Mastering Free-Response Questions in AP Calculus AB

What is the integral from A to B of fime of X DX typically equal to?

• F(a) - F(b)

• None of the above

• F(b) - F(a)

• F(x) + C

What is the primary purpose of the yellow sheet mentioned in the video?

• To provide answers

• To serve as a reference

• To distribute grades

• To collect student feedback

What does the differential equation dy/dx = 1 - 2x^2 * (y - -1) imply when x = 1 and y = 2?

• Slope = 2

• Slope = -1

• Slope = 0

• Slope = 1

What is the slope at the point (2,2) for the given differential equation?

• -1

• 1

• 0

• 0.5

What is the correct sketching approach for a slope field with undefined points?

• Use a ruler for precision

• Guess the slopes

• Exclude slopes at undefined points

• Include slopes at undefined points

How should the slopes in the slope field be drawn?

• With precise measurements

• Using a computer

• Approximately correct

• Without regard to scale

What method is used to solve the differential equation presented in the video?

• Integration by parts

• Separation of variables

• Partial fractions

• Graphical method

What does the integral of 1 over y - 1 simplify to?

• ln|y + 1| + C

• 1/(y - 1) + C

• y - 1 + C

• ln|y - 1| + C

What is the value of C when using the initial condition F(1) = 2?

• 1

• 0

• -3

• 3

What is the final expression for y in terms of x after solving the differential equation?

• y = 1 - e^(x + 2/x - 3)

• y = e^(x + 2/x - 3) - 1

• y = 1 + e^(x + 2/x - 3)

• y = e^(x + 2/x + 3)