高中数学 http://xuewuyou.com/math/high zh-hans 高中数学解答题的通用答题套路,必须掌握! http://xuewuyou.com/math/detail/47.html <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--math.html.twig x field--node--title.html.twig * field--node--math.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>高中数学解答题的通用答题套路,必须掌握!</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--math.html.twig x field--node--uid.html.twig * field--node--math.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <span lang="" about="/index.php/user/6" typeof="schema:Person" property="schema:name" datatype="">学无忧</span> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--math.html.twig x field--node--created.html.twig * field--node--math.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>周三, 12/04/2019 - 02:50</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/xwy/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/xwy/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--body--math.html.twig * field--node--body.html.twig * field--node--math.html.twig * field--body.html.twig * field--text-with-summary.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/xwy/templates/field/field.html.twig' --> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p class="p1"><span class="s2">1</span><span class="s1">、三角变换与三角函数的性质问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">不同角化同角。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">降幂扩角。</span></p> <p class="p4"><span class="s3">§ </span><span class="s4">化</span><span class="s3">f</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)=</span><span class="s3">Asin</span><span class="s4">(</span><span class="s3">ωx</span><span class="s4">+</span><span class="s3">φ</span><span class="s4">)+</span><span class="s3">h</span><span class="s4">。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">结合性质求解。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">化简:三角函数式的化简,一般化成</span><span class="s3">y</span><span class="s4">=</span><span class="s3">Asin</span><span class="s4">(</span><span class="s3">ωx</span><span class="s4">+</span><span class="s3">φ</span><span class="s4">)+</span><span class="s3">h</span><span class="s4">的形式,即化为“一角、一次、一函数”的形式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">整体代换:将</span><span class="s3">ωx</span><span class="s4">+</span><span class="s3">φ</span><span class="s4">看作一个整体,利用</span><span class="s3">y</span><span class="s4">=</span><span class="s3">sin x</span><span class="s4">,</span><span class="s3">y</span><span class="s4">=</span><span class="s3">cos x</span><span class="s4">的性质确定条件。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求解:利用</span><span class="s3">ωx</span><span class="s4">+</span><span class="s3">φ</span><span class="s4">的范围求条件解得函数</span><span class="s3">y</span><span class="s4">=</span><span class="s3">Asin</span><span class="s4">(</span><span class="s3">ωx</span><span class="s4">+</span><span class="s3">φ</span><span class="s4">)+</span><span class="s3">h</span><span class="s4">的性质,写出结果。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">反思:反思回顾,查看关键点,易错点,对结果进行估算,检查规范性。</span></p> <p class="p1"><span class="s2">2</span><span class="s1">、解三角函数问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">化简变形;用余弦定理转化为边的关系;变形证明。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">用余弦定理表示角;用基本不等式求范围;确定角的取值范围。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">定条件:即确定三角形中的已知和所求,在图形中标注出来,然后确定转化的方向。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">定工具:即根据条件和所求,合理选择转化的工具,实施边角之间的互化。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求结果。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">再反思:在实施边角互化的时候应注意转化的方向,一般有两种思路:一是全部转化为边之间的关系;二是全部转化为角之间的关系,然后进行恒等变形。</span></p> <p class="p1"><span class="s2">3</span><span class="s1">、数列的通项、求和问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">先求某一项,或者找到数列的关系式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求通项公式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求数列和通式。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">找递推:根据已知条件确定数列相邻两项之间的关系,即找数列的递推公式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求通项:根据数列递推公式转化为等差或等比数列求通项公式,或利用累加法或累乘法求通项公式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">定方法:根据数列表达式的结构特征确定求和方法(如公式法、裂项相消法、错位相减法、分组法等)。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">写步骤:规范写出求和步骤。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">再反思:反思回顾,查看关键点、易错点及解题规范。</span></p> <p style="text-align: center"> </p> <p class="p1"><span class="s2">4</span><span class="s1">、利用空间向量求角问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">建立坐标系,并用坐标来表示向量。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">空间向量的坐标运算。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">用向量工具求空间的角和距离。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">找垂直:找出(或作出)具有公共交点的三条两两垂直的直线。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">写坐标:建立空间直角坐标系,写出特征点坐标。