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高中一年级试题

高中一年级试题
高中一年级试题

银川一中

一、选择题:(本大题共12小题,每小题3分,共36分.在每小题给出的四个选

项中,只有一项是符合要求的.)

1.集合M={x|x 2

-4=0},N={-2,0,2},则M 与N 的关系为( )

A .M N

B .M N

C .M=N

D .M ?N 2.如下图,可表示函数y=f(x)的图象的可能是( )

3.已知:f(x)=??

???>-≤+)0( 2)

0( 12x x x x ,若f(a)=10,则a 的值为( )

A .-1

B .1

C .-3

D .3 4.设y 1=40.9

,y 2=8

0.48

,y 3=5.1)2

1

(-,则( )

A .y 3>y 1>y 2

B .y 2>y 1>y 3

C .y 1>y 2>y 3

D . y 1>y 3>y 2 5. 已知:f (x 1)=1

1+x ,则f (2)的值为( ) A.

31 B.32 C.3 D.2

3 6. 下列说法错误的个数为( )

①图像关于原点对称的函数是奇函数 ②图像关于y 轴对称的函数是偶函数

③奇函数图像一定过原点 ④偶函数图像一定与y 轴相交 A .4 B 。3 C 。2 D.0

7. 下列函数中,值域为[0,+∞)的函数是( ) A .y=2x

B.y=x 2

C.y=x

-2

D. y=log a x(a>0,且a ≠1)

8.若函数f(x)=x 2

+2(a-1)x+2在区间(-∞,4)上是减函数,则实数a 的取值范围是( )

A .a ≤-3

B .a ≥-3

C .a ≤5

D .a ≥3 9.若lg2=a ,lg3=b ,则log 524等于( )

A .a b a ++13

B .13++a b a

C .a b a -+13

D .a

b

a -+13 10.已知a>0,a ≠0,函数y=a x

与y=log a (-x)的图象只能是( ) A . B . C . D .

11.已知函数f(x)=12++m x m x 的定义域是R ,则m 的取值范围是( )

A .0

B .0≤m ≤1

C .m ≥4

D .0≤m ≤4 12. 若方程

x x lg 1

1

=+两根为21,x x ,则( ) A. 021?x x 二、填空题:(每空4分,共16分) 13.y=log 3x 的反函数是____________.

14.若集合A={y|y=log 3x,x>1},B={y|y=1,)2

1

(>x x },则A ∩B=__________。

15.函数y=|x-2|的单调递增区间是____________。

16.设f(x)是定义在R 上的奇函数,且当x>0时,f(x)=2x

-2,则f(-2)=___________.

? ≠ ?

三、解答题: 17.计算(8分)

(1)0

121

32

)32()25(10)002.0()8

33(-+-?-+----

(2)3log 12522ln 100

1

lg

625log ++++e 18.(8分)函数f(x)定义在R 上的偶函数,当x ≥0时,f(x)=x )2

1

(

(1)写出f(x)单调区间;(2)函数的值域;

19.(8分)“水”这个曾经被人认为“取之不尽用之不竭”的资源,竟然到了严重

制约我国经济发展,严重影响人民生活的程度。因为缺水,每年给我国工业造成的损失达2000亿元,给我国农业造成的损失达1500亿元,严重缺水困扰全国三分之二的城市。为了节约用水,某市打算出台一项水费政策,规定每季度每人用水量不超过5吨时,每吨水费1.2元,若超过5吨而不超过6吨时,超过的部分的水费加收200%,若超过6吨而不超过7吨时,超过部分的水费加收400%。(1)如果某人本季度实际用水量为6.5吨,试计算本季度他应交的的水费。(2)如果某人本季度实际用水量为(7)x x ≤吨,写出本季度他应交的的水费y 的函数关系(单位:元)。 20.(8分)定义在[1,4]上的函数f(x)=x 2

-2bx+4

b

(1)b=2时,求函数的最值;

(2)若函数是单调函数,求b 的取值范围. 21.(12分)f(x)=-x|x|+px (1)判断并证明函数的奇偶性;

(2)当p=2时,判断函数f(x)在(-1,0)上单调性并加以证明; (3)当p=2时,画出函数的图象并指出单调区间.

22.(12分)已知函数2

2

2

(1)log 2a x f x x

-=-(0,1)a a >≠且 (1)求函数()f x 的解析式,并判断()f x 的奇偶性; (2)解关于x 的方程1()log a

f x x

=

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