2022年中考数学模拟试卷.docx

精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载2022 中考数学模拟试卷留意事项：本卷共八大题,计23 小题,满分 150 分,考试时间 120 分钟一、挑选题（此题共10 小题,每道题 4 分,满分 40 分）D a 2·a31. 11 2的确定值是 A2 B1C1D2 222以下运算正确选项 Aa 3÷ a2aa 6 Ba3a2a5 Ca 3 2a5 3以下几何体,正 主视图是三角形的是 ABCD4以下命题是假命题的是 A等角的补角相等 B内错角相等 C两点之间,线段最短 D两点确定一条直线2 25关于 x 的一元二次方程 a 1 x ax a 1 0 的一个根是 0,就 a 的值为A1 B. 0 C. 1 D. ± 1 6假如等边三角形的边长为 6,那么它的内切圆的半径为（）A3 B3 C 2 3 D 3 37以下图形中能确定 12 的是 ABCD8甲、乙、丙三人参与央视的“ 幸运52” .幸运的是,他们都得到了一件精致的礼物.其过程是这样的：墙上挂着两串礼物（如图）,每次只能从其中一串的最下端取一件,直到礼物取完为止 .甲第一个取得礼物,然后,乙、丙依次取得第 2 件、第3 件礼物 .事后他们打开这些礼物认真比较发觉礼物B 最精致,那么取得礼物 B 可名师归纳总结 能性最大的是B乙C丙D无法确定BCA甲A第 1 页,共 10 页- - - - - - -精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载k 19反比例函数 yx 的图象,在每个象限内, y 的值随 x 值的增大而增大,就 k 的值可 A0 B1 C2 D3 10用四个全等的矩形和一个小正方形拼成如下列图的大正方形,已知大正方形的面积是 144,小正方形的面积是 4, x 如用 x,y 表示矩形的长和宽 xy,就以下关系式中不正确的是y A. x+y=12 B. xy=2C. xy=3 D. x 2 y 2 =144第 10 题图二、填空题（此题共 4 小题,每道题 5 分,满分 20 分）11. 我 国 的 国 土 面 积 为 9596960 平 方 千 米 , 这 个 数 用 科 学 记 数 法 表 示 为_平方千米 保留三个有效数字 1 12. 如图,半圆的直径AB=_- 2 B - 1 0 1 A第 12 题图13. 将抛物线y2 x 的图像向右平移3 个单位,就平移后的抛物线的解析式为_ 14观看表一,查找规律表二、表三分别是从表一中选取的一部分,就 为 _a+b 的值0 1 2 3 1 3 5 7 11 112 5 8 11 1 3 14 3 7 11 15 1b a 7 表一表二表三三（此题共 2 小题,每道题 8 分,满分 16 分）15. 先化简代数式aa2a22÷a214,然后选取一个合适的 a 值,代入求值名师归纳总结 第 2 页,共 10 页- - - - - - -精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载16. “ 方程” 是现实生活中特别重要的数学模型请结合你的生活实际编写一道二元一次方程组的应用题, 并使所列出的二元一次方程组为x2y, ,并写出求解过程60xy四、（此题共 2 小题,每道题 8 分,满分 16 分）17.1按要求在网格中画图：画出图形“” 关于直线 l 的对称图形,再将所画图形与原图形组成的图案向右平移 2 格；2依据以上构成的图案,请写一句简短、贴切的解说词：；18. 某公司经过市场调研,打算从明年起对甲、乙两种产品实行“ 限产压库”,方案这两种产品全年共生产 20 件,这 20 件的总产值 P 不少于 1140 万元,且不多于 1170 万元；已知有关数据如下表所示：产品 每件产品的产值甲 45 万元乙 75 万元（1） 设支配生产甲产品X 件（X 为正整数）,写出 X 应满意的不等式组；名师归纳总结 - - - - - - -第 3 页,共 10 页精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载（2） 请你帮忙设计出全部符合题意的生产方案；五、（此题共 2 小题,每道题 10 分,满分 20 分）19、如图 RtABO中,A30,OB2,假如将 RtABO在坐标平面内,绕原点 O按顺时针方向旋转到OA B 的位置（1）求点 B 的坐标（2）求顶点 A 从开头到 A 点终止经过的路径长A y BB O Ax 20、声音在空气传播的速度 温的音速 : ym/s是气温 x的一次函数 ,下表列出了一组不同气气 温0 5 10 15 20 x 音 速331 334 337 340 343 ym/s 1求 y 与 x 之间的函数关系式 ; 2气温 x=23时,某人看到烟花燃放 距多远 . 5s 后才听到声响 ,那么此人与烟花燃放地约相名师归纳总结 - - - - - - -第 4 页,共 10 页精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载六、（此题满分 12 分）21、三角形中位线定理,是我们特别熟识的定理请你在下面的横线上,完整地表达出这个定理：依据这个定理画出图形,写出已知和求证,并对该定理给出证明.七、（此题满分 12 分）C E 22、如图, AB 为 O 的直径,弦 CDAB于点 M ,过 B 点作A O M B BECD,交 AC 的延长线于点E ,连接 BC ；（1）求证： BE 为 O 的切线；（2）假如CD6 tanBCD1,求 O 的直径；D 2八、（此题满分 14 分）23| 、如图, 一元二次方程x22x30的二根x 1,x 2（x 1x ）是抛物线yax2bxc 与x 轴的两个交点B,C的横坐标,且此抛物线过点A , （1）求此二次函数的解析式（2）设此抛物线的顶点为P,对称轴与线段AC 相交于点 Q ,求点 P 和点 Q 的坐标第 5 页,共 10 页（3）在 x 轴上有一动点 M ,当 MQMA 取得最小值时,求M 点的坐标名师归纳总结 - - - - - - -精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载 y A（3,6）Q C O B x P 数学参考答案及评分标准一挑选题（此题共10 小题,每道题 4 分,满分 40 分）8 9 10 题号1 2 3 4 5 6 7 答案C A C B C B C C A D 二填空题（此题共4 小题,每道题 5 分,满分 20 分）6 11、9.60× 1012、2213 yx3214、37 三（此题共 2 小题,每道题 8 分,满分 16 分）15、解: 方法一：原式aa a2 aa2 a2 2 162 a2 2 aa24aa2422a2 2 aa24分名师归纳总结 （注：分步给分,化简正确给5 分）第 6 页,共 10 页- - - - - - -精选学习资料 - - - - - - - - - 方法二：原式a2a优秀学习资料a欢迎下载 6 分822a22 aaa22 a2 a24取 a1,得 7 分原式 5 分（注：答案不唯独假如求值这一步,取a2 或 2,就不给分）16、应用题：我家里有 60 棵树,其中杨树是柳树的 2 倍,求杨树和柳树各有多少棵？····················································································································································· 5 分解答过程：设杨树 x 棵,柳树 y 棵 ····························································································6 分x y 60 x 40依题意：解得···················································································7 分x 2 y y 20答：我家有杨树 40 棵,柳树 20 棵 ························································································8 分四、（此题共 2 小题,每道题 8 分,共 16 分）17、1按步骤给分,每步 3 分 6 分递或我们心连心 2解说合理即可,如爱心传等 8 分18、（1）114045x+7520-x1170 4 分211x12 5 分x 为正整数当 x=11 时,20-11=9 当 x=12 时 20-12=8 生产甲产品 11 件,生产乙产品 9 件名师归纳总结 或 生产甲产品 12 件,生产乙产品 8 件； 8 分第 7 页,共 10 页- - - - - - -精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载五、 此题共 2 小题,每道题 10 分,满分 20 分 19. 