Calculus Help & Past Papers
AP Calculus BC Multiple Choice 2012 Questions - complete paper (pdf)
AP Calculus BC 2012 MCQ Part A Solutions
The function f, whose graph is shown above, is defined on the interval -2 ≤ x ≤ 2. Which of the following statements about f is false?
(A) f is continuous at x = 0.
(B) f is differentiable at x = 0.
(C) f has a critical point at x = 0.
(D) f has an absolute minimum at x = 0.
(E) The concavity of the graph of f changes at x = 0.
Let f and g be the functions given by f(x) = ex and g(x) = x4. On what intervals is the rate of change of f(x) greater than the rate of change of g(x)) ?
The graph of the piecewise linear function f is shown above.
Let f be a function having derivatives of all orders for x > 0 such that f(3)= 2, f'(3) = 1, f''(3) = 6, and f'''(3) = 12. Which of the following is the third-degree Taylor polynomial for f about x = 3 ?
The graph of f', the derivative of the function f, is shown above. Which of the following statements must be true?
Let f be a function that is twice differentiable on -2 < x < 2 and satisfies the conditions in the table above. If f(x) = f(-x) , what are the x-coordinates of the points of inflection of the graph of f on -2 < x < 2?
What is the average value of y = √cos x on the interval 0 ≤ x ≤ π/2?
If the function f is continuous at x = 3, which of the following must be true?
For -1.5 < x < 1.5, let f be a function with first derivative given by f'(x) = e(x4 - 2x2 + 1) - 2. Which of the following are all intervals on which the graph of f is concave down?
The fuel consumption of a car, in miles per gallon (mpg), is modeled by where s is the speed of the car, in miles per hour. If the car is traveling at 50 miles per hour and its speed is changing at the rate of 20 miles / hour2 , what is the rate at which its fuel consumption is changing?
If f'(x) > 0 for all real numbers x
Let R be the region in the first quadrant bounded above by the graph of y = ln(3 - x) for 0 < x < 2. R is the base of a solid for which each cross section perpendicular to the x-axis is a square. What is the volume of the solid?
The derivative of a function f is increasing for x < 0 and decreasing for x > 0. Which of the following could be the graph of f?
A particle moves along a line so that its acceleration for t ≥ 0 is given by
If the series
The figure above shows the graphs of the polar curves r = 2cos 3θ and r = 2. What is the sum of the areas of the shaded regions?
The function h is differentiable, and for all values of x, h(x) = h(x - 2). Which of the following statements must be true?
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