名校
1 . 记实数
,
中的最小值为
,例如
,当
取任意实数时,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c954fef3c9af71c228f22c4f5e3f00de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0aeb68789d2079c6d1e22dc0fd74fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6071ec2ffa6e87cc39fba8c7e95a1c.png)
A.5 | B.4 | C.3 | D.2 |
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2 . 汽车的“燃油效率”是指汽车每消耗1升汽油最多可行驶的公里数,如图描述了A、B两辆汽车在不同速度下的燃油效率情况,根据图中信息,下面4个推断中,合理的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/e4bce3e3-c2e5-4d21-9379-a11093723afe.jpg?resizew=231)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/e4bce3e3-c2e5-4d21-9379-a11093723afe.jpg?resizew=231)
A.消耗1升汽油,A车最多可行驶5千米 |
B.B车以40千米/小时的速度行驶1小时,最少消耗4升汽油 |
C.对于A车而言,行驶速度越快越省油 |
D.某城市机动车最高限速80千米/小时,相同条件下,在该市驾驶B车比驾驶A车更省油 |
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3 . 反比例函数
其中
的部分图象记为曲线
,将
沿y轴翻折,得到曲线
,直线
与
、
一共只有两个公共点,则b的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c5dbbd1a7f9932567099ee67f2443f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8e09440ba8161cda6b60eb3ca5dfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bd144e0e96e4236a14523e0729cacb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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4 . 如图1所示的图形是一个轴对称图形,且每个角都是直角,长度如图所示,小明按图2所示方法玩拼图游戏,两两相扣,相互间不留空隙,那么小明用9个这样的图形拼出来的图形的总长度是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/ab4a14b2-f8c7-4d2f-8f41-6904555d42eb.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/ab4a14b2-f8c7-4d2f-8f41-6904555d42eb.png?resizew=314)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
5 . 已知m为已知常数,且
,如图对称轴为直线
的二次函数
的图象与x轴交于A、B两点,与y轴交于C点,B点的坐标为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/9612b1ad-5370-4c8b-a6e6-35e5ff9d401d.png?resizew=190)
(1)求此二次函数的解析式;
(2)在直线
上找一点P,使
的周长最小,并求出点P的坐标;
(3)现定义一个新运算,
,且
,当
时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f5f4ded389ecab2fe3b3cc44977993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32d26c8d44f5fb4813a19c1030a9f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/9612b1ad-5370-4c8b-a6e6-35e5ff9d401d.png?resizew=190)
(1)求此二次函数的解析式;
(2)在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(3)现定义一个新运算,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9267ac6f792b25bf6c6ab56b78d7299a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4796d015853d5db00e1f2567da9ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d2343c81fcad8f99284b6c464dd280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd00f42a62756926ff484cabc368ef9c.png)
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解题方法
6 . 当
时,求函数
的最小值(其中t为常数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966d9dd819cba29980da3700422c2497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90d292b1a550a873c9b1b57e128da49.png)
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7 . 按要求计算:
(1)分解因式:
;
(2)已知
,求
的值;
(3)
;
(4)已知
,求
的值.
(1)分解因式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfdb71089c581d4a65a944f18fcfc40.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ccf1328602bd22b09ca55faa023a3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac0218b480ef3eeec90ad04bdffb55f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875e9e322ab55609bf86fbc632175bda.png)
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80236b37de6f299b5ff05d1ff29850c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31f3398b18fc1b3285129af356f48e1.png)
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解题方法
8 . 已知关于x一元二次方程
有两个实根
,
,(1)若
比3大,
比3小,则a的取值范围是______ ;(2)把
写成用含a表达式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9d53db986fa98cf9391c6d30870338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
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9 . 根式运算:①若
,则x的取值范围是______ ;②化简![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6befb2396e904f04041bc022fc139383.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffbb00106dcc4f1b80a6e00dcc3b9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6befb2396e904f04041bc022fc139383.png)
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10 . 图①,在
中,
,
,
.求作菱形
,使点
在边
上,点
、
在边
上,点
在边
上.根据小明的作法,下列说法中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/c81620dc-cb79-41d2-948d-1a0aeb36a4dc.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/c81620dc-cb79-41d2-948d-1a0aeb36a4dc.png?resizew=164)
小明的作法 1.如图②,在边 ![]() ![]() ![]() ![]() ![]() ![]() 2.以点 ![]() ![]() ![]() ![]() 3.在 ![]() ![]() ![]() ![]() ![]() |
A.按照小明的作法,一定能作出菱形![]() |
B.当![]() |
C.当只能作出一个菱形时,![]() |
D.作出的菱形周长最大为![]() |
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