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2013年北京市中学生数学竞赛初赛高一试题

适用年级:高一试卷类型:竞赛试题总数:14浏览次数:48上传日期:2019/7/11
一、单选题
1 . 已知集合eqIdd88af72f19194a72b490b485675a589aeqId51c32131c6614cfe80e4ad384c697280则集合eqId1d412809cf6b4fac9e9ebf29252bafcf,且关于eqIdc12aac8c2448479687a40735b3572a23的方程eqId640c11dbe21f4a1fa84271074e206b65有实根}的元素个数为(    ).
A.7B.8C.9D.10
难度系数:0.85使用:5次题型:单选题更新:2019/7/11
2 . 已知eqIda64291f9946742a7922db7cb6ec69f4f.则eqId06a6a51471c4437289973a1d5b5aa12d(    )
A.7B.8C.9D.10
难度系数:0.94使用:8次题型:单选题更新:2019/7/11
3 . 如图,矩形eqId5ce7a06ae7a34393b92b5277978ac014的对角线eqId1b51efe7c2fa42748ac5a6be262e2fa4经过坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b,矩形的边分别平行于坐标轴,点eqId19a4eb16029e4550a14f2afe4741a3c3在反比例函数eqIdb04e412fa1de480da87aed788ac0cbcc的图像上若eqIdc36e323c7e6d400b8a5b4ee8a2914a90,则eqIdf3ccc5889ff44339b4e5a8c578f48e0e(    )
figure
A.2B.1C.0D.-1
难度系数:0.65使用:7次题型:单选题更新:2019/7/11
4 . 定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的偶函数eqId4837c94ef0ff4dcf9b1dda4df363275a,满足eqId0cbb5b9ded8c4ad8b4e6ca06b5d4648f,且在区间eqId0038ddcca427496bbaf235d2535158c3上递增,则(    ).
A.eqIdbc27391583214b4d908055a208049b52B.eqIdffa629e1b3f440cba74e5b163a86f9a5
C.eqIde307c3b4ae9c470e97c03d6abd6b8787D.eqIddb79279edd83423ab9196fab0c4f4470
难度系数:0.85使用:8次题型:单选题更新:2019/7/11
5 . 由1开始的连续n个正整数相乘,简记为eqId2fc389b163664a47b316dbb441128387,如eqId6e5d83eda06d42e1848d49cf1b735415eqId20cb83a501e844d3aee8fbde6975dd12(    )
A.eqIddb97b8fea1ba43c5ac8e4a8e62802a69B.eqId592d104bf20442b4b7e36ff3888ddf56C.eqId9f77ae31d1fb4902aee003e9fead424dD.eqId2fcdd5c8482a47269b9b2f5d8f3ceb54
难度系数:0.85使用:5次题型:单选题更新:2019/7/11
6 . 如图,正方形eqId5ce7a06ae7a34393b92b5277978ac014内接于eqId7e5bed1e22f647e39f6f360a21451327eqIdd7be5abad1e34f6db17a56660de8d54f为劣弧eqIde29dca1dc76b42e791635f885e7ea97d上一点,eqId6f782d71f5a7422aa78bd8204949ce26eqId1b51efe7c2fa42748ac5a6be262e2fa4交于点eqId2381423d4cd146cab95f55527681a766eqIde9b50933e347462ea824ccc9bf51fc93eqIdcf2da96900c948a1b3ce7cbfd420c080交于点eqId517584fed25c413ba8b7bb33ffa2d5c6,记eqId28161ba190a64254bd83e4605388672d,若eqId24b7c47bf3c64ecb9142c8a0182e76c3,则eqId95ea4a7a864540698d34fc3aab511d5e(    )
figure
A.1B.eqId5f816d038c584dc7a249120298677ef3C.eqIddb6b28cbd8a14caa9cf1146f6f7916c0D.eqIdfc2bc31fcbdf4db399efd669abc4d214
难度系数:0.65使用:5次题型:单选题更新:2019/7/11
二、填空题
7 . 计算:
eqId93936904bbf2474dbf82f7910ea9e647______.
