 he y1d ff9 fs5 fc1 sc0 ls0 ws0">x</div><div class="t m8 x41 hf y1b ffa fs5 fc1 sc0 ls0 ws0">-</div><div class="t m8 x42 hf y1c ffa fs5 fc1 sc0 ls0 ws0">=<span class="_ _24"> </span>=<span class="_ _f"> </span>-<span class="_ _1a"> </span><</div><div class="t m8 x43 hf y1d ffa fs5 fc1 sc0 ls0 ws0">+</div><div class="t m8 x0 h10 y1c ffb fs5 fc1 sc0 ls0 ws0">Q<span class="_ _25"> </span>„<span class="_ _26"> </span>„</div></div><div class="t m0 x44 ha y2e ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x1 y30 w10 h1c"><div class="t m9 x1b h1d y31 ff2 fsc fc1 sc0 ls0 ws0">{<span class="_ _5"> </span>|<span class="_ _27"> </span>1</div><div class="t m9 x45 h1e y32 ff9 fsd fc1 sc0 ls0 ws0">R</div><div class="t m9 x42 h1f y31 ff9 fsc fc1 sc0 ls0 ws0">A<span class="_ _8"> </span>x<span class="_ _28"> </span>x<span class="_ _29"></span><span class="ffa">\<span class="_ _2a"> </span>=<span class="_ _2b"> </span>-<span class="_ _2c"></span><span class="ffb">„<span class="_ _2d"></span>ð</span></span></div></div><div class="t m0 x46 ha y33 ff1 fs3 fc2 sc0 ls0 ws0">或</div><div class="c x47 y34 w11 h11"><div class="t ma x1a h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">4<span class="_ _7"></span>}<span class="_ _2e"></span><span class="ff9">x<span class="_"> </span><span class="ffa">></span></span></div></div><div class="t m0 x48 ha y33 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x1 y35 w12 h11"><div class="t mb x3e h20 y1f ff2 fs6 fc1 sc0 ls0 ws0">{<span class="_ _5"> </span>|<span class="_ _9"> </span>5<span class="_ _a"> </span>4<span class="_ _7"></span>}<span class="_ _b"></span><span class="ff9">B<span class="_ _c"> </span>x<span class="_ _d"> </span>x<span class="_ _e"></span><span class="ffa">=<span class="_ _f"> </span>-<span class="_ _5"> </span><<span class="_ _10"> </span><<span class="_ _2f"></span><span class="ffb">Q</span></span></span></div></div><div class="t m0 x49 ha y36 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x1 y37 w13 h13"><div class="t mc x4a h14 y21 ff2 fs7 fc1 sc0 ls0 ws0">(<span class="_ _c"> </span>)<span class="_ _d"> </span>{<span class="_ _5"> </span>|<span class="_ _9"> </span>5<span class="_ _30"> </span>1<span class="_ _31"></span>}</div><div class="t mc x4b h15 y22 ff9 fs8 fc1 sc0 ls0 ws0">R</div><div class="t mc x4c h16 y21 ff9 fs7 fc1 sc0 ls0 ws0">A<span class="_ _c"> </span>B<span class="_ _8"> </span>x<span class="_ _d"> </span>x<span class="_ _32"></span><span class="ffa">\<span class="_ _33"> </span>=<span class="_ _f"> </span>-<span class="_ _28"> </span><<span class="_ _34"> </span>-</span></div><div class="t mc x4d h17 y23 ffb fs9 fc1 sc0 ls0 ws0">I</div><div class="t mc x4e h18 y21 ffb fs7 fc1 sc0 ls0 ws0">„<span class="_ _35"></span>ð</div></div><div class="t m0 x4f ha y38 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y39 ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e y3a wd h1b"><div class="t m0 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">D</div></div><div class="t m0 x50 ha y39 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y3b ff2 fs3 fc1 sc0 ls0 ws0">2<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）<span class="_ _4"></span><span class="ffc">“</span></span></div><div class="c x51 y3c w14 h11"><div class="t m0 x4c h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">0<span class="_ _2e"></span><span class="ff9">x<span class="_ _13"></span>y<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x52 ha y3b ff8 fs3 fc1 sc0 ls0 ws0">”是“</div><div class="c x53 y3c w15 h21"><div class="t md x31 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _36"> </span>2</div><div class="t md x1e h23 y3e ff2 fsf fc1 sc0 ls0 ws0">0<span class="_ _37"></span><span class="ff9">x<span class="_ _38"> </span>y<span class="_ _39"></span><span class="ffa">+<span class="_ _16"> </span>=</span></span></div></div><div class="t m0 x54 ha y3b ff8 fs3 fc1 sc0 ls0 ws0">”的</div><div class="c x55 y3c w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 x56 ha y3b ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c x44 y3c w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha y3f ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．充分不必要条件<span class="_ _3a"> </span></span>B<span class="ff8">．必要不充分条件</span></div><div class="t m0 x2d ha y40 ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．充分必要条件<span class="_ _3b"> </span></span>D<span class="ff8">．既不充分也不必要条件</span></div><div class="t m0 x1 ha y41 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b y42 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x1 ha y43 ff1 fs3 fc2 sc0 ls0 ws0">【分析】根据</div><div class="c x30 y44 w16 h11"><div class="t me x4c h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">0<span class="_ _3c"> </span>0<span class="_ _3d"></span><span class="ff9">xy<span class="_ _3e"> </span>x<span class="_ _3f"></span><span class="ffa">=<span class="_ _10"> </span>Û<span class="_ _c"> </span>=</span></span></div></div><div class="t m0 x57 ha y43 ff1 fs3 fc2 sc0 ls0 ws0">或</div><div class="c x4 y44 w17 h11"><div class="t mf x1a h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">0<span class="_ _40"></span><span class="ff9">y<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x11 ha y43 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x15 y45 w18 h21"><div class="t m10 x31 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _36"> </span>2</div><div class="t m10 x1e h23 y3e ff2 fsf fc1 sc0 ls0 ws0">0<span class="_ _41"> </span>0<span class="_ _42"></span><span class="ff9">x<span class="_ _38"> </span>y<span class="_ _43"> </span>x<span class="_ _44"> </span>y<span class="_ _45"></span><span class="ffa">+<span class="_ _16"> </span>=<span class="_ _10"> </span>Û<span class="_ _c"> </span>=<span class="_ _12"> </span>=</span></span></div></div><div class="t m0 x58 ha y43 ff1 fs3 fc2 sc0 ls0 ws0">，即可求解．</div><div class="t m0 x1 ha y46 ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：</div><div class="c x30 y47 w19 h11"><div class="t m0 x59 h20 y1f ff2 fs6 fc1 sc0 ls0 ws0">0<span class="_ _3c"> </span>0<span class="_ _3d"></span><span class="ff9">xy<span class="_ _3e"> </span>x<span class="_ _3f"></span><span class="ffa">=<span class="_ _10"> </span>Û<span class="_ _c"> </span>=<span class="_ _46"></span><span class="ffb">Q</span></span></span></div></div><div class="t m0 x5a ha y46 ff1 fs3 fc2 sc0 ls0 ws0">或</div><div class="c x5b y47 w17 h11"><div class="t mf x1a h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">0<span class="_ _40"></span><span class="ff9">y<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x5c ha y46 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x5d y48 w18 h21"><div class="t m10 x31 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _36"> </span>2</div><div class="t m10 x1e h23 y3e ff2 fsf fc1 sc0 ls0 ws0">0<span class="_ _41"> </span>0<span class="_ _42"></span><span class="ff9">x<span class="_ _38"> </span>y<span class="_ _43"> </span>x<span class="_ _44"> </span>y<span class="_ _45"></span><span class="ffa">+<span class="_ _16"> </span>=<span class="_ _10"> </span>Û<span class="_ _c"> </span>=<span class="_ _12"> </span>=</span></span></div></div><div class="t m0 x5e ha y46 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x1 y49 w1a h24"><div class="t m0 x0 h25 y4a ffa fs10 fc1 sc0 ls0 ws0">\</div></div><div class="t m0 x5f h9 y4b ff2 fs3 fc2 sc0 ls0 ws0"> </div><div class="t m0 x60 ha y4c ffd fs3 fc2 sc0 ls0 ws0">“</div><div class="c x61 y4d w14 h11"><div class="t m0 x4c h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">0<span class="_ _2e"></span><span class="ff9">x<span class="_ _13"></span>y<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x51 ha y4c ff1 fs3 fc2 sc0 ls0 ws0">”是“</div><div class="c x62 y4e w15 h21"><div class="t md x31 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _36"> </span>2</div><div class="t md x1e h23 y3e ff2 fsf fc1 sc0 ls0 ws0">0<span class="_ _37"></span><span class="ff9">x<span class="_ _38"> </span>y<span class="_ _39"></span><span class="ffa">+<span class="_ _16"> </span>=</span></span></div></div><div class="t m0 x63 ha y4c ff1 fs3 fc2 sc0 ls0 ws0">”的必要不充分条件．