全一卷
1.若等式(x+6)x+1=1成立,那么满足等式成立的x的值的个数有( )
A.5个 | B.4个 | C.3个 | D.2个 |
2.下列代数式中,属于分式的是( )
A.5x | B.![]() | C.![]() | D.![]() |
3.某厂准备加工500个零件,在加工了100个零件后,引进了新机器,使每天的工作效率是原来的2倍,结果共用6天完成了任务.若设该厂原来每天加工x个零件,则由题意可列出方程()
A.![]() | B.![]() |
C.![]() | D.![]() |
4.已知
=
,
=
,则
的值为( )
![](http://static.xuejinqu.com/qimg/5d1/5d164328dd93fe8f10f600ca5f21879a.png)
![](http://static.xuejinqu.com/qimg/fb7/fb759a9c263d0eb035dbb669dc5e42d3.png)
![](http://static.xuejinqu.com/qimg/506/50660197866ce4ac893a27105416c73f.png)
![](http://static.xuejinqu.com/qimg/b44/b446a191d971edf7809885a7e2e82d71.png)
![](http://static.xuejinqu.com/qimg/7ba/7baf3a2994d6a8b3c761ec5a099acfec.png)
A.3 | B.4 | C.6 | D.9 |
5.已知
,
,则
的值为( )
![](https:///quesimg/Upload/formula/bbc5b4357fd97fc6a2328953fe45a294.png)
![](https:///quesimg/Upload/formula/9f1fdbad317df15d8e41eff4009f9d24.png)
![](https:///quesimg/Upload/formula/eaf459a7d8a317bc28235c0473c4b6aa.png)
A.6 | B.![]() | C.0 | D.1 |
6.如图,在△ABC和△ADE中,∠BAC=∠DAE=90°,AB=AC,AD=AE,C,D,E三点在同一条直线上,连接BD,则下列结论错误的是( )
![](//static.xuejinqu.com/qimg/b61/b61819fde91563274260764dade89359.png)
![](http://static.xuejinqu.com/qimg/b61/b61819fde91563274260764dade89359.png)
A.△ABD≌△ACE | B.∠ACE+∠DBC=45° |
C.BD⊥CE | D.∠BAE+∠CAD=200° |
7.如图,在直角三角形ABC中,AC=8,BC=6,∠ACB=90°,点E是AC的中点,点D在AB上,且DE⊥AC于E,则CD=( )
![](//static.xuejinqu.com/qimg/ec1/ec10f7c246066d001521f05ddf34203c.png)
![](http://static.xuejinqu.com/qimg/ec1/ec10f7c246066d001521f05ddf34203c.png)
A.3 | B.4 | C.5 | D.6 |
8.在△ABC中,∠BAC=115°,DE、FG分别为AB、AC的垂直平分线,则∠EAG的度数为( )
![](//static.xuejinqu.com/qimg/fc7/fc7fb99c882cb82d289238174f5b66d9.png)
![](http://static.xuejinqu.com/qimg/fc7/fc7fb99c882cb82d289238174f5b66d9.png)
A.50° | B.40° | C.30° | D.25° |
9.如图,已知AB=AC,AD⊥BC,AE=AF,图中共有( )对全等三角形.
![](//static.xuejinqu.com/qimg/fdc/fdc94337e86ca3c25d13ea2f9546739b.png)
![](http://static.xuejinqu.com/qimg/fdc/fdc94337e86ca3c25d13ea2f9546739b.png)
A.5 | B.6 | C.7 | D.8 |
10.如图,在△ABC,∠C=90°,AD平分∠BAC交CB于点D,过点D作DE⊥AB,垂足恰好是边AB的中点E,若AD=3cm,则BE的长为( )
![](//static.xuejinqu.com/qimg/d48/d48a15321a7277d34a48ae552d196a17.png)
![](http://static.xuejinqu.com/qimg/d48/d48a15321a7277d34a48ae552d196a17.png)
A.![]() | B.4cm | C.3![]() | D.6cm |
11.某广场准备用边长相等的正方形和正三角形两种地砖铺满地面,在每个顶点的周围,正方形和正三角形地砖的块数分别是( )
A.1、2 | B.2、1 | C.2、2 | D.2、3 |
12.已知实数
,
满足
,则以
,
的值为两边长的等腰三角形周长是( )
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/ae3/ae3d592441dc4632c35d8b7efe75dba7.png)
![](http://static.xuejinqu.com/qimg/9e4/9e4b97c104b40ed0e247ff635c3d1166.png)
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/ae3/ae3d592441dc4632c35d8b7efe75dba7.png)
A.20或16 | B.20 | C.16 | D.以上答案均不对 |
13.以下列数据为长度的三条线段,能组成三角形的是( )
A.2 cm、3cm、5cm | B.2 cm、3 cm、4 cm |
C.3 cm、5 cm、9 cm | D.8 cm、4 cm、4 cm |
14.将长方形纸片按如图所示的方式折叠,BC、BD为折痕,若∠ABC=35°,则∠DBE的度数为
![](//static.xuejinqu.com/qimg/f98/f986f464f2d42d837f65db66c3343743.png)
![](http://static.xuejinqu.com/qimg/f98/f986f464f2d42d837f65db66c3343743.png)
A.55° | B.50° | C.45° | D.60° |
15.下列多项式中,能分解因式的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
16.当x______时,分式
有意义.
