AP-Style Practice QuestionsAP 风格练习题
Topics主题 8.1 - 8.12AB
Show all supporting work on scratch paper. On the AP Exam, Section I is split into a no-calculator and a calculator-allowed part, each question below is labeled accordingly.请在草稿纸上写出所有解题步骤。AP 考试第一部分分为不允许使用计算器和允许使用计算器两部分，每道题已注明。
The average value of $f(x)=x^{2}$ on $[0,3]$ is$f(x)=x^{2}$ 在 $[0,3]$ 上的平均值为
A particle moves along the $x$-axis with velocity $v(t)=t-2$ for $0\le t\le 3$. The displacement of the particle on this interval is一质点沿 $x$ 轴运动，速度为 $v(t)=t-2$，$0\le t\le 3$。该质点在此区间上的位移为
A particle moves with velocity $v(t)=t-2$ for $0\le t\le 3$. The total distance traveled is一质点的速度为 $v(t)=t-2$，$0\le t\le 3$。该质点走过的总路程为
Water flows into a tank at a rate of $r(t)=4+\sin(t)$ gallons per minute, for $0\le t\le 6$. The tank initially contains $50$ gallons. The amount in the tank at $t=6$ is closest to水以 $r(t)=4+\sin(t)$ 加仑/分钟的速率流入水箱，$0\le t\le 6$。水箱初始容量为 $50$ 加仑。$t=6$ 时水箱中的水量最接近
The area enclosed by $y=x$ and $y=x^{2}$ is$y=x$ 与 $y=x^{2}$ 所围的面积为
Which integral gives the area enclosed by $x=y^{2}$ and $x=y+2$?下列哪个积分表示 $x=y^{2}$ 与 $x=y+2$ 所围的面积？
The total area of the regions enclosed between $y=x^{3}-x$ and the $x$-axis is$y=x^{3}-x$ 与 $x$ 轴所围各区域的总面积为
The base of a solid is the region in the $xy$-plane bounded by $y=x$, $y=0$, and $x=2$. Cross sections perpendicular to the $x$-axis are squares. The volume of the solid is某立体的底面是 $xy$ 平面上由 $y=x$、$y=0$ 和 $x=2$ 所围的区域。垂直于 $x$ 轴的截面为正方形。该立体的体积为
The base of a solid is the region bounded by $y=\sqrt{x}$ and the $x$-axis on $[0,4]$. Cross sections perpendicular to the $x$-axis are equilateral triangles. The volume is某立体的底面是 $[0,4]$ 上由 $y=\sqrt{x}$ 与 $x$ 轴所围的区域。垂直于 $x$ 轴的截面为等边三角形。该立体的体积为
The region bounded by $y=\sqrt{x}$, $y=0$, and $x=4$ is revolved about the $x$-axis. The volume is由 $y=\sqrt{x}$、$y=0$ 和 $x=4$ 所围的区域绕 $x$ 轴旋转一周。体积为
The region bounded by $y=x^{2}$, $y=0$, and $x=2$ is revolved about the line $y=-1$. Which integral gives the volume?由 $y=x^{2}$、$y=0$ 和 $x=2$ 所围的区域绕直线 $y=-1$ 旋转一周。下列哪个积分表示其体积？
Let $R$ be the region enclosed by $y=x$ and $y=x^{2}$. The volume of the solid formed when $R$ is revolved about the $x$-axis is设 $R$ 为 $y=x$ 与 $y=x^{2}$ 所围的区域。将 $R$ 绕 $x$ 轴旋转一周所得立体的体积为
Let $R$ be the region bounded by $y=x^{2}$ and $y=4$. Which integral gives the volume of the solid generated when $R$ is revolved about the line $y=5$?设 $R$ 为 $y=x^{2}$ 与 $y=4$ 所围的区域。下列哪个积分表示将 $R$ 绕直线 $y=5$ 旋转一周所得立体的体积？
The rate at which people enter a park is modeled by $E(t)$ people per hour, where $t$ is hours since opening. Selected values:进入公园的人数速率由 $E(t)$（人/小时）建模，其中 $t$ 为开放后的小时数。部分数值如下：
| $t$ (hr小时) | $0$ | $2$ | $4$ | $6$ | $8$ |
|---|---|---|---|---|---|
| $E(t)$ | $100$ | $240$ | $380$ | $300$ | $150$ |
Using a left Riemann sum with the four subintervals of equal length, the approximate total number of people who entered during the $8$ hours is利用四个等长子区间的左黎曼和，在 $8$ 小时内进入公园的总人数近似为
If $f(x)=4x$, the average value of $f$ on $[1,3]$ is若 $f(x)=4x$，则 $f$ 在 $[1,3]$ 上的平均值为
A particle has velocity $v(t)=3t^{2}-6t$ and initial position $x(0)=2$. Then $x(2)=$一质点的速度为 $v(t)=3t^{2}-6t$，初始位置为 $x(0)=2$。则 $x(2)=$
The area enclosed by $y=4-x^{2}$ and the $x$-axis is$y=4-x^{2}$ 与 $x$ 轴所围的面积为
The base of a solid is the region under $y=\sqrt{x}$ on $[0,4]$. Cross sections perpendicular to the $x$-axis are semicircles with diameter in the base. The volume is某立体的底面是 $[0,4]$ 上 $y=\sqrt{x}$ 下方的区域。垂直于 $x$ 轴的截面为直径在底面上的半圆。体积为
Free-response answers must include setup, units, and interpretation in context where appropriate. A calculator is permitted unless marked otherwise.自由回答题须包含解题设置、单位，以及在适当时对结果的情境解释。除非特别注明，否则允许使用计算器。
A particle moves along the $x$-axis with velocity $v(t)=t^{2}-4t+3$ for $0\le t\le 4$. The particle is at position $x=2$ when $t=0$.一质点沿 $x$ 轴运动，速度为 $v(t)=t^{2}-4t+3$，$0\le t\le 4$。$t=0$ 时质点位于 $x=2$。
Let $R$ be the region in the first quadrant bounded by the graphs of $y=\sin(\pi x)$ and $y=x-x^{2}$.设 $R$ 为第一象限中由 $y=\sin(\pi x)$ 与 $y=x-x^{2}$ 所围的区域。
Water is being pumped into a tank at a rate of $P(t)=20+5\sin(t/2)$ gallons per minute. At the same time, water is leaking out at a rate of $L(t)=2+0.5t$ gallons per minute, for $0\le t\le 30$. At time $t=0$, the tank contains $400$ gallons of water.水以 $P(t)=20+5\sin(t/2)$ 加仑/分钟的速率泵入水箱，同时以 $L(t)=2+0.5t$ 加仑/分钟的速率漏出，$0\le t\le 30$。$t=0$ 时水箱中有 $400$ 加仑水。
Let $R$ be the region enclosed by the graphs of $y=e^{-x^{2}}$ and $y=\dfrac{1}{2}$.设 $R$ 为 $y=e^{-x^{2}}$ 与 $y=\dfrac{1}{2}$ 所围的区域。
A car travels along a straight road for $12$ seconds. The car's velocity $v(t)$, in meters per second, is differentiable. Selected values are given.一辆汽车沿直路行驶 $12$ 秒。汽车速度 $v(t)$（米/秒）可微，部分数值如下。
| $t$ (sec秒) | $0$ | $3$ | $6$ | $9$ | $12$ |
|---|---|---|---|---|---|
| $v(t)$ (m/s) | $0$ | $12$ | $20$ | $15$ | $6$ |