</div><div class="t m0 x1 ha y4f ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e y50 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x64 ha y4f ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y51 ff2 fs3 fc1 sc0 ls0 ws0">3<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）三个数</span></div><div class="c x65 y52 w1b h1c"><div class="t m11 x66 h1e y32 ff2 fsd fc1 sc0 ls0 ws0">2</div><div class="t m11 x4b h26 y31 ff2 fsc fc1 sc0 ls0 ws0">log<span class="_ _47"> </span>0.7<span class="_ _48"></span><span class="ff9">a<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x67 ha y51 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x68 y53 wa h11"><div class="t m0 x59 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2</div><div class="t m0 x4b h12 y55 ff2 fs6 fc1 sc0 ls0 ws0">0.3<span class="_ _49"></span><span class="ff9">b<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x69 ha y51 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x6a y53 w1c h11"><div class="t m12 x4c h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">0.3</div><div class="t m12 x4b h12 y55 ff2 fs6 fc1 sc0 ls0 ws0">2<span class="_ _40"></span><span class="ff9">c<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 xa ha y51 ff8 fs3 fc1 sc0 ls0 ws0">的大小关系为</div><div class="c x6b y52 w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 x6c ha y51 ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c x6d y52 w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha y56 ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．</span></div><div class="c x2e y57 w1d h28"><div class="t m13 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">a<span class="_ _10"> </span>b<span class="_ _4a"> </span>c<span class="_ _1c"></span><span class="ffa"><<span class="_ _4b"> </span><</span></div></div><div class="t m0 x6e ha y56 ff2 fs3 fc1 sc0 ls0 ws0">B<span class="ff8">．</span></div><div class="c x6f y57 w1d h28"><div class="t m13 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">b<span class="_ _4a"> </span>a<span class="_ _4a"> </span>c<span class="_ _4c"></span><span class="ffa"><<span class="_ _10"> </span><</span></div></div><div class="t m0 x32 ha y56 ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．</span></div><div class="c x33 y57 w1d h28"><div class="t m13 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">a<span class="_ _4a"> </span>c<span class="_ _10"> </span>b<span class="_ _1c"></span><span class="ffa"><<span class="_ _4d"> </span><</span></div></div><div class="t m0 x70 ha y56 ff2 fs3 fc1 sc0 ls0 ws0">D<span class="ff8">．</span></div><div class="c x71 y57 w1d h28"><div class="t m13 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">b<span class="_ _10"> </span>c<span class="_ _4a"> </span>a<span class="_ _1c"></span><span class="ffa"><<span class="_ _18"> </span><</span></div></div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89649381/bg2.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div></div><div class="c x2 y5 w2 h4"><div class="t m0 x0 h5 y6 ff2 fs1 fc1 sc0 ls0 ws0">2</div></div><div class="t m0 x1 ha y59 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b y5a we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x1 ha y5b ff1 fs3 fc2 sc0 ls0 ws0">【分析】利用指数、对数函数的性质可解．</div><div class="t m0 x1 ha y5c ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：</div><div class="c x30 y5d w1e h1c"><div class="t m14 x72 h1e y32 ff2 fsd fc1 sc0 ls0 ws0">2<span class="_ _4e"> </span>2</div><div class="t m14 x73 h1f y31 ff2 fsc fc1 sc0 ls0 ws0">log<span class="_ _47"> </span>0.7<span class="_ _10"> </span>log<span class="_ _4f"> </span>1<span class="_ _4d"> </span>0<span class="_ _50"></span><span class="ff9">a<span class="_"> </span><span class="ffa">=<span class="_ _51"> </span><<span class="_ _23"> </span>=<span class="_ _52"></span><span class="ffb">Q</span></span></span></div></div><div class="t m0 x74 ha y5c ff1 fs3 fc2 sc0 ls0 ws0">，故</div><div class="c x75 y5e w1f h28"><div class="t m15 x4b h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">0<span class="_ _40"></span><span class="ff9">a<span class="_"> </span><span class="ffa"><</span></span></div></div><div class="t m0 x76 ha y5c ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y5f ff1 fs3 fc2 sc0 ls0 ws0">又</div><div class="c x77 y60 w20 h11"><div class="t m0 x59 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2<span class="_ _53"> </span>0</div><div class="t m0 x4b h12 y55 ff2 fs6 fc1 sc0 ls0 ws0">0.3<span class="_ _8"> </span>0.3<span class="_ _54"> </span>1<span class="_ _55"></span><span class="ff9">b<span class="_"> </span><span class="ffa">=<span class="_ _21"> </span><<span class="_ _21"> </span>=</span></span></div></div><div class="t m0 x78 ha y5f ff1 fs3 fc2 sc0 ls0 ws0">，且</div><div class="c x3 y61 w1f h28"><div class="t m15 x4b h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">0<span class="_ _40"></span><span class="ff9">b<span class="_"> </span><span class="ffa">></span></span></div></div><div class="t m0 x79 ha y5f ff1 fs3 fc2 sc0 ls0 ws0">，故</div><div class="c x7a y61 w21 h28"><div class="t m16 x26 h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">0<span class="_ _53"> </span>1<span class="_ _56"></span><span class="ff9">b<span class="_ _57"></span><span class="ffa"><<span class="_ _4d"> </span><</span></span></div></div><div class="t m0 x7b ha y5f ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y62 ff1 fs3 fc2 sc0 ls0 ws0">又</div><div class="c x77 y63 w16 h11"><div class="t me x4c h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">0.3<span class="_ _58"> </span>0</div><div class="t me x4b h12 y55 ff2 fs6 fc1 sc0 ls0 ws0">2<span class="_ _59"> </span>2<span class="_ _5a"> </span>1<span class="_ _5b"></span><span class="ff9">c<span class="_"> </span><span class="ffa">=<span class="_ _5c"> </span>><span class="_ _8"> </span>=</span></span></div></div><div class="t m0 x7c ha y62 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y64 ff1 fs3 fc2 sc0 ls0 ws0">故</div><div class="c x77 y65 w1d h28"><div class="t m13 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">c<span class="_ _4a"> </span>b<span class="_ _4a"> </span>a<span class="_ _5d"></span><span class="ffa">><span class="_ _4b"> </span>></span></div></div><div class="t m0 x7d ha y64 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y66 ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e y67 we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x64 ha y66 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y68 ff2 fs3 fc1 sc0 ls0 ws0">4<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）函数</span></div><div class="c x7e y69 w22 hd"><div class="t m17 x7f he y1b ff2 fs5 fc1 sc0 ls0 ws0">(<span class="_ _16"> </span>2)</div><div class="t m17 x27 he y1c ff2 fs5 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)</div><div class="t m17 x80 he y1d ff2 fs5 fc1 sc0 ls0 ws0">1</div><div class="t m17 x4d he y1b ff9 fs5 fc1 sc0 ls0 ws0">ln<span class="_ _5e"> </span>x</div><div class="t m17 x81 he y1c ff9 fs5 fc1 sc0 ls0 ws0">f<span class="_ _5"> </span>x</div><div class="t m17 x1e he y1d ff9 fs5 fc1 sc0 ls0 ws0">x</div><div class="t m17 x43 hf y1b ffa fs5 fc1 sc0 ls0 ws0">+</div><div class="t m17 x29 hf y1c ffa fs5 fc1 sc0 ls0 ws0">=</div><div class="t m17 x82 hf y1d ffa fs5 fc1 sc0 ls0 ws0">-</div></div><div class="t m0 x83 ha y68 ff8 fs3 fc1 sc0 ls0 ws0">的图象大致是</div><div class="c x84 y6a w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 x85 ha y68 ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c x86 y6a w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha y6b ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．<span class="_ _5f"> </span></span>B<span class="ff8">．</span></div><div class="t m0 x2d ha y6c ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．<span class="_ _60"> </span></span>D<span class="ff8">．</span></div><div class="t m0 x1 ha y6d ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b y6e wd h1b"><div class="t m0 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">D</div></div><div class="t m0 x1 ha y6f ff1 fs3 fc2 sc0 ls0 ws0">【分析】对比选项中的图象，再分别计算</div><div class="c x87 y70 w23 h28"><div class="t m18 x88 h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">1<span class="_ _61"></span><span class="ff9">x<span class="_"> </span><span class="ffa">></span></span></div></div><div class="t m0 x85 ha y6f ff1 fs3 fc2 sc0 ls0 ws0">和</div><div class="c xa y70 w1f h28"><div class="t m15 x4b h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">0<span class="_ _62"></span><span class="ff9">x<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x89 ha y6f ff1 fs3 fc2 sc0 ls0 ws0">时，</div><div class="c x35 y71 w24 h11"><div class="t m0 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _63"></span><span class="ff9">f<span class="_ _5"> </span>x</span></div></div><div class="t m0 x6c ha y6f ff1 fs3 fc2 sc0 ls0 ws0">的取值情况，即可作出选择．