解：（1）过点 B 作 B D x 轴于 D·················································································3 分由题意知,A 30° ,A OB 60°,OB 2,OA 4 1 2 分A y OD OB cos60°2 1 4 分2 BDB OB sin 60°22 3 3 5 分 B O D A x B 的坐标为：B 1,3 6 分（2）AOB 60°,AOA 180°60°120°······················································7 分A 由开头到终止所经过的路径长为：120 4 8·······················································10 分180 320解：（1）y=kx+bb5 k 331,b 334.k=3 5. y 3x 331 （7 分）5（2）当 x=23 时, y 323 331 344.8 . 55× 344.8=1724. 此人与烟花燃放地相距约 六、（此题满分 12 分）1724m （ 3 分）21、（1）三角形的中位线平行于第三边且等于第三边的一半DE············································2 分（2）已知： DE 是ABC的中位线求证：DEBC,1 2BC······················································································································································5 分证明：延长 DE 到 F ,使 EF 连接 CFDE························································································6 分AE CE,AED CEFADECEF··················································································································7 分AD CF,ADE CFE······························································································8 分ADCF································································································································9 分AD BDBD CF·······························································································································10 分四边形 BCFD 是平行四边形······························································································11 分1DEBC,DE BC ····································································································12 分2七、（此题满分 12 分）名师归纳总结 第 8 页,共 10 页- - - - - - -精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载22. 证明：BECD, AB CD ,AB BE又 AB为直径,BE 为 O 的切线 ·················································································································3 分（2）AB为直径, AB CD ,1 1CM CD 6 3 ·····································································································5 分2 2BC BD BAC BCD tan BCD 1,BM 12 CM 21 3BM CM ················································································································8 分2 2CM 1tan BAC tan BCD,AM 2AM 6······························································································································10 分O 的直径 AB AM BM 6 3 15 ········································································12 分2 2八、（此题满分 14 分）223. 解：（1）解方程 x 2 x 3 0得 x 1 3,x 2 1···························································································································1 分抛物线与 x 轴的两个交点坐标为：C 3 0,B 10,·····························································2 分设抛物线的解析式为y a x 3 x 1·························································································································3 分A 3 6, 在抛物线上6 a 3 3 3 1a 1································································································4 分2抛物线解析式为：y 1x 2x 3·························································································5 分2 2（2）由 y 1 x 2x 3 1 x 1 22·······················································································6 分2 2 2抛物线顶点 P 的坐标为： 1,2,对称轴方程为：x 1·············································7 分设直线 AC 的方程为：y kx bA 3 6,C 3 0, 在该直线上3 k b 6 b 3解得直线 AC 的方程为：y x 3·····················································9 分3 k b 0 k 1将 x 1 代入 y x 3 得 y 2Q 点坐标为 1 2, ···················································································································10 分（3）作 A 关于 x 轴的对称点 A 3,6,连接 A Q ； A Q 与 x 轴交于点 M 即为所求的点····················································································································································11 分名师归纳总结 - - - - - - -第 9 页,共 10 页精选学习资料 - - - - - - - - - 优秀学习资料 欢迎下载设直线 A Q 方程为 y kx b3 k b 6 b 0解得k b 2 k 2直线A C：y 2 x ··············································································································12 分令 x 0,就 y 0·······················································································································13 分M 点坐标为 0 0,···················································································································14 分y A（3,6）Q C O B x P 名师归纳总结 A ,6第 10 页,共 10 页- - - - - - -