江苏省南京外国语学校2018-2019届高一年级(上)数学试题

适用年级:高一
试卷号:529063

试卷类型:月考
试卷考试时间:2018/12/25

1.选择题(共5题)

1.如图,已知点A,B,C,D,E,F是边长为1的正六边形的顶点,连接任意两点均可得到一条线段.在连接两点所得的所有线段中任取一条线段,取到长度为 3 的线段的概率为(   )

2.如图,已知点A,B,C,D,E,F是边长为1的正六边形的顶点,连接任意两点均可得到一条线段.在连接两点所得的所有线段中任取一条线段,取到长度为 3 的线段的概率为(   )

3.求使函数y=2sin3x+1,x∈R取得最大值的自变量x的集合,并说出最大值是什么?
4.根据短文内容,选择最佳答案。

    Car companies are developing vehicles that will plug into electric sockets, ust like many laptops, digital cameras, cell phones and Mp4 do. Called “plug-in vehicles”, these cars will get most of their power from electricity. Their drivers won't have to stop at gas stations as often as usual.

    The technology is more than just cool. In our car-filled world, plug-in vehicles could reduce the amount of gas we use, which keeps rising in cost now and then. Besides, driving around in these vehicles may even help the environment. Gas-burning cars produce a lot of greenhouse gas, which causes global warming.

    The first company-produced plug-in vehicles could hit the roads by 2020. But engineers still have a lot of work to do to make the technology practical and inexpensive.

    Batteries are the biggest challenge. In the plug-in-vehicle world,Li-ion(锂离子)batteries are getting the most attention. These batteries can store a large amount of energy in a small package, and they last a longer time between charges. Li-ion batteries can fit laptops, cell phones, heart instruments and other similar pocket ones.

    But because cars are so big and heavy, it would still require a suitcase-sized Li-ion batteries to power about 12km of driving. What's more, the batteries are much expensive.

    “A car filled with batteries could go a long distance,” says Ted Bohn, an electrical engineer in Chicago. “But it couldn't pull any people, and it would cost $100,000.” So researchers need to work out how to make batteries smaller and cheaper, among other questions.

    “The answers don't exist yet,” Bohn says, “As a kid, I thought someone someplace knows the answer to everything. All of these questions haven't been decided. That's what engineering is about-making a guess, running tests and getting fine results.”

5.根据短文内容,选择最佳答案。

    Car companies are developing vehicles that will plug into electric sockets, ust like many laptops, digital cameras, cell phones and Mp4 do. Called “plug-in vehicles”, these cars will get most of their power from electricity. Their drivers won't have to stop at gas stations as often as usual.

    The technology is more than just cool. In our car-filled world, plug-in vehicles could reduce the amount of gas we use, which keeps rising in cost now and then. Besides, driving around in these vehicles may even help the environment. Gas-burning cars produce a lot of greenhouse gas, which causes global warming.

    The first company-produced plug-in vehicles could hit the roads by 2020. But engineers still have a lot of work to do to make the technology practical and inexpensive.

    Batteries are the biggest challenge. In the plug-in-vehicle world,Li-ion(锂离子)batteries are getting the most attention. These batteries can store a large amount of energy in a small package, and they last a longer time between charges. Li-ion batteries can fit laptops, cell phones, heart instruments and other similar pocket ones.

    But because cars are so big and heavy, it would still require a suitcase-sized Li-ion batteries to power about 12km of driving. What's more, the batteries are much expensive.

    “A car filled with batteries could go a long distance,” says Ted Bohn, an electrical engineer in Chicago. “But it couldn't pull any people, and it would cost $100,000.” So researchers need to work out how to make batteries smaller and cheaper, among other questions.

    “The answers don't exist yet,” Bohn says, “As a kid, I thought someone someplace knows the answer to everything. All of these questions haven't been decided. That's what engineering is about-making a guess, running tests and getting fine results.”

2.填空题(共13题)

6.
设集合 则=____.
7.
已知集合A={x|2x+a>0},若1∉A,则实数a的取值范围是_____.
8.
已知集合,则中元素的个数为_______.
9.
已知函数f(x)=x2+mx+1是偶函数,则m=_____.
10.
指数函数f(x)=(a﹣1)x在R上是增函数,则a的取值范围是_____.
11.
若函数在区间 单调递增,则实数的取值范围为__________.
12.
函数的定义域为_____.
13.
设P(x0,y0)是函数f(x)图象上任意一点,且y02≥x02,则f(x)的解析式可以是_____.(填序号)
①f(x)=x﹣②f(x)=ex﹣1(e≈2.718,是一个重要常数)③f(x)=x+④y=x2
14.
已知是偶函数,且 .
15.
若函数f(x)=x2-ax-a在区间[0,2]上的最大值为1,则实数a等于________.
16.
已知二次函数f(x)满足f (2+x)=f (2﹣x),且f(x)在[0,2]上是增函数,若f(a)≥f (0)则实数a的取值范围是_____.
17.
已知函数的图象恒过定点,则
18.
f(x)=ex-1,g(x)=-x2+4x-3,若有f(a)=g(b),则b的取值范围为________.

3.解答题(共6题)

19.
已知函数是奇函数.
(1)求实数的值;
(2)若函数在区间上单调递增,求实数的取值范围.
20.
设函数,且f(﹣2)=3,f(﹣1)=f (1).
(1)求f(x)的解析式;
(2)画出f(x)的图象,写出函数的单调增区间.
21.
已知函数f(x)=ax2+bx+c(a>0,b∈R,c∈R).
(1)若函数f(x)的最小值是f(﹣1)=0,且c=1,求f (2)的值;
(2)若a=1,c=0,且|f(x)|≤1在区间(0,1]上恒成立,试求b的取值范围.
22.
已知定义域为R的函数是奇函数.
(1)求a,b的值;
(2)解关于t的不等式f(t2-2t)+f(2t2-1)<0.
23.
已知f(x)=(x≠a).
(1)若a=﹣2,试证明f(x)在(﹣∞,﹣2)内单调递增;
(2)若a>0,且x∈(﹣∞,0),请直接写出f(x)的值域.
24.
已知f(x)=2x,g(x)是一次函数,并且点(2,2)在函数f[(g(x)]的图象上,点(2,5)在函数g[f(x)]的图象上,则g(x)的解析式为_____.
试卷分析
  • 【1】题量占比

    选择题:(5道)

    填空题:(13道)

    解答题:(6道)

  • 【2】:难度分析

    1星难题:0

    2星难题:0

    3星难题:0

    4星难题:0

    5星难题:0

    6星难题:0

    7星难题:0

    8星难题:0

    9星难题:19