</div><div class="t m0 x1 ha y72 ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：当</div><div class="c x8a y73 w23 h28"><div class="t m18 x88 h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">1<span class="_ _61"></span><span class="ff9">x<span class="_"> </span><span class="ffa">></span></span></div></div><div class="t m0 x8b ha y72 ff1 fs3 fc2 sc0 ls0 ws0">时，</div><div class="c x8c y74 w25 h11"><div class="t m19 x4a h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _16"> </span>2)<span class="_ _4a"> </span>0<span class="_ _64"></span><span class="ff9">ln<span class="_ _5e"> </span>x<span class="_ _1"> </span><span class="ffa">+<span class="_ _54"> </span>></span></span></div></div><div class="t m0 x8d ha y72 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x8e y73 w21 h28"><div class="t m16 x8f h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">1<span class="_ _4d"> </span>0<span class="_ _65"></span><span class="ff9">x<span class="_ _1"> </span><span class="ffa">-<span class="_ _1b"> </span>></span></span></div></div><div class="t m0 xa ha y72 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x86 y74 w26 h11"><div class="t m0 x4b h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _4a"> </span>0<span class="_ _66"></span><span class="ff9">f<span class="_ _5"> </span>x<span class="_ _67"></span><span class="ffa">\<span class="_ _a"> </span>></span></span></div></div><div class="t m0 x58 ha y72 ff1 fs3 fc2 sc0 ls0 ws0">，排除选项</div><div class="c x90 y75 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x91 ha y72 ff1 fs3 fc2 sc0 ls0 ws0">和</div><div class="c x92 y73 we h28"><div class="t m1a x26 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">C</div></div><div class="t m0 x93 ha y72 ff1 fs3 fc2 sc0 ls0 ws0">；</div><div class="t m0 x1 ha y76 ff1 fs3 fc2 sc0 ls0 ws0">当</div><div class="c x77 y77 w1f h28"><div class="t m15 x4b h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">0<span class="_ _62"></span><span class="ff9">x<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x94 ha y76 ff1 fs3 fc2 sc0 ls0 ws0">时，</div><div class="c x95 y78 w27 hd"><div class="t m1b x7f he y1b ff2 fs5 fc1 sc0 ls0 ws0">2</div><div class="t m1b x27 he y1c ff2 fs5 fc1 sc0 ls0 ws0">(0)<span class="_ _68"> </span>2<span class="_ _10"> </span>0</div><div class="t m1b x72 he y1d ff2 fs5 fc1 sc0 ls0 ws0">1</div><div class="t m1b x4d he y1b ff9 fs5 fc1 sc0 ls0 ws0">ln</div><div class="t m1b x81 hf y1c ff9 fs5 fc1 sc0 ls0 ws0">f<span class="_ _25"> </span>ln<span class="_ _48"></span><span class="ffa">=<span class="_ _69"> </span>=<span class="_"> </span>-<span class="_ _c"> </span><</span></div><div class="t m1b x96 hf y1d ffa fs5 fc1 sc0 ls0 ws0">-</div></div><div class="t m0 x97 ha y76 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x98 y79 w1a h24"><div class="t m0 x0 h25 y4a ffa fs10 fc1 sc0 ls0 ws0">\</div></div><div class="t m0 x74 ha y76 ff1 fs3 fc2 sc0 ls0 ws0">选项</div><div class="c x75 y7a we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x9 ha y76 ff1 fs3 fc2 sc0 ls0 ws0">错误，</div><div class="t m0 x1 ha y7b ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e y7c wd h1b"><div class="t m0 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">D</div></div><div class="t m0 x50 ha y7b ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y7d ff2 fs3 fc1 sc0 ls0 ws0">5<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_ _6a"> </span></span>分）<span class="_ _4"></span>在正方体</span></div><div class="c x99 y7e w10 h1c"><div class="t m9 x40 h1e y32 ff2 fsd fc1 sc0 ls0 ws0">1<span class="_ _47"> </span>1<span class="_ _28"> </span>1<span class="_ _5"> </span>1</div><div class="t m9 x1c h26 y31 ff9 fsc fc1 sc0 ls0 ws0">ABCD<span class="_ _12"> </span>A<span class="_ _6b"> </span>B<span class="_ _6b"> </span>C<span class="_ _2"> </span>D<span class="_ _6c"></span><span class="ffa">-</span></div></div><div class="t m0 x9a ha y7d ff8 fs3 fc1 sc0 ls0 ws0">中，<span class="_ _4"></span>三棱锥</div><div class="c x85 y7e w28 h1c"><div class="t m1c x29 h1e y32 ff2 fsd fc1 sc0 ls0 ws0">1<span class="_ _6d"> </span>1</div><div class="t m1c x1c h26 y31 ff9 fsc fc1 sc0 ls0 ws0">A<span class="_ _4b"> </span>B<span class="_ _6b"> </span>CD<span class="_ _6e"></span><span class="ffa">-</span></div></div><div class="t m0 x34 ha y7d ff8 fs3 fc1 sc0 ls0 ws0">的表面积为</div><div class="c x36 y7f w29 h1c"><div class="t m1d x26 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">4<span class="_ _5"> </span>3</div></div><div class="t m0 x9b ha y7d ff8 fs3 fc1 sc0 ls0 ws0">，<span class="_ _4"></span>则正方体外接球的体积为</div><div class="c x9c y7e w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 x9d ha y7d ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c x9e y7e w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha y81 ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．</span></div><div class="c x2e y82 w2a h1c"><div class="t m1e x26 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">4<span class="_ _5"> </span>3</div><div class="t m1f x1a h2b y80 ffe fs13 fc1 sc0 ls0 ws0">p</div></div><div class="t m0 x6e ha y81 ff2 fs3 fc1 sc0 ls0 ws0">B<span class="ff8">．</span></div><div class="c x6f y82 w23 h1c"><div class="t m20 x27 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">6</div><div class="t m21 x45 h2c y80 ffe fs14 fc1 sc0 ls0 ws0">p</div></div><div class="t m0 x32 ha y81 ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．</span></div><div class="c x33 y82 w2b h1c"><div class="t m22 x26 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">32<span class="_ _5"> </span>3</div><div class="t m23 x4c h2d y80 ffe fs15 fc1 sc0 ls0 ws0">p</div></div><div class="t m0 x70 ha y81 ff2 fs3 fc1 sc0 ls0 ws0">D<span class="ff8">．</span></div><div class="c x71 y82 w2a h1c"><div class="t m1e x26 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">8<span class="_ _5"> </span>6</div><div class="t m1f x4b h2b y80 ffe fs13 fc1 sc0 ls0 ws0">p</div></div><div class="t m0 x1 ha y83 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b y84 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x1 ha y85 ff1 fs3 fc2 sc0 ls0 ws0">【分析】根据三棱锥的表面积，求出正方体的棱长，由正方体的对角线即为外接球的直径，求得正方体的</div><div class="t m0 x1 ha y86 ff1 fs3 fc2 sc0 ls0 ws0">外接球的半径，由球的体积公式计算可得所求值．</div><div class="t m0 x1 ha y87 ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：设正方体的棱长为</div><div class="c x9f y88 w2c h24"><div class="t m24 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xa0 ha y87 ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c x15 y8a w2d h1c"><div class="t m25 x96 h26 y80 ff2 fsc fc1 sc0 ls0 ws0">2<span class="_ _6f"></span><span class="ff9">BD<span class="_ _70"> </span>a<span class="_ _71"></span><span class="ffa">=</span></span></div></div><div class="t m0 x17 ha y87 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y8b ff1 fs3 fc2 sc0 ls0 ws0">由于三棱锥</div><div class="c x2f y8c w28 h1c"><div class="t m1c x29 h1e y32 ff2 fsd fc1 sc0 ls0 ws0">1<span class="_ _6d"> </span>1</div><div class="t m1c x1c h26 y31 ff9 fsc fc1 sc0 ls0 ws0">A<span class="_ _4b"> </span>B<span class="_ _6b"> </span>CD<span class="_ _6e"></span><span class="ffa">-</span></div></div><div class="t m0 xa1 ha y8b ff1 fs3 fc2 sc0 ls0 ws0">的表面积为</div><div class="c xa2 y8c w29 h1c"><div class="t m1d x26 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">4<span class="_ _5"> </span>3</div></div><div class="t m0 xa3 ha y8b ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y8d ff1 fs3 fc2 sc0 ls0 ws0">则</div><div class="c x77 y8e w2e h2f"><div class="t m0 x77 h27 y8f ff2 fs11 fc1 sc0 ls0 ws0">2</div><div class="t m0 x4c h19 y90 ff2 fs6 fc1 sc0 ls0 ws0">3</div><div class="t m0 x26 h19 y91 ff2 fs6 fc1 sc0 ls0 ws0">4<span class="_ _3c"> </span>(<span class="_ _1b"> </span>2<span class="_ _47"> </span>)<span class="_ _16"> </span>4<span class="_ _5"> </span>3</div><div class="t m0 xa4 h19 y92 ff2 fs6 fc1 sc0 ls0 ws0">4</div><div class="t m0 xa5 h12 y91 ff9 fs6 fc1 sc0 ls0 ws0">a<span class="_ _64"></span><span class="ffa">´<span class="_ _34"> </span>´<span class="_ _72"> </span>=</span></div></div><div class="t m0 x3 ha y8d ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y93 ff1 fs3 fc2 sc0 ls0 ws0">解得</div><div class="c xf y94 w2b h1c"><div class="t m22 xa6 h26 y80 ff2 fsc fc1 sc0 ls0 ws0">2<span class="_ _4c"></span><span class="ff9">a<span class="_ _2"> </span><span class="ffa">=</span></span></div></div><div class="t m0 xa7 ha y93 ff1 fs3 fc2 sc0 ls0 ws0">，</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89649381/bg3.