当前位置:首页 > 八年级 > 数学试卷

【330339】2020年青海省中考数学试题

时间:2025-02-09 10:58:52 作者: 字数:25013字

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 青海省2020年初中毕业升学考试数学试卷

一、填空题

1.(-3+8)的相反数是________ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的平方根是________

【答案】 (1).  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (2).  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

1空:先计算-3+8的值,根据相反数的定义写出其相反数;

2空:先计算 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的值,再写出其平方根.

【详解】第1空:∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则其相反数为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2空:∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则其平方根为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了相反数,平方根,熟知相反数,平方根的知识是解题的关键.

2.分解因式: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ________;不等式组 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的整数解为________

【答案】 (1).  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (2).  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

综合利用提取公因式法和公式法即可得;先分别求出两个不等式的解,再找出它们的公共部分得出不等式组的解集,由此即可得出答案.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解不等式①得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解不等式②得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

则不等式组的解为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

因此,不等式组的整数解 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了利用提取公因式法和公式法分解因式、求一元一次不等式组的整数解,熟练掌握因式分解的方法和一元一次不等式组的解法是解题关键.

3.岁末年初,一场突如其来的新型冠状病毒肺炎疫情席卷全球,我国在党中央的坚强领导下,全国人民团结一心、众志成城,取得了抗击疫情的阶段性胜利;据科学研究表明,新型冠状病毒颗粒的最大直径为125纳米;125纳米用科学记数法表示为________米(1纳米 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 米)

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

绝对值小于1的正数也可以利用科学记数法表示,一般形式为a×10-n,与较大数的科学记数法不同的是其所使用的是负指数幂,指数由原数左边起第一个不为零的数字前面的0的个数所决定.

【详解】解:将数据125纳米用科学记数法表示为:125×10-9=1.25×10-7米.

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查用科学记数法表示较小的数,一般形式为a×10-n,其中1≤|a|10n为由原数左边起第一个不为零的数字前面的0的个数所决定.

4.如图,将周长为8 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 沿BC边向右平移2个单位,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的周长为________

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】12

【解析】

【分析】

先根据平移的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,再根据三角形的周长公式可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,然后根据等量代换即可得.

【详解】由平移的性质得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的周长为8

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

则四边形ABFD的周长为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为:12

【点睛】本题考查了平移的性质等知识点,掌握理解平移的性质是解题关键.

5.如图所示ΔABC中,AB=AC=14cm,AB的垂直平分线MNACD,ΔDBC的周长是24cm,BC=___________cm

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】10

【解析】

【分析】

MNAB的垂直平分线可得AD=BD,于是将△BCD的周长转化为BC与边长AC的和来解答.

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

BD+DC+BC=24cm

MN垂直平分AB

AD=BD

AD+DC+BC=24cm

AC+BC=24cm

又∵AC=14cm

BC=24-14=10cm

故答案为:10

点睛:解答本题 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 关键是熟练掌握垂直平分线的性质:垂直平分线上的点到线段两端的距离相等.此题将垂直平分线的性质与三角形的周长问题相结合,体现了转化思想在解题时的巨大作用.

6.如图,在矩形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中,对角线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 相交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的长为________cm

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】6cm

【解析】

【分析】

根据矩形的性质可得对角线相等且平分,由 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 所对直角边是斜边的一半即可得到结果.

【详解】∵四边形ABCD是矩形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

Rt△ABC中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为6cm

【点睛】本题主要考查了矩形的性质应用,准确利用直角三角形的性质是解题的关键.

7.已知abc <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的三边长.bc满足 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,且a为方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的解,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的形状为________三角形.

【答案】等腰三角形

【解析】

【分析】

根据绝对值和平方的非负性可得到bc的值,再根据式子解出a的值,即可得出结果.

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

a是方程的解且abc <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的三边长,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 是等腰三角形.

【点睛】本题主要考查了根据三角形三边判断三角形的性质,准确求解题中的式子是解题的关键.

8.在解一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 时,小明看错了一次项系数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,得到的解为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;小刚看错了常数项 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,得到的解为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> .请你写出正确的一元二次方程_________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

根据题意列出二元一次方程组求解即可得出答案.

【详解】解:将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 代入一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

小明看错了一次项,

c的值为6

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 代入一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

小刚看错了常数项,

b=-5

一元二次方程为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了二元一次方程组的解法,熟练掌握二元一次方程组的解法是解题关键.

