DP IB数学:AI HL练习试卷问题2021(中等)|保存我的考试必威体育网址下载

问题1

分数:2

Scotpop博士正在调查苏格兰水獭的数量。

根据历史数据，这位医生发现水獭的数量，P{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P" style="vertical-align:-6px;height:22px;width:12px">的模型P=7500+A1.09t{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P = 7500 + A，左括号，1.09右括号，t次方" style="vertical-align:-6px;height:23px;width:145px">在哪里A{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:15px">是常数，并且t≥0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="T大于等于0" style="vertical-align:-6px;height:22px;width:32px">是从2000年开始算起的年数。

一)

在2000年初，苏格兰水獭的数量是8000只。
求这个常数的值

A{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:15px">．

问题1 b

分数:2

b)

找出2020年初苏格兰水獭的数量。

问题1 c

分数:2

c)

斯考特波普博士估计，苏格兰水獭的最高数量是15 500只。算出斯科特波普博士预计水獭数量达到峰值的年份。

问题2

分数:1

一位商店经理想知道顾客们花了多少钱。
经理进行了一项调查，询问顾客他们花了多少钱。

数据如下表所示。

消费金额(以英镑计)£p{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="£p" style="vertical-align:-6px;height:22px;width:24px" loading="lazy">）	购物人数
£0≤p<£2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="小于或等于p小于2英镑的0英镑" style="vertical-align:-6px;height:22px;width:87px" loading="lazy">	5
£2≤p<£5{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="小于或等于p小于5英镑" style="vertical-align:-6px;height:22px;width:87px" loading="lazy">	14
£5≤p<£10{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="小于或等于p小于10英镑" style="vertical-align:-6px;height:22px;width:96px" loading="lazy">	20.
£10≤p<£20{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="小于或等于p小于20英镑" style="vertical-align:-6px;height:22px;width:105px" loading="lazy">	s{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="年代" style="vertical-align:-6px;height:22px;width:9px" loading="lazy">
£20≤p<£50{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="小于或等于20英镑p小于50英镑" style="vertical-align:-6px;height:22px;width:105px" loading="lazy">	3.

一)

解释为什么只有估计消费者的平均消费金额可以通过表中的数据找到(即使当消费者的消费金额为

s{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="年代" style="vertical-align:-6px;height:22px;width:9px" loading="lazy">是已知的)。

问题2 b

标志:4

顾客的平均消费额估计为£8.58{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="£8.58" style="vertical-align:-6px;height:22px;width:46px" loading="lazy">．

b)

找到…的价值

s{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="年代" style="vertical-align:-6px;height:22px;width:9px" loading="lazy">．

问题2摄氏度

分数:1

在某一天询问商店里的每一位购物者是不现实的，所以经理在商店出口站了一个小时，问其中一些(而不是全部)购物者他们花了多少钱。

c)

确定调查中使用的抽样技术。

问题3

分数:2

护林员利用空中图像来帮助定位大草原上的大型猫科动物。这周飞机无法起飞，所以他们必须使用上周的照片，这张照片显示了5只公猫最后已知的位置A1, 3, B3, 11, C5, 7, D9, 9{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="直A开括号1逗号空格3闭括号逗号空格直B开括号3逗号空格11闭括号逗号空格直C开括号5逗号空格7闭括号逗号空格直D开括号9逗号空格9闭括号" style="vertical-align:-6px;height:22px;width:243px" loading="lazy">而且E11, 1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="直E，开括号11个，空格1个，闭括号" style="vertical-align:-6px;height:22px;width:60px" loading="lazy">如下面的坐标轴所示。

水平比例尺:1单位代表1公里。垂直尺度:1单位代表1公里。

q3a1-ib-practice-paper-set-a-1

公猫坚守在非常严格的领地上，与其他公猫保持距离，以避免对抗。使用上图，护林员画三条直线形成一个不完整的Voronoi图。

q3a2-ib-practice-paper-set-a-1

一)

计算线段CD的梯度。

问题3 b

分数:3

b)

