天天资源网 / 初中数学 / 三轮冲刺 / 2021年中考数学及格冲刺试卷
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中考数学及格冲刺试卷
一、填空题（每题 3 分，共 30 分）
1、方程 x－3 ＝7 的解是 ．
2、当 x____________时，二次根式 32 x 有意义
3、已知函数 y＝kx＋b，当 x＝2 时，y＝－2；当 x＝－
2
1 时，y＝3，则函数解析式为____ __．
4、一汽车在 a 小时内走 x 千米，用同样的速度，b 分钟可以走 千米．
5、等腰三角形底边长 10cm，周长为 36cm，则一底角的余弦值为 .
6、等腰三角形一边等于 5，另一边等于 8，则周长是 ；
7、0.1 是数 a 的立方根，则 a＝_________．
8、在数据－1，0，4，5，8 中插入一个数 x，使这组数据的中位数为 3，则 x＝_______．
9、关于 x 方程（k－1）x2－4x＋5＝0 有两个不相等的实数根，则 k 取值范围为 ；
10、已知不等式 mx－n＞0，当 m__ _时，解集是 x＜
m
n ；
二、选择题（每题 3 分，共 30 分）
1、当 a＜0 时，化简|2a－ 2a |的结果是（ ）
（A）a （B）－a （C）3a （D）－3a
2、若点 P（a，b）在第四象限，则点 Q（－a，b－4）在象限是（ ）
（A）第一象限 （B）第二象限 （C）第三象限 （D）第四象限
3、矩形的边长为 10 cm 和 15 cm，其中一内角平分线分长边为两部分，这两部分的长为（ ）
（A）6 cm 和 9 cm （B）5 cm 和 10 cm
（C）4 cm 和 11 cm （D）7 cm 和 8 cm
4、如图，在 Rt△ABC 中，CD 是斜边 AB 上的高，则图中的相似三角形共有（ ）
（A）1 对 （B）2 对 （C）3 对 （D）4 对
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拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城，拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场，建设规模占地约128亩，建筑面积约25万平方米，项目总投资约5亿元人民币。经过1--2年的开发建设，能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家，预计年交易额实现68亿元人民币，每年实现税收8000—10000万元人民币，每年实现利润1.68亿元人民币，实现就业和创业人员约2万以上。
经济增长：在优化结构、提高效益和降低消耗的基础上，“十一五”期市GDP年均增长12%以上（现14%以上），2010年达到650亿元以上，人均GDP力争1000美元；财政收入达到80亿元；规模以上工业销售达到550亿以上；全社会固定资产投资年均长20%，五年累计1000亿元；社会消费品销售额260亿元，年均增长20%，外贸进口总额2.5亿美元，年均增长15%；五年累计招商引资突破500亿元，力争达到600亿元
5、若|2 x－5|＝5－2 x，则 x 的取值是（ ）
（A）x＞
2
5 （B）x≥
2
5 （C）x＜
2
5 （D）x≤
2
5
6、从 1，2，3，4 这四个数字中，任意抽取两个不同数字组成一个两位数，则这个两位数能被 3 整除的概率是（ ）
(A) 1
3
(B) 1
4
(C) 1
6
(D) 1
12
7、下列运算正确的是（ ）
（A）（－2ab）·（－3ab）3＝－54a4b4 （B）5x2·（3x3）2＝15x12
（C）（－0.1 b）·（－10b2）3＝－b7 （D）（2×10n）（
2
1 ×10n）＝102n
8、某商店出售下列四种形状的地砖：①正三角形；②正方形；③正五边形；④正六边形．若只选购其中一种地砖镶嵌
地面，可供选择的地砖共有（ ）．
（A）4 种 （B）3 种 （C）2 种 （D）1 种
9、将抛物线
2y x 向左平移 2 个单位后，得到的抛物线的解析式是（ ）
（A）
2( 2)y x （B）
2 2y x （C）
2( 2)y x （D）
2 2y x
10、四边形 ABCD 中，对角线 AC、BD 相交于点 O，给出下列四组条件：①AB∥CD，AD∥BC；②AB=CD，AD=BC；③AO=CO，
BO=DO；④AB∥CD，AD=BC．其中一定能判断这个四边形是平行四边形的条件共有（ ）
（A）1 组 （B）2 组 （C）3 组 （D）4 组
三、解答题：
1、某校去年一年级男生比女生多 80 人，今年女生增加 20%，男生减少 25%，结果女生又比男生多 30 人，求去年一年
级男生、女生各多少人．（6 分）
