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【323453】2023九年级数学上册 第二章 一元二次方程1 认识一元二次方程(1)练习(新版)北师

时间:2025-01-16 18:35:43 作者: 字数:3200字
简介:


2.1 认识一元二次方程(1

班级:__________ 姓名:__________

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 、判断题(下列方程中,是一元二次方程的在括号内划“√”,不是一元二次方程的,在括号内划“×”

( )1. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 5x2+1=0

( )2. 3x2+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> +1=0

( )3. 4x2=ax(其中a为常数)

( )4. 2x2+3x=0

( )5.  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> =2x

( )6.  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> =2x

( )7. x2+2x=4

二、填空题

1. 一元二次方程的一般形式是__________.

2. 将方程-5x2+1=6x化为一般形式为__________.

3. 将方程(x+1)2=2x化成一般形式为__________.

4. 方程2x2=8化成一般形式后,一次项系数为__________,常数项为__________.

5. 方程5(x2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 1)=3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x+2的一般形式是__________,其二次项是__ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> ________,一次项是__________,常数项是__________.

6. ab≠0,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x2+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x=0的常数项是_ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> _________.

7. 如果方程ax2+5=(x+2)(x1)是关于x的一元二次方程,则a__________.

8. 关于x的方程(m4)x2+(m+4)x+2m+3=0,当m__________时,是一元二次方程,当m__________时, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 是一元一次方程.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 、选择题

1. 下列方程中,不是一元二次方程的是

A. 2x2+7=0

B. 2x2+2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x+1=0

C. 5x2+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> +4=0

D. 3x2+(1+x)  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> +1=0

2. 方程x22(3x2)+(x+1)=0的一般形式是

A. x25x+5=0 B. x2+5x+5=0

C. x2+5x5=0 D. x2+5= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 0

3. 一元二次方程7x22x=0的二次项、一次项、常数项依次是

A. 7x2,2x,0 B. 7x2,2x,无常数项

C. 7x2,0,2x D. 7x2,2x,0

4. 方程x2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> =( <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> )x化为一般形式,它的各项系数之和可能是

A. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> B. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> C. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> D. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a>

5. 若关于x的方程(a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x+b(dcx)=m(ac≠0)的二次项系数是ac,则常数项为

A. m B. bd C. bdm D. (bdm)

6. 若关于x的方程a(x1)2=2x22是一元二次方程,则a的值是

A. 2 B. 2 C. 0 D. 不等于2

7. 关于x2=2的说法,正确的是

A.由于x2≥0,故x2不可能等于-2,因此这不是一个方程

B.x2=2是一个方程,但它没有一次项,因此不 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 是一元二次方程

C.x2=2是一个一元二次方程

D.x2=2是一个一元二次方程,但不能解

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 四、解答题

现有长40米、宽30米场地,欲在中央建一游泳池,周围是等宽的便道及休息区,且游泳池与周围部分面积之比为3∶ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 2,请给出这块场地建设的设计方案,并用图形及相关尺寸表示出来。


参考答案

一、1 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> .√ 2.× 3.√ 4.√ 5.√ 6.√ 7.√

二、1. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> ax2+bx+c=0(a≠0)

2. 5x2+6x1=0

3. x2+1=0 4. 0 8

5. 5x22 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x+3=0 5x2 2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> x 3

6. 0 7. ≠1

8. ≠4 =4

三、1.C 2.A 3.D 4.D 5.D 6.A 7. C

四、设计方案:即 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> 求出满足条件的便道及休息区的宽度.

若设便道及休息区宽度为x米,则游泳池面积为(402x)(302x)2,便道及休息区面积为240x+(302x)x]米2,依题意,可得方程:

(402x)(302x)∶240x+(302x)x=3∶2

由此可求得x的值,即可得游泳池长与宽.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/53/" title="认识" class="c1" target="_blank">认识</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a>

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