9.已知⊙O的直径为10cmABCD是⊙O的两条弦, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 之间的距离为________cm

【答案】71

【解析】

【分析】

分两种情况考虑:当两条弦位于圆心O同一侧时,当两条弦位于圆心O两侧时;利用垂径定理和勾股定理分别求出OEOF的长度,即可得到答案.

【详解】解:分两种情况考虑:

当两条弦位于圆心O一侧时,如图1所示,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>
OOE⊥CD,交CD于点E,交AB于点F,连接OCOA
∵AB∥CD
,∴OE⊥AB
∴E
F分别为CDAB的中点,
∴CE=DE=
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> CD=3cmAF=BF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> AB=4cm
Rt△AOF中,OA=5cmAF=4cm
根据勾股定理得:OF=3cm
Rt△COE中,OC=5cmCE=3cm
根据勾股定理得:OE═4cm
EF=OE
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> OF=4cm <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 3cm=1cm
当两条弦位于圆心O两侧时,如图2所示,
同理可得EF=4cm+3cm=7cm
综上,弦ABCD的距离为7cm1cm

故答案为:71

【点睛】此题考查了垂径定理,勾股定理,利用了分类讨论的思想,熟练掌握垂径定理是解本题的关键.

10. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的内切圆的半径为__________

【答案】1

【解析】

【详解】如图,设ABC的内切圆与各边相切于DEF,连接ODOEOF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

OE⊥BCOF⊥ABOD⊥AC

设半径为rCD=r

∵∠C=90°BC=4AC=3

AB=5

BE=BF=4-rAF=AD=3-r

4-r+3-r=5

r=1

∴△ABC的内切圆的半径为 1

11.对于任意不相等的两个实数ab a > b )定义一种新运算a※b= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,如3※2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,那么12※4=______

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

按照规定的运算顺序与计算方法化为二次根式的混合运算计算即可.

【详解】解:12※4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】此题考查二次根式的化简求值,理解规定的运算顺序与计算方法是解决问题的关键.

12.观察下列各式的规律:① <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;② <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;③ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> .请按以上规律写出第4个算式________.用含有字母的式子表示第n个算式为________

【答案】 (1).  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (2).  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

1)按照前三个算式的规律书写即可;

2)观察发现,算式序号与比序号大2的数的积减去比序号大1的数的平方,等于-1,根据此规律写出即可;

【详解】(1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2)第n个式子为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题主要考查了规律性数字变化类知识点,准确分析是做题的关键.

二、选择题

13.下面是某同学在一次测试中的计算:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;② <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;③ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;④ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,其中运算正确 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 个数为(

A. 4 B. 3 C. 2 D. 1

【答案】D

【解析】

【分析】

根据整式的减法、整式的乘除法、幂的乘方逐个判断即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 不是同类项,不可合并,则①错误

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则②错误

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则③错误

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则④正确

综上,运算正确的个数为1

故选:D

【点睛】本题考查了整式的减法、整式的乘除法、幂的乘方,熟记整式的运算法则是解题关键.

14.等腰三角形的一个内角为70°,则另外两个内角的度数分别是(

A. 55°55° B. 70°40°70°55° C. 70°40° D. 55°55°70°40°

【答案】D

【解析】

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 分析】

先根据等腰三角形的定义,分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的内角为顶角和 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的内角为底角两种情况,再分别根据三角形的内角和定理即可得.

【详解】(1)当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的内角为这个等腰三角形的顶角

则另外两个内角均为底角,它们的度数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2)当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的内角为这个等腰三角形的底角

则另两个内角一个为底角,一个为顶角

底角为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,顶角为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

综上,另外两个内角的度数分别是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故选:D

【点睛】本题考查了等腰三角形的定义、三角形的内角和定理,根据等腰三角形的定义,正确分两种情况讨论是解题关键.

15.根据图中给出的信息,可得正确的方程是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】A

【解析】

【分析】

根据题意可得相等关系的量为“水的体积”,然后利用圆柱体积公式列出方程即可.

【详解】解:大量筒中的水的体积为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

小量筒中的水的体积为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

则可列方程为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> .

故选A.

【点睛】本题主要考查列方程,解此题的关键在于准确找到题中相等关系的量,然后利用圆柱的体积公式列出方程即可.

16.将一张四条边都相等的四边形纸片按下图中①②的方式沿虚线依次对折后,再沿图③中的虚线裁剪,最后将图④中的纸片打开铺平,所得图案应是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】A

【解析】

【分析】

对于此类问题,学生只要亲自动手操作,答案就会很直观地呈现.

