一、<strong><span>选择题</span></strong><strong><span>(</span></strong><strong><span>本大题共6小题</span></strong><strong><span>,</span></strong><strong><span>每小题4分</span></strong><strong><span>,</span></strong><strong><span>共24分.每小题只有一个正确选项</span></strong><strong><span>)</span></strong>
-
1.
从正面观察如图所示的几何体,看到的形状图是( )
![](//tikupic.21cnjy.com/2023/11/29/2b/af/2baf5d43d483795f2dbd018f022c0235_129x117.png)
-
2.
比-1小2的数是( )
A . 1
B . -1
C . -3
D . 3
-
3.
下列说法中正确的有( )
①若
,
互为相反数,则
;
②在数轴上到原点的距离为4个单位长度的点有两个,它们表示的数分别为4和-4;
③若
, 则
.
A . 0个
B . 1个
C . 2个
D . 3个
-
-
-
6.
已知有理数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 下列各式中成立的是( )
二、填空题<strong><span>(</span></strong><strong><span>本大题共6小题</span></strong><strong><span>,</span></strong><strong><span>每小题4分</span></strong><strong><span>,</span></strong><strong><span>共24分</span></strong><strong><span>)</span></strong>
-
7.
把向南走8m记作+8m,那么向北走5m可表示为米.
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8.
一个正方体所有相对面上的两数之和相等,它的表面展开图如图所示,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
的值为
.
![](//tikupic.21cnjy.com/2023/11/29/4a/fd/4afd0bab56894695475367081b4f3897_158x106.png)
-
9.
太阳中心的温度可达15500000℃.15500000可用科学记数法表示为.
-
10.
随着服装市场竞争日益激烈,某商场销售的一款运动装每套标价a元,第一次打折价格下调了25%,销售时每套又降价b元,则该运动装的实际售价是元.
-
-
12.
如图,剪去图中一个正方形,使剩余的部分恰好能折成一个正方体,应剪去
号小正方形.
![](//tikupic.21cnjy.com/2023/11/29/cf/b2/cfb2840dedd844907d1e4203e0c1a314_155x118.png)
三、<strong><span>(</span></strong><strong><span>本大题共3小题</span></strong><strong><span>,</span></strong><strong><span>每小题7分</span></strong><strong><span>,</span></strong><strong><span>共21分</span></strong><strong><span>)</span></strong>
-
13.
如图所示,这是用6个小正方体搭成的立体图形,请你从正面、左面、上面观察这个几何体,分别画出你所看到的几何体的形状图.
![](//tikupic.21cnjy.com/2023/11/29/4a/b3/4ab3edebd6b560d1721ed119e02ed4da_161x126.png)
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14.
计算:
-
(1)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
-
(2)
-
15.
将下列各数在数轴上表示出来,并用“
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3C%2Fmath%3E)
”把它们连接起来.
,
,
, 2,![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
![](//tikupic.21cnjy.com/2023/11/29/ef/e4/efe486236106fcfbdd7d417a28061bce_398x63.png)
四、<strong><span>(</span></strong><strong><span>本大题共3小题</span></strong><strong><span>,</span></strong><strong><span>每小题9分</span></strong><strong><span>,</span></strong><strong><span>共27分</span></strong><strong><span>)</span></strong>
-
16.
如图所示,把一个底面半径是5cm、高是8cm的圆柱放在水平桌面上.
![](//tikupic.21cnjy.com/2023/11/29/fc/31/fc31b2868e09b09f94342c87d9b7c194_94x106.png)
-
(1)
若用一个平面沿水平方向去截这个圆柱,所得的截面是;
-
(2)
若用一个平面沿竖直方向去截这个圆柱,所得的截面是;
-
(3)
若用一个平面去截这个圆柱,使截得的截面是长方形,且长方形的截面面积最大,请写出截法,并求出此时截面的面积.
-
-
18.
将8袋优质大米的质量以每袋50kg为基准,超过的记为正,不足的记为负,称重记录如下:
+4.5,-4,+2.3,-1.3,+2.5,-1,-4.5,+2.
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-
五、<strong><span>(</span></strong><strong><span>本大题共11分</span></strong><strong><span>)</span></strong>
-
19.
甲、乙两家超市以相同的价格出售同样的商品.为了吸引顾客,各自推出不同的优惠方案:在甲超市累计购买商品超出300元之后,超出部分按原价九折优惠;在乙超市累计购买商品超出200元之后,超出部分按原价九五折优惠.设顾客
购物
元.
-
(1)
请用含
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
的式子分别表示顾客在两家超市购物所付的费用.
-
(2)
李明准备购买700元的商品,你认为他应该去哪家超市?请说明理由.
六、(本大题共13分)
-
20.
小赵同学在查阅大数学家高斯的资料时,知道了高斯如何求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
.小赵于是对从1开始的连续奇数的和进行研究,发现了如下式子:
第1个等式:
;
第2个等式:
;
第3个等式:
;
……
探索以上等式的规律,解决以下问题.
-
(1)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
(
).
-
(2)
写出第
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmath%3E)
个等式:
.
-
(3)
利用(2)中的等式计算:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmath%3E)
.