1 . 若复数
满足
(
为虚数单位),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35845a775881218a4d0a4944dee85ed9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c9e1505c8957fde08b7ee6638bb818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35845a775881218a4d0a4944dee85ed9.png)
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解题方法
2 . 已知向量
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c243b5d0d732650434997b83e43ff1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec0d2c49c287c9fca50c90252a2735b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c243b5d0d732650434997b83e43ff1.png)
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解题方法
3 . 设
是数列
的前
项和(其中
为正整数),已知
,且数列
是等差数列,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed51d0dcfb266e60acc0249cb8971d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
4 . 函数
的部分图像的示意图如图所示,已知
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5dac6977823733308100a1c267e3bf6.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29602cbc73377b9e6dde14a1cccbf05a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6d9f798a99a7b28888820716549f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe66a5de3864adef925142cbd08fc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5dac6977823733308100a1c267e3bf6.png)
您最近一年使用:0次
5 . 在某一个十字路口,每次亮绿灯的时长为
(
为时间单位:秒),那么每次绿灯亮时,在同一条直行道路上同方向能有多少辆汽车通过该十字路口?
该问题涉及车长、车距、车速,前方堵塞状况包括行人非机动车等因素.为了将问题简化,在路况车况驾驶状态等都良好的前提下,提出如下基本假设:
1.通过路口的车辆长度都相等;
2.等待通行时,前后相邻两辆车的车距都相等;
3.绿灯亮时,汽车都是沿同方向从静止状态匀加速启动,到达最高限速汽车开始匀速行驶;
4.离路口信号灯最近的第一辆车在绿灯亮后延迟
时间开始动起来.前一辆车启动后,下一辆车启动的延迟时间相等,在延迟时间内,车辆保持静止;
5.按照交通安全法规行驶,行车秩序良好,没有碰擦或堵塞等现象发生.
1.车长设为
,取
,车距设为
,取
,第一辆车离停车线距离为
;
2.加速度记作
,取
,汽车在匀加速运动
时段行驶路程
;
3.前后车启动延迟时间记为
,取
;
4.第
辆车启动延迟时间为
;
5.该十字路口限速
,换算为
;
6.第
辆车到达最高限速的时间为
取
.
设第
辆车在绿灯持续
时间内驶离停车线的距离为
.根据上述假设与数据,
,依次类推.请你解决下列问题:
(1)求
;(结果保留一位小数,单位:
)
(2)对于第
辆车,写出函数
的分段表达式;
(3)求在亮绿灯的
内,这一条直行道路上同方向能有多少辆汽车通过该十字路口.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6fd3aa935cffb2a4526ed28f47e4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2065bdd4392601a18d1ef1fc1fdb13ce.png)
该问题涉及车长、车距、车速,前方堵塞状况包括行人非机动车等因素.为了将问题简化,在路况车况驾驶状态等都良好的前提下,提出如下基本假设:
1.通过路口的车辆长度都相等;
2.等待通行时,前后相邻两辆车的车距都相等;
3.绿灯亮时,汽车都是沿同方向从静止状态匀加速启动,到达最高限速汽车开始匀速行驶;
4.离路口信号灯最近的第一辆车在绿灯亮后延迟
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9206b8d3214e21a3115c6bc9886d03.png)
5.按照交通安全法规行驶,行车秩序良好,没有碰擦或堵塞等现象发生.
1.车长设为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd09cd596379a9b81dd6cd74e123fd13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97599b586b7decae67a55cd008b9091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651a6747032c07c0ac12257e6fe8b254.png)
2.加速度记作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d90ff2ab2472b25fd95756e144f861d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a54eb2123d9eafa3b923287abe8b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2c53ba413678dc85ab3a6f0faf3c9e.png)
3.前后车启动延迟时间记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9206b8d3214e21a3115c6bc9886d03.png)
4.第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ac4aec03431ef10172065c4a4fad20.png)
5.该十字路口限速
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d55f3eb3475ce28862370d286ebc4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e29784992adeb6014c71cbb551e0652.png)
6.第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b0b9925db981df603f7e863189fe3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e1ccd5ed2a995b0162013014396321f.png)
设第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a54eb2123d9eafa3b923287abe8b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f48ae649161e580a4f96966f92abbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b865e8598fcbb953b40dbb143576640d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a3dc3e602639ccbf1a2e9c82a68e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
(2)对于第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f48ae649161e580a4f96966f92abbc.png)
(3)求在亮绿灯的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6fd3aa935cffb2a4526ed28f47e4ee.png)
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解题方法
6 . 已知一元二次方程
.
(1)在复数范围内解该方程;
(2)设这个方程的两个复数根
在复平面上所对应的向量分别为
(
为坐标原点),求
与
夹角
的大小.(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ce5f1be547bd7e6852875d3aa4ad77.png)
(1)在复数范围内解该方程;
(2)设这个方程的两个复数根
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02bf8659b535ca7ffc2f4647dde72a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8cbdd6bad9c05c3bee467655d32f538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1640d3fff861f45c5eb4019943b000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
解题方法
7 . 已知角
的终边经过点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6f607f3471373bc9e851ac8a579c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b81ce0c95f338dffecd185a981ec20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
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8 . 已知函数
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8148d19a676998fefef19fcea22a3972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afaa9cf5610f785f5873d01ea0c1cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d514174b3d31834dd436ba2bd1d8d1.png)
A.11 | B.14 | C.17 | D.20 |
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9 . 如图的实线部分是江南某公园内的一个月亮门的正面外部轮廓,它由三部分构成:①水平地平线
;②位于地平线
与离地
高的水平线
之间的是长半轴长为
的同一个椭圆的左、右两侧的一部分;③水平线
以上是半径为
的半圆.
(2)某货运公司计划搬运一批大型包装箱通过此门,包装箱能否通过此门取决于其横截面的形状和大小,若包装箱的横截面分别为正方形或正三角形,搬运过程中要求包装箱保持水平状态(横截面与地面垂直,且有一边保持水平),为方便搬运,你会提前告诉货运公司哪些信息?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56045dacb47a5909c193ad70beb81806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b4f2a143735077f598fbab4f1452ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
(2)某货运公司计划搬运一批大型包装箱通过此门,包装箱能否通过此门取决于其横截面的形状和大小,若包装箱的横截面分别为正方形或正三角形,搬运过程中要求包装箱保持水平状态(横截面与地面垂直,且有一边保持水平),为方便搬运,你会提前告诉货运公司哪些信息?为什么?
您最近一年使用:0次
解题方法
10 . (1)请写出由拋物线的定义推导抛物线的标准方程
的过程;
(2)设直线
与抛物线
交于
两点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d3113c33d21b940f2fc864a79ca4b2.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d3113c33d21b940f2fc864a79ca4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b004f3c29ca828a163255c25323e7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次