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div></div><div class="c x2 y5 w2 h4"><div class="t m0 x0 h5 y6 ff2 fs1 fc1 sc0 ls0 ws0">3</div></div><div class="t m0 x1 ha y95 ff1 fs3 fc2 sc0 ls0 ws0">又</div><div class="c x77 y96 w2f h1c"><div class="t m26 x26 h26 y80 ff2 fsc fc1 sc0 ls0 ws0">2<span class="_ _73"> </span>3<span class="_ _27"> </span>6<span class="_ _74"></span><span class="ff9">R<span class="_ _75"> </span>a<span class="_ _2e"></span><span class="ffa">=<span class="_ _21"> </span>=</span></span></div></div><div class="t m0 x46 ha y95 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y97 ff1 fs3 fc2 sc0 ls0 ws0">即</div><div class="c x77 y98 wa h2f"><div class="t m0 x3e h19 y90 ff2 fs6 fc1 sc0 ls0 ws0">6</div><div class="t m0 x29 h19 y92 ff2 fs6 fc1 sc0 ls0 ws0">2</div><div class="t m0 x26 h12 y91 ff9 fs6 fc1 sc0 ls0 ws0">R<span class="_"> </span><span class="ffa">=</span></div></div><div class="t m0 xa8 ha y97 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y99 ff1 fs3 fc2 sc0 ls0 ws0">所以正方体的外接球的体积为</div><div class="c xa9 y9a w30 h2f"><div class="t m27 xaa h27 y8f ff2 fs11 fc1 sc0 ls0 ws0">3</div><div class="t m27 x1c h19 y90 ff2 fs6 fc1 sc0 ls0 ws0">4<span class="_ _2b"> </span>4<span class="_ _58"> </span>3<span class="_ _5"> </span>6</div><div class="t m27 x50 h19 y91 ff2 fs6 fc1 sc0 ls0 ws0">6</div><div class="t m27 x1c h19 y92 ff2 fs6 fc1 sc0 ls0 ws0">3<span class="_ _76"> </span>3<span class="_ _77"> </span>4</div><div class="t m27 x88 h19 y91 ff9 fs6 fc1 sc0 ls0 ws0">R</div><div class="t m28 x20 h30 y90 ffe fs16 fc1 sc0 ls0 ws0">p</div><div class="t m28 x27 h30 y91 ffe fs16 fc1 sc0 ls0 ws0">p<span class="_ _78"> </span>p</div><div class="t m27 xab h12 y91 ffa fs6 fc1 sc0 ls0 ws0">=<span class="_ _f"> </span>´<span class="_ _70"> </span>=</div></div><div class="t m0 xac ha y99 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y9b ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e y9c we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x64 ha y9b ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y9d ff2 fs3 fc1 sc0 ls0 ws0">6<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）若</span></div><div class="c xad y9e w31 h21"><div class="t m29 xab h22 y3d ff2 fse fc1 sc0 ls0 ws0">5</div><div class="t m29 x26 h23 y3e ff2 fsf fc1 sc0 ls0 ws0">(<span class="_ _79"> </span>)<span class="_ _7a"></span><span class="ff9">x<span class="_ _4a"> </span>a<span class="_ _1f"></span><span class="ffa">+</span></span></div></div><div class="t m0 x12 ha y9d ff8 fs3 fc1 sc0 ls0 ws0">的二项式展开式中</div><div class="c x69 y9f w32 h11"><div class="t m2a x31 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2</div><div class="t m2a x26 h19 y55 ff9 fs6 fc1 sc0 ls0 ws0">x</div></div><div class="t m0 x75 ha y9d ff8 fs3 fc1 sc0 ls0 ws0">的系数为<span class="_ _7b"> </span><span class="ff2">10</span>，则</div><div class="c x35 y9e w23 h11"><div class="t m2b x4b h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _56"></span><span class="ff9">a<span class="_ _2"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x6c ha y9d ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c x6d y9e w6 h11"><div class="t m4 x26 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha ya0 ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．</span>1<span class="_ _7c"> </span>B<span class="ff8">．</span></div><div class="c x6f ya1 w33 h1b"><div class="t m2c x31 h31 y2b ff2 fsb fc1 sc0 ls0 ws0">1<span class="_ _1e"></span><span class="ffa">-</span></div></div><div class="t m0 x32 ha ya0 ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．</span></div><div class="c x33 ya1 w33 h1b"><div class="t m2c x31 h31 y2b ff2 fsb fc1 sc0 ls0 ws0">1<span class="_ _1e"></span><span class="ffa">±</span></div></div><div class="t m0 x70 ha ya0 ff2 fs3 fc1 sc0 ls0 ws0">D<span class="ff8">．</span></div><div class="c x71 ya1 w2 h1b"><div class="t m0 x31 h31 y2b ff2 fsb fc1 sc0 ls0 ws0">2<span class="_ _1e"></span><span class="ffa">+</span></div></div><div class="t m0 x1 ha ya2 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b ya3 we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x1 ha ya4 ff1 fs3 fc2 sc0 ls0 ws0">【分析】依题意，可得</div><div class="c xae ya5 w34 h21"><div class="t m2d x27 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _28"> </span>3</div><div class="t m2d xaf h22 ya6 ff2 fse fc1 sc0 ls0 ws0">5</div><div class="t m2d x4d h23 y3e ff2 fsf fc1 sc0 ls0 ws0">10<span class="_ _7d"></span><span class="ff9">C<span class="_ _7e"> </span>a<span class="_ _5"> </span><span class="ffa">=</span></span></div></div><div class="t m0 xb0 ha ya4 ff1 fs3 fc2 sc0 ls0 ws0">，解之即可．</div><div class="t m0 x1 ha ya7 ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：</div><div class="c x30 ya8 w31 h21"><div class="t m29 xab h22 y3d ff2 fse fc1 sc0 ls0 ws0">5</div><div class="t m29 x26 h23 y3e ff2 fsf fc1 sc0 ls0 ws0">(<span class="_ _79"> </span>)<span class="_ _7a"></span><span class="ff9">x<span class="_ _4a"> </span>a<span class="_ _1f"></span><span class="ffa">+</span></span></div></div><div class="t m0 xa1 ha ya7 ff1 fs3 fc2 sc0 ls0 ws0">的二项式展开式中</div><div class="c xb1 ya9 w32 h11"><div class="t m2a x31 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2</div><div class="t m2a x26 h19 y55 ff9 fs6 fc1 sc0 ls0 ws0">x</div></div><div class="t m0 x56 ha ya7 ff1 fs3 fc2 sc0 ls0 ws0">的系数为</div><div class="c x2 ya8 w24 h21"><div class="t m2e x27 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _28"> </span>3</div><div class="t m2e xaf h22 ya6 ff2 fse fc1 sc0 ls0 ws0">5</div><div class="t m2e x26 h32 y3e ff9 fsf fc1 sc0 ls0 ws0">C<span class="_ _7e"> </span>a</div></div><div class="t m0 x24 ha ya7 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha yaa ff1 fs3 fc2 sc0 ls0 ws0">依题意，得</div><div class="c x2f yab w19 h21"><div class="t m2e x27 h22 y3d ff2 fse fc1 sc0 ls0 ws0">2<span class="_ _28"> </span>3<span class="_ _7f"> </span>3</div><div class="t m2e xaf h22 ya6 ff2 fse fc1 sc0 ls0 ws0">5</div><div class="t m2e x4d h23 y3e ff2 fsf fc1 sc0 ls0 ws0">10<span class="_ _59"> </span>10<span class="_ _80"></span><span class="ff9">C<span class="_ _7e"> </span>a<span class="_ _81"> </span>a<span class="_ _82"></span><span class="ffa">=<span class="_ _53"> </span>=</span></span></div></div><div class="t m0 xb2 ha yaa ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha yac ff1 fs3 fc2 sc0 ls0 ws0">解得</div><div class="c xf yad w23 h28"><div class="t m18 x88 h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">1<span class="_ _56"></span><span class="ff9">a<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 xb3 ha yac ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha yae ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e yaf we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x64 ha yae ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha yb0 ff2 fs3 fc1 sc0 ls0 ws0">7<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）已知</span></div><div class="c x7e yb1 we h24"><div class="t m2f xb4 h33 y89 ffe fs17 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xb5 ha yb0 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xb6 yb2 we h11"><div class="t m30 x26 h34 y1f ffe fs18 fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xb7 ha yb0 ff8 fs3 fc1 sc0 ls0 ws0">是两个不同的平面，</div><div class="c xb8 yb1 wd h24"><div class="t m31 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">m</div></div><div class="t m0 x16 ha yb0 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xb9 yb1 w2c h24"><div class="t m24 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">n</div></div><div class="t m0 xba ha yb0 ff8 fs3 fc1 sc0 ls0 ws0">是两条不同的直线，则下列说法正确的是</div><div class="c xbb yb2 w6 h11"><div class="t m4 xb4 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 xbc ha yb0 ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c xbd yb2 w6 h11"><div class="t m4 xb4 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha yb3 ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．