难度系数:0.85使用:5次题型:填空题更新:2019/7/11
8 . 设eqId4837c94ef0ff4dcf9b1dda4df363275a是定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的奇函数,当eqId26126945e23544d9b0cecaf9cf4809ac时,eqId9c45fccfdf46452f80c0dbe9c2a8850d(eqIdaea992e70d4943e49e893817eb885ed7为常数).则eqId45144b6004f8463fa88fec33fe5e06e6______.
难度系数:0.85使用:7次题型:填空题更新:2019/7/11
9 . 若实数eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5feqId2cd9e2fe3d6540df9399dbefe49ada54满足方程eqId27a2b56e06204e6f8cdb73084094631e,则eqId09788ed90c0646fb84803aed8b1fe94f的个位数字为______.
难度系数:0.65使用:5次题型:填空题更新:2019/7/11
10 . 如图,正方形eqId5ce7a06ae7a34393b92b5277978ac014被分成了面积相等的8个三角形,若eqId7770dea60061411ea1488b43a38f489c,则正方形eqId5ce7a06ae7a34393b92b5277978ac014的面积eqId37abcf0d52514fdb9825ab5a3972485a______.figure
难度系数:0.4使用:7次题型:填空题更新:2019/7/11
11 . 已知实数eqId3a4208e0040c42ed8b09de2cae9d562eeqIdf458db68122849abb588feb2e682d9ac满足eqId2fb32d2a8d7e48b2a4908f7cd29bb201eqIdc9a4fd1b6248409495f2babd4a067582为素数,若eqIdc9a4fd1b6248409495f2babd4a067582的最大值为eqId70a27b6ddf6b478285353abb3b1f3741,最小值为eqIdaea992e70d4943e49e893817eb885ed7,则eqId9b95de2c62e54f599ac66f8b52442cba______.
难度系数:0.65使用:3次题型:填空题更新:2019/7/11
12 . 如图,在eqId992fe44057cf4492895193f3f5398449的边eqId0627be51821d4be7b3e024a354815d64上有一点eqId0cd8063abf2b458f80091bc51b75a904eqId5dcb86e9e0284be3af33cca7f3e7834b的外心,且四边形eqIddeb9e2d176e6454aaaa8db174580baca面积是eqId992fe44057cf4492895193f3f5398449面积的eqIddda48cced83d424b89b7d8f8c62b1056.则eqId162d1f4a770343de9591156bd124a3aa______.figure
难度系数:0.65使用:4次题型:填空题更新:2019/7/11
13 . 设eqId225e4a7685934061a844267c0bb81f9c表示自然数eqIdc12aac8c2448479687a40735b3572a23的数字和,则方程eqId470472e0d7b54224b1dff8b3aa080730的解集为______.
难度系数:0.65使用:3次题型:填空题更新:2019/7/11
14 . 在eqIdd54d2df8a6a94238aeb732c4aa5e311d中,内切圆eqId7e5bed1e22f647e39f6f360a21451327与斜边eqId99a3187c2b8f4bcc9703c74c3b72f1f3切于点eqId0cd8063abf2b458f80091bc51b75a904,分别与eqId0627be51821d4be7b3e024a354815d64eqId1eb64606273a4d63bfa90e56f9a3f5c2切于点eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdd5b10b2a13f148b78e0d5a1b820538fd,作eqId4618799a3e8245a2beb84946067d9caa于点eqId06e60c1a2261437ba646a9bc18a212b1eqIdfc22be29873141d2aeafa56e8f0c7e82于点eqIdd7be5abad1e34f6db17a56660de8d54f.已知eqId807f101531df4eafb4b219b169bd3e94eqId6bf79e3783334fc5aad65b8f9dff1525.用eqId3a4208e0040c42ed8b09de2cae9d562eeqIdf458db68122849abb588feb2e682d9ac表示矩形eqIdbe892c878336434989c35ab8bb6549f2的面积eqId1b7d8b87b50e4cfdbf89d48980209a52为______.
难度系数:0.65使用:4次题型:填空题更新:2019/7/11
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