找出完成Voronoi单元包含位置的直线方程C．
在表格里填写你的答案

ax+by+d=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="ax + b y + d = 0" style="vertical-align:-6px;height:22px;width:108px" loading="lazy">在哪里

a, b, d∈ℤ{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="A，空格，b，空格，d元素的直整数" style="vertical-align:-6px;height:22px;width:75px" loading="lazy">．

问题3 c

分数:1

c)

在问题的背景下，解释Voronoi细胞包含位点的意义C．

问题4

分数:1

矩形的周长P{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P" style="vertical-align:-6px;height:22px;width:12px" loading="lazy">它的宽是高的两倍，可以用函数表示PA=6A2, A≥0,{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P个开括号A个闭括号等于6个根号A除以2个底根逗号空格一个大于等于0的逗号" style="vertical-align:-11px;height:39px;width:153px" loading="lazy">在哪里A{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:15px" loading="lazy">是矩形的面积。函数的图像P{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P" style="vertical-align:-6px;height:22px;width:12px" loading="lazy">显示为0≤A≤32.{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="0小于等于A小于等于32。" style="vertical-align:-6px;height:22px;width:79px" loading="lazy">

q4a1-ib-practice-paper-set-a-1

一)

写下的值

P32{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P个开括号32个闭括号" style="vertical-align:-6px;height:22px;width:42px" loading="lazy">．

问题4 b

分数:3

b)

在上面的坐标轴上，画出逆函数的图形，

P-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P的- 1次方的末端指数" style="vertical-align:-6px;height:23px;width:29px" loading="lazy">．

问题4摄氏度

分数:1

c)

在问题的上下文中，解释…的意思

P-112=8{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P的- 1次方结束指数开括号12闭括号等于8" style="vertical-align:-6px;height:23px;width:85px" loading="lazy">．

问题5

分数:1

一个粒子A，移动速度(v ms-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="V (ms) ^(- 1)末端指数" style="vertical-align:-6px;height:23px;width:53px" loading="lazy">)在时间t{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="t" style="vertical-align:-6px;height:22px;width:7px" loading="lazy">秒由v=3 cos t{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="V = 3空间cos空间t" style="vertical-align:-6px;height:22px;width:75px" loading="lazy">，t≥0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="T大于等于0" style="vertical-align:-6px;height:22px;width:32px" loading="lazy">．

动能(E{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="E" style="vertical-align:-6px;height:22px;width:13px" loading="lazy">)，以焦耳(J)为单位，由E=2v2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="E = 2v方" style="vertical-align:-6px;height:23px;width:56px" loading="lazy">．

一)

写下一个表达式

E{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="E" style="vertical-align:-6px;height:22px;width:13px" loading="lazy">作为时间的函数。

问题5 b

分数:2

b)

因此,找到

dEdt{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="分子d E除以分母d t结束分数" style="vertical-align:-17px;height:47px;width:31px" loading="lazy">．

问题5度

分数:2

c)

因此，求动能第一次以10js的速率变化的时间^－1．

问题6

标志:4

亚历克斯被委托用50根圆柱形的金属条和一个纵向的楔形切割来创作一个艺术雕塑。每一块的长度为3.8米，半径为12.6厘米，如下图所示，其中O表示圆形截面的中心。

q6a1-ib-practice-paper-set-a-1

整个雕塑将使用7.15米^3.的金属。

一)

找到角度

θ°{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="θ程度" style="vertical-align:-6px;height:22px;width:19px" loading="lazy">定义楔子的大小，每个棒必须从它切割出来。

问题6 b

分数:1

b)

将(a)部分的答案转换成弧度。

问题7

分数:2

剧院的照明设备上正在安装一个新的聚光灯。灯光工作人员必须调整光束的角度，并标记出演员可以站立的位置，以确保他们得到适当的照明。聚光灯位于舞台前面D点正上方的A点。灯光所覆盖的区域如下图中三角形ABC所围成的阴影区域所示，可以通过改变角度来调节CA^B{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="笔直的，笔直的，笔直的" style="vertical-align:-6px;height:26px;width:38px" loading="lazy">．

q7-ib-practice-paper-set-a-1

灯光工作人员调整灯光，使A点到B点的距离为10米，A点到C点的距离为8米，B点到C点之间覆盖的舞台地板长度为5.2米。

一)

