北师大版八年级下册《第5章 分式与分式方程》单元检测卷A（一）

1、北师大版八年级下册第5章 分式与分式方程2014年单元检测卷a（一）一、选择题（每小题4分，共48分）1下列各式x23，1y+2，a21a1，3m中，分式有（）a1个b2个c3个d4个2分式x21x+1的值为零，则x的值为（）a-1b0c1d13把分式ab+c的a、b、c的值都扩大为原来的3倍，则分式的值（）a不变b变为原来的3倍c变为原来的13d变为原来的164下列计算错误的是（）a0.2a+b0.7ab2a+b7abbx3y2x2y3xycabba1d1c+2c3c5化简2xx29+13x的结果是（）a1x3b1x+3c13xd3x+3x296化简（x-2x1x）（1-1x）的结果是（）a

2、1xbx-1cx1xdxx17为了帮助遭受自然灾害的地区重建家园，某学校号召同学们自愿捐款已知第一次捐款总额为4800元，第二次捐款总额为5000元，第二次捐款人数比第一次多20人，而且两次人均捐款额恰好相等，如果设第一次捐款人数是x人，那么x满足的方程是（）a4800x5000x20b4800x=5000x+20c4800x205000xd4800x+205000x8分式方程1x1+2xx+1=2的解是（）a1b-1c3d无解9对于非零的实数a、b，规定ab=1b-1a若2（2x-1）=1，则x=（）a56b54c32d-1610若方程xx3-2=kx3有增根，则k=（）a-2b0c1d31

3、1关于x的分式方程mx+11的解是负数，则m的取值范围是（）am-1bm-1且m0cm-1dm-1且m012如图，设k=甲图中阴影部分面积乙图中阴影部分面积（ab0），则有（）ak2b1k2c12k1d0k12二、填空题（每小题4分，共24分）13要使分式2xx3有意义，则x须满足的条件为14计算：(1+4a24)aa2=15杭州到北京的铁路长1487千米火车的原平均速度为x千米/时，提速后平均速度增加了70千米/时，由杭州到北京的行驶时间缩短了3小时，则可列方程为16已知1a1b12，则abab的值是17若关于x的方程axx2=4x2+1无解，则a的值是18已知三个数x，y，z满足xyx+y

4、2，yzy+z43，zxz+x43，则xyzxy+yz+zx的值为三、解答题（19题6分，20题8分，共14分）19计算：（1）2aa291a3；（2）(1a1b)a2b2ab20解分式方程：（1）23x1136x2；（2）3x1x+3x10四、解答题（每小题10分，共40分）21先化简，再求值：aba（a-2abb2a），其中a、b满足式子|a-2|+（b-3）2=022我市新城区环形路的拓宽改造工程项目，经投标决定由甲、乙两个工程队共同完成这一工程项目已知乙队单独完成这项工程所需天数是甲队单独完成这项工程所需天数的2倍；该工程如果由甲队先做6天，剩下的工程再由甲、乙两队合作16天可以完成求

5、甲、乙两队单独完成这项工程各需要多少天？23a玉米试验田是边长为a米的正方形减去一个边长为1米的正方形蓄水池后余下部分，b玉米试验田是边长为（a-1）米的正方形，两块试验田的玉米都收获了500千克（1）哪种玉米的单位面积产量高？（2）高的单位面积产量是低的单位面积产量的多少倍？24兴发服装店老板用4500元购进一批某款t恤衫，由于深受顾客喜爱，很快售完，老板又用4950元购进第二批该款式t恤衫，所购数量与第一批相同，但每件进价比第一批多了9元（1）第一批该款式t恤衫每件进价是多少元？（2）老板以每件120元的价格销售该款式t恤衫，当第二批t恤衫售出45时，出现了滞销，于是决定降价促销，若要使第

6、二批的销售利润不低于650元，剩余的t恤衫每件售价至少要多少元？（利润=售价-进价）五、解答题（每小题12分，共24分）25先观察下列等式，然后用你发现的规律解答下列问题11211212312131341314（1）计算112+123+134+145+156=；（2）探究112+123+134+1n(n+1)=；（用含有n的式子表示）（3）若113+135+157+1(2n1)(2n+1)的值为1735，求n的值26阅读下面材料，并解答问题材料：将分式x4x2+3x2+1拆分成一个整式与一个分式（分子为整数）的和的形式解：由分母为-x2+1，可设-x4-x2+3=（-x2+1）（x2+a）+b

7、则-x4-x2+3=（-x2+1）（x2+a）+b=-x4-ax2+x2+a+b=-x4-（a-1）x2+（a+b）对应任意x，上述等式均成立，a11a+b3，a=2，b=1x4x2+3x2+1(x2+1)(x2+2)+1x2+1=(x2+1)(x2+2)x2+1+1x2+1=x2+2+1x2+1这样，分式x4x2+3x2+1被拆分成了一个整式x2+2与一个分式1x2+1的和解答：（1）将分式x46x2+8x2+1拆分成一个整式与一个分式（分子为整数）的和的形式（2）当x（-1，1），试说明x46x2+8x2+1的最小值为8 tgz7r4i30ka1dkaghn3xtkknbycudxqa7f

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