![](http://static.xuejinqu.com/qimg/032/032cbb909f731dba5df17e9a7d5e9e14.png)
17.分解因式![](https:///quesimg/Upload/formula/aa71a1e99492f62331c9b40341dac9b5.png)
___________
![](https:///quesimg/Upload/formula/aa71a1e99492f62331c9b40341dac9b5.png)
18.如图,在
中,
,
,
,将
绕点
逆时针旋转
得到
,连接
,则
的长为__________.![](//static.xuejinqu.com/qimg/152/152b0c721a58010ec87567e0b09745fc.png)
![](http://static.xuejinqu.com/qimg/547/547e4e827293fa2dc1b30a135813da74.png)
![](http://static.xuejinqu.com/qimg/306/306e2318cfe30d5d46336147049f6a97.png)
![](http://static.xuejinqu.com/qimg/799/7991d298ab1eb90b2f899912e3fbf608.png)
![](http://static.xuejinqu.com/qimg/60d/60da5f1595a2fb87c7ee172070101c6e.png)
![](http://static.xuejinqu.com/qimg/547/547e4e827293fa2dc1b30a135813da74.png)
![](http://static.xuejinqu.com/qimg/ab7/ab72679ea85827cb304a921700da16f8.png)
![](http://static.xuejinqu.com/qimg/0cf/0cfa89cd5ef703a9ee630a52a662c6af.png)
![](http://static.xuejinqu.com/qimg/400/40008bca77744c2c7a2505f8bb91256d.png)
![](http://static.xuejinqu.com/qimg/065/065646d91cb4e3f4b958ed9e5abc3028.png)
![](http://static.xuejinqu.com/qimg/065/065646d91cb4e3f4b958ed9e5abc3028.png)
![](http://static.xuejinqu.com/qimg/152/152b0c721a58010ec87567e0b09745fc.png)
19.在△ABC中,∠A=∠B+∠C,∠B=2∠C﹣6°,则∠C的度数为_____ .
20.如图,在
中,
,
是
的中点,
,垂足为
,
,则
的度数是______ .
![](https://img./dksih/QBM/2019/8/5/2262324716511232/2262421931343873/STEM/d17f0c8c73444fdba139a79d48f5c04a.png?resizew=122)
![](https:///quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https:///quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https:///quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https:///quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https:///quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https:///quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https:///quesimg/Upload/formula/456e0f77d83975fdbdb60b499cb5b521.png)
![](https:///quesimg/Upload/formula/23dc2d2dd56fcc67698c45a6e0e48f80.png)
![](https://img./dksih/QBM/2019/8/5/2262324716511232/2262421931343873/STEM/d17f0c8c73444fdba139a79d48f5c04a.png?resizew=122)
21.已知
,
,若
,试求
的值.
![](http://static.xuejinqu.com/qimg/529/529bf8a97402b8fead2e04c6692cf998.png)
![](http://static.xuejinqu.com/qimg/c3c/c3cf8fdebb7883c3ad957d98b68518ab.png)
![](http://static.xuejinqu.com/qimg/3b8/3b857b849fa897bff729acfb6eec9d30.png)
![](http://static.xuejinqu.com/qimg/38f/38f807ebd7f07b3ae5d02330beec4e4e.png)
22.阅读下面的材料:
我们可以用配方法求一个二次三项式的最大值或最小值,例如:求代数式
的最小值.方法如下:
∵
,由
,得
;
∴代数式
的最小值是4.
(1)仿照上述方法求代数式
的最小值.
