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www.4852.com:专题3.1.1 倾斜角与斜率(测)-2016-2017学年高二数学同步精品课堂(提升版)(必修二)(原卷版)

3.1.1 倾斜角与斜率 (时间:25 分,满分 55 分) 班级 一、选择题 1.对于下列命题 ①若 α 是直线 l 的倾斜角,则 0° ≤α<180° ; ②若 k 是直线的斜率,则 k∈R; ③任一条直线都有倾斜角,但不一定有斜率; ④任一条直线都有斜率,但不一定有倾斜角. 其中正确命题的个数是( A.1 B.2 ) C.3 D.4 ) 姓名 得分 2.斜率为 2 的直线经过点 A(3,5)、B(a,7)、C(-1,b)三点,则 a、b 的值为( A.a=4,b=0 C.a=4,b=-3 B.a=-4, b=-3 D.a=-4,b=3 3.设直线 l 过坐标原点,它的倾斜角为 α,如果将 l 绕坐标原点按逆时针方向旋转 45° ,得到直线 l1, 那么 l1 的倾斜角为( A.α+45° B.α-135° C.135° -α D.当 0° ≤α<135° 时,倾斜角为 α+45° ;当 135° ≤α<180° 时,倾斜角为 α-135° 4.直线 l 过原点(0,0),且不过第三象限,那么 l 的倾斜角 α 的取值范围是( A.[0°,90°] C.[90°,180°)或 α=0° B.[90° ,180° ) D.[90°,135°] ) ) ) 5.若图中直线 l1、l2、l3 的斜率分别为 k1、k2、k3,则( A.k1<k2<k3 C.k3<k2<k1 B.k3<k1<k2 D.k1<k3<k2 ) 6.直线 mx+ny-1=0 同时过第一、三、四象限的条件是( A.mn>0 C.m>0,n<0 二、填空题 B.mn<0 D.m<0,n<0 7.若 A(?2,3) , B (3,?2) , C ( , m) 三点共线,则 m 的值为_________ 2 1 8.直线过点 A(1, 2) ,且不经过第四象限,那么直线的斜率的取值范围是_________ 9.已知直线 l 的倾斜角为 α-20° ,则 α 的取值范围是________________________. f?a? f?b? f?c? 10.已知函数 f(x)=log2(x+1),a>b>c>0,则 , , 的大小关系是________________. a b c f?c? f?b? f?a? > > c b a 三、解答题 11.如图所示,菱形 ABCD 中,∠BAD=60° ,求菱形 ABCD 各边和两条对角线所在直线的倾斜角和斜 率. y 12.已知实数 x,y 满足 y=-2x+8,当 2≤x≤3 时,求 的最大值和最小值. x :

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