解题方法
1 . (1)计算:
;
(2)已知
,计算
的值并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03174be2aeab05cb62ce0202313fe2b8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d00f77341badaa94a3a56e410d0985b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f0b84ee4ed90face0993d4f4dda379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ae5638d85483b26edfd69a0a4abaae.png)
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2 . 节约资源和保护环境是中国的基本国策.某化工企业,积极响应国家要求,探索改良工艺,使排放的废气中含有的污染物数量逐渐减少.已知改良工艺前所排放的废气中含有的污染物数量为
,首次改良后所排放的废气中含有的污染物数量为
. 设改良工艺前所排放的废气中含有的污染物数量为
,首次改良工艺后所排放的废气中含有的污染物数量为
,第
次改良后所排放的废气中的污染物数量
,可由函数模型
给出,其中
是指改良工艺的次数.
(1)试求改良后所排放的废气中含有的污染物数量的函数模型;
(2)依据国家环保要求,企业所排放的废气中含有的污染物数量不能超过
,试问至少进行多少次改良工艺后,才能使得该企业所排放的废气中含有的污染物数量达标?
(参考数据:取
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643207cd7705652c36db22289d705b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f8280862bb1304584434473624df1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2833ddbe58a6f4e7585c69c698f0d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135cb036833400f3fa1edc92d5ce410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997569581677dceec538af7380a813af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)试求改良后所排放的废气中含有的污染物数量的函数模型;
(2)依据国家环保要求,企业所排放的废气中含有的污染物数量不能超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84435639f617a49386c9115985b5c55e.png)
(参考数据:取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcc4e8297d10c1344a4cdaf67eee268.png)
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3 . 已知
.
(1)分别求
和
;
(2)若
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798807f971504a4ddb00898dbef09886.png)
(1)分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ffbece8eaa48d6f874ad33257a0da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871c01f016b80a7af493e05c06bab4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
4 . (1)计算:
;
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6280e5a7f70ff2dbdc8a678e24507303.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9174586826fb9bf2f4ba4ee3efb967d6.png)
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5 . “宸宸”“琮琮”“莲莲”是2023年杭州亚运会吉祥物,组合名为“江南忆”,出自唐朝诗人白居易的名句“江南忆,最忆是杭州”,它融合了杭州的历史人文、自然生态和创新基因.某中国企业可以生产杭州亚运会吉祥物“宸宸”“琮踪”“莲莲”,根据市场调查与预测,投资成本x(百万元)与利润y(百万元)的关系如下表:
当投资成本
不高于12(百万元)时,利润
(百万元)与投资成本
(百万元)的关系有两个函数模型
与
可供选择.
(1)当投资成本
不高于12(百万元)时,选出你认为最符合实际的函数模型,并求出相应的函数解析式;
(2)当投资成本
高于12(百万元)时,利润
(百万元)与投资成本
(百万元)满足关系
,结合第(1)问的结果,要想获得不少于一千万元的利润,投资成本
(百万元)应该控制在什么范围.(结果保留到小数点后一位)(参考数据:
)
![]() | ![]() | 2 | ![]() | 4 | ![]() | 12 | ![]() |
![]() | ![]() | 0.4 | ![]() | ![]() | ![]() | 12.8 | ![]() |
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29eefd206a1f3a11c0c11c1062f4f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d60ebf0ccf455866ac61b83632d43d1.png)
(1)当投资成本
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当投资成本
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e48328ebaff6f11ddded3ec01a8b216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5869279eabecd2e4e6d5e050d1928151.png)
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2024-01-16更新
|
239次组卷
|
6卷引用:江苏省2023-2024学年高一上学期期末全真模拟数学试题01
名校
6 . 计算:
(1)
;
(2)已知
,
,用
,
表示
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663795d79c8d978deeeb9d45e4301340.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd46be4851d0e2092c0c796dda3fe9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57115371320bf8c2b5cde136392696c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e7eab8d85898d409414297d5f11a50.png)
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名校
7 . 数学运算是指在明晰运算对象的基础上依据运算法则解决数学问题的素养,因为运算,数的威力无限;没有运算,数就只是个符号.对数运算与指数幂运算是两类重要的运算.
(1)试利用对数运算性质计算
的值;
(2)已知x,y,z为正数,若
,求
的值.
(1)试利用对数运算性质计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d04fb0e77ae84eac3778e2515e07ff0.png)
(2)已知x,y,z为正数,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f1a77df4f43746a2e3fa334503ae0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46de8d6705dca5188ff5b0cdbfcb5a1.png)
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8 . 计算下列各式:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d8fc2664cdd4b52de57c87dfc05a8c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a1f49b3588b9f2088ccb289228ad3c.png)
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9 . 化简或计算下列各式:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c4168b323a70f344e86af88df93048.png)
(2)已知
,用a,b表示
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c4168b323a70f344e86af88df93048.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d586be112cea35ce289229e22bef7dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4e679588b85d84a96167c731a33008c.png)
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名校
10 . 求下列各式的值(写出化简步骤),其中(3)(4)问用分数指数幂表示并计算下列各式(式中字母均正数),写出化简步骤.
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b4ca0b9487d9cbec64b2eafbe1279d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51dafb540faa2a641cd2698f9a2d58b4.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecffa4066f604e2cc1ed89e4ca70832.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b405ea8de95df494101e8a635a33a9e4.png)
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