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2019年中考数学数与式专题复习讲义_整式专练_2018年中考数学真题汇编

16.下列运算正确的是\((\)  \()\)

A.\(2a – a = 1\)                                                          

B.\(2a + b = 2ab\)                                                     

C.\({({a^4})^3} = {a^7}\)                                    

D.\((-a)^{2}· (-a)^{3}=-a^{5}\)

【解答】解:\(A\)、\(2a – a = a\),故本选项错误;

\(B\)、\(2a\)与\(b\)不是同类项,不能合并,故本选项错误;

\(C\)、\({({a^4})^3} = {a^{12}}\),故本选项错误;

\(D\)、\((-a)^{2}· (-a)^{3}=-a^{5}\),故本选项正确.

故选:\(D\).

【总结】考查了合并同类项,幂的乘方与积的乘方,同底数幂的乘法,属于基础题,熟记计算法则即可解答.

17.计算:\((2a)· (ab)=(\)  \()\)

A.\(2ab\)                       

B.\(2{a^2}b\)              

C.\(3ab\)                        

D.\(3{a^2}b\)

【解答】解:\((2a)· (ab)=2a^{2}b\).

故选:\(B\).

【总结】此题主要考查了单项式乘以单项式,正确掌握运算法则是解题关键.

18.下列运算正确的是\((\)  \()\)

A.\({({b^2})^3} = {b^5}\)                                   

B.\({x^3} \div {x^3} = x\)                                    

C.\(5y^{3}· 3y^{2}=15y^{5}\)                           

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

【解答】解:\(A\)、\({({b^2})^3} = {b^6}\),故此选项错误;

\(B\)、\({x^3} \div {x^3} = 1\),故此选项错误;

\(C\)、\(5y^{3}· 3y^{2}=15y^{5}\),正确;

\(D\)、\(a + {a^2}\),无法计算,故此选项错误.

故选:\(C\).

【总结】此题主要考查了幂的乘方运算以及同底数幂的除法运算、单项式乘以单项式和合并同类项,正确掌握相关运算法则是解题关键.

19.下列运算中,正确的是\((\)  \()\)

A.\(a^{2}· a^{3}=a^{5}\)                                     

B.\(2a – a = 2\)            

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

D.\(2a + 3b = 5ab\)

【解答】解:\(A\)、\(a^{2}· a^{3}=a^{5}\),正确;

\(B\)、\(2a – a = a\),错误;

\(C\)、\({(a + b)^2} = {a^2} + 2ab + {b^2}\),错误;

\(D\)、\(2a + 3b = 2a + 3b\),错误;

故选:\(A\).

【总结】此题主要考查了整式的运算能力,对于相关的整式运算法则要求学生很熟练,才能正确求出结果.

20.下列运算正确的是\((\)  \()\)

A .\({a^2} + {a^3} = {a^5}\)                           

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

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

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

【解答】解:\(A\)、\({a^2} + {a^3} = {a^2} + {a^3}\),错误;

\(B\)、\({a^2} \times {a^3} = {a^5}\),错误;

\(C\)、\({(a + b)^2} = {a^2} + 2ab + {b^2}\),错误;

\(D\)、\({({a^2})^3} = {a^6}\),正确;

故选:\(D\).

【总结】此题主要考查了整式的运算能力, 对于相关的整式运算法则要求学生很熟练, 才能正确求出结果 .

21.下列运算错误的是\((\)  \()\)

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

B.\({a^{10}} \div {a^9} = a\)                              

C.\(x^{3}· x^{5}=x^{8}\)                                    

D.\({a^4} + {a^3} = {a^7}\)

【解答】解:\(A\)、\({({m^2})^3} = {m^6}\),正确;

\(B\)、\({a^{10}} \div {a^9} = a\),正确;

\(C\)、\(x^{3}· x^{5}=x^{8}\),正确;

\(D\)、\({a^4} + {a^3} = {a^4} + {a^3}\),错误;

故选:\(D\).

【总结】此题主要考查了合并同类项法则以及单项式乘以单项式运算法则和同底数幂的除法运算法则等知识,正确掌握运算法则是解题关键.

22.下列运算正确的是\((\)  \()\)

A.\({( – \frac{1}{3})^2} = 9\)                             

B.\({2018^0} – \sqrt[3]{{ – 8}} =  – 1\)          

C.\(3a^{3}· 2a^{-2}=6a(a\ne 0)\)                       

D.\(\sqrt {18}  – \sqrt {12}  = \sqrt 6 \)

【解答】解:\(A\)、\({( – \frac{1}{3})^2} = \frac{1}{9}\),错误;

\(B\)、\({2018^0} – \sqrt[3]{{ – 8}} = 1 – ( – 2) = 3\),错误;

\(C\)、\(3a^{3}· 2a^{-2}=6a(a\ne 0)\),正确;

\(D\)、\(\sqrt {18}  – \sqrt {12}  = 3\sqrt 2  – 2\sqrt 3 \),错误;

故选:\(C\).

【总结】此题主要考查了二次根式以及单项式乘以单项式运算法则和实数的计算等知识,正确掌握运算法则是解题关键.

23.下列计算正确的是\((\)  \()\)

A.\(2x – x = 1\)           

B.\(x( – x) =  – 2x\)  

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

D.\({x^2} + x = 2\)

【解答】解:\(A\)、\(2x – x = x\),错误;

\(B\)、\(x( – x) =  – {x^2}\),错误;

\(C\)、\({({x^2})^3} = {x^6}\),正确;

\(D\)、\({x^2} + x = {x^2} + x\),错误;

故选:\(C\).

