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江苏省启东中学2019届高三上学期第一次月考数学试题 Word版含解析


2018-2019 学年 一、填空题:本大题共 14 小题,每小题 5 分,共 70 分.金榜题名,高考必胜!蝉鸣声里勾起高考记忆三年的生活,每天睡眠不足六 个小时,十二节四十五分钟的课加上早晚自习,每天可以用完一支中性笔,在无数杯速溶咖啡的刺激下,依然活蹦乱跳,当我穿过昏暗的清晨走向教学楼时,我看到了远方地平线上渐渐升起的黎 明充满自信,相信自己很多考生失利不是输在知识技能上而是败在信心上,觉得自己不行。临近考试前可以设置完成一些小目标,比如说今天走 1 万步等,考试之前给自己打气,告诉自己“我一 定行”! 1.已知集合 A ? ?1, 2, 4? , B ? ?x | ( x ? 1)( x ? 3)≤0? ,则 A B? .最新试卷十年寒窗苦,踏上高 最新试卷多少汗水曾洒下,多少期待曾播种,终是在高考交卷的一刹尘埃落地,多少记忆梦中惦记,多少青春付与流水,人生,总有一次这样的成败,才算长大。 考路,心态放平和,信心要十足,面对考试卷,下笔如有神,短信送祝福,愿你能高中,马到功自成,金榜定题名。 【答案】 ?1, 2? 考点:集合的运算. 2.“ ?x ? [0, ??) , x 2 ? 3 ”的否定是 【答案】 ?x ? [0, ??) , x 2 ≤3 【解析】 试题分析:“ ?x ? [0, ??) , x 2 ? 3 ”的否定是“ ?x ? [0, ??) , x 2 ≤3 ” 考点:的否定. 3.在 3 和 243 中间插入 3 个实数 a1 , a 2 , a3 ,使这 5 个数成等比数列,则 a2 ? 【答案】27 【解析】 试题分析: a2 ? 3 ? 243 ? 27 ,又 a2 与 2,243 同号,所以 a2 ? 27 . 2 2 . . 考点:等比数列的性质. 4.已知 sin ? ? cos ? ? ? 【答案】 ? 【解析】 7 π , ? ? (? ,0) ,则 tan? ? 13 2 . 12 5 试题分析:由 sin ? ? cos ? ? ? 7 49 60 2 得 (sin ? ? cos ? ) ? ,所以 sin ? cos ? ? ? ,因 13 169 169 7 ? 12 ? sin ? ?cos ? ? ? sin ? ? ? ? ? ? ? 13 ? 13 为 ? ? ( ? , 0) ,所以 sin ? ? 0,cos ? ? 0 ,由 ? 得? ,所以 2 ?sin ?cos ? ? ? 60 ?cos ? ? 5 ? ? 169 13 ? ? tan ? ? sin ? 12 ?? . cos ? 5 考点:同角间的三角函数关系. 5.函数 f ( x) ? ln x ? 2x ? 3 在区间 (1, 2) 上的零点个数为 【答案】1 . 考点:函数的零点. 6 . 已 知 定 义 在 R 上 的 函 数 f ( x) ? ax2 ? 2 x ? 3 的 值 域 为 [ 2 ,?? ), 则 f ( x) 的 单 调 增 区 间 为 . 【答案】 [?1, ??) ( (?1, ??) 也对) 【解析】 ?a ? 0 ? 2 2 试题分析:由已知 ?12a ? 4 ,解得 a ? 1 , f ( x) ? x ? 2x ? 3 ? ( x ? 1) ? 2 ,所以其增 ?2 ? ? 4a 区间为 [?1, ??) . 考点:二次函数的性质. 3] 上的最大值与最小值之和是 7.函数 f ( x) ? 8 ? 12 x ? x3 在区间 [?3, . 【答案】16 【解析】 g ( x) 试题分析: 设在区间 [?3,3] 上 f ( x ) 的最大值为 M , 最小值为 m , 再设 g ( x) ? f ( x) ? 8 , 3 的最大值为 M ? 8 ,最小值为 m ? 8 ,又 g ( x) ? 12x ? x 是奇函数,所以在区间 [?3,3] 上 g ( x)max ? g ( x)min ? 0 ,即 (M ? 8) ? (m ? 8) ? 0 , M ? m ? 16 . 考点:函数的奇偶性. 8 . 等 差 数 列 ?an ? 的 前 m 项 的 和 为 30 , 前 2 m 项 的 和 为 100 , 求 它 的 前 3m 项 的 和 为 【答案】210 【解析】 试题分析:因为 {an } 是等差数列,所以 Sm , S2m ? Sm , S3m ? S2m 也成等差数列,即 . 2(S2m ? Sm ) ? Sm ? (S3m ? S2m ) ,所以 S3m ? 3(S2m ? Sm ) ? 3? (100 ? 30) ? 210 . 考点:等差数列的性质. 9.若 ? 、 ? 均为锐角,且 cos ? ? 【答案】 1 47 , cos(? ? ? ) ? ? ,则 cos ? ? 17 51 . 1 3 考点:两角和与差的余弦公式. 【名师点睛】三角函数的给值求值,关键是把待求角用已知角表示: (1)已知角为两个时,待求角一般表示为已知角的和或差. (2)已知角为一个时,待求角一般与已知角成“倍”的关系或“互余互补”的关系. (3)在求值的过程中“拼凑角”对求值往往起到“峰回路转”的效果.通过适当地拆角、凑 角来利用所给条件.常见的变角技巧有 π π ?π +α = -? -α 4 2 ?4 β ? ?α α +β ? ? =?α - ?-? -β ?,α =(α -β )+β , 2? ?2 2 ? ? ?,15°=45°-30°等. ? ? x ,3 ) 时, f ? x ? ? 2 , 10.函数 y ? f ? x ? 是 R 上的奇函数,满足 f ?3 ? x ? ? f ?3 ? x ? ,当 x ? (0 则 f (?5) ? . 【答案】 ?2 【解析】 试题分析:由题意 f (5) ? f (3 ? 2) ? f (3 ? 2)

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