2022年数学历年高考题 .pdf
Do the following three main poi nts: 1 find out the weak. Review process is to sum up the knowledge on the one hand, make the knowledge more coherent system and regularity, but also let the students themselves, looks up the deficiencies. So, we teachers to understand the students knowledge of the situation prior to the review, students not only found widespread deficiencies, but also some shortcoming s, for these well designe d programs, reasonable arrangement of time, this review is more targeted and more effective. For example, you can design a form for investgation, understanding students weaknesses i n each knowledge, put it as a review of key, combined with the problem of textbooks to reviewboth to avoid casting a net tihaizhanshu, a nd improve the efficiency of review. 2, good collation. Throug h six years of study, students in the basics, reading method, exercises, and so alrea dy have a certain degree of accumulation, the review stage, teachers should knowhow to guide the stude nts to label the accumulation, process, form a system of knowledge networks. Exercises for students to be representative, fine, complete, to live, and earnestly do a problem learning a method, class of pass was to get time efficient review results. 3, pay attention to use. The accumulation of knowledge is ultimately to use, t herefore, review the situation and life situation t o be created in a variety of languages, gui de students on the basis of the previous accumulation of knowledge to use to the maximum, and really apply what they have learned. Second, review the content and strategy of the first part: the basics (a) 1, review the main points of Hanyu Pinyin is a ble to recite a nd write down the alphabet of Hanyu Pinyin; accurate spelling pronunciation (after reading cacuminal, nasal sound, light, and retroflex sounds), the correct write consonants, vowels and syllables. 2,. main types according to the order of the alpha bet of Hanyu Pinyialphabetical order; fill in the appropriate uppercase and l owerca se letters; see phonetic writing words; pinyin to write sentences with dot to select the corre ct pronunciation of the word; to bring some initial consonants or vowels, word selection. Second, the main types of words (1) Ruby written words; (2) to bring Word to select the correct pronunciation; (3) use a sequencer and radical character lookup method 2009 年一、选择题：1. 10i2-iA. -2+4iB. -2-4iC. 2+4iD. 2-4i解：原式10i(2+i)24(2-i)(2+i)i.故选 A.2. 设集合1|3 ,|04xAx xBxx，则ABI= A. B. 3,4C.2,1D. 4.解：1|0| (1)(4)0|144xBxxxxxxx.(3,4)ABI.故选 B. 3. 已知ABC中，12cot5A， 则cosAA. 1213B.513C.513D. 1213解：已知ABC中，12cot5A，(, )2A. 221112cos1351tan1()12AA故选 D. 4.曲线21xyx在点1,1处的切线方程为A. 20 xyB. 20 xyC.450 xyD. 450 xy解：111222121|1(21)(21)xxxxxyxx, 故切线方程为1(1)yx,即20 xy故选 B. 5. 已知正四棱柱1111ABCDA B C D中，12AAAB，E为1AA中点，则异面直线BE与1CD所成的角的余弦值为A. 1010B. 15C. 3 1010D. 35精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 35 页Do the following three main poi nts: 1 find out the weak. Review process is to sum up the knowledge on the one hand, make the knowledge more coherent system and regularity, but also let the students themselves, looks up the deficiencies. So, we teachers to understand the students knowledge of the situation prior to the review, students not only found widespread deficiencies, but also some shortcoming s, for these well designe d programs, reasonable arrangement of time, this review is more targeted and more effective. For example, you can design a form for investigation, understanding students weaknesses i n each knowledge, put it as a review of key, combined with the problem of textbooks to reviewboth to avoid casting a net tihaizhanshu, a nd improve the efficiency of review. 