【总结】此题主要考查了合并同类项法则以及单项式乘以单项式运算法则和幂的乘方运算法则等知识,正确掌握运算法则是解题关键.

24.按一定规律排列的单项式:\(a\),\( – {a^2}\),\({a^3}\),\( – {a^4}\),\({a^5}\),\( – {a^6}\),\( \ldots  \ldots \),第\(n\)个单项式是\((\)  \()\)

A.\({a^n}\)                   

B.\( – {a^n}\)               

C.\({( – 1)^{n + 1}}{a^n}\)                                  

D.\({( – 1)^n}{a^n}\)

【解答】解:\(a\),\( – {a^2}\),\({a^3}\),\( – {a^4}\),\({a^5}\),\( – {a^6}\),\( \ldots  \ldots \),\((-1)^{n+1}· a^{n}\).

故选:\(C\).

【总结】考查了单项式,数字的变化类,注意字母\(a\)的指数为奇数时,符号为正;系数字母\(a\)的指数为偶数时,符号为负.

25.下列运算一定正确的是\((\)  \()\)

A.\({(m + n)^2} = {m^2} + {n^2}\)                 

B.\({(mn)^3} = {m^3}{n^3}\)                            

C.\({({m^3})^2} = {m^5}\)                                 

D.\(m· m^{2}=m^{2}\)

【解答】解:\(A\)、\({(m + n)^2} = {m^2} + 2mn + {n^2}\),故此选项错误;

\(B\)、\({(mn)^3} = {m^3}{n^3}\),正确;

\(C\)、\({({m^3})^2} = {m^6}\),故此选项错误;

\(D\)、\(m· m^{2}=m^{3}\),故此选项错误;

故选:\(B\).

【总结】此题主要考查了完全平方公式以及积的乘方运算、同底数幂的乘除运算,正确掌握运算法则是解题关键.

26.下列计算结果为\({a^6}\)的是\((\)  \()\)

A.\(a^{2}· a^{3}\)    

B.\({a^{12}} \div {a^2}\)                                     

C.\({({a^2})^3}\)      

D.\({( – {a^2})^3}\)

【解答】解:\(A\)、\(a^{2}· a^{3}=a^{5}\),此选项不符合题意;

\(B\)、\({a^{12}} \div {a^2} = {a^{10}}\),此选项不符合题意;

\(C\)、\({({a^2})^3} = {a^6}\),此选项符合题意;

\(D\)、\({( – {a^2})^3} =  – {a^6}\),此选项不符合题意;

故选:\(C\).

【总结】本题主要考查幂的运算,解题的关键是掌握同底数幂相乘、同底数幂相除、幂的乘方的运算法则.

27.下列运算正确的是\((\)  \()\)

A.\(a(a + 1) = {a^2} + 1\)                                                          

B.\({({a^2})^3} = {a^5}\)                                   

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

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

【解答】解:\(A\)、\(a(a + 1) = {a^2} + a\),故本选项错误;

\(B\)、\({({a^2})^3} = {a^6}\),故本选项错误;

\(C\)、不是同类项不能合并,故本选项错误;

\(D\)、\({a^5} \div {a^2} = {a^3}\),故本选项正确.

故选:\(D\).

【总结】此题考查了单项式乘多项式、合并同类项、同底数幂的除法以及幂的乘方,熟练掌握运算法则是解题的关键.

28.下列运算正确的是\((\)  \()\)

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

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

C.\(x^{3}· x^{4}=x^{7}\)                                    

D.\(2{x^3} – {x^3} = 1\)

【解答】解:\(A\)、\({( – {x^2})^3} =  – {x^6}\),此选项错误;

\(B\)、\({x^2}\)、\({x^3}\)不是同类项,不能合并,此选项错误;

\(C\)、\(x^{3}· x^{4}=x^{7}\),此选项正确;

\(D\)、\(2{x^3} – {x^3} = {x^3}\),此选项错误;

故选:\(C\).

【总结】本题主要考查整式的运算,解题的关键是掌握幂的乘方、同类项概念、同底数幂相乘及合并同类项法则.

29.下列运算正确的是\((\)  \()\)

A .\({( – {a^2})^3} =  – {a^5}\)                    

B .\(a^{3}· a^{5}=a^{15}\)                        

C .\({( – {a^2}{b^3})^2} = {a^4}{b^6}\)    

D .\(3{a^2} – 2{a^2} = 1\)

【解答】解:\(A\)、\({( – {a^2})^3} =  – {a^6}\),故此选项错误;

\(B\)、\(a^{3}· a^{5}=a^{8}\),故此选项错误;

\(C\)、\({( – {a^2}{b^3})^2} = {a^4}{b^6}\),正确;

\(D\)、\(3{a^2} – 2{a^2} = {a^2}\),故此选项错误;

故选:\(C\).

【总结】此题主要考查了积的乘方运算以及同底数幂的乘除运算、 合并同类项, 正确掌握相关运算法则是解题关键 .

30.下列计算结果为\({a^6}\)的是\((\)  \()\)

A.\({a^7} – a\)            

B.\(a^{2}· a^{3}\)     

C.\({a^8} \div {a^2}\)                                            

D.\({({a^4})^2}\)

【解答】解:\(A\)、\({a^7}\)与\(a\)不能合并,\(A\)错误;

\(B\)、\(a^{2}· a^{3}=a^{5}\),\(B\)错误;

\(C\)、\({a^8} \div {a^2} = {a^6}\),\(C\)正确;

\(D\)、\({({a^4})^2} = {a^8}\),\(D\)错误;

故选:\(C\).

【总结】本题考查的是同底数幂的乘除法、幂的乘方、合并同类项,掌握它们的运算法则是解题的关键.

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