标题

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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

31.下列计算正确的是\((\)  \()\)

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

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

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

D.\({(ab)^3} = a{b^3}\)

【解答】解:\(A\)、\(a^{2}· a^{3}=a^{5}\),故此选项错误;

\(B\)、\({({a^2})^2} = {a^4}\),正确;

\(C\)、\({a^8} \div {a^4} = {a^4}\),故此选项错误;

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

故选:\(B\).

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

32.下列等式成立的是\((\)  \()\)

A.\({x^2} + 3{x^2} = 3{x^4}\)                          

B.\(0.00028 = 2.8 \times {10^{ – 3}}\)             

C.\({({a^3}{b^2})^3} = {a^9}{b^6}\)             

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

【解答】解:\(A\)、\({x^2} + 3{x^2} = 4{x^2}\),故此选项错误;

\(B\)、\(0.00028 = 2.8 \times {10^{ – 4}}\),故此选项错误;

\(C\)、\({({a^3}{b^2})^3} = {a^9}{b^6}\),正确;

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

故选:\(C\).

【总结】此题主要考查了平方差公式以及科学记数法、积的乘方运算,正确掌握运算法则是解题关键.

33.计算\(a^{2}· a^{3}\),结果正确的是\((\)  \()\)

A.\({a^5}\)                   

B.\({a^6}\)                   

C.\({a^8}\)                   

D.\({a^9}\)

【解答】解:\(a^{2}· a^{3}=a^{5}\),

故选:\(A\).

【总结】此题考查同底数幂的乘法,关键是根据同底数的幂的乘法解答.

34.下列运算正确的是\((\)  \()\)

A.\( – {(x – y)^2} =  – {x^2} – 2xy – {y^2}\)

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

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

D.\({(x{y^2})^2} = {x^2}{y^4}\)

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

\(B\)、\({a^2} + {a^2} = 2{a^2}\),此选项错误;

\(C\)、\(a^{2}· a^{3}=a^{5}\),此选项错误;

\(D\)、\({(x{y^2})^2} = {x^2}{y^4}\),此选项正确;

故选:\(D\).

【总结】本题主要考查整式的运算,解题的关键是掌握完全平方公式、合并同类项法则、同底数幂的乘法、积的乘方与幂的乘方.

35.下列计算正确的是\((\)  \()\)

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

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

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

D.\({(a – 2)^2} = {a^2} – 4\)

【解答】解:\(A\)、\(a^{2}· a^{2}=a^{4}\),此选项错误;

\(B\)、\({( – {a^2})^3} =  – {a^6}\),此选项正确;

\(C\)、\(3{a^2} – 6{a^2} =  – 3{a^2}\),此选项错误;

\(D\)、\({(a – 2)^2} = {a^2} – 4a + 4\),此选项错误;

故选:\(B\).

【总结】本题主要考查整式的运算,解题的关键是掌握同底数幂相乘、幂的乘方、合并同类项法则及完全平方公式.

36.下列运算正确的是\((\)  \()\)

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

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

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

D.\({( – 2{x^2})^3} =  – 8{x^6}\)

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

\(B\)、\(x^{2}· x^{3}=x^{5}\),故\(B\)错误;

\(C\)、\({x^3} \div x = {x^2}\),故\(C\)错误;

\(D\)、\({( – 2{x^2})^3} =  – 8{x^6}\),故\(D\)正确.

故选:\(D\).

【总结】本题考查合并同类项、同底数幂的乘法、同底数幂的除法、积的乘方,熟练掌握运算性质和法则是解题的关键.

37.下列计算正确的是\((\)  \()\)

A.\(3x – x = 3\)                                                          

B.\({a^3} \div {a^4} = \frac{1}{a}\)                 

C.\({(x – 1)^2} = {x^2} – 2x – 1\)                       

D.\({( – 2{a^2})^3} =  – 6{a^6}\)

【解答】解:(A)原式\( = 2x\),故\(A\)错误;

(C)原式\( = {x^2} – 2x + 1\),故\(C\)错误;

(D)原式\( =  – 8{a^6}\),故\(D\)错误;

故选:\(B\).

【总结】本题考查整式的运算,解题的关键是熟练运用整式的运算法则,本题属于基础题型.

38.下列运算正确的是\((\)  \()\)

A.\({( – 3.14)^0} = 0\)                                            

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

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

D.\(2a^{2}· a^{-1}=2a\)

【解答】解:\(A\)、\({( – 3.14)^0} = 1\),故此选项错误;

\(B\)、\(x^{2}· x^{3}=x^{5}\),故此选项错误;

\(C\)、\({(a{b^2})^3} = {a^3}{b^6}\),故此选项错误;

\(D\)、\(2a^{2}· a^{-1}=2a\),正确.