【详解】严格按照图中的顺序,向右对折,向上对折,从斜边处剪去一个直角三角形,从直角顶点处剪去一个等腰直角三角形,展开后实际是从原菱形的四边处各剪去一个直角三角形,从菱形的中心剪去一个和菱形位置基本一致的正方形,得到结论.

故选A

【点睛】本题主要考查学生的动手能力及空间想象能力.

17.在一张桌子上摆放着一些碟子,从3个方向看到的3种视图如图所示,则这个桌子上的碟共有(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A. 4 B. 8 C. 12 D. 17

【答案】C

【解析】

【分析】

先根据俯视图得出碟子共有3摞,再根据主视图和俯视图得出每摞上碟子的个数,由此即可得.

【详解】由俯视图可知,碟子共有3

由主视图和左视图可知,这个桌子上碟子的摆放为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,其中,数字表示每摞上碟子的个数

则这个桌子上的碟共有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (个)

故选:C

【点睛】本题考查了由三视图判断几何体的组成,掌握理解3种视图的定义是解题关键.

18. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则正比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 与反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 在同一平面直角坐标系中的大致图像可能是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】B

【解析】

【分析】

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 异号,若图象中得到的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 异号则成立,否则不成立.

【详解】A. 由图象可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,故A错误;

B. 由图象可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,故B正确;

C. 由图象可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,但正比例函数图象未过原点,故C错误;

D. 由图象可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,故D错误;

故选:B

【点睛】本题考查了根据已知参数的取值范围确定函数的大致图象的问题,熟知参数对于函数图象的影响是解题的关键.

19.如图是一个废弃的扇形统计图,小明同学利用它的阴影部分制作一个圆锥,则这个圆锥的底面半径是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A. 3.6 B. 1.8 C. 3 D. 6

【答案】A

【解析】

【分析】

先计算阴影部分的圆心角度数,再计算阴影部分的弧长,再利用弧长计算圆锥底面的半径.

【详解】由图知:阴影部分的圆心角的度数为:360° <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 252°=108°

阴影部分的弧长为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

设阴影部分构成的圆锥的底面半径为r:则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故选:A

【点睛】本题考查了扇形的弧长与其构成的圆锥之间的对应关系,熟练的把握这一对应关系是解题的关键.

20.将一盛有部分水的圆柱形小水杯放入事先没有水的大圆柱形容器内,现用一注水管沿大容器内壁匀速注水(如图所示),则小水杯内水面的高度 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 与注水时间 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的函数图象大致为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】B

【解析】

【分析】

用排除法可直接得出答案.

【详解】圆柱形小水杯事先盛有部分水,起点处小水杯内水面的高度 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 必然是大于0的,用排除法可以排除掉AD

注水管沿大容器内壁匀速注水,在大容器内水面高度到达h之前,小水杯中水边高度保持不变,大容器内水面高度到达h后,水匀速从大容器流入小容器,小容器水面高度匀速上升,达到最大高度h后,小容器内盛满了,水面高度一直保持h不变,因此可以排除C,正确答案选B.

考点:1.函数;2.数形结合;3.排除法.

三、解答题

21.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

根据负整数指数幂,绝对值的性质,零指数幂,立方根,特殊角的三角函数值进行计算即可

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了负整数指数幂,绝对值的性质,零指数幂,立方根,特殊角的三角函数值,熟知以上计算是解题的关键.

22.化简求值: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;其中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,1

【解析】

【分析】

括号内先通分,合并同类项,括号外进行因式分解,之后变除为乘进行约分,之后利用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 代入计算即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

原式= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了分式的化简,及整体代入求值的应用,熟知以上计算是解题的关键.

23.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

1)尺规作图:作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的外接圆 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的角平分线交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 于点D,连接AD.(不写作法,保留作图痕迹)

2)若AC =6BC =8,求AD的长.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】1)见解析;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

1)根据外接圆,角平分线的作法作图即可;

2)连接ADOD,根据CD平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> °,根据圆周角与圆心角的关系得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> °,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中计算AB,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中,计算AD

【详解】(1)作图如下:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2)连接ADOD,如图所示

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

由(1)知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> °

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> °

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> °

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了三角形的外接圆,角平分线,以及利用圆周角与圆心角的关系,及勾股定理计算线段长度的方法,熟知以上方法是解题的关键.

24.某市为了加快5G网络信号覆盖,在市区附近小山顶架设信号发射塔,如图所示.小军为了知道发射塔 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 高度,从地面上的一点A测得发射塔顶端P点的仰角是45°,向前走60米到达B点测得P点的仰角是60°,测得发射塔底部Q点的仰角是30°.请你帮小军计算出信号发射塔PQ的高度.(结果精确到0.1 米, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】94.6

【解析】

【分析】

先根据题意得出AC=PCBQ=PQCQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> BQ,设BQ=PQ=x,则CQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> BQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> x,根据勾股定理可得BC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> x,根据AB+BC=PQ+QC即可得出关于x的方程求解即可.

