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

一、2018年中考真题整式专题知识点分析

2018年全国各省市整式选择题中考真题汇编知识点分析
知识点 题量 占比
合并同类项 28 56.00%
同底数幂的乘法 8 16.00%
完全平方公式 1 2.00%
整式 1 2.00%
幂的乘方与积的乘方 2 4.00%
单项式乘单项式 1 2.00%
实数的运算 1 2.00%
规律型:数字的变化类 1 2.00%
科学记数法—表示较小的数 1 2.00%
算术平方根 1 2.00%
整式的混合运算 3 6.00%
有理数的乘方 1 2.00%
整式的加减 1 2.00%

二、 2018年中考真题整式专题难易度分析

试题难易度题量题号题量占比
431,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43
86%
较易644,45,46,47,48,4912%
中档1502%
较难000%
000%

2019年中考数学数与式专题复习_2018中考整式真题汇编复习讲义(一)

一.选择题(共50小题)

1.下列运算正确的是\((\)  \()\)

A.\(7a – a = 6\)            

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

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

D.\({(ab)^4} = a{b^4}\)

【解答】解:\(A\)、\(7a – a = 6a\),此选项错误;

\(B\)、\(a^{2}· a^{3}=a^{5}\),此选项正确;

\(C\)、\({({a^3})^3} = {a^9}\),此选项错误;

\(D\)、\({(ab)^4} = {a^4}{b^4}\),此选项错误;

故选:\(B\).

【总结】本题主要考查幂的运算,解题的关键是掌握合并同类项法则、同底数幂的乘法、幂的乘方、积的乘方.

2.下列运算正确的是\((\)  \()\)

A.\(x^{3}· x^{3}=x^{9}\)                                    

B.\({x^8} \div {x^4} = {x^2}\)                           

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

D.\({(2x)^3} = 8{x^3}\)

【解答】解:\(A\)、错误.应该是\(x^{3}· x^{3}=x^{6}\);

\(B\)、错误.应该是\({x^8} \div {x^4} = {x^4}\);

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

\(D\)、正确.

故选:\(D\).

【总结】本题考查同底数幂的乘除法法则,幂的乘方,积的乘方等知识,解题的关键是熟练掌握基本知识,属于中考基础题.

3.下列计算正确的是\((\)  \()\)

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

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

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

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

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

\(B\)、\({(ab)^2} = {a^2}{b^2}\),故\(B\)错误;

\(C\)、\({a^2}\)与\({a^3}\)不是同类项,不能合并,故\(C\)错误;

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

故选:\(D\).

【总结】本题考查幂的乘方与积的乘方,合并同类项,熟练掌握运算性质和法则是解题的关键.

4.下列运算正确的是\((\)  \()\)

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

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

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

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

【解答】解:\(A\)、\({x^2} + {x^2} = 2{x^2}\),故本选项不符合题意;

\(B\)、\(x^{2}· x^{3}=x^{5}\),故本选项不符合题意;

\(C\)、\({({x^2})^3} = {x^6}\),故本选项符合题意;

\(D\)、\({(2{x^2})^3} = 8{x^6}\),故本选项不符合题意;

故选:\(C\).

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

5.计算\(x^{2}· x^{3}\)结果是\((\)  \()\)

A.\(2{x^5}\)                

B.\({x^5}\)                   

C.\({x^6}\)                   

D.\({x^8}\)

【解答】解:\(x^{2}· x^{3}=x^{5}\).

故选:\(B\).

【总结】此题主要考查了同底数幂的乘法运算,正确掌握运算法则是解题关键.

6.下列运算正确的是\((\)  \()\)

A.\(2x + 3y = 5xy\)   

B.\({(x + 3)^2} = {x^2} + 9\)                              

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

D.\({x^{10}} \div {x^5} = {x^2}\)

【解答】解:\(A\)、原式不能合并,错误;

\(B\)、\({(x + 3)^2} = {x^2} + 6x + 9\),错误;

\(C\)、\({(x{y^2})^3} = {x^3}{y^6}\),正确;

\(D\)、\({x^{10}} \div {x^5} = {x^5}\),错误;

故选:\(C\).

【总结】此题考查了同底数幂的乘除法,完全平方公式,以及合并同类项,熟练掌握公式及运算法则是解本题的关键.

7.下列运算结果是\({a^5}\)的是\((\)  \()\)

A.\({a^{10}} \div {a^2}\)                                     

B.\({({a^2})^3}\)      

C.\({( – a)^5}\)           

D.\(a^{3}· a^{2}\)

【解答】解:\(A\)、\({a^{10}} \div {a^2} = {a^8}\),错误;

\(B\)、\({({a^2})^3} = {a^6}\),错误;

\(C\)、\({( – a)^5} =  – {a^5}\),错误;

\(D\)、\(a^{3}· a^{2}=a^{5}\),正确;

故选:\(D\).

