问题 解答题
我们把平面直角坐标系中,函数y=f(x),x∈D上的点P(x,y),满足x∈N*,y∈N*的点称为函数y=f(x)的“正格点”.
(1)请你选取一个m的值,使对函数f(x)=sinmx,x∈R的图象上有正格点,并写出函数的一个正格点坐标
(2)若函数f(x)=sinmx,x∈R,m∈(1,2),与函数g(x)=lgx的图象有正格点交点,求m的值,并写出两个函数图象的所有交点个数.
(3)对于(2)中的m值,函数f(x)=sinx,x∈[0,
5
9
]时,不等式logax>sinmx恒成立,求实数a的取值范围.
答案

(1)若取m=

π
2
时,

正格点坐标(1,1),(5,1)(9,1)等(答案不唯一)…(2分)

(2)作出两个函数图象,可知函数f(x)=sinmx,x∈R,与函数g(x)=lgx的图象有正格点交点只有一个点为(10,1)(4分)

2kπ+

π
2
=10m,m=
4k+1
20
π,(k∈z),m∈(1,2),

m=

20
.…(6分)

根据图象可知:两个函数图象的所有交点个数为5个.(注意:最后两个点非常接近,几乎粘合在一起.)…(7分)

(3)由(2)知f(x)=sin

20
x,x∈[0,
5
9
],

∴①当a>1时,不等式logax>sinmx不能成立…(8分)

②当0<a<1时,由图(2)可知loga

5
9
>sin
π
4
=
2
2
,∴(
5
9
)
2
<a<1
…(10分)

单项选择题
完形填空

第二节:任务型阅读:(6选5)(共5小题;每小题2分,满分10分)

You say you are old enough to stay out late on weekends while they say you have to be home early. __71___while they say you can’t see it . You say you have met some nice kids and you’d like to go out with them, but they say they’d like to see your friends first.

When you’re a teenager, it seems that every time you say “I want to ” , they will certainly answer “No, you can’t .” Also, no part of your life is safe from the “prying eyes” of your parents.15-year –old Debbie says, “My dad always wants to know where I am, what time I’m going home. Most parents do that .Do they have to know everything? _72____”

__73__ When something goes wrong, most parents just don’t believe in their children. Without asking why, they think their kids are wrong. And not many parents would allow their kids to choose for themselves.

__74__ But remember that not too long ago you were really a child. Your parents still remember the childish mistakes you used to make.  They want to protect you though you do not want them to do so. And when something seems to threaten your well-being, they worry.

So, if you want to get more freedom, please try to understand your parents and do not just lie. __75__If you want them to allow you to stay out late, don’t just say, “All the other kids can stay out late.” Tell them as much as you can about what you want to do and where you’ll be and why it’s important for you to stay out later…, they might just say yes.

A.Yes, it is true that your parents sometimes treat you like a small child.

B.No one likes being troubled.

C.They should give us more freedom.

D.Try a more friendly way.E. Young people further complain that their parents do not respect them.

F. You say you want to see a film.