【详解】∵∠PAC=45°,∠PCA=90°

AC=PC

∵∠PBC=60°,∠QBC=30°,∠PCA=90°

∴∠BPQ=∠PBQ=30°

BQ=PQCQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> BQ

BQ=PQ=x,则CQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> BQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> x

根据勾股定理可得BC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> x

AB+BC=PQ+QC

60+ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> x=x+ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> x

解得:x=60+ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> =60+20×1.732=94.64≈94.6

PQ的高度为94.6米.

【点睛】本题考查了等腰三角形的性质,勾股定理,含30度角的直角三角形的性质,找出等量关系是解题关键.

25.如图,已知AB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的直径,直线BC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 相切于点B,过点AAD//OC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 于点D,连接CD

1)求证:CD <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的切线.

2)若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,直径 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,求线段BC的长.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】1)证明见解析;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

1)如图(见解析),先根据等腰三角形的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,又根据平行线的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,从而可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,再根据圆的切线的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,然后根据三角形全等的判定定理与性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,最后根据圆的切线的判定即可得证;

2)如图(见解析),先根据圆周角定理得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,再根据勾股定理可得BD的长,然后根据相似三角形的判定与性质即可得.

【详解】(1)如图,连接OD,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 直线BC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 相切于点B

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的半径

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的切线;

2)如图,连接BD

由圆周角定理得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了圆周角定理、圆的切线的判定与性质、三角形全等的判定定理与性质、相似三角形的判定与性质等知识点,较难的是题(2),通过作辅助线,构造相似三角形是解题关键.

26.每年626日是“国际禁毒日”.某中学为了让学生掌握禁毒知识,提高防毒意识,组织全校学生参加了“禁毒知识网络答题”活动.该校德育处对八年级全体学生答题成绩进行统计,将成绩分为四个等级:优秀、良好、一般、不合格;并绘制成如下不完整的统计图.请你根据图1、图2中所给的信息解答下列问题:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

1)该校八年级共有_________名学生,“优秀”所占圆心角的度数为_________

2)请将图1中的条形统计图补充完整.

3)已知该市共有15000名学生参加了这次“禁毒知识网络答题”活动,请以该校八年级学生答题成绩统计情况估计该市大约有多少名学生在这次答题中成绩不合格?

4)德育处从该校八年级答题成绩前四名甲、乙、丙、丁学生中随机抽取2名同学参加全市现场禁毒知识竞赛,请用树状图或列表法求出必有甲同学参加的概率.

【答案】1500,108°;(2)见解析;(31500名;(4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【解析】

【分析】

1)由条形统计图和扇形统计图得到良好的人数及其所对应的百分比,即可得到该校八年级总人数;通过计算优秀人员所占比例,即可得到其所对的圆心角;

2)计算出等级“一般”的学生人数,补充图形即可;

3)用该校八年级成绩及格的比例乘以该市的学生人数即可;

4)画出树状图,根据概率公式求概率即可.

【详解】(1)由条形统计图知:等级“良好”的人数为:200

由扇形统计图知:等级“良好”的所占的比例为:40%

则该校八年级总人数为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (名)

由条形统计图知:等级“优秀”的人数为:150

其站该校八年级总人数的比例为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

所以其所对的圆心角为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故答案为:500108°

2)等级“一般”的人数为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (名)

补充图形如图所示:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

3)该校八年级中不合格人数所占的比例为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

故该市15000名学生中不合格的人数为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> (名)

4)从甲,乙,丙,丁四名学生中任取选出两人,所得基本事件有:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

共计12种,

其中必有甲同学参加的有6种,

必有甲同学参加的概率为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【点睛】本题考查了统计与概率的综合,熟知以上知识是解题的关键.

27. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> BA的延长线于点G

特例感知:

1)将一等腰直角三角尺按图1所示的位置摆放,该三角尺的直角顶点为F,一条直角边与AC重合,另一条直角边恰好经过点B.通过观察、测量BFCG的长度,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> .请给予证明.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

猜想论证:

2)当三角尺沿AC方向移动到图2所示的位置时,一条直角边仍与AC边重合,另一条直角边交BC于点D,过点D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 垂足为E.此时请你通过观察、测量DEDFCG的长度,猜想并写出DEDFCG之间存在的数量关系,并证明你的猜想.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

联系拓展:

3)当三角尺在图2的基础上沿AC方向继续移动到图3所示的位置(点F在线段AC上,且点F与点C不重合)时,请你判断(2)中的猜想是否仍然成立?(不用证明)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】1)证明见详解;(2DE+DF=CG,证明见详解;(3)成立.

