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中考复习:2018年全国各省市中考真题汇编—分式(一)

一、2018年中考真题分式计算知识点分析

知识点题量占比
同底数幂的乘法12.00%
合并同类项510.00%
分式的基本性质12.00%
分式的混合运算48.00%
完全平方公式24.00%
约分12.00%
分式的化简求值48.00%
分式的加减法1326.00%
分式的乘除法12.00%
分式的值为零的条件510.00%
零指数幂24.00%
分式的值36.00%
分式有意义的条件816.00%

二、 2018年中考真题分式计算难易度分析

试题难易度题量题号题量占比
232,3,4,6,7,11,12,13,14,15,17,18,20,23,
24,25,26,27,29,34,44,48,49
46%
较易211,5,8,9,10,16,19,21,22,28,30,31,37,38,
40,41,42,43,45,46,47
42%
中档632,33,35,36,39,5012%
较难000%
000%

2018年全国各省市分式中考真题汇编—分式(一)

一.选择题(共26小题)

1.(2018•牡丹江)下列运算正确的是\((\)  \()\)

A.\(2a^{-3}· a^{4}=2a^{-12}\)                           

B.\({( – 3{a^2})^3} =  – 9{a^6}\)                     

C.\({a^2} \div a \times \frac{1}{a} = {a^2}\)

D.\(a· a^{3}+a^{2}· a^{2}=2a^{4}\)

2.(2018•梧州)下列各式计算正确的是\((\)  \()\)

A.\(a + 2a = 3a\)        

B.\(x^{4}· x^{3}=x^{12}\)                                  

C.\({(\frac{1}{x})^{ – 1}} =  – \frac{1}{x}\) 

D.\({({x^2})^3} = {x^5}\)

3.(2018•莱芜)若\(x\),\(y\)的值均扩大为原来3倍, 则下列分式的值保持不变的是\((\)  \()\)

A .\(\frac{{2 + x}}{{x – y}}\)                      

B .\(\frac{{2y}}{{{x^2}}}\)                         

C .\(\frac{{2{y^3}}}{{3{x^2}}}\)                

D .\(\frac{{2{y^2}}}{{{{(x – y)}^2}}}\)

4.(2018•苏州)计算\((1 + \frac{1}{x}) \div \frac{{{x^2} + 2x + 1}}{x}\)的结果是\((\)  \()\)

A.\(x + 1\)                    

B.\(\frac{1}{{x + 1}}\)                                           

C.\(\frac{x}{{x + 1}}\)                                           

D.\(\frac{{x + 1}}{x}\)

5.(2018•云南)已知\(x + \frac{1}{x} = 6\),则\({x^2} + \frac{1}{{{x^2}}} = (\)  \()\)

A.38                               

B.36                                

C.34                                

D.32

6.(2018•曲靖)下列计算正确的是\((\)  \()\)

A.\(a^{2}· a=a^{2}\)                                              

B.\({a^6} \div {a^2} = {a^3}\)                           

C.\({a^2}b – 2b{a^2} =  – {a^2}b\)                 

D.\({( – \frac{3}{{2a}})^3} =  – \frac{9}{{8{a^3}}}\)

7.(2018•山西)下列运算正确的是\((\)  \()\)

A.\({( – {a^3})^2} =  – {a^6}\)                          

B.\(2{a^2} + 3{a^2} = 6{a^2}\)                         

C.\(2a^{2}· a^{3}=2a^{6}\)                                 

D.\({( – \frac{{{b^2}}}{{2a}})^3} =  – \frac{{{b^6}}}{{8{a^3}}}\)

8.(2018•河北)老师设计了接力游戏,用合作的方式完成分式化简,规则是:每人只能看到前一人给的式子,并进行一步计算,再将结果传递给下一人,最后完成化简.过程如图所示:

接力中,自己负责的一步出现错误的是\((\)  \()\)

A.只有乙                      

B.甲和丁                      

C.乙和丙                      

D.乙和丁

9.(2018•北京)如果\(a – b = 2\sqrt 3 \),那么代数式\((\frac{{a}^{2}+{b}^{2}}{2a}-b)· \frac{a}{a-b}\)的值为\((\)  \()\)

A.\(\sqrt 3 \)                

B.\(2\sqrt 3 \)              