(2)代数式
有最大值还是最小值?请用配方法求出这个最值.
我们可以用配方法求一个二次三项式的最大值或最小值,例如:求代数式
![](http://static.xuejinqu.com/qimg/3ae/3aed8b3c2839615822e50a1b42effba2.png)
∵
![](http://static.xuejinqu.com/qimg/b24/b24b8251103a126b6a90606604d08f34.png)
![](http://static.xuejinqu.com/qimg/73d/73d43fafeffd4ac3fa2fa6b5d851c1e7.png)
![](http://static.xuejinqu.com/qimg/bde/bdeb9897342c8e903e82e36c4334425e.png)
∴代数式
![](http://static.xuejinqu.com/qimg/3ae/3aed8b3c2839615822e50a1b42effba2.png)
(1)仿照上述方法求代数式
![](http://static.xuejinqu.com/qimg/cfb/cfb39136291c703b48470ec2a9a21efc.png)
(2)代数式
![](http://static.xuejinqu.com/qimg/8f4/8f445529f36f7a9ab90ab8935518d5c0.png)
23.如图,A(0,4)是直角坐标系y轴上一点,动点P从原点O出发,沿x轴正半轴运动,速度为每秒1个单位长度,以P为直角顶点在第一象限内作等腰Rt△APB.设P点的运动时间为t秒.
![](//static.xuejinqu.com/qimg/932/932c31aaa5b7486d19174d5bf408a294.png)
(1)若AB//x轴,求t的值;
(2)当t=3时,坐标平面内有一点M(不与A重合),使得以M、P、B为顶点的三角形和△ABP全等,请求出点M的坐标;
![](http://static.xuejinqu.com/qimg/932/932c31aaa5b7486d19174d5bf408a294.png)
(1)若AB//x轴,求t的值;
(2)当t=3时,坐标平面内有一点M(不与A重合),使得以M、P、B为顶点的三角形和△ABP全等,请求出点M的坐标;
24.如图,点
是等边
内一点,
,
,将
绕点
顺时针方向旋转
得到
,连接
,
.
![](//static.xuejinqu.com/qimg/e2d/e2d104606d5730097e7d34f8c2462b7c.png)
(1)当
时,判断
的形状,并说明理由;
(2)求
的度数;
(3)请你探究:当
为多少度时,
是等腰三角形?
![](http://static.xuejinqu.com/qimg/878/8782c97902a9f447b53fed3ac5e0bc64.png)
![](http://static.xuejinqu.com/qimg/547/547e4e827293fa2dc1b30a135813da74.png)
![](http://static.xuejinqu.com/qimg/90d/90d04796ae24a2fd5e39d042255b2bcb.png)
![](http://static.xuejinqu.com/qimg/7c2/7c29028c107b198231f1607272ee022e.png)
![](http://static.xuejinqu.com/qimg/910/910979cac833b5cc2b6b0b981eb1b91e.png)
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
![](http://static.xuejinqu.com/qimg/138/138829c6863509860cdf2e44dcd5a930.png)
![](http://static.xuejinqu.com/qimg/189/1890bf5725bcfede5cc42dbd7c2c6501.png)
![](http://static.xuejinqu.com/qimg/eb7/eb78d09521489c0947493bab21f20031.png)
![](http://static.xuejinqu.com/qimg/d3d/d3d4a13ed195f38e13d1324a1cf312a9.png)
![](http://static.xuejinqu.com/qimg/e2d/e2d104606d5730097e7d34f8c2462b7c.png)
(1)当
![](http://static.xuejinqu.com/qimg/ae5/ae56cda57a3de98ed0c19165d1c643d7.png)
![](http://static.xuejinqu.com/qimg/218/2180159227109cd025e8070a370e1323.png)
(2)求
![](http://static.xuejinqu.com/qimg/265/265eb1bad5253dc602ed50585c4634a7.png)
(3)请你探究:当
![](http://static.xuejinqu.com/qimg/2ba/2ba0ceb45b366219a93be82cee70b97a.png)
![](http://static.xuejinqu.com/qimg/218/2180159227109cd025e8070a370e1323.png)
25.如图,AB∥EF,AD平分∠BAC,且∠C=45°,∠CDE=125°,求∠ADF的度数.![](//static.xuejinqu.com/qimg/725/725eb4b1de4e8f18732cf210e0c28a46.png)
![](http://static.xuejinqu.com/qimg/725/725eb4b1de4e8f18732cf210e0c28a46.png)