AP Calculus AB Review (For BC Semester 1 Final)

Question 1

Evaluate ∫ x2 dx on the interval [0, 2]

Accepted Answer

8/3

Question 2

Find the area between the curves x = 4 - y2 and x = y - 2

Accepted Answer

20.833

Question 3

Evaluate ∫( 1 / (3-x)) dx

Accepted Answer

-ln|3-x| + C

Question 4

∫( 5 / (1 + x2)) dx =

Accepted Answer

5tan-1(x) + C, 5arctan(x) + C

Question 5

∫(1 / (16 + x2)) dx =

Accepted Answer

(1/4)arctan(x/4) + C, (1/4)tan-1(x/4) + C

Question 6

Find the derivative of ∫ t3 dt when the bounds are [-2, ex]

Accepted Answer

e4x

Question 7

∫ e6x dx =

Accepted Answer

(1/6)e6x + C

Question 8

USE YOUR CALCULATOR

Accepted Answer

14

Question 9

∫(1/2)sec2(4x) dx =

Accepted Answer

(1/8)tan(4x) + C

Question 10

Given the position function s(t)=4t3-12t2, find the velocity when acceleration = 0

Accepted Answer

-12

Question 11

CALCULATOR: Given rate = 2100sin2((π/8)x) gallons/hour, find total gallons pumped after 5 hours

Accepted Answer

6195

Question 12

Equation of the line tangent to the graph of y = (2x+1) / (5x -4) at the point (1, 3) is

Accepted Answer

y - 3 = (-13)(x-1)

Question 13

Base of a solid bounded by x and y-axis and y = -2x + 4. Cross sections are squares. Volume = ?

Accepted Answer

10.667

Question 14

Find the limit as x approaches 4 of (x2 - 16) / (x - 4)

Accepted Answer

8

Question 15

Find the limit as x approaches infinity of (3x2 - 1) / (x2 + 30x)

Accepted Answer

3

Question 16

Find the limit as x approaches -∞ of ex + 1

Accepted Answer

1

Question 17

Given a(t) = -32t, what is the speed at t = 2? Given: v(0) = 10

Accepted Answer

54

Question 18

Evaluate ∫ (x3)/(x4 + 1) dx on the interval [0,1].

Accepted Answer

(1/4)ln2

Question 19

Solve dy/dx = 2x/y for y

Accepted Answer

√(2x2 + C)

Question 20

Given that F(7) = 7 and ∫(ln(12x)(x1/2)(e-3x) dx = 0 on the interval [3, 7], find F(3).

Accepted Answer

7

Question 21

∫ (x + sin(x)) dx on the interval [0, π] =

Accepted Answer

(1/2)π2 + 2

Question 22

Find the area under the curve below on the interval [0, 3].

Accepted Answer

5/2, 2.5

Question 23

Find the derivative of sin-1(5x)

Accepted Answer

5 / √(1 - 25x2)

Question 24

Find the position at t = 5 given s(0) = 4 and v(t) = 2t

Accepted Answer

29

Question 25

Find the derivative of 2x

Accepted Answer

(2x)ln(2)

AP Calculus AB Review (For BC Semester 1 Final)

Questions 25

AP Calculus AB Review (For BC Semester 1 Final)

Questions 25