若</span></div><div class="c x3b yb4 w11 h28"><div class="t m32 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">m<span class="_ _83"> </span>n<span class="_ _84"></span><span class="ffa">^</span></div></div><div class="t m0 x7e ha yb3 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x65 yb4 w14 h28"><div class="t m26 x26 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">m</div><div class="t m33 xa4 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div><div class="t m26 xbe h29 y58 ffa fs12 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xbf ha yb3 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xc0 yb5 w2a h11"><div class="t m34 x26 h19 y1f ff9 fs6 fc1 sc0 ls0 ws0">n</div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div><div class="t m34 x27 h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xb0 ha yb3 ff8 fs3 fc1 sc0 ls0 ws0">，则</div><div class="c x74 yb5 w14 h11"><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _8"> </span>b</div><div class="t m37 x1f h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m37 x32 ha yb3 ff2 fs3 fc1 sc0 ls0 ws0">B<span class="ff8">．若</span></div><div class="c x89 yb4 w2a h28"><div class="t m38 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m<span class="_ _85"> </span>n</span></div></div><div class="t m0 xc1 ha yb3 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xc2 yb4 w14 h28"><div class="t m26 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m</span></div><div class="t m33 x42 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xc3 ha yb3 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xc4 yb5 w2a h11"><div class="t m34 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _2c"></span><span class="ff9">n</span></div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xc5 ha yb3 ff8 fs3 fc1 sc0 ls0 ws0">，则</div><div class="c xc6 yb5 w14 h11"><div class="t m0 x1f h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">/<span class="_"> </span>/</div><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _54"> </span>b</div></div><div class="t m0 x2d ha yb6 ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．若</span></div><div class="c x3b yb7 w11 h28"><div class="t m32 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">m<span class="_ _83"> </span>n<span class="_ _84"></span><span class="ffa">^</span></div></div><div class="t m0 x7e ha yb6 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x65 yb7 w14 h28"><div class="t m26 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m</span></div><div class="t m33 x42 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xbf ha yb6 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xc0 yb8 w14 h11"><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _8"> </span>b</div><div class="t m37 x1f h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m37 x97 ha yb6 ff8 fs3 fc1 sc0 ls0 ws0">，则</div><div class="c xa3 yb8 w2a h11"><div class="t m34 x26 h19 y1f ff9 fs6 fc1 sc0 ls0 ws0">n</div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div><div class="t m34 x27 h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 x32 ha yb6 ff2 fs3 fc1 sc0 ls0 ws0">D<span class="ff8">．若</span></div><div class="c xac yb7 w2a h28"><div class="t m38 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m<span class="_ _85"> </span>n</span></div></div><div class="t m0 xc1 ha yb6 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xc2 yb7 w14 h28"><div class="t m26 x26 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">m</div><div class="t m33 xa4 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div><div class="t m26 xbe h29 y58 ffa fs12 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xc3 ha yb6 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c xc4 yb8 w14 h11"><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _8"> </span>b</div><div class="t m37 x1f h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m37 xc7 ha yb6 ff8 fs3 fc1 sc0 ls0 ws0">，则</div><div class="c xc8 yb8 w2a h11"><div class="t m34 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _2c"></span><span class="ff9">n</span></div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div></div><div class="t m0 x1 ha yb9 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b yba we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x1 ha ybb ff1 fs3 fc2 sc0 ls0 ws0">【分析】根据题意，由空间中线线、线面、面面之间的位置关系依次分析选项，综合可得答案．</div><div class="t m0 x1 ha ybc ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：根据题意，依次分析选项：</div><div class="t m0 x1 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">对于</div><div class="c xf ybe we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x2e ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，若</div><div class="c x2f ybf w14 h28"><div class="t m26 x26 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">m</div><div class="t m33 xa4 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div><div class="t m26 xbe h29 y58 ffa fs12 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xc9 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c xca yc0 w2a h11"><div class="t m34 x26 h19 y1f ff9 fs6 fc1 sc0 ls0 ws0">n</div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div><div class="t m34 x27 h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xcb ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，设直线</div><div class="c xcc yc1 wd h24"><div class="t m31 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">m</div></div><div class="t m0 xcd ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c xce yc1 w2c h24"><div class="t m24 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">n</div></div><div class="t m0 x56 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">的方向向量分别为</div><div class="c xcf yc2 w7 h38"><div class="t m39 x27 h39 yc3 ff2 fs1c fc1 sc0 ls0 ws0">,<span class="_ _86"></span><span class="ff9">m<span class="_ _87"> </span>n</span></div><div class="t m39 x81 h3a yc4 ffb fs1c fc1 sc0 ls0 ws0">r<span class="_ _5"> </span>r</div></div><div class="t m0 xd0 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，则平面</div><div class="c x2b yc1 we h24"><div class="t m2f xb4 h33 y89 ffe fs17 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xd1 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c xd2 yc0 we h11"><div class="t m30 x26 h34 y1f ffe fs18 fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xc6 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">对应法向量为</div><div class="c xd3 yc2 w7 h38"><div class="t m39 x27 h39 yc3 ff2 fs1c fc1 sc0 ls0 ws0">,<span class="_ _86"></span><span class="ff9">m<span class="_ _87"> </span>n</span></div><div class="t m39 x81 h3a yc4 ffb fs1c fc1 sc0 ls0 ws0">r<span class="_ _5"> </span>r</div></div><div class="t m0 xd4 ha ybd ff1 fs3 fc2 sc0 ls0 ws0">，由</div><div class="c x1 yc5 w11 h28"><div class="t m32 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">m<span class="_ _83"> </span>n<span class="_ _84"></span><span class="ffa">^</span></div></div><div class="t m0 xd5 ha yc6 ff1 fs3 fc2 sc0 ls0 ws0">，即</div><div class="c x7d yc5 w11 h28"><div class="t m32 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">m<span class="_ _83"> </span>n<span class="_ _84"></span><span class="ffa">^</span></div><div class="t m32 x81 h3b yc7 ffb fs12 fc1 sc0 ls0 ws0">r<span class="_ _8"> </span>r</div></div><div class="t m0 xd6 ha yc6 ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c xd7 yc8 w14 h11"><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _8"> </span>b</div><div class="t m37 x1f h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m37 xd8 ha yc6 ff1 fs3 fc2 sc0 ls0 ws0">，故</div><div class="c x97 yc9 we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 xd9 ha yc6 ff1 fs3 fc2 sc0 ls0 ws0">正确；</div><div class="t m0 x1 ha yca ff1 fs3 fc2 sc0 ls0 ws0">对于</div><div class="c xf ycb we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x2e ha yca ff1 fs3 fc2 sc0 ls0 ws0">，若</div><div class="c x2f ycc w2a h28"><div class="t m38 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m<span class="_ _85"> </span>n</span></div></div><div class="t m0 x65 ha yca ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x18 ycc w14 h28"><div class="t m26 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m</span></div><div class="t m33 x42 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xcb ha yca ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x6f ycd w2a h11"><div class="t m34 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _2c"></span><span class="ff9">n</span></div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xda ha yca ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c xdb yce we h24"><div class="t m2f xb4 h33 y89 ffe fs17 