找到照明人员调整的角度

CA^B{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="笔直的，笔直的，笔直的" style="vertical-align:-6px;height:26px;width:38px" loading="lazy">出现。

问题7 b

标志:6

C点距离舞台前面d点1.2米。为了确保演员从C点方向走向B点时知道在哪里停下来，灯光工作人员在地板上标记了一个点，任何身高在1.9米以下的演员都可以站在那里并保持完全照明。

b)

找到最远的距离从舞台前面灯光师应该做标记。

问题8

分数:1

列奥纳多构造了一个带有六个扇形标签的偏置转轮0, 1, 1, 2, 3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="0，空格1，空格1，空格2，空格3" style="vertical-align:-6px;height:22px;width:82px" loading="lazy">和5。

旋转器在六个扇区中每个扇区着陆的概率如下表所示:

扇区编号	0	1	1	2	3.	5
概率	620{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="6 / 20" style="vertical-align:-17px;height:47px;width:27px" loading="lazy">	p{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="p" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">	320{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="3 / 20" style="vertical-align:-17px;height:47px;width:27px" loading="lazy">	520{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="5 / 20" style="vertical-align:-17px;height:47px;width:27px" loading="lazy">	320{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="3 / 20" style="vertical-align:-17px;height:47px;width:27px" loading="lazy">	120{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="1 / 20" style="vertical-align:-17px;height:47px;width:27px" loading="lazy">

一)

求的确切值

p{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="p" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">．

问题8 b

分数:2

莱昂纳多正在和他的偏心旋转器玩一个游戏。游戏的分数是旋转者在旋转后落在的数字。

莱昂纳多玩了一次这个游戏。

b)

计算期望分数

问题8 c

分数:3

莱昂纳多玩了两次游戏，把两个分数加在一起。

c)

求列奥纳多有a的概率总计2分。

问题9

分数:2

飞机以速度飞行v=-3-124{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="V等于左括号表行单元格- 3结束单元格行单元格- 12结束单元格第4行结束表右括号" style="vertical-align:-34px;height:80px;width:81px" loading="lazy">变成有速度的风w=4k2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="W等于右括号表第4行k行第2行结束表右括号" style="vertical-align:-34px;height:80px;width:64px" loading="lazy">，k∈ℝ.{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="K个实数元素。" style="vertical-align:-6px;height:22px;width:45px" loading="lazy">

一)

考虑到

v{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="v" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">垂直于

w{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="w" style="vertical-align:-6px;height:22px;width:15px" loading="lazy">，求的值

k{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="k" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">．

问题9 b

标志:4

平面上的升力垂直于平面和风，由矢量方程给出L=av×w, a∈ℝ+{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="斜体加粗的L等于v叉乘斜体加粗的w，加粗的空格一个实数元素的正次方" style="vertical-align:-6px;height:23px;width:140px" loading="lazy">．

b)

考虑到

L=88{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="打开竖条加粗斜体L关闭竖条等于88" style="vertical-align:-6px;height:22px;width:61px" loading="lazy">，求的值

a{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:10px" loading="lazy">．

问题10

分数:2

科学家们正在实验室的一个大培养皿中培养X和Y两种细菌的菌落。两种细菌所覆盖区域的变化率，其中x{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="x" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">是X和所覆盖的区域吗y{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="y" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">为Y所覆盖的面积，由下式给出:

dxdt=19x-9y{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="分子dx除以分母dt端分数等于19x - 9y" style="vertical-align:-17px;height:47px;width:110px" loading="lazy">

dydt=9x-11y{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="分子dy除以分母dt，末端分数等于9x - 11y" style="vertical-align:-17px;height:47px;width:110px" loading="lazy">

矩阵19-99-11{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="开括号表第19行单元格- 9结束单元格第9行单元格- 11结束单元格结束表闭括号" style="vertical-align:-21px;height:54px;width:80px" loading="lazy">是否有特征值16和-8对应的特征向量31{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="左括号表第3行第1行结束表右括号" style="vertical-align:-21px;height:54px;width:32px" loading="lazy">而且13{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="开括号表第1行第3行结束表闭括号" style="vertical-align:-21px;height:54px;width:32px" loading="lazy">．

