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1 . 解方程
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cef1c6de51e6d2f0aae7518a632fe0f.png)
(2)
.
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59554131f22c1f06174cfbecf5cd4457.png)
(4)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cef1c6de51e6d2f0aae7518a632fe0f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6a3247eeb7b1d40d6e43e203f25d0a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59554131f22c1f06174cfbecf5cd4457.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bbe7170aebb6d15d04768271f35d13.png)
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2 . (1)先化简,再求值:
,其中
.
(2)先化简;再求值:当
时;求代数式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee6c509313fac5387d910b661e5ff1.png)
(3)关于
的代数式
的值与
无关,求
的值.
(4)求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb05868da64493f9a2c4dc3871011a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8f878ab71705ccae99bfc9a32c8b8e.png)
(2)先化简;再求值:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad202ed8c2aea4e055f9dc62f581bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee6c509313fac5387d910b661e5ff1.png)
(3)关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f9c5f751a21b4c026144b6f2782e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(4)求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe924053218702aa2a43139bf611c2f.png)
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3 . 如图,在平面直角坐标系中,
分别为
轴、
轴正半轴上的点,以
、OC为边,在第一象限内作矩形OABC,且
.将矩形OABC翻折,使点
与原点重合,折痕为
,点
的对应点
落在第四象限,过
点的反比例函数
,其图象恰好过
的中点,则点的
坐标为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036399ffc4595e843dfbd93049238dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1410e0a731a4a6cdd55ef6f38aee40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f647db75e79757c4031b749613f344f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/13/dc5f0ef7-dc42-438b-82f4-fc3ecc54253c.png?resizew=223)
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2022-10-08更新
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97次组卷
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2卷引用:江苏省无锡市市北高级中学2021-2022学年高一上学期期初检测数学试题
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4 . 如果
互为相反数,
互为倒数,
的绝对值是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aaf880270275f2dedb42a8c7d28de0c.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca31577dd76afbc1b720cdcad88ffd16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aaf880270275f2dedb42a8c7d28de0c.png)
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5 . 若
,则对
的任何值,多项式
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634092b6a8694adb8211f6230566a0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f26fef2b28ef0e0c22a0bef893319a9.png)
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6 . 《算法统宗》中记有“李白沽酒”的故事.诗云:今携一壶酒,游春郊外走.逢朋加一倍,入店饮半斗.相逢三处店,饮尽壶中酒.试问能算士:如何知原有?(古代一斗是10升)大意是:李白在郊外春游时,做出这样一条约定:遇见朋友,先到酒店里将壶里的酒增加一倍,再喝掉其中的5升酒.按照这样的约定,在第3个店里遇到朋友正好喝光了壶中的酒.则李白的酒壶中原有___________ 升酒.
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7 . 某校将举行“咏经典”诗文比赛,决赛阶段只剩下甲、乙、丙、丁实力相当的四名同学,则甲、乙同学获得前两名的概率是___________ .
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2022-10-08更新
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92次组卷
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2卷引用:江苏省无锡市市北高级中学2021-2022学年高一上学期期初检测数学试题
8 . 下列图中阴影部分面积与算式
的结果相同的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0cc84890abe9142b41c656b248c976.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
9 . 已知曲线
上一动点
到两定点
,
的距离之和为
,过点
的直线
与曲线
相交于点
,
.
(1)求曲线
的方程;
(2)动弦
满足:
,求点
的轨迹方程;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f7a7cf83fb9706134edb619d8aa90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cc3f576dcf32e3ec2de59ea8059a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14dd75003428d5b4071aabbaa4d11cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)动弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55899a55390743a4dd830402641d2122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979df095c33a0d8edce5c1fab7cad04.png)
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382次组卷
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2卷引用:上海市行知中学2022届高三上学期开学考试数学试题
10 . 在“立体几何”知识中:①两直线所成角的取值范围是
;②直线与平面所成角的取值范围是
;③二面角的平面角取值范围是
.在“解析几何”知识中;④直线的倾斜角取值范围是
;⑤两直线的夹角取值范围是
;在“向量”知识中:⑥两向量的夹角的取值范围是
;以上概念叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa898d5280ab56f52aeedc2cce370bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14bdd7f2b48c0ce6ba8696c89fbf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b1d28a098ea5555c89b332fad25b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917ae6fcf56fa6b4fc9852854cd8f78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
A.②①④⑤ | B.②③④⑥ | C.③④⑤⑥ | D.②③④⑤ |
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