2, good collation. Throug h six years of study, students in the basics, reading method, exercises, and so alrea dy have a certain degree of accumulation, the review stage, teachers should knowhow to guide the stude nts to label the accumulation, process, form a system of knowledge networks. Exercises for students to be representative, fine, complete, to live, and earnestly do a problem learning a method, class of pass was to get time efficient review results. 3, pay attention to use. The accumulation of knowledge is ultimately to use, t herefore, review the situation and life situation to be created in a variety of languages, gui de students on the basis of the previous accumulation of knowledge to use to the maximum, and really apply what they have learned. Second, review the content and strategy of the first part: the basics (a) 1, review the main points of Hanyu Pinyin is a ble to recite and write down the alphabet of Hanyu Pinyin; accurate spelling pronunciation (after reading cacuminal, nasal sound, light, and retroflex sounds), the correct write consonants, vowels and syllables. 2,. main types according to the order of the alpha bet of Hanyu Pinyin alphabetical order; fill in the appropriate uppercase and l owerca se letters; see phonetic writing words; pinyin to write sentences with dot to select the corre ct pronunciation of the word; to bring some initial consonants or vowels, word selection. Second, the main types of words (1) Ruby written words; (2) to bring Word to select the correct pronunciation; (3) use a sequencer and radical character lookup method解：令1AB则12AA,连1A B1C DQ1A B异面直线BE与1CD所成的角即1A B与BE所成的角。在1A BE中由余弦定理易得13 10cos10A BE。故选 C 6. 已知向量2,1 ,10,| 5 2aa bab，则|bA. 5B. 10C.5D. 25解：222250|2|520|abaa bbbrrrr rrrQg| 5br。故选 C7. 设323log,log3,log2abc，则A. abcB. acbC. bacD. bca解：322log2log2log3bcQ2233log3log 2log 3logababc.故选 A.8. 若 将 函 数tan04yx的 图 像 向 右 平 移6个 单 位 长 度 后 ， 与 函 数tan6yx的图像重合，则的最小值为A16B. 14C. 13D. 12解：6tantan(ta)6446nyxyxx向右平移个单位164()662kkkZ，又min102Q.故选 D9. 已知直线20yk xk与抛物线2:8Cyx相交于AB、两点，F为C的焦点， 若| 2 |FAFB，则kA. 13B.23C. 23D. 2 23解 ： 设 抛 物 线2:8Cyx的 准 线 为:2l x直 线20yk xk恒过定点P2,0.如图过AB、分 别作AMl于M,BNl精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 35 页Do the following three main poi nts: 1 find out the weak. Review process is to sum up the knowledge on the one hand, make the knowledge more coherent system and regularity, but also let the students themselves, looks up the deficiencies. So, we teachers to understand the students knowledge of the situation prior to the review, students not only found widespread deficiencies, but also some shortcoming s, for these well designe d programs, reasonable arrangement of time, this review is more targeted and more effective. For example, you can design a form for investigation, understanding students weaknesses i n each knowledge, put it as a review of key, combined with the problem of textbooks to reviewboth to avoid casting a net tihaizhanshu, a nd improve the efficiency of review. 2, good collation. Throug h six years of study, students in the basics, reading method, exercises, and so alrea dy have a certain degree of accumulation, the review stage, teachers should knowhow to guide the stude nts to label the accumulation, process, form a system of knowledge networks. Exercises for students to be representative, fine, complete, to live, and earnestly do a problem learning a method, class of pass was to get time efficient review results. 3, pay attention to use. The accumulation of knowledge is ultimately to use, t herefore, review the situation and life situation t o be created in a variety of languages, gui de students on the basis of the previous accumulation of knowledge to use to the maximum, and really apply what they have learned. Second, review the content and strategy of the first part: the basics (a) 1, review the main points of Hanyu Pinyin is a ble to recite a nd write down the alphabet of Hanyu Pinyin; accurate spelling pronunciation (after reading cacuminal, nasal sound, light, and retroflex sounds), the correct write consonants, vowels and syllables. 