C.\(3\sqrt 3 \)              

D.\(4\sqrt 3 \)

10.(2018•孝感)已知\(x + y = 4\sqrt 3 \),\(x – y = \sqrt 3 \),则式子\((x – y + \frac{{4xy}}{{x – y}})(x + y – \frac{{4xy}}{{x + y}})\)的值是\((\)  \()\)

A.48                               

B.\(12\sqrt 3 \)           

C.16                                

D.12

11.(2018•淄博)化简\(\frac{{{a^2}}}{{a – 1}} – \frac{{1 – 2a}}{{1 – a}}\)的结果为\((\)  \()\)

A.\(\frac{{a + 1}}{{a – 1}}\)                                

B.\(a – 1\)                     

C.\(a\)                            

D.1

12.(2018•江西)计算\((-a)^{2}· \frac{b}{{a}^{2}}\)的结果为\((\)  \()\)

A.\(b\)                           

B.\( – b\)                       

C.\(ab\)                         

D.\(\frac{b}{a}\)

13.(2018•株洲)下列运算正确的是\((\)  \()\)

A.\(2a + 3b = 5ab\)  

B.\({( – ab)^2} = {a^2}b\)                                    

C.\(a^{2}· a^{4}=a^{8}\)                                     

D.\(\frac{{2{a^6}}}{{{a^3}}} = 2{a^3}\)

14.(2018•温州)若分式\(\frac{{x – 2}}{{x + 5}}\)的值为0,则\(x\)的值是\((\)  \()\)

A.2                                  

B.0                                  

C.\( – 2\)                        

D.\( – 5\)

15.(2018•陇南)若分式\(\frac{{{x^2} – 4}}{x}\)的值为0,则\(x\)的值是\((\)  \()\)

A.2或\( – 2\)               

B.2                                  

C.\( – 2\)                        

D.0

16.(2018•天津)计算\(\frac{{2x + 3}}{{x + 1}} – \frac{{2x}}{{x + 1}}\)的结果为\((\)  \()\)

A.1                                  

B.3                                  

C.\(\frac{3}{{x + 1}}\)                                           

D.\(\frac{{x + 3}}{{x + 1}}\)

17.(2018•广州)下列计算正确的是\((\)  \()\)

A.\({(a + b)^2} = {a^2} + {b^2}\)                    

B.\({a^2} + 2{a^2} = 3{a^4}\)                            

C.\({x^2}y \div \frac{1}{y} = {x^2}(y \ne 0)\)   

D.\({( – 2{x^2})^3} =  – 8{x^6}\)

18.(2018•台州)计算\(\frac{{x + 1}}{x} – \frac{1}{x}\),结果正确的是\((\)  \()\)

A.1                                  

B.\(x\)                            

C.\(\frac{1}{x}\)        

D.\(\frac{{x + 2}}{x}\)

19.(2018•威海)化简\((a-1)\div (\frac{1}{a}-1)· a\)的结果是\((\)  \()\)

A.\( – {a^2}\)              

B.1                                  

C.\({a^2}\)                   

D.\( – 1\)

20.(2018•泰安)计算:\( – ( – 2) + {( – 2)^0}\)的结果是\((\)  \()\)

A.\( – 3\)                       

B.0                                  

C.\( – 1\)                        

D.3

21.(2018•南充)已知\(\frac{1}{x} – \frac{1}{y} = 3\),则代数式\(\frac{{2x + 3xy – 2y}}{{x – xy – y}}\)的值是\((\)  \()\)

A.\( – \frac{7}{2}\)    

B.\( – \frac{{11}}{2}\)                                            

C.\(\frac{9}{2}\)        

D.\(\frac{3}{4}\)

22.(2018•内江)已知:\(\frac{1}{a} – \frac{1}{b} = \frac{1}{3}\),则\(\frac{{ab}}{{b – a}}\)的值是\((\)  \()\)

A.\(\frac{1}{3}\)        

B.\( – \frac{1}{3}\)    

C.3                                  

D.\( – 3\)

23.(2018•绵阳)\({( – 2018)^0}\)的值是\((\)  \()\)

A.\( – 2018\)               

B.2018                        

C.0                                

D.1

24.(2018•武汉)若分式\(\frac{1}{{x + 2}}\)在实数范围内有意义,则实数\(x\)的取值范围是\((\)  \()\)

