解题方法
1 . 在半径为1的圆
中,以圆心
为中心作一个正六边形
,再分别以其各边为底边,圆
上的点为顶点作等腰三角形
,如图,沿虚线剪开后,分别以
为折痕折起
,使
重合,得到六棱锥,则当六棱锥体积最大时,正六边形的边长为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239eab132ad665ff850eb3534ee19b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80edb3049a8391c224dba21094954766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239eab132ad665ff850eb3534ee19b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c5465c3be81e4156ff7cc7fb1f3559.png)
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2 . 用平行于棱锥底面的平面去截棱锥,把底面和截面之间的那部分多面体叫做棱台.在正三棱台
中,侧棱
,则侧棱
与底面ABC所成角的正弦值为_____________ ,该三棱台的体积为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944f00d2d962252c286827fd47b4b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
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3 . 袋中有4个红球,
个黄球,
个绿球.所有球除颜色不同外,形状,大小,质量完全一样.现从中任取两个球,若取出的两个球都是红球的概率为
,记取出的红球数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d419c30ff40e9b368a3f151f639dac8f.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d419c30ff40e9b368a3f151f639dac8f.png)
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4 . 等比数列
的前
项和为
,且数列
的公比为32,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e030e6477f83384109416cbde2479bf7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051392edad70a34634b89bdac068f67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e030e6477f83384109416cbde2479bf7.png)
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解题方法
5 . 函数
,
,则
的值域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2492e103144fed2161e1b8c9d6bab212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aef458f2367b76432719f6f56275d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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6 . 已知圆
和圆
,M、N分别是圆C、D上的动点,P为x轴上的动点,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42a8ef4cb2c0338bff440837e4cfa87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6735579eb7453c5691cf738fdd1c467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1b3031d7393a63719166285314d73f.png)
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7 . 已知函数
,
的部分图象如图所示.若将函数
的图象向右平移
个单位长度,得到函数
的图象.若函数
为奇函数,则
的最小值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024d0af0c008ea76f5f5991723dfe784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e5dbf1c6e8c37604704bc27eeb93d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebd1d359040a1172a944ded96ed0127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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8 . 蚊香具有悠久的历史,我国蚊香的发明与古人端午节的习俗有关,如图为某校数学社团用数学软件制作的“蚊香”.画法如下:在水平直线上收长度为1的线段
,作一个等边三角形
,然后以点
为圆心,
为半径逆时针画圆弧交线段
的延长线于点
(第一段圆弧),再以点
为圆心,
为半径逆时针画圆弧交线段
的延长线于点
,再以点
为圆心,
为半径逆时针画圆弧……以此类推,当得到的“蚊香”恰好有15段圆弧时,“蚊香”的长度为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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9 . 已知
,
,若有且只有一组数对
满足不等式
,则实数
的取值集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ecd6c836ea6552b5d8f30db1abbc83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f142f51af74a591255d2cba7b14396c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5006c39a681747e6653e93589b5a467b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a104d2f91774c27a0810d20bd4799bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 在三棱锥中
,
,且
.记直线
,
与平面
所成角分别为
,
,已知
,当三棱锥
的体积最小时,则三棱锥
外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4959250cb4f4289b7c5400c7bee0426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae8179359f73d7202df34aa62748c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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