2,. main types according to the order of the alpha bet of Hanyu Pinyin alphabetical order; fill in the appropriate uppercase and l owerca se letters; see phonetic writing words; pinyin to write sentences with dot to select the corre ct pronunciation of the word; to bring some initial consonants or vowels, word selection. Second, the main types of words (1) Ruby written words; (2) to bring Word to select the correct pronunciation; (3) use a sequencer and radical character lookup method 于N, 由| 2 |FAFB, 则|2|AMBN,点B为AP的 中 点 . 连 结OB, 则1|2OBAF, | |OBBF点B的 横 坐 标 为1, 故 点B的 坐 标 为2 202 2(1,2 2)1 ( 2)3k, 故选 D10. 甲、乙两人从4 门课程中各选修2门。则甲、乙所选的课程中至少有1 门不相同的选法共有A. 6 种B. 12 种C. 30 种D. 36 种解：用间接法即可.22244430CCC种. 故选 C11. 已知双曲线222210,0 xyCabab：的右焦点为F,过F且斜率为3的直线交C于AB、两点，若4AFFB,则C的离心率为m A65B. 75C. 58D. 95解：设双曲线22221xyCab：的右准线为l,过AB、分 别作AMl于M,BNl于N, BDAMD于,由直 线AB的 斜 率 为3,知 直 线AB的 倾 斜 角 为16060 ,|2BADADAB, 由双曲线的第二定义有1| |(|)AMBNADAFFBeu uu ruuu r11|(|)22ABAFFBuu u ruuu r. 又15643|25AFFBFBFBeeuu u ruu u rQ故选 A12.纸制的正方体的六个面根据其方位分别标记为上、下、东、南、西、北。现有沿该正方体的一些棱将正方体剪开、外面朝上展平，得到右侧的平面图形，则标“”的面的方位是A. 南B. 北C. 西D. 下精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 35 页Do the following three main poi nts: 1 find out the weak. Review process is to sum up the knowledge on the one hand, make the knowledge more coherent system and regularity, but also let the students themselves, looks up the deficiencies. So, we teachers to understand the students knowledge of the situation prior to the review, students not only found widespread deficiencies, but also some shortcoming s, for these well designe d programs, reasonable arrangement of time, this review is more targeted and more effective. For example, you can design a form for investigation, understanding students weaknesses i n each knowledge, put it as a review of key, combined with the problem of textbooks to reviewboth to avoid casting a net tihaizhanshu, a nd improve the efficiency of review. 2, good collation. Throug h six years of study, students in the basics, reading method, exercises, and so alrea dy have a certain degree of accumulation, the review stage, teachers should knowhow to guide the stude nts to label the accumulation, process, form a system of knowledge networks. Exercises for students to be representative, fine, complete, to live, and earnestly do a problem learning a method, class of pass was to get time efficient review results. 3, pay attention to use. The accumulation of knowledge is ultimately to use, t herefore, review the situation and life situation to be created in a variety of languages, gui de students on the basis of the previous accumulation of knowledge to use to the maximum, and really apply what they have learned. Second, review the content and strategy of the first part: the basics (a) 1, review the main points of Hanyu Pinyin is a ble to recite and write down the alphabet of Hanyu Pinyin; accurate spelling pronunciation (after reading cacuminal, nasal sound, light, and retroflex sounds), the correct write consonants, vowels and syllables. 2,. main types according to the order of the alpha bet of Hanyu Pinyin alphabetical order; fill in the appropriate uppercase and l owerca se letters; see phonetic writing words; pinyin to write sentences with dot to select the corre ct pronunciation of the word; to bring some initial consonants or vowels, word selection. Second, the main types of words (1) Ruby written words; (2) to bring Word to select the correct pronunciation; (3) use a sequencer and radical character lookup method解：展、折问题。