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xdc ha yca ff1 fs3 fc2 sc0 ls0 ws0">与</div><div class="c xdd ycd we h11"><div class="t m30 x26 h34 y1f ffe fs18 fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xde ha yca ff1 fs3 fc2 sc0 ls0 ws0">可能平行或相交，故</div><div class="c xdf ycb we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x70 ha yca ff1 fs3 fc2 sc0 ls0 ws0">错误；</div><div class="t m0 x1 ha ycf ff1 fs3 fc2 sc0 ls0 ws0">对于</div><div class="c xf yd0 we h28"><div class="t m1a xb4 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">C</div></div><div class="t m0 x2e ha ycf ff1 fs3 fc2 sc0 ls0 ws0">，若</div><div class="c x2f yd0 w11 h28"><div class="t m32 x26 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">m<span class="_ _83"> </span>n<span class="_ _84"></span><span class="ffa">^</span></div></div><div class="t m0 xb5 ha ycf ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c xb6 yd0 w14 h28"><div class="t m26 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m</span></div><div class="t m33 x42 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xc0 ha ycf ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x67 yd1 w14 h11"><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _8"> </span>b</div><div class="t m37 x1f h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m37 xcc ha ycf ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c x8e yd1 w11 h11"><div class="t ma x26 h19 y1f ff9 fs6 fc1 sc0 ls0 ws0">n</div><div class="t m3a x42 h3c y1f ffe fs1d fc1 sc0 ls0 ws0">b</div><div class="t ma x27 h12 y1f ffa fs6 fc1 sc0 ls0 ws0">Ì</div></div><div class="t m0 xde ha ycf ff1 fs3 fc2 sc0 ls0 ws0">，或</div><div class="c xe0 yd1 w2a h11"><div class="t m34 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _2c"></span><span class="ff9">n</span></div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xe1 ha ycf ff1 fs3 fc2 sc0 ls0 ws0">，或</div><div class="c xe2 yd2 w2c h24"><div class="t m24 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">n</div></div><div class="t m0 x6c ha ycf ff1 fs3 fc2 sc0 ls0 ws0">与</div><div class="c xe3 yd1 we h11"><div class="t m30 x26 h34 y1f ffe fs18 fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xe4 ha ycf ff1 fs3 fc2 sc0 ls0 ws0">相交，故</div><div class="c xe5 yd0 we h28"><div class="t m1a xb4 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">C</div></div><div class="t m0 xe6 ha ycf ff1 fs3 fc2 sc0 ls0 ws0">错误；</div><div class="t m0 x1 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">对于</div><div class="c xf yd4 wd h1b"><div class="t m0 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">D</div></div><div class="t m0 xe7 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">，若</div><div class="c xa7 yd5 w2a h28"><div class="t m38 x1f h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _63"></span><span class="ff9">m<span class="_ _85"> </span>n</span></div></div><div class="t m0 x65 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x18 yd5 w14 h28"><div class="t m26 x26 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">m</div><div class="t m33 xa4 h35 y58 ffe fs19 fc1 sc0 ls0 ws0">a</div><div class="t m26 xbe h29 y58 ffa fs12 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xc0 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c x83 yd5 w2a h28"><div class="t m38 x26 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">n</div><div class="t m3b x4b h3d y58 ffe fs1e fc1 sc0 ls0 ws0">a</div><div class="t m38 x27 h29 y58 ffa fs12 fc1 sc0 ls0 ws0">^</div></div><div class="t m0 xe8 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">，又</div><div class="c xdc yd6 w14 h11"><div class="t m36 xb4 h37 y1f ffe fs1b fc1 sc0 ls0 ws0">a<span class="_ _8"> </span>b</div><div class="t m37 x1f h12 y1f ffa fs6 fc1 sc0 ls0 ws0">^</div></div><div class="t m37 xe9 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c xea yd6 w2a h11"><div class="t m34 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">/<span class="_"> </span>/<span class="_ _2c"></span><span class="ff9">n</span></div><div class="t m35 x1a h36 y1f ffe fs1a fc1 sc0 ls0 ws0">b</div></div><div class="t m0 xeb ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">或</div><div class="c x58 yd6 w11 h11"><div class="t ma x26 h19 y1f ff9 fs6 fc1 sc0 ls0 ws0">n</div><div class="t m3a x42 h3c y1f ffe fs1d fc1 sc0 ls0 ws0">b</div><div class="t ma x27 h12 y1f ffa fs6 fc1 sc0 ls0 ws0">Ì</div></div><div class="t m0 x36 ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x37 yd4 wd h1b"><div class="t m0 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">D</div></div><div class="t m0 xec ha yd3 ff1 fs3 fc2 sc0 ls0 ws0">错误．</div><div class="t m0 x1 ha yd7 ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e yd8 we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x64 ha yd7 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha yd9 ff2 fs3 fc1 sc0 ls0 ws0">8<span class="ff8">．<span class="_ _4"></span>（<span class="ff2">5<span class="_"> </span></span>分）已知函数</span></div><div class="c x18 yda w20 hd"><div class="t m17 x27 he y1c ff2 fs5 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _10"> </span>sin(<span class="_ _88"> </span>)</div><div class="t m17 xed he y1d ff2 fs5 fc1 sc0 ls0 ws0">3</div><div class="t m17 x81 he y1c ff9 fs5 fc1 sc0 ls0 ws0">f<span class="_ _5"> </span>x<span class="_ _15"> </span>x</div><div class="t m3c x5f h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p</div><div class="t m17 x29 hf y1c ffa fs5 fc1 sc0 ls0 ws0">=<span class="_ _89"> </span>+</div></div><div class="t m0 xee ha yd9 ff8 fs3 fc1 sc0 ls0 ws0">．给出下列结论：</div><div class="t m0 x1 ha ydb ff1 fs3 fc1 sc0 ls0 ws0">①</div><div class="c x77 ydc w24 h11"><div class="t m0 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _63"></span><span class="ff9">f<span class="_ _5"> </span>x</span></div></div><div class="t m0 xef ha ydb ff8 fs3 fc1 sc0 ls0 ws0">的最小正周期为</div><div class="c xf0 ydd w35 h28"><div class="t m3d x26 h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">2</div><div class="t m3e xf1 h3f y58 ffe fs20 fc1 sc0 ls0 ws0">p</div></div><div class="t m0 xf2 ha ydb ff8 fs3 fc1 sc0 ls0 ws0">；</div><div class="t m0 x1 ha yde ff1 fs3 fc1 sc0 ls0 ws0">②</div><div class="c x77 ydf w36 hd"><div class="t m17 x27 he y1c ff2 fs5 fc1 sc0 ls0 ws0">(<span class="_ _8a"> </span>)</div><div class="t m17 x45 he y1d ff2 fs5 fc1 sc0 ls0 ws0">2</div><div class="t m17 x81 he y1c ff9 fs5 fc1 sc0 ls0 ws0">f</div><div class="t m3f xf3 h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p</div></div><div class="t m0 xf4 ha yde ff8 fs3 fc1 sc0 ls0 ws0">是</div><div class="c xf5 ye0 w24 h11"><div class="t m0 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _63"></span><span class="ff9">f<span class="_ _5"> </span>x</span></div></div><div class="t m0 xf6 ha yde ff8 fs3 fc1 sc0 ls0 ws0">的最大值；</div><div class="t m0 x1 ha ye1 ff1 fs3 fc1 sc0 ls0 ws0">③<span class="ff8">把函数</span></div><div class="c x3b ye2 w1d h11"><div class="t m40 x4b h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">sin<span class="_ _8b"></span><span class="ff9">y<span class="_ _81"> </span>x<span class="_ _8c"></span><span class="ffa">=</span></span></div></div><div class="t m0 x65 ha ye1 ff8 fs3 fc1 sc0 ls0 ws0">的图象上的所有点向左平移</div><div class="c xf7 ye3 wd hd"><div class="t m41 x81 he y1d ff2 fs5 fc1 sc0 ls0 ws0">3</div><div class="t m42 x26 h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p</div></div><div class="t m0 x32 ha ye1 ff8 fs3 fc1 sc0 ls0 ws0">个单位长度，可得到函数</div><div class="c xf8 ye2 w37 h11"><div class="t m43 x73 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _8d"></span><span class="ff9">y<span class="_ _8e"> </span>f<span class="_ _5"> </span>x<span class="_ _7a"></span><span class="ffa">=</span></span></div></div><div class="t m0 xf9 ha ye1 ff8 fs3 fc1 sc0 ls0 ws0">的图象．</div><div class="t m0 x1 ha ye4 ff8 fs3 fc1 sc0 ls0 ws0">其中所有正确结论的序号是</div><div class="c xfa ye5 w6 h11"><div class="t m4 xb4 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 x6f ha ye4 ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c xfb ye5 w6 h11"><div class="t m4 xb4 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89649381/bg4.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div><div class="t m0 x1 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">学科网（北京）股份有限公司</div></div><div class="c x2 y5 w2 h4"><div class="t m0 x0 h5 y6 ff2 fs1 fc1 sc0 ls0 ws0">4</div></div><div class="t m0 x2d ha y59 ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．