中考试题专项测试卷
中考数学专项测试卷
方程与不等式
一、选择（每小题3分，共15分）
1. 已知关于方程432x m -=的解是x m =，则m 的值是
A.2
B.2-
C.27
D.27
- 2. 一元一次不等式2(x ＋1)≥4的解在数轴上表示为
A ．
B ．
C ．
D ．
3. 今年来某县加大了对教育经费的投入，2013年投入2500万元，2015 年投入3500万元. 假设该县投入教育经费的年平均增长率为x ，根据 题意列方程，则下列方程正确的是
A.225003500x =
B.()2250013500x +=
C.()225001%3500x +=
D.()()225001250013500x x +++= 4. 一元二次方程2810x x --=配方后可变形为
A.()2417x +=
B.()2
415x += C.()2417x -= D.()2415x -= 5. 已知2是关于x 的方程2230x mx m -+=的一个根，并且这个方程的两 个根恰好是等腰三角形ABC 的两条边长，则三角形ABC 的周长为
A.10
B.14
C.10或14
D.8或10
二、填空题（每小题3分，共15分）
6. 已知关于x 的方程250x a --=的解是2x =-，则a 的值为
. 7. 已知132m x y --与12n m n x y +是同类项，那么()2013n m -=
. 8. 方程()2x x x -=的根是
. 9. 用换元法解方程222216()101x x x x -++=-时，如果设2
21
x y x =-，那么原 方程可化为 .
10. 定义运算“*”，规定2x y ax by *=+，其中a ，b 为常数，且125*=，
216*=，则23*= .
三‘解答题（一）（每小题6分，共8分）
11. 解不等式：
4113x x --＞，并马解集表示在数轴上.
12. 解方程：
2111
x x x =-+-.
13. 解方程组：241x y y +=??-=-?
.
14. 解不等式组：426113
9x x x x -??-+???＞≤，并把解集在数轴上表示出来
15. 解一元二次方程：2253x x -=.
四、解答题（二）（每小题8分，共40分）
16. 已知关于x 的一元二次方程()2310x m x m ++++=，求证：
无论m 取何值时，原方程总有两个不相等的实数根.
17. 某工厂计划生产A ，B 两种产品共10件，其生产成本利润如下表：
若工厂计划获利14万元，问A ，B 两种产品应分别生产多少件？
18. 某工厂计划在规定时间内生产24000个零件，若每天比原计划多生产
30个零件则在规定时间内
可以多生产300个零件.
(1) 求原计划每天生产的零件个数和规定的天数；
(2) 为了提前完成生产任务，工厂在安排原有工人按原计划正常生产
的同时，引进5组机器人生产流水线共同参与零件生产，已知每组机 器人生产流水线每天生产零件的个数比20个工人原计划每
天生产的零件总数还多20%，按此测算，恰好提前两天完成24000个零件的生产任务，求原计划安排的工人人数.
19. 某商店把进价为8元的商品按每件10元售出，每天可销售200件，现采用提高售价，减少进货量的办法增加利润，已知这种商品每涨价0.5 元，其每天销售量就减少10件，若经营的这种商品要达到每天获利640 元，售价应定为多少？
20. P表示n边形的对角线的交点个数（指落在其内部的交点），如果这些交点都不重合，那么P与n 的关系式是：
P=
()()
2
1
24
n n
n an b
-
-+
g（其中，a，b是常数）
(1) 填空：通过画图可得：四边形时，P= (填数字)，五边形时，P= (填数字)
(2) 请根据四边形和五边形对角线交点的个数，结合关系式，求a，b 的值.（注：本题的多边形均指
凸多边形）
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