最初x=5 cm2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X等于5cm方" style="vertical-align:-6px;height:23px;width:70px" loading="lazy">而且y=7 cm2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Y = 7cm²" style="vertical-align:-6px;height:23px;width:70px" loading="lazy">．

一)

找到…的价值

dydx{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="分子dy除以分母dx的分数" style="vertical-align:-17px;height:47px;width:29px" loading="lazy">当

t=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="T = 0" style="vertical-align:-6px;height:22px;width:33px" loading="lazy">．

问题10 b

标志:4

b)

在下面的坐标轴上，描绘出两种菌落生长的可能轨迹，明确任何渐近行为。

问题11

标志:6

客户投诉电话持续的时间长度可以用正态分布建模，其均值为2.4分钟，方差为0.63分钟²．

Jennifer完成了5个客户电话，一个接一个。

求出完成这些电话的总时间超过13分钟的概率。

清楚地陈述你所做的任何假设。

问题12

分数:3

一)

的图形

y=-x3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Y = - x³" style="vertical-align:-6px;height:23px;width:62px" loading="lazy">变换到的图上

y=45-0.015x3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Y = 45 - 0.015 x³" style="vertical-align:-6px;height:23px;width:121px" loading="lazy">通过翻译

a{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:10px" loading="lazy">单位垂直方向和平行方向拉伸

x{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="x" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">比例因子的-轴

b{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="b" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">．

(i)写下的值a{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:10px" loading="lazy">．

求的值b{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="b" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">．

问题12 b

分数:5

b)

罗科正在为他的微型战争游戏俱乐部建造一座空心的山堡。山的外表面呈直径40厘米的半球形状，由高度25厘米的垂直墙壁支撑。山的内表面可以通过旋转曲线来建模

y=45-0.015x3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Y = 45 - 0.015 x³" style="vertical-align:-6px;height:23px;width:121px" loading="lazy">通过

360°{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="360度" style="vertical-align:-6px;height:22px;width:36px" loading="lazy">关于

y{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="y" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">设在之间

y=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Y = 0" style="vertical-align:-6px;height:22px;width:37px" loading="lazy">而且

y=45{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Y = 45" style="vertical-align:-6px;height:22px;width:46px" loading="lazy">，如图所示。

求出山的内外表面之间的空间体积。

问题13

分数:1

玛丽卡是一头优秀的松露狩猎猪的主人。她的猪在一小时内可以在特定的林地区域发现松露的数量可以用泊松分布来模拟。

玛丽卡称，她的猪平均每小时能发现12颗松露。

里卡多是一只竞争对手猪的主人，他认为玛丽卡的猪平均不到12头。他决定做个测试。玛丽卡的猪将有一个小时的时间去寻找松露，如果猪发现的松露少于8块，里卡多就会拒绝玛丽卡的要求。

(a)为李嘉图检验提出合适的零假设和替代假设。

问题13 b

分数:2

b)

求第一类错误的概率。

问题13 c

分数:3

玛丽卡的猪在一小时内发现的松露平均数量为11.3块。

(c)求第二类错误的概率。

问题14

分数:2

一家公司生产内置可充电电池的健身追踪器。为了保证质量，我们测试了25个充满电的追踪器样本，以确定充满电的健身追踪器的电池寿命。样品的平均电池寿命为70.6小时，标准差为2.3小时。

一)

找到

sn-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="S下标n - 1末端下标" style="vertical-align:-12px;height:28px;width:36px" loading="lazy">对于这个样本。

问题14 b

分数:2

b)

求总体均值的95%置信区间。

问题14 c

分数:1

该公司声称，一个充满电的健身追踪器在需要充电之前可以使用整整3天。

c)

就你在(b)部份的回答，评论这项申索。

问题15

标志:7

生物学家认为，二氧化硅含量的变化(s{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="年代" style="vertical-align:-6px;height:22px;width:9px" loading="lazy">)对每厘米的种群有影响^3.一种特定类型的细菌(B{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="B" style="vertical-align:-6px;height:22px;width:14px" loading="lazy">)．他从三个不同的区域收集样本，结果如下表所示。

区域	二氧化硅,s{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="年代" style="vertical-align:-6px;height:22px;width:9px" loading="lazy">（%）	细菌,B (没有。每厘米^3.）
1	25	32
2	34	186
3.	12	3.