易判断选B第 II卷（非选择题，共90 分）二、填空题：本大题共4 小题，每小题5 分，共 20 分。把答案填在答题卡上。13. 4xyyx的展开式中33x y的系数为 6 。解：4224()xyyxx yxy，只需求4()xy展开式中的含xy项的系数：246C14. 设等差数列na的前n项和为nS，若535aa则95SS9 . 解：naQ为等差数列，9553995SaSa15.设OA是球O的半径，M是OA的中点，过M且与OA成 45角的平面截球O的表面得到圆C。若圆C的面积等于74，则球O的表面积等于8. 解：设球半径为R，圆C的半径为r，2277.444rr, 得由因为22224ROCR。由2222217()484RRrR得22R.故球O的表面积等于8. 16. 已知ACBD、为圆O:224xy的两条相互垂直的弦，垂足为1,2M,则四边形ABCD的面积的最大值为。解：设圆心O到ACBD、的距离分别为12dd、,则222123ddOM+. 四边形ABCD的面积222212121| | 2 (4)8()52SABCDdddd)(4-三、解答题：本大题共6 小题，共70 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10 分）设ABC的内角A、B、C的对边长分别为a、b、c，3cos()cos2ACB，2bac，求B。分 析：由3cos()cos2ACB， 易想到先将()BAC代入精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 35 页Do the following three main poi nts: 1 find out the weak. Review process is to sum up the knowledge on the one hand, make the knowledge more coherent system and regularity, but also let the students themselves, looks up the deficiencies. So, we teachers to understand the students knowledge of the situation prior to the review, students not only found widespread deficiencies, but also some shortcoming s, for these well designe d programs, reasonable arrangement of time, this review is more targeted and more effective. For example, you can design a form for investigation, understanding students weaknesses i n each knowledge, put it as a review of key, combined with the problem of textbooks to reviewboth to avoid casting a net tihaizhanshu, a nd improve the efficiency of review. 2, good collation. Throug h six years of study, students in the basics, reading method, exercises, and so alrea dy have a certain degree of accumulation, the review stage, teachers should knowhow to guide the stude nts to label the accumulation, process, form a system of knowledge networks. Exercises for students to be representative, fine, complete, to live, and earnestly do a problem learning a method, class of pass was to get time efficient review results. 3, pay attention to use. The accumulation of knowledge is ultimately to use, t herefore, review the situation and life situation t o be created in a variety of languages, gui de students on the basis of the previous accumulation of knowledge to use to the maximum, and really apply what they have learned. Second, review the content and strategy of the first part: the basics (a) 1, review the main points of Hanyu Pinyin is a ble to recite a nd write down the alphabet of Hanyu Pinyin; accurate spelling pronunciation (after reading cacuminal, nasal sound, light, and retroflex sounds), the correct write consonants, vowels and syllables. 2,. main types according to the order of the alpha bet of Hanyu Pinyin alphabetical order; fill in the appropriate uppercase and l owerca se letters; see phonetic writing words; pinyin to write sentences with dot to select the corre ct pronunciation of the word; to bring some initial consonants or vowels, word selection. Second, the main types of words (1) Ruby written words; (2) to bring Word to select the correct pronunciation; (3) use a sequencer and radical character lookup method 3cos()cos2ACB得3cos()cos()2ACAC然后利用两角和与差的余弦公式展开得3sinsin4AC； 又由2bac， 利用正弦定理进行边角互化，得2sinsinsinBAC，进而得3sin2B.故233B或。 大部分考生做到这里忽略了检验，事实上，当23B时，由1coscos()2BAC，进而得3cos()cos()212ACAC，矛盾，应舍去。也可利用若2bac则babc或从而舍去23B。不过这种方法学生不易想到。评析 ：本小题考生得分易，但得满分难。18（本小题满分12 分）如图，直三棱柱111ABCA B C中，,ABAC D、E分别为1AA、1B C的中点，DE平面1BCC（I）证明：ABAC（II ）设二面角ABDC为 60，求1B C与平面BCD所成的角的大小。（I）分析一 ：连结 BE，111ABCA B CQ为直三棱柱，190 ,B BCEQ为1B C的中点，BEEC。又DE平面1BCC，BDDC（射影相等的两条斜线段相等）而DA平面ABC，ABAC（相等的斜线段的射影相等）。分析二 ：取BC的中点F，证四边形AFED为平行四边形，进而证AFDE，AFBC，得ABAC也可。分析三 ：利用空间向量的方法。具体解法略。（II ）分析一 ：求1B C与平面BCD所成的线面角，只需求点1B到面BDC的距离即可。作AGBD于G， 连GC， 则GCBD，AGC为二面角ABDC的平面角，60AGC.不妨设2 3AC，则2
