The test will have somewhere between 8 and 10 problems. I guarantee there will be problems on the following topics:

Finding inflection points: Take two derivatives in order to find the critical points and inflection points of a function on an interval. Apply either the First or Second Derivative Test to decide whether each critical point is a local max, min, or neither. Section 4.6: 31-50. Section 4.MP: 29-33.

Curve sketching: Given a function, find its critical points and inflection points, as well as its asymptotes, both horizontal and vertical (this will involve some limit computations). Sketch a graph of the function. Section 4.7: 1-16 (for asymptote computations), 29-54. Section 4.MP: 53-72.

Antiderivatives and initial-value problems: Find the general antiderivative for a given function. If an initial value of the function is given, solve for the specific antiderivative with this initial value. Section 5.2: 1-30, 35-46. Section 5.MP: 1-30.

Position, velocity, acceleration: Knowing the