江苏省赣榆高级中学2008—2009学年度第二学期期中考试高二数学试题(文科)参考答案一．填空题：1．（4）2．演绎3．4．15．6．-237．8．9．10．1111．直线12．13．14．25二．解答题：15．（本小题满分14分）解：（1）设由z＋2i为实数知··················3分同理可算得·················6分所以·················7分（2）·················10分而它在复平面上对应的点在第一象限，所以满足···············12分解得·················14分16．（本小题满分14分）解：（1）设则······················3分因为所以所以所以·······································用心爱心专心·············6分（2）当a≥1时，对称轴，此时················9分当a＜1时，在上单调递减，此时··············12分综上可知··································14分17．（本小题满分15分）解：（1）设函数，将点代入得所以·····················5分（2）因为，所以≥0，即函数的定义域不关于原点对称，所以函数是非奇非偶函数。····················9分（3）函数在上单调递增，·····················12分图略·····················15分18．（本小题满分15分）解：┅┅······················6分将以上各式分别相加得：················9分整理得：·····················15分19．（本小题满分16分）解：（1）证明：任取，则用心爱心专心，，，，即函数在内单调递增.……8分（2）[解法一]，……11分当时，，的取值范围是.……16分[解法二]解方程，得，……11分，解得.的取值范围是.……16分20．（本小题满分16分）（1）证令x=y=0.则f(0)=f(0)+f(0)所以f(0)=0……………2分（2）令y=-x,则f(0)=f(-x)+f(x)即f(-x)=-f(x)故f(x)为奇函数；……………4分例如：；……………6分（3）用心爱心专心a)任取x10f(x2-x1)=f(x2)+f(-x1)=f(x2)-f(x1)<0则该函数f(x2)0时，有两解；……………12分当a=0时，有一解；……………14分当a<0时，无解；……………16分用心爱心专心