故选:\(D\).

【总结】此题主要考查了幂的乘方运算以及同底数幂的乘法运算,正确掌握相关运算法则是解题关键.

39.下列各式中,运算正确的是\((\)  \()\)

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

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

C.\({a^6} \div {a^2} = {a^4}\)                          

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

【解答】解:\(A\)、错误.\({({a^3})^2} = {a^5}\);

\(B\)、错误.\({(a – b)^2} = {a^2} – 2ab + {b^2}\);

\(C\)、正确.

\(D\)、错误.\({a^2} + {a^2} = 2{a^2}\)

故选:\(C\).

【总结】本题考查同底数幂的乘法、除法法则,合并同类项法则,幂的乘方,乘法公式等知识,解题的关键是熟练掌握基本知识,属于中考常考题型.

40.下列运算正确的是\((\)  \()\)

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

B.\(\sqrt {{{( – 5)}^2}}  =  – 5\)                     

C.\(a^{3}· a^{4}=a^{12}\)                                   

D.\({(\pi  – 3)^0} = 1\)

【解答】解:\(A\)、错误.\(2a + 3a = 5a\);

\(B\)、错误.\(\sqrt {{{( – 5)}^2}}  = 5\);

\(C\)、错误.\(a^{3}· a^{4}=a^{7}\);

\(D\)、正确.∵\( \pi -3\ne 0\),

∴\( {(\pi  – 3)^0} = 1\).

故选:\(D\).

【总结】本题考查合并同类项法则、同底数幂乘法、不等于零的数的零次幂等于1、二次根式的性质等知识,解题的关键是熟练掌握基本知识,属于中考常考题型.

41.下列计算或运算中,正确的是\((\)  \()\)

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

B.\({( – 2{a^2})^3} =  – 8{a^3}\)                     

C.\((a – 3)(3 + a) = {a^2} – 9\)                             

D.\({(a – b)^2} = {a^2} – {b^2}\)

【解答】解:\(A\)、\({a^6} \div {a^2} = {a^4}\),此选项错误;

\(B\)、\({( – 2{a^2})^3} =  – 8{a^6}\),此选项错误;

\(C\)、\((a – 3)(3 + a) = {a^2} – 9\),此选项正确;

\(D\)、\({(a – b)^2} = {a^2} – 2ab + {b^2}\),此选项错误;

故选:\(C\).

【总结】本题主要考查整式的混合运算,解题的关键是掌握同底数幂的除法、积的乘方与幂的乘方、平方差公式、完全平方公式.

42.下列计算正确的是\((\)  \()\)

A .\(2a· 3b=5ab\)                                                

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

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

D .\({a^4} \div {a^2} + {a^2} = 2{a^2}\)

【解答】解:\(A\)、\(2a· 3b=6ab\),故此选项错误;

\(B\)、\(a^{3}· a^{4}=a^{7}\),故此选项错误;

\(C\)、\({( – 3{a^2}b)^2} = 9{a^4}{b^2}\),故此选项错误;

\(D\)、\({a^4} \div {a^2} + {a^2} = 2{a^2}\),正确 .

故选:\(D\).

【总结】此题主要考查了单项式乘以单项式以及积的乘方运算和合并同类项, 正确掌握相关运算法则是解题关键 .

43.下列运算正确的是\((\)  \()\)

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

B.\(a(b – 1) = ab – a\)                                               

C.\(3{a^{ – 1}} = \frac{1}{{3a}}\)                    

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

【解答】解:\(A\)、\({a^2}\)、\({a^3}\)不是同类项,不能合并,错误;

\(B\)、\(a(b – 1) = ab – a\),正确;

\(C\)、\(3{a^{ – 1}} = \frac{3}{a}\),错误;

\(D\)、\((3{a^2} – 6a + 3) \div 3 = {a^2} – 2a + 1\),错误;

故选:\(B\).

【总结】本题主要考查整式的运算,解题的关键是掌握合并同类项法则、单项式乘多项式、负整数指数幂及多项式除以单项式法则.

44.下列运算正确的是\((\)  \()\)

A .\(2{m^2} + {m^2} = 3{m^4}\)                  

B .\({(m{n^2})^2} = m{n^4}\)                        

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

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

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

\(B\)、\({(m{n^2})^2} = {m^2}{n^4}\),故此选项错误;

\(C\)、\(2m· 4m^{2}=8m^{3}\),故此选项错误;

\(D\)、\({m^5} \div {m^3} = {m^2}\),正确 .