【解析】

【分析】

1)通过条件证明△BFC≌△CGB,即可得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2)过点BBM⊥CFCF延长线于M,过点DDH⊥BMH,通过△BMC≌△CGB,得到BM=CG,然后由四边形MHDF为矩形,MH=DF,最后再证明△BDH≌△DBE,得到BH=DE,即可得到结论;

3)同(2)中的方法.

【详解】(1)∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴∠ABC=∠ACB

在△BFC和△CGB中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴△BFC≌△CGB

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2DE+DF=CG

如图,过点BBM⊥CFCF延长线于M,过点DDH⊥BMH

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴∠ABC=∠ACB

BMCCGB中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

BMC≌CGB

BM=CG

由题意和辅助线可知,∠M=90°,∠MFD=90°,∠MHD=90°

四边形MHDF为矩形,

MH=DFDH∥MF

∴∠HDB=∠MCB

∴∠HDB=∠ABC

在△BDH和△DBE中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴△BDH≌△DBE

BH=DE

BM=CGBM=BH+HM

DE+DF=CG

3)成立,

如图,过点BBM⊥CFCF延长线于M,过点DDH⊥BMH

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

同(2)中的方法

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴∠ABC=∠ACB

在△BMC和△CGB中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴△BMC≌△CGB

BM=CG

由题意和辅助线可知,∠M=90°,∠MFD=90°,∠MHD=90°

四边形MHDF为矩形,

MH=DFDH∥MF

∴∠HDB=∠MCB

∴∠HDB=∠ABC

在△BDH和△DBE中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

∴△BDH≌△DBE

BH=DE

BM=CGBM=BH+HM

DE+DF=CG

【点睛】本题考查了全等三角形的性质和判定,属于几何动态问题,能够正确的构造辅助线找到全等三角形是解题的关键.

28.如图1(注:与图2完全相同)所示,抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 经过BD两点,与x轴的另一个交点为A,与y轴相交于点C

1)求抛物线的解析式.

2)设抛物线的顶点为M,求四边形ABMC的面积(请在图1中探索)

3)设点Qy轴上,点P在抛物线上.要使以点ABPQ为顶点的四边形是平行四边形,求所有满足条件的点P的坐标(请在图2中探索)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ;(3)点P的坐标为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 或(4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> )或( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ).

【解析】

【分析】

1)由图可知点B、点D的坐标,利用待定系数法,即可求出抛物线的解析式;

2)过点MME⊥AB于点E,由二次函数的性质,分别求出点ACM的坐标,然后得到OEBE的长度,再利用切割法求出四边形的面积即可;

3)由点Qy轴上,设Q0y),由平行四边形的性质,根据题意可分为:①当AB为对角线时;②当BQ2为对角线时;③当AQ3为对角线时;分别求出三种情况的点P的坐标,即可得到答案.

【详解】解:(1)根据题意,抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 经过BD两点,

D为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ),点B为(30),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

抛物线的解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

2)∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

M的坐标为(12

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 0);

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

C为(0 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> );

OA=1OC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

过点MME⊥AB于点E,如图:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

3)根据题意,点Qy轴上,则设点Q为(0y),

P在抛物线上,且以点ABPQ为顶点的四边形是平行四边形,

如图所示,可分为三种情况进行分析:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

AB为对角线时,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 为对角线;

由平行四边形的性质,

EAB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 的中点,

E为(10),

Q1为(0y),

P1的横坐标为2

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 时,代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

BQ2是对角线时,AP也是对角线,

B30),点Q20y),

BQ2中点的横坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

A为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 0),

P2的横坐标为4

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 时,代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

P2的坐标为(4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> );

AQ3为对角线时,BP3也是对角线;

A为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 0),点Q30y),

AQ3的中点的横坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

B30),

P3的横坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 时,代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>

P3的坐标为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> );

综合上述,点P的坐标为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> 或(4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> )或( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1133/" title="青海省" class="c1" target="_blank">青海省</a> ).

【点睛】本题考查了二次函数的性质,平行四边形的性质,解一元二次方程,以及坐标与图形等知识,解题的关键是熟练掌握二次函数的性质进行解题,注意利用分类讨论和数形结合的思想进行分析.