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mi168168com:高一(下)数学期末综合测试一及答案

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高一(下)数学期末综合测试一 (时间 120 分钟,满分 150 分) 第Ⅰ卷(选择题 共 60 分) 一、选择题(本大题共 12 小题,每小题 5 分,共 60 分,在每小题给出的四个选择项 中,只有一项符合题目要求的) 1. 已知e1、e2是两个单位向量,下列 命题中正确的是 A. e1 ? e 2 ? 1 B. e1 ? e 2 2 C. e1 ? e2 2 ?    ? D. e1 // e 2 2.下列命题中:①若 a 与 b 互为负向量,则 a+b=0;②若 k 为实数,且 k· a=0,则 a=0 或 k=0;③若 a· b=0,则 a=0 或 b=0;④若 a 与 b 为平行的向量,则 a· b=|a||b|;⑤若|a| =1,则 a=±1.其中假命题的个数为() A.5 个 B.4 个 ?? ? ?? ? C.3 个 D.2 个 3. 在Δ ABC中, a ? 5,b ? 8,C ? 60?,则 BC ? CA 的值等于 A. 20 B. ? 20 ?    ? D. ? 20 3 ( ) C. 20 3 4.设|a|=1,|b|=2,且 a、b 夹角 120°,则|2a+b|等于 A. 2 B. 4 C. 12 D. 2 3 5. 已知△ABC 的顶点坐标为 A (3, 4) , B (-2, -1) , C (4, 5) , D 在 BC 上, 且 S ?ABC ? 3S ?ABD , 则 AD 的长为 ( ) A. A.3 2 B. 2 2 B.-1 C. 3 2 C.-1 或 3 D. 7 2 2 ( ) 6.已知 a=(2,1) ,b=(3,λ ) ,若(2a-b)⊥b,则λ 的值为 D.-3 或 1 ( ) 7.向量 a=(1,-2) ,|b|=4|a|,且 a、b 共线,则 b 可能是 A. (4,8) ?? ? B. (-4,8) ?? ? C. (-4,-8) D. (8,4) 8.已知△ABC 中, ( ) A.30° AB ? a , AC ? b, a ? b ? 0, S ?ABC ? 15 ,a ? 3, b ? 5 4 ,则 a 与 b 的夹角为 D.30°或 150° B.-150° C.150° 9. 若 a ? b ? 41 ? 20 3 ,a ? 4,b ? 5,则a ? b ? ?    ? D. 10 A. 10 3 B. ? 10 3 C. 10 2 ( 10. 将函数 y=f (x) 的图象先向右平移 a 个单位, 然后向下平移 b 个单位 (a>0, b>0) . 设 点 P(a,b)在 y=f(x)的图象上,那么 P 点移动到点 A. (2a,0) B. (2a,2b) C. (0,2b) ) D. (0,0) ?? ? ?? ? 3 11. 若点P分 AB 所成的比为 ,则A分 BP 所得的比是 4 ?    ? 1 A. 3 7 B. 7 3 a?b a ?b 2 2 C. ? 7 3 D. ? 3 7 12. 已知a ? ?x,1?,b ? ?2,3x?,那么 的取值范围是 ? 2? B. ?0, ? ? 4 ? ? ? ?    ? A. ?,2 2 ? ? ? 2 2? C. ?? , ? ? ? 4 4 ? ? D. 2 2 ,?? ? ? 第Ⅱ卷(非选择题 共 90 分) 二、填空题(本大题共 4 小题,每小题 4 分,共 16 分,把答案填在题中横线上) 13.向量 a=(2k+3,3k+2)与 b=(3,k)共线,则 k=___________. ?9 ? 14. 已知a ? ? ,k ?,b ? ?k,8?,且a与b为互相平行的 向量,则k的值为__ ___________. ?2 ? 15.向量 a=(1,1) ,且 a 与(a+2b)的方向相同,则 a· b 的取值范围是________. ?? ? ?? ? ?? ? 16. AB ? 8, AC ? 12, 则 BC 取值范围用区间表示为___________ . 三、解答题(本大题共 6 小题,共 74 分,解答应写出文字说明,证明过程或演算步骤) 17. (本小题满分 12 分) 设 O 为原点, OA ? ?3,1?, OB ? ?? 1,2?, OC ? OB, BC// OA ,试求满足 OD? OA ? OC 的 ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? OD 的坐标. 18. (本小题满分 12 分) 设 e 1 和 e 2 是两个单位向量,夹角是 60°,试求向量 a ? 2e1 ? e 2 和 b ? ?3e1 ? 2e 2 的夹 角. 19. (本小题满分 12 分) 已知 AC ? 5.6, BC ? 4.2, AC 与 AB 的夹角为 40°,求 AC? BC 与 CB 的夹角 ?? ? ?? ? ?? ? ??? ?? ? ?? ? ?? ? ??? | BC? AC| (长度保留四位有效数字,角度精确到′) . 20. (本小题满分 12 分) ?? ? ?? ? ①如果 AB ? e1 ? e 2 , BC ? 2e1 ? 8e2 , CD ? 3?e1 ? e 2 ?, 设两个非零向量e 1与e2 不共线, ?? ? ?? ? ?? ? 使ke1 ? e2和e1 ? ke2 共线. 求证:A、B、D 三点共线. ②试确定实数k的值, 21. (本小题满分 12 分) 已知 a,b 是两个非零向量,当 a+tb(t∈R)的模取最小值时, 2 ①求 t 的值。②已知 a 与 b 共线且同向,求证:b 与 a+tb 垂直. 22. (本小题满分 14 分) 2 2 将函数 y ? 2x 进行平移, 使得到的图形与函数 y ? ?2x ?

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