故选:\(D\).

【总结】此题主要考查了合并同类项以及积的乘方运算、 整式的乘除运算, 正确掌握相关运算法则是解题关键 .

45.下列运算正确的是\((\)  \()\)

A.\({x^3} + {x^5} = {x^8}\)                               

B.\((y + 1)(y – 1) = {y^2} – 1\)                            

C.\({a^{10}} \div {a^2} = {a^5}\)                     

D.\({( – {a^2}b)^3} = {a^6}{b^3}\)

【解答】解:\(A\)、\({x^3} + {x^5}\),无法计算,故此选项错误;

\(B\)、\((y + 1)(y – 1) = {y^2} – 1\),正确;

\(C\)、\({a^{10}} \div {a^2} = {a^8}\),故此选项错误;

\(D\)、\({( – {a^2}b)^3} =  – {a^6}{b^3}\),故此选项错误.

故选:\(B\).

【总结】此题主要考查了合并同类项以及积的乘方运算、整式的乘除运算,正确掌握相关运算法则是解题关键.

46.下列运算正确的是\((\)  \()\)

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

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

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

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

【解答】解:\(A\)、原式\( = ( – {a^2} – {b^2} + 2ab) \times {a^2} – {b^2} = [ – {(a – b)^2}] \times ({a^2} – {b^2})\)

\(B\)、\({a^3} + {a^4} = {a^7}\),底数相同,指数不同不能相加,故本选项错误;

\(C\)、\(a^{3}· a^{2}=a^{5}\),运算正确;

\(D\)、\({2^3} = 2 \times 2 \times 2 = 8\),故本选项错误;

故选:\(C\).

【总结】此题考查了有理数的乘方和整式的混合运算,熟练掌握运算法则是解本题的关键.

47.下列各运算中,计算正确的是\((\)  \()\)

A.\({a^{12}} \div {a^3} = {a^4}\)                    

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

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

D.\(2a· 3a=6a^{2}\)

【解答】解:\(A\)、原式\( = {a^9}\),不符合题意;

\(B\)、原式\( = 27{a^6}\),不符合题意;

\(C\)、原式\( = {a^2} – 2ab + {b^2}\),不符合题意;

\(D\)、原式\( = 6{a^2}\),符合题意.

故选:\(D\).

【总结】此题考查了整式的混合运算,熟练掌握运算法则是解本题的关键.

48.下列运算正确的是\((\)  \()\)

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

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

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

D.\( – 2(a – 1) =  – 2a + 1\)

【解答】解:\(A\)、原式\( = {a^2}\),所以\(A\)选项正确;

\(B\)、原式\( =  – 4{a^2}\),所以\(B\)选项错误;

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

\(D\)、原式\( =  – 2a + 2\),所以\(D\)选项错误.

故选:\(A\).

【总结】本题考查了幂的乘方与积的乘方:幂的乘方法则:底数不变,指数相乘:\({({a^m})^n} = {a^{mn}}(m\),\(n\)是正整数);积的乘方法则:把每一个因式分别乘方,再把所得的幂相乘:\({(ab)^n} = {a^n}{b^n}(n\)是正整数).也考查了整式的加减.

49.下列运算正确的是\((\)  \()\)

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

B.\({( – 2{a^3})^2} = 4{a^5}\)                           

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

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

【解答】解:\(A\)、错误.不是同类项不能合并;

\(B\)、错误.应该是\({( – 2{a^3})^2} = 4{a^6}\);

\(D\)、错误.应该是\({(a + b)^2} = {a^2} + 2ab + {b^2}\);

故选:\(C\).

【总结】本题考查多项式的乘法法则、幂的乘方与积的乘方、完全平方公式、合并同类项法则等知识,解题的关键是熟练掌握基本知识,属于中考常考题型.

50.下列运算中正确的是\((\)  \()\)

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

B.\((2x + 1)(2x – 1) = 2{x^2} – 1\)                     

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

D.\({(a – 3)^2} = {a^2} – 6a + 9\)

【解答】解:\(A\)、结果是\({a^6}\),故本选项不符合题意;

\(B\)、结果是\(4{x^2} – 1\),故本选项不符合题意;

\(C\)、结果是\({a^{10}}\),故本选项不符合题意;

\(D\)、结果是\({a^2} – 6a + 9\),故本选项符合题意;

故选:\(D\).

【总结】本题考查了幂的乘方、同底数幂的乘法、平方差公式和完全平方公式等知识点,能正确求出每个式子的值是解此题的关键.

2019.3.22




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2019年中考第一轮中考复习数与式模块复习(分式专题讲义)_2018年中考分式真题汇编

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