2、按下列条件，求二次函数的解析式：
（1）图象经过 A（0，1），B（1，3），C（－1，1）；
（2）图象经过（3，1），且当 x＝2 时有最大值为 3．（8 分）
3、已知：如图，矩形 ABCD 中，E、F 是 AB 上的两点，且 AF＝BE．求证：∠ADE＝∠BCF．（8 分）
4、已知满足不等式 3（x－2）＋5＜4（x－1）＋6 的最小整数是方程 2 x－ax＝3 的解，求代数式 4a－
a
14 的值．（8 分）
拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城，拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场，建设规模占地约128亩，建筑面积约25万平方米，项目总投资约5亿元人民币。经过1--2年的开发建设，能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家，预计年交易额实现68亿元人民币，每年实现税收8000—10000万元人民币，每年实现利润1.68亿元人民币，实现就业和创业人员约2万以上。
经济增长：在优化结构、提高效益和降低消耗的基础上，“十一五”期市GDP年均增长12%以上（现14%以上），2010年达到650亿元以上，人均GDP力争1000美元；财政收入达到80亿元；规模以上工业销售达到550亿以上；全社会固定资产投资年均长20%，五年累计1000亿元；社会消费品销售额260亿元，年均增长20%，外贸进口总额2.5亿美元，年均增长15%；五年累计招商引资突破500亿元，力争达到600亿元
5、如图，在△ABC 中，∠ACB=90°，∠A=30°，BC=2．将△ABC 绕点 C 按顺时针方向旋转 n 度后得到△EDC，此时点 D 在 AB 边上，
斜边 DE 交 AC 边于点 F．
（1）求 DC 的长和旋转的角度 n；
（2）求图中阴影部分的面积．（10 分）
答案：
一、填空题
题号 1 2 3 4 5 6 7 8 9 10
答案 10 x≥3/2 Y=-2x+2 Xb/60a 18 或 21 5/9 0.001 2 k≤9/5 m＜0
二、选择题
题号 1 2 3 4 5 6 7 8 9 10
答案 D C B C D A D B A C
三、解答题
1、1.2x-0.75(x+80)=30
解得 x=200
所以男生 280 人，女生 200 人
2、（1）y=x2+x+1
（2）y=2（x-2）2+3
3、证明：∵四边形 ABCD 是矩形，
∴AD=BC，∠A=∠B=90°．
∵AF=BE，
∴AF-EF=BE-EF．即 AE=BF．
在△ADE 和△BCF 中，
拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城，拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场，建设规模占地约128亩，建筑面积约25万平方米，项目总投资约5亿元人民币。经过1--2年的开发建设，能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家，预计年交易额实现68亿元人民币，每年实现税收8000—10000万元人民币，每年实现利润1.68亿元人民币，实现就业和创业人员约2万以上。
经济增长：在优化结构、提高效益和降低消耗的基础上，“十一五”期市GDP年均增长12%以上（现14%以上），2010年达到650亿元以上，人均GDP力争1000美元；财政收入达到80亿元；规模以上工业销售达到550亿以上；全社会固定资产投资年均长20%，五年累计1000亿元；社会消费品销售额260亿元，年均增长20%，外贸进口总额2.5亿美元，年均增长15%；五年累计招商引资突破500亿元，力争达到600亿元
AD=BC
∠A=
∠B
AE=BF
∴△ADE-≌△BCF．
∴∠ADE=∠BCF．
4、10
5、解：（1）根据旋转的性质可得 DC=CB=2，
∵∠ACB=90°，∠A=30°，
∴∠B=90°-30°=60°，
∴△BCD 是等边三角形，
∴旋转的角度 n=∠BCD=60°；
（2）∵∠ACB=90°，∠A=30°，BC=2，
∴AB=2BC=4， ∴AD=4-2=2，∴AD=CD，
∴∠A=∠DCA=30°，又∵∠EDC=∠B=60°，∴∠CFD=180°-30°-60°=90°，∴DF⊥AC，∵BC=2，AB=4，∴AC=2 3
∴AF=FC=
AC= 3
∴DF=1，
阴影部分的面积=
1/2AF•DF= 3 /2
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仅供参考
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