9. The driver was at ______ loss when ________ word came that he was forbidden to
drive for speeding.
A. a, the B. / , / C. the, the D. a, /
8. - Did you enjoy yourself at the party?
- Yes. I’ve never been to _________ one before.
A. a more excited B. the more excited
C. a more exciting D. the most exciting
7. Fitness is important in sport, but of at least ________ importance are skills.
A. fair B. reasonable C. equal D. proper
6. It’s usually warm in my hometown in March, but it _____ be rather cold sometimes.
A. must B. can C. should D. would
5. I have ________ all my papers but I still can’t find my notes.
A. looked through B. looked for
C. looked after D. looked out
4. - Now that you like computers very much, isn’t that a good idea to get a ______?
- Well, I’d like to, but I can’t afford such an expensive computer at present.
A. one B. them C. it D. that
3. I have many friends, _______ some are businessmen.
A. of them B. from which C. of who D. of whom
2. The car has been well maintained and is ________ excellent condition.
A. in B. under C. on D. with
第一节 单项填空(共15小题;每小题1分,满分15分)
从A、B、C、D四个选项中,选出可以填入空白处的最佳选项。
1. - Why was Professor Johnson unhappy those days?
- Can’t you see it clearly? The only reason was that the theory he stuck to________ wrong.
A. proving B. being proved
C. proved D. was proved
20. (本小题满分12分)已知数列的前n项和为设集合
,
(1) 求数列的通项公式;
(2) 若以集合A中的元素作为点的坐标,则这些点是否都在同一条直线上? 并说明理由;
(3) “至多只有一个元素”是否正确? 如果正确, 请给予证明; 如果不正确, 请举
例说明.
20(本小题满分12分)如图所示,将一矩形花坛ABCD扩建成一个更大的矩形花园AMPN,要求B在AM上,D在AN上,且对角线MN过C点,|AB|=3米,|AD|=2米,
(I)要使矩形AMPN的面积大于32平方米,则AN的长应在什么范围内?
(II)若AN的长度不少于6米,则当AM、AN的长度是多少时,矩形AMPN的面积最小?并求出最小面积.
21(本题满分12分)已知函数(1)求证:函数上是增函数.
(2)若上恒成立,求实数a的取值范围.
(3)若函数上的值域是,求实数a的取值范围.
22(本小题满分14分)以为原点,所在直线为轴,建立如图所示的直角坐标系。
设,点的坐标为,点的坐标为。
(Ⅰ)求关于的函数的表达式,并判断函数的单调性(不必证明);
(Ⅱ)设的面积,若以为中心,为焦点的椭圆经过点,
求当取得最小值时椭圆的方程;
(Ⅲ)在(Ⅱ)的条件下,若点的坐标为,、是椭圆上的两点,
且求实数的取值范围。