【总结】本题考查了同底数幂的乘法、除法以及幂的乘方法则,是基础题,熟记运算法则是解题的关键.

8.已知实数\(a\)、\(b\)满足\(a + b = 2\),\(ab = \frac{3}{4}\),则\(a – b = (\)  \()\)

A.1                                  

B.\( – \frac{5}{2}\)   

C.\( \pm 1\)                  

D.\( \pm \frac{5}{2}\)

【解答】解:∵\(a+b=2\),\(ab = \frac{3}{4}\),

∴\({(a + b)^2} = 4 = {a^2} + 2ab + {b^2}\),

∴\({a^2} + {b^2} = \frac{5}{2}\),

∴\( {(a – b)^2} = {a^2} – 2ab + {b^2} = 1\),

∴\( a – b =  \pm 1\),

故选:\(C\).

【总结】本题考查了完全平方公式的运用,熟记公式结构是解题的关键.

9.下列运算正确的是\((\)  \()\)

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

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

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

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

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

\(B\)、\({a^2} + {a^2} = 2{a^2}\),错误;

\(C\)、\({({a^3})^2} = {a^6}\),正确;

\(D\)、\({a^8} \div {a^2} = {a^6}\),错误;

故选:\(C\).

【总结】本题考查了整式的除法,单项式的乘法,合并同类项法则,是基础题,熟记运算法则是解题的关键.

10.下列代数式中,整式为\((\)  \()\)

A.\(x + 1\)                    

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

C.\(\sqrt {{x^2} + 1} \)                                          

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

【解答】解:\(A\)、\(x + 1\)是整式,故此选项正确;

\(B\)、\(\frac{1}{{x + 1}}\),是分式,故此选项错误;

\(C\)、\(\sqrt {{x^2} + 1} \)是二次根式,故此选项错误;

\(D\)、\(\frac{{x + 1}}{x}\),是分式,故此选项错误;

故选:\(A\).

【总结】此题主要考查了整式、分式、二次根式的定义,正确把握相关定义是解题关键.

11.计算\({({x^3})^2}\)的结果是\((\)  \()\)

A.\({x^5}\)                 

B.\(2{x^3}\)               

C.\({x^9}\)                 

D.\({x^6}\)

【解答】解:\({({x^3})^2} = {x^6}\),

故选:\(D\).

【总结】本题主要考查幂的乘方,底数不变,指数相乘的性质,熟练掌握性质是解题的关键.

12.下列运算正确的是\((\)  \()\)

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

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

C.\(2{({x^2})^3} = 8{x^6}\)                               

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

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

\(B\)、\(x^{2}· x^{3}=x^{5}\),正确;

\(C\)、\(2{({x^2})^3} = 2{x^6}\),错误;

\(D\)、\({(x + 1)^2} = {x^2} + 2x + 1\),错误;

故选:\(B\).

【总结】本题考查了单项式的乘法,合并同类项法则,是基础题,熟记运算法则是解题的关键.

13.下列计算正确的是\((\)  \()\)

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

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

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

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

【解答】解:\(A\)、\(3{a^2} – 4{a^2} =  – {a^2}\),错误;

\(B\)、\(a^{2}· a^{3}=a^{5}\),错误;

\(C\)、\({a^{10}} \div {a^5} = {a^5}\),错误;

\(D\)、\({({a^2})^3} = {a^6}\),正确;

故选:\(D\).

【总结】本题考查了整式的除法,单项式的乘法,合并同类项法则,是基础题,熟记运算法则是解题的关键.

14.下列运算正确的是\((\)  \()\)

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

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

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

D.\({( – 2{a^3})^2} = 4{a^6}\)

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

\(B\)、\({({a^2})^3} = {a^6}\),错误;

\(C\)、\({a^2} \div {a^{ – 2}} = {a^4}\),错误;

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

故选:\(D\).

【总结】本题考查了整式的除法,单项式的乘法,是基础题,熟记运算法则是解题的关键.

15.下列运算正确的是\((\)  \()\)

A .\(3x + 4y = 7xy\)                                             

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

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

D .\({m^{10}} \div {m^7} = {m^3}\)

【解答】解:\(A\)、\(3x\)、\(4y\)不是同类项, 不能合并, 此选项错误;

\(B\)、\((-a)^{3}· a^{2}=-a^{5}\),此选项错误;

\(C\)、\({({x^3}y)^5} = {x^{15}}{y^5}\),此选项错误;

\(D\)、\({m^{10}} \div {m^7} = {m^3}\),此选项正确;

故选:\(D\).

【总结】本题主要考查整式的运算, 解题的关键是掌握同类项的定义、 幂的运算法则 .

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