<span class="ff1">①<span class="_ _8f"> </span></span></span>B<span class="ff8">．<span class="ff1">①③<span class="_ _90"> </span></span></span>C<span class="ff8">．<span class="ff1">②③<span class="_ _91"> </span></span></span>D<span class="ff8">．<span class="ff1">①②③</span></span></div><div class="t m0 x1 ha y5b ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b ye6 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x1 ha ye7 ff1 fs3 fc2 sc0 ls0 ws0">【分析】由已知结合正弦函数的周期公式可判断①，结合函数最值取得条件可判断②，结合函数图象的平</div><div class="t m0 x1 ha ye8 ff1 fs3 fc2 sc0 ls0 ws0">移可判断③．</div><div class="t m0 x1 ha ye9 ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：因为</div><div class="c xfc yea w20 hd"><div class="t m17 x27 he y1c ff2 fs5 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _10"> </span>sin(<span class="_ _88"> </span>)</div><div class="t m17 xed he y1d ff2 fs5 fc1 sc0 ls0 ws0">3</div><div class="t m17 x81 he y1c ff9 fs5 fc1 sc0 ls0 ws0">f<span class="_ _5"> </span>x<span class="_ _15"> </span>x</div><div class="t m3c x5f h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p</div><div class="t m17 x29 hf y1c ffa fs5 fc1 sc0 ls0 ws0">=<span class="_ _89"> </span>+</div></div><div class="t m0 x98 ha ye9 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha yeb ff1 fs3 fc2 sc0 ls0 ws0">①由周期公式可得，</div><div class="c x12 yec w24 h11"><div class="t m0 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _63"></span><span class="ff9">f<span class="_ _5"> </span>x</span></div></div><div class="t m0 x48 ha yeb ff1 fs3 fc2 sc0 ls0 ws0">的最小正周期</div><div class="c xfd yed w2b h28"><div class="t m26 x1a h2a y58 ff2 fs12 fc1 sc0 ls0 ws0">2<span class="_ _92"></span><span class="ff9">T</span></div><div class="t m44 xaa h35 y58 ffe fs19 fc1 sc0 ls0 ws0">p</div><div class="t m26 x1f h29 y58 ffa fs12 fc1 sc0 ls0 ws0">=</div></div><div class="t m0 xfe ha yeb ff1 fs3 fc2 sc0 ls0 ws0">，故①正确；</div><div class="t m0 x1 ha yee ff1 fs3 fc2 sc0 ls0 ws0">②</div><div class="c x77 yef w38 hd"><div class="t m17 x2f he y1b ff2 fs5 fc1 sc0 ls0 ws0">5<span class="_ _93"> </span>1</div><div class="t m17 x27 he y1c ff2 fs5 fc1 sc0 ls0 ws0">(<span class="_ _8a"> </span>)<span class="_ _10"> </span>s<span class="_ _0"></span>in(<span class="_ _94"> </span>)<span class="_ _10"> </span>s<span class="_ _0"></span>in</div><div class="t m17 x45 he y1d ff2 fs5 fc1 sc0 ls0 ws0">2<span class="_ _3e"> </span>2<span class="_ _8e"> </span>3<span class="_ _72"> </span>6<span class="_ _c"> </span>2</div><div class="t m17 x81 he y1c ff9 fs5 fc1 sc0 ls0 ws0">f</div><div class="t m42 xf3 h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p<span class="_ _72"> </span>p<span class="_ _8e"> </span>p<span class="_ _51"> </span>p</div><div class="t m17 x3e hf y1c ffa fs5 fc1 sc0 ls0 ws0">=<span class="_ _95"> </span>+<span class="_ _34"> </span>=<span class="_ _2b"> </span>=</div></div><div class="t m0 x5b ha yee ff1 fs3 fc2 sc0 ls0 ws0">，不是</div><div class="c x69 yf0 w24 h11"><div class="t m0 x27 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _63"></span><span class="ff9">f<span class="_ _5"> </span>x</span></div></div><div class="t m0 x9 ha yee ff1 fs3 fc2 sc0 ls0 ws0">的最大值，故②错误；</div><div class="t m0 x1 ha yf1 ff1 fs3 fc2 sc0 ls0 ws0">③根据函数图象的平移法则可得，函数</div><div class="c x23 yf2 w1d h11"><div class="t m40 x4b h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">sin<span class="_ _8b"></span><span class="ff9">y<span class="_ _81"> </span>x<span class="_ _8c"></span><span class="ffa">=</span></span></div></div><div class="t m0 xff ha yf1 ff1 fs3 fc2 sc0 ls0 ws0">的图象上的所有点向左平移</div><div class="c x100 yf3 wd hd"><div class="t m41 x81 he y1d ff2 fs5 fc1 sc0 ls0 ws0">3</div><div class="t m42 x26 h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p</div></div><div class="t m0 xe5 ha yf1 ff1 fs3 fc2 sc0 ls0 ws0">个单位长度，可得到函数</div><div class="c x1 yf4 w37 h11"><div class="t m43 x73 h12 y1f ff2 fs6 fc1 sc0 ls0 ws0">(<span class="_ _47"> </span>)<span class="_ _8d"></span><span class="ff9">y<span class="_ _8e"> </span>f<span class="_ _5"> </span>x<span class="_ _7a"></span><span class="ffa">=</span></span></div></div><div class="t m0 x101 ha yf5 ff1 fs3 fc2 sc0 ls0 ws0">的图象，故③正确．</div><div class="t m0 x1 ha yf6 ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e yf7 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x64 ha yf6 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha yf8 ff2 fs3 fc1 sc0 ls0 ws0">9<span class="ff8">．<span class="_ _96"></span>（<span class="ff2">5<span class="_ _2"> </span></span>分）设</span></div><div class="c x102 yf9 w39 h28"><div class="t m45 xaf h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">ABC<span class="_ _71"></span><span class="ffa">D</span></div></div><div class="t m0 x18 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">的内<span class="_ _0"></span>角</div><div class="c xf2 yfa we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x103 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x104 yfa we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x3c ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x22 yf9 we h28"><div class="t m1a xb4 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">C</div></div><div class="t m0 x69 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">所对<span class="_ _0"></span>的边分别<span class="_ _0"></span>为</div><div class="c x105 yf9 w2c h24"><div class="t m24 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">a</div></div><div class="t m0 xe1 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x106 yf9 w2c h28"><div class="t m46 xb4 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">b</div></div><div class="t m0 x25 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="c x107 yf9 w2c h24"><div class="t m24 x26 h2e y89 ff9 fs10 fc1 sc0 ls0 ws0">c</div></div><div class="t m0 x108 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">，已<span class="_ _0"></span>知</div><div class="c x90 yf9 w3a h11"><div class="t m47 x45 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2<span class="_ _6"> </span>2<span class="_ _3e"> </span>2</div><div class="t m47 xb4 h12 y55 ff2 fs6 fc1 sc0 ls0 ws0">sin<span class="_ _70"> </span>sin<span class="_ _97"> </span>sin<span class="_ _98"> </span>sin<span class="_ _4d"> </span>si<span class="_ _0"></span>n<span class="_ _99"></span><span class="ff9">B<span class="_ _95"> </span>C<span class="_ _9a"> </span>A<span class="_ _73"> </span>B<span class="_ _c"> </span>C<span class="_ _9b"></span><span class="ffa">+<span class="_ _9c"> </span>-<span class="_ _9d"> </span>=</span></span></div></div><div class="t m0 x109 ha yf8 ff8 fs3 fc1 sc0 ls0 ws0">，</div><div class="t m0 x1 ha yfb ff8 fs3 fc1 sc0 ls0 ws0">且</div><div class="c x77 yfc w1f h28"><div class="t m15 x4b h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">2<span class="_ _40"></span><span class="ff9">a<span class="_"> </span><span class="ffa">=</span></span></div></div><div class="t m0 x94 ha yfb ff8 fs3 fc1 sc0 ls0 ws0">，则</div><div class="c x95 yfc w39 h28"><div class="t m45 xaf h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">ABC<span class="_ _71"></span><span class="ffa">D</span></div></div><div class="t m0 x62 ha yfb ff8 fs3 fc1 sc0 ls0 ws0">的面积的最大值为</div><div class="c xe8 yfd w6 h11"><div class="t m4 xb4 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(</div></div><div class="t m0 x23 ha yfb ff8 fs3 fc1 sc0 ls0 ws0">　　</div><div class="c xb8 yfd w6 h11"><div class="t m4 xb4 h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">)</div></div><div class="t m0 x2d ha yfe ff2 fs3 fc1 sc0 ls0 ws0">A<span class="ff8">．</span>1<span class="_ _7c"> </span>B<span class="ff8">．</span></div><div class="c x6f yff w35 h1c"><div class="t m0 xaf h1d y80 ff2 fsc fc1 sc0 ls0 ws0">3</div></div><div class="t m0 x32 ha yfe ff2 fs3 fc1 sc0 ls0 ws0">C<span class="ff8">．</span>2<span class="_ _9e"> </span>D<span class="ff8">．</span></div><div class="c x71 yff w29 h1c"><div class="t m1d x26 h1d y80 ff2 fsc fc1 sc0 ls0 ws0">2<span class="_ _5"> </span>3</div></div><div class="t m0 x1 ha y100 ff1 fs3 fc2 sc0 ls0 ws0">【答案】</div><div class="c x3b y101 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x1 ha y102 ff1 fs3 fc2 sc0 ls0 ws0">【分析】利用正弦定理化角为边，结合余弦定理求得角</div><div class="c x10a y103 we h1b"><div class="t m7 x1c h9 y2b ff9 fsb fc1 sc0 ls0 ws0">A</div></div><div class="t m0 x10b ha y102 ff1 fs3 fc2 sc0 ls0 ws0">，利用余弦定理结合基本不等式求得</div><div class="c x10c y104 w33 h28"><div class="t m48 xb4 h2a y58 ff9 fs12 fc1 sc0 ls0 ws0">bc</div></div><div class="t m0 x10d ha y102 ff1 fs3 fc2 sc0 ls0 ws0">的最大值，</div><div class="t m0 x1 ha y105 ff1 fs3 fc2 sc0 ls0 ws0">再根据三角形的面积公式，即可得出答案．