AP Calculus AB Final Exam Review Part 2

The base of a solid is the region in the first quadrant enclosed by the parabola 𝑦 = 4𝑥² , the line 𝑥 = 1, and the 𝑥-axis. Each plane section of the solid perpendicular to the 𝑥-axis is a square. The volume of the solid is…

• 4/3

• 16/5

• 4

• 16

Find the length of the curve described by  $y=\frac{2}{3}x^{\frac{3}{2}}$  for  $0\le x\le8.$  

•  $\frac{26}{3}$  

•  $\frac{52}{3}$  

•  $\frac{512\sqrt{2}}{15}$  

• 96

A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t². If the particle is at position p=7 at t=1, what is the position of the particle at t=2?

• -10

• -5

• -3

• 3

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.) 

• 5(3) + 1(4) + 2(5) + 1(7)
• 5(4) + 1(5) + 2(7) + 1(6)
• 5(3) + 6(4) + 8(5) + 9(7)
• 0(3) + 5(4) + 6(5) + 8(7)

Use a trapezoidal sum with four intervals from the table to estimate the integral of 0 to 9 of V(t).

• 64

• 67

• 93

• 151/2

• -1
• -2
• 1/2
• -1/2

Tags

CCSS.HSA.REI.D.10

• -4
• 28
• 40
• 20

Tags

CCSS.HSA.SSE.A.1

Let $A\left(x\right)=\int_0^x\sqrt{9-x^2}dx$  find  $A'\left(0\right)$  

• 3

• 0

• 9

• -3

Find the average value of the function  $f\left(x\right)=x+3$  on the interval  $\left[3,9\right]$  

•  $54$  

•  $67.5$  

•  $7.5$  

•  $9$  

Tags

CCSS.HSA.SSE.A.1

 What is the value of the definite integral :   $\int_0^{\frac{\pi}{2}}\cos\left(x\right)\ dx$ 

• -1

• 1

•  $\pi$  

•  $\frac{\pi}{2}$  

Tags

CCSS.HSF.TF.A.1