AP Calculus AB Readiness Test

10 questions, balanced across the exam's topics. Answer each one, then submit for your practice readiness estimate and per-topic breakdown. This is a practice estimate — not a prediction or guarantee of your official exam result.

Question 1

What is the derivative of f(x) = (3x + 4)^4?

12(3x + 4)^3 4(3x + 4)^3 12(3x + 4)^4 (3x + 4)^3

Question 2

Which concept is described by the following? "The application of derivatives to find maximum or minimum values of a quantity subject to constraints."

optimization mean value theorem increasing function local maximum

Question 3

Which of the following pairings of a concept with its description is correct?

quotient rule — the expression [f(a + h) - f(a)]/h whose limit as h → 0 gives the derivative at a differentiability — the rule that the derivative of f/g is (f'·g - f·g')/g^2 difference quotient — the property of having a derivative at a point, which requires the function to be continuous and have no corner, cusp, or vertical tangent there derivative — the instantaneous rate of change of a function, defined as the limit of the average rate of change as the interval shrinks to zero

Question 4

Which concept is described by the following? "A method for the volume of a solid of revolution with a hole, using V = π ∫ ([R(x)]^2 - [r(x)]^2) dx."

average value of a function disk method washer method volume by cross sections

Question 5

Which of the following pairings of a concept with its description is correct?

fundamental theorem of calculus, part 2 — a function defined by a definite integral with a variable upper limit, representing accumulated change indefinite integral — the theorem that a definite integral equals F(b) - F(a) for any antiderivative F of the integrand accumulation function — the family of all antiderivatives of a function, written with a constant of integration +C trapezoidal sum — an approximation of a definite integral using trapezoids over subintervals, which is the average of the left and right Riemann sums

Question 6

A particle moves along a line with position s(t) = 2t^3 - 4t. What is its velocity at t = 2?

20 24 4 8

Question 7

The concept "squeeze theorem" is most closely associated with which part of the course?

Applications of Integration Differentiation: Definition and Properties Composite, Implicit, and Inverse Differentiation Limits and Continuity

Question 8

Which concept is described by the following? "A technique for solving differential equations by moving all y terms to one side and all x terms to the other, then integrating."

separation of variables particular solution general solution differential equation

Question 9

The phrase "the result that the derivative of an inverse function at a point is the reciprocal of the original function's derivative at the corresponding point" is the definition of which of the following?

implicit differentiation chain rule derivative of inverse function washer method

Question 10

What is the meaning of "second derivative test"?

A diagram recording where a derivative is positive or negative to determine where a function increases, decreases, or is concave A method using the value of f'' at a critical point: positive indicates a local minimum, negative a local maximum The direction a graph bends, determined by the sign of the second derivative: up when f'' > 0, down when f'' < 0 A function whose values rise as x increases on an interval, which occurs when its derivative is positive there

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