A.\(x >  – 2\)              

B.\(x <  – 2\)              

C.\(x =  – 2\)              

D.\(x \ne  – 2\)

25.(2018•金华)若分式\(\frac{{x – 3}}{{x + 3}}\)的值为0,则\(x\)的值为\((\)  \()\)

A.3                                  

B.\( – 3\)                        

C.3或\( – 3\)                

D.0

26.(2018•葫芦岛)若分式\(\frac{{{x^2} – 1}}{{x + 1}}\)的值为0,则\(x\)的值为\((\)  \()\)

A.0                                  

B.1                                  

C.\( – 1\)                        

D.\( \pm 1\)

二.填空题(共24小题)

27.(2018•甘孜州)已知\(m + n = 3mn\),则\(\frac{1}{m} + \frac{1}{n}\)的值为  

28.(2018•绥化)当\(x = 2\)时,代数式\((\frac{{2x + 1}}{x} + x) \div \frac{{x + 1}}{x}\)的值是  

29.(2018•镇江)若分式\(\frac{5}{{x – 3}}\)有意义,则实数\(x\)的取值范围是  

30.(2018•乐山)化简\(\frac{a}{{b – a}} + \frac{b}{{a – b}}\)的结果是  

31.(2018•攀枝花)如果\(a + b = 2\),那么代数式\((a – \frac{{{b^2}}}{a}) \div \frac{{a – b}}{a}\)的值是  

32.(2018•贵港)若分式\(\frac{2}{{x + 1}}\)的值不存在,则\(x\)的值为  

33.(2018•包头)化简:\(\frac{{{x^2} – 4x + 4}}{{{x^2} + 2x}} \div (\frac{4}{{x + 2}} – 1) = \)  

34.(2018•昆明)若\(m + \frac{1}{m} = 3\),则\({m^2} + \frac{1}{{{m^2}}} = \)  

35.(2018•沈阳)化简:\(\frac{{2a}}{{{a^2} – 4}} – \frac{1}{{a – 2}} = \)  

36.(2018•大庆)已知\(\frac{{3x – 4}}{{(x – 1)(x – 2)}} = \frac{A}{{x – 1}} + \frac{B}{{x – 2}}\),则实数\(A = \)  

37.(2018•永州)化简:\((1 + \frac{1}{{x – 1}}) \div \frac{{{x^2} + x}}{{{x^2} – 2x + 1}} = \)  

38.(2018•武汉)计算\(\frac{m}{{{m^2} – 1}} – \frac{1}{{1 – {m^2}}}\)的结果是  

39.(2018•湖州)当\(x = 1\)时,分式\(\frac{x}{{x + 2}}\)的值是  

40.(2018•襄阳)计算\(\frac{{5x + 3y}}{{{x^2} – {y^2}}} – \frac{{2x}}{{{x^2} – {y^2}}} = \)  

41.(2018•常州)化简:\(\frac{a}{{a – b}} – \frac{b}{{a – b}} = \)  

42.(2018•宁波)要使分式\(\frac{1}{{x – 1}}\)有意义,\(x\)的取值应满足  

43.(2018•长沙)化简:\(\frac{m}{{m – 1}} – \frac{1}{{m – 1}} = \)  

44.(2018•衡阳)计算:\(\frac{{{x^2}}}{{x + 1}} – \frac{1}{{x + 1}} = \)  

45.(2018•咸宁)如果分式\(\frac{1}{{x – 2}}\)有意义,那么实数\(x\)的取值范围是  

46.(2018•江西)若分式\(\frac{1}{{x – 1}}\)有意义,则\(x\)的取值范围为  

47.(2018•滨州)若分式\(\frac{{{x^2} – 9}}{{x – 3}}\)的值为0,则\(x\)的值为  

48.(2018•湘西州)要使分式\(\frac{1}{{x + 2}}\)有意义,则\(x\)的取值范围为  

49.(2018•盐城)要使分式\(\frac{1}{{x – 2}}\)有意义,则\(x\)的取值范围是  

50.(2017•衡阳)化简:\(\frac{{{x^2} + 2x + 1}}{{x + 1}} – \frac{{{x^2} + x}}{x} = \)   

2019.3.20



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