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求向量:求直线的方向向量或平面的法向量。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求夹角:计算向量的夹角。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">得结论:得到所求两个平面所成的角或直线和平面所成的角。</span></p> <p class="p1"><span class="s2">5</span><span class="s4">、</span><span class="s1">圆锥曲线中的范围问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">设方程。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">解系数。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">得结论。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">提关系:从题设条件中提取不等关系式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">找函数:用一个变量表示目标变量,代入不等关系式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">得范围:通过求解含目标变量的不等式,得所求参数的范围。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">再回顾:注意目标变量的范围所受题中其他因素的制约。</span></p> <p class="p1"><span class="s2">6</span><span class="s1">、解析几何中的探索问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">一般先假设这种情况成立(点存在、直线存在、位置关系存在等)。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">将上面的假设代入已知条件求解。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">得出结论。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">先假定:假设结论成立。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">再推理:以假设结论成立为条件,进行推理求解。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">下结论:若推出合理结果,经验证成立则肯。定假设;若推出矛盾则否定假设。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">再回顾:查看关键点,易错点(特殊情况、隐含条件等),审视解题规范性。</span></p> <p class="p1"><span class="s2">7</span><span class="s1">、离散型随机变量的均值与方法</span></p> <p class="p3"><span class="s4">①解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">标记事件;对事件分解;计算概率。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">确定</span><span class="s3">ξ</span><span class="s4">取值;计算概率;得分布列;求数学期望。</span></p> <p class="p3"><span class="s4">②构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">定元:根据已知条件确定离散型随机变量的取值。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">定性:明确每个随机变量取值所对应的事件。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">定型:确定事件的概率模型和计算公式。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">计算:计算随机变量取每一个值的概率。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">列表:列出分布列。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求解:根据均值、方差公式求解其值。</span></p> <p class="p1"><span class="s2">8</span><span class="s1">、函数的单调性、极值、最值问题</span></p> <p class="p1"><span class="s2">①</span><span class="s1">解题路线图</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">先对函数求导;计算出某一点的斜率;得出切线方程。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">先对函数求导;谈论导数的正负性;列表观察原函数值;得到原函数的单调区间和极值。</span></p> <p class="p1"><span class="s2">②</span><span class="s1">构建答题模板</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">求导数:求</span><span class="s3">f</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)的导数</span><span class="s3">f′</span><span class="s4">(</span><span class="s3">x</span><span class="s4">),注意</span><span class="s3">f</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)的定义域。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">解方程:解</span><span class="s3">f′</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)=</span><span class="s3">0</span><span class="s4">,得方程的根。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">列表格:利用</span><span class="s3">f′</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)=</span><span class="s3">0</span><span class="s4">的根将</span><span class="s3">f</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)定义域分成若干个小开区间,并列出表格。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">得结论:从表格观察</span><span class="s3">f</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)的单调性、极值、最值等。</span></p> <p class="p3"><span class="s3">§ </span><span class="s4">再回顾:对需讨论根的大小问题要特殊注意,另外观察</span><span class="s3">f</span><span class="s4">(</span><span class="s3">x</span><span class="s4">)的间断点及步骤规范性。</span></p> <p class="p1"><span class="s1">遇到大题怎么做</span></p> <p class="p1"><span class="s2">1</span><span class="s1">、做</span><span class="s2">——</span><span class="s1">常规题目直接做</span></p> <p class="p3"><span class="s4">在理解题意后,立即思考问题属于哪一章节?与这一章节的哪个类型比较接近?解决这个类型有哪些方法?哪个方法可以首先拿来试用?这样一想,做题的方向就有了。</span></p> <p class="p1"><span class="s2">2</span><span class="s1">、套</span><span class="s2">——</span><span class="s1">陌生题目往熟套</span></p> <p class="p3"><span class="s4">高考题目一般而言,很少会出怪题、偏题。很多题目乍一看是新题型,没见过;但是换个角度思考一下;或者试着往下面运算两步、做一下变形,就会回到你熟悉的套路上去。因此遇到没做过的题型,不要慌张,尝试往自己做过的题目上套。</span></p> <p class="p1"><span class="s2">3</span><span class="s1">、推</span><span class="s2">——</span><span class="s1">正面难解反向推</span></p> <p class="p3"><span class="s4">后面的大题,尤其是一些证明题,不少同学会发现正面推到一半推不下去了。这时候不妨尝试从结果开始反向推理证明。或者想一想,想要得出结果,需要哪些已知条件,这些条件能够通过哪些方式获得。从两头入手,向中间挤压、合拢,尽可能完成题目。</span></p> </div> <!-- END OUTPUT from 'themes/xwy/templates/field/field.html.twig' --> Wed, 04 Dec 2019 02:50:39 +0000 学无忧 47 at http://xuewuyou.com