</div><div class="t m0 x1 ha y106 ff1 fs3 fc2 sc0 ls0 ws0">【解答】解：</div><div class="c x30 y107 w3b h11"><div class="t m0 x4c h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2<span class="_ _6"> </span>2<span class="_ _3e"> </span>2</div><div class="t m0 x4a h20 y55 ff2 fs6 fc1 sc0 ls0 ws0">sin<span class="_ _70"> </span>sin<span class="_ _97"> </span>sin<span class="_ _98"> </span>sin<span class="_ _4d"> </span>si<span class="_ _0"></span>n<span class="_ _99"></span><span class="ff9">B<span class="_ _95"> </span>C<span class="_ _9a"> </span>A<span class="_ _73"> </span>B<span class="_ _c"> </span>C<span class="_ _9b"></span><span class="ffa">+<span class="_ _9c"> </span>-<span class="_ _9d"> </span>=<span class="_ _9f"></span><span class="ffb">Q</span></span></span></div></div><div class="t m0 x10e ha y106 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y108 ff1 fs3 fc2 sc0 ls0 ws0">由正弦定理得</div><div class="c x30 y109 w3c h11"><div class="t m49 x31 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2<span class="_ _a0"> </span>2<span class="_ _58"> </span>2</div><div class="t m49 xb4 h12 y55 ff9 fs6 fc1 sc0 ls0 ws0">b<span class="_ _8"> </span>c<span class="_ _8"> </span>a<span class="_ _c"> </span>bc<span class="_ _a1"></span><span class="ffa">+<span class="_ _54"> </span>-<span class="_ _5a"> </span>=</span></div></div><div class="t m0 x103 ha y108 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y10a ff1 fs3 fc2 sc0 ls0 ws0">由余弦定理得</div><div class="c x30 y10b w3d h40"><div class="t m4a x7f h41 y10c ff2 fs21 fc1 sc0 ls0 ws0">2<span class="_ _a0"> </span>2<span class="_ _58"> </span>2</div><div class="t m4a x3b h42 y10d ff2 fs22 fc1 sc0 ls0 ws0">1</div><div class="t m4a x26 h42 y10e ff2 fs22 fc1 sc0 ls0 ws0">cos</div><div class="t m4a x43 h42 y10f ff2 fs22 fc1 sc0 ls0 ws0">2<span class="_ _a2"> </span>2</div><div class="t m4a x96 h42 y10d ff9 fs22 fc1 sc0 ls0 ws0">b<span class="_ _8"> </span>c<span class="_ _c"> </span>a</div><div class="t m4a x4b h42 y10e ff9 fs22 fc1 sc0 ls0 ws0">A</div><div class="t m4a x21 h42 y10f ff9 fs22 fc1 sc0 ls0 ws0">bc</div><div class="t m4a x10f h43 y10d ffa fs22 fc1 sc0 ls0 ws0">+<span class="_ _54"> </span>-</div><div class="t m4a x73 h43 y10e ffa fs22 fc1 sc0 ls0 ws0">=<span class="_ _a3"> </span>=</div></div><div class="t m0 x22 ha y10a ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y110 ff1 fs3 fc2 sc0 ls0 ws0">又</div><div class="c x77 y111 w3e h11"><div class="t m4b x1a h19 y1f ff2 fs6 fc1 sc0 ls0 ws0">(0,<span class="_ _9"> </span>)<span class="_ _a4"></span><span class="ff9">A</span></div><div class="t m4c x59 h44 y1f ffe fs23 fc1 sc0 ls0 ws0">p</div><div class="t m4b x4a h12 y1f ffa fs6 fc1 sc0 ls0 ws0">Î</div></div><div class="t m0 x51 ha y110 ff1 fs3 fc2 sc0 ls0 ws0">，则</div><div class="c x110 y112 w14 hd"><div class="t m17 x111 he y1d ff2 fs5 fc1 sc0 ls0 ws0">3</div><div class="t m17 x1c he y1c ff9 fs5 fc1 sc0 ls0 ws0">A</div><div class="t m3c x42 h3e y1b ffe fs1f fc1 sc0 ls0 ws0">p</div><div class="t m17 x1f hf y1c ffa fs5 fc1 sc0 ls0 ws0">=</div></div><div class="t m0 x112 ha y110 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x1 y113 w3f h28"><div class="t m4d x73 h3b y58 ff2 fs12 fc1 sc0 ls0 ws0">2<span class="_ _40"></span><span class="ff9">a<span class="_"> </span><span class="ffa">=<span class="_ _a5"></span><span class="ffb">Q</span></span></span></div></div><div class="t m0 x113 ha y114 ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y115 ff1 fs3 fc2 sc0 ls0 ws0">由余弦定理得</div><div class="c x30 y116 w40 h11"><div class="t m0 x31 h27 y54 ff2 fs11 fc1 sc0 ls0 ws0">2<span class="_ _58"> </span>2<span class="_ _a0"> </span>2</div><div class="t m0 x114 h12 y55 ff2 fs6 fc1 sc0 ls0 ws0">2<span class="_ _12"> </span>cos<span class="_ _a6"></span><span class="ff9">a<span class="_ _c"> </span>b<span class="_ _8"> </span>c<span class="_ _69"> </span>bc<span class="_ _f"> </span>A<span class="_ _a7"></span><span class="ffa">=<span class="_ _5a"> </span>+<span class="_ _54"> </span>-</span></span></div></div><div class="t m0 x9a ha y115 ff1 fs3 fc2 sc0 ls0 ws0">，即</div><div class="c xce y117 w41 h1c"><div class="t m4e x4c h1e y118 ff2 fsd fc1 sc0 ls0 ws0">2<span class="_ _38"> </span>2</div><div class="t m4e x26 h1f y119 ff2 fsc fc1 sc0 ls0 ws0">4<span class="_ _10"> </span><span class="ff9">b<span class="_ _8"> </span>c<span class="_ _5a"> </span>bc<span class="_ _20"> </span>bc<span class="_ _45"></span><span class="ffa">=<span class="_ _5a"> </span>+<span class="_ _6d"> </span>-<span class="_ _4a"> </span><span class="ffb">…</span></span></span></div></div><div class="t m0 x115 ha y115 ff1 fs3 fc2 sc0 ls0 ws0">，当且仅当</div><div class="c xe y11a w1d h28"><div class="t m13 x4d h29 y58 ff2 fs12 fc1 sc0 ls0 ws0">2<span class="_ _8d"></span><span class="ff9">b<span class="_ _10"> </span>c<span class="_ _a8"></span><span class="ffa">=<span class="_ _4d"> </span>=</span></span></div></div><div class="t m0 x116 ha y115 ff1 fs3 fc2 sc0 ls0 ws0">时等号成立，</div><div class="c x1 y11b w3f h38"><div class="t m4f x3e h3a yc3 ff2 fs1c fc1 sc0 ls0 ws0">4<span class="_ _a9"></span><span class="ff9">bc<span class="_ _62"></span><span class="ffa">\<span class="_ _8e"> </span><span class="ffb">„</span></span></span></div></div><div class="t m0 x113 ha y11c ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="t m0 x1 ha y11d ff1 fs3 fc2 sc0 ls0 ws0">则</div><div class="c x77 y11e w42 h2f"><div class="t m0 x1b h19 y90 ff2 fs6 fc1 sc0 ls0 ws0">1<span class="_ _aa"> </span>3</div><div class="t m0 x1 h19 y91 ff2 fs6 fc1 sc0 ls0 ws0">sin<span class="_ _24"> </span>3</div><div class="t m0 x1b h19 y92 ff2 fs6 fc1 sc0 ls0 ws0">2<span class="_ _ab"> </span>4</div><div class="t m0 x1f h27 y11f ff9 fs11 fc1 sc0 ls0 ws0">ABC</div><div class="t m0 x26 h19 y91 ff9 fs6 fc1 sc0 ls0 ws0">S<span class="_ _ac"> </span>bc<span class="_ _38"> </span>A<span class="_ _89"> </span>bc</div><div class="t m0 x31 h45 y11f ffa fs11 fc1 sc0 ls0 ws0">D</div><div class="t m0 x73 h20 y91 ffa fs6 fc1 sc0 ls0 ws0">=<span class="_ _ad"> </span>=<span class="_ _23"> </span><span class="ffb">„</span></div></div><div class="t m0 x83 ha y11d ff1 fs3 fc2 sc0 ls0 ws0">，</div><div class="c x1 y120 w43 h28"><div class="t m26 x88 h29 y58 ff9 fs12 fc1 sc0 ls0 ws0">ABC<span class="_ _8d"></span><span class="ffa">\<span class="_ _87"> </span>D</span></div></div><div class="t m0 x117 ha y121 ff1 fs3 fc2 sc0 ls0 ws0">的面积的最大值为</div><div class="c xc0 y122 w35 h1c"><div class="t m0 xaf h1d y80 ff2 fsc fc1 sc0 ls0 ws0">3</div></div><div class="t m0 x118 ha y121 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x1 ha y123 ff1 fs3 fc2 sc0 ls0 ws0">故选：</div><div class="c x2e y124 we h1b"><div class="t m7 x26 h9 y2b ff9 fsb fc1 sc0 ls0 ws0">B</div></div><div class="t m0 x64 ha y123 ff1 fs3 fc2 sc0 ls0 ws0">．</div><div class="t m0 x3c hb y125 ff6 fs4 fc1 sc1 ls0 ws0">第二部分（非<span class="_ _0"></span>选择题</div><div class="t m0 x119 h46 y126 ff7 fs4 fc1 sc0 ls0 ws0"> </div><div class="t m0 xeb hb y125 ff6 fs4 fc1 sc1 ls0 ws0">共</div><div class="t m0 x6b h46 y126 ff7 fs4 fc1 sc0 ls0 ws0">105</div><div class="t m0 xd hb y125 ff6 fs4 fc1 sc1 ls0 ws0">分）</div><div class="t m0 x1 ha y127 ff6 fs3 fc1 sc1 ls0 ws0">二、填空题：<span class="_ _0"></span>本题共</div><div class="t m0 x11a hc y128 ff7 fs3 fc1 sc0 ls0 ws0">6</div><div class="t m0 xae ha y127 ff6 fs3 fc1 sc1 ls0 ws0">小题，每小题</div><div class="t m0 xe8 hc y128 ff7 fs3 fc1 sc0 ls0 ws0">5</div><div class="t m0 x69 ha y127 ff6 fs3 fc1 sc1 ls0 ws0">分，共</div><div class="t m0 xde hc y128 ff7 fs3 fc1 sc0 ls0 ws0">30</div><div class="t m0 x11b ha y127 ff6 fs3 fc1 sc1 ls0 ws0">分</div><div class="t m0 x33 hc y128 ff7 fs3 fc1 sc0 ls0 ws0">.</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div>

100+评论昵称:

captcha

基于PHP的水质管理系统（用户端、管理员端）
基于php、html、mysql、bootstrap、layui进行全栈式开发。项目完成了前端用户平台、后端管理员平台，以乡村水质检测为主题设立。项目用户页面包括“用户首页”、“关于我们”、“水质新闻”、“水质检测报告”四个模块。水质检测宣传、项目产品、项目服务、未来计划、项目团队、指导团队、成就展示、水质新闻展示、水质报告增删改查的各项功能。项目管理员页面包括“数据展示”、“用户管理”、“水域管理”三个模块。实现了后台数据库数据可视化展示、数据库全用户管理以及权限分配、水域分配以及管理的各项功能。项目登录登出与注册页面实现了用户和管理员权限区分，登录后进入不同平台的功能。语言：php、html、css、javascript工具：Wampserver、Mysql、Dreamever。框架与样式库：bootstrap、echarts、jquery、layui、popper。
后端
php水质管理系统源码.zip 72.87KB
10 月前