这位生物学家认为，二氧化硅浓度与细菌数量之间的关系可以用这个方程来模拟

Bs=asebs a,b∈ℝ {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="B开括号s闭括号等于a se的B次方空间空间结束指数空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间a, B的直实数元素空间空间空间空间空间空间空间空间空间空间空间空间空间" style="vertical-align:-6px;height:23px;width:211px" loading="lazy">

基于生物学家的方程提出了两个相互竞争的模型，但参数不同a{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:10px" loading="lazy">而且b{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="b" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">如下图所示:

模型:a=0.006, b=0.2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="A = 0.006，空格b = 0.2" style="vertical-align:-6px;height:22px;width:127px" loading="lazy">

模型:a=0.09, b=0.12{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="A = 0.09，空格b = 0.12" style="vertical-align:-6px;height:22px;width:127px" loading="lazy">

生物学家将选择残差平方和值最小的模型。

确定生物学家将选择哪种模型。

问题16

标志:6

率,一个固定温度下化学反应的，与两种化合物的浓度有关，B而且C，由

A=k Bx Cy, {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="A等于k空间B的x次方C的y次方，空间" style="vertical-align:-6px;height:23px;width:105px" loading="lazy">在哪里x, y, k∈ℝ{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X，空间y，空间k个实数元素" style="vertical-align:-6px;height:22px;width:78px" loading="lazy">．

科学家在反应过程中三次测量这三个变量，得到以下值。

实验	Amol l-1s-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="A，开括号，mol空间l的- 1次幂s的- 1次幂，闭括号" style="vertical-align:-6px;height:23px;width:106px" loading="lazy">	Bmol l-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="B，开括号，mol空间，l的负1次方，结束指数，闭括号" style="vertical-align:-6px;height:23px;width:80px" loading="lazy">	Cmol l-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="C，开括号，mol空间，l的- 1次方，结束指数，闭括号" style="vertical-align:-6px;height:23px;width:80px" loading="lazy">
1	7.21	1．8	3．1
2	3.25	1.3	2.7
3.	0.827	0.4	1.7

找到x, y{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X，空格y" style="vertical-align:-6px;height:22px;width:30px" loading="lazy">而且k{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="k" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">．

问题17

分数:5

让w=aeπ3i{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="W等于a e的/ 3次方I的末端指数" style="vertical-align:-6px;height:36px;width:67px" loading="lazy">,在那里a∈ℝ+{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="正数的正数次方的一种元素" style="vertical-align:-6px;height:23px;width:49px" loading="lazy">．

一)

为

a=3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="A等于根3" style="vertical-align:-6px;height:26px;width:54px" loading="lazy"> ，

(我)

求的值

w2, w3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="W的平方，空间W的立方" style="vertical-align:-6px;height:23px;width:52px" loading="lazy"> 而且

w4{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="W的4次方" style="vertical-align:-6px;height:23px;width:22px" loading="lazy"> ；

(2)

画

w2, w3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="W的平方，空间W的立方" style="vertical-align:-6px;height:23px;width:52px" loading="lazy">而且

w4{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="W的4次方" style="vertical-align:-6px;height:23px;width:22px" loading="lazy">在下面的阿根图上。

问题17 b

分数:2

让z=w1+i{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="Z等于分子w除以分母1加上I端分数" style="vertical-align:-17px;height:47px;width:66px" loading="lazy">．

b)

求的连续幂的值

z{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="z" style="vertical-align:-6px;height:22px;width:10px" loading="lazy">躺成一个圈。

问题18

分数:2

莱拉收藏了26颗水晶。有8个白色晶体，5个红色晶体，其余是蓝色晶体。

每天，蕾拉都会随机选择一块水晶放在她的桌子上。

一)

求她在1月份10次选择白色水晶的概率。

问题18 b

标志:4

莱拉把她和姐姐的水晶收藏品结合在一起，所以她们总共有54颗水晶。Leila计算出在第一周内选到一个蓝色水晶5次的概率是0.201063，精确到小数点后6位。

b)

找出组合集合中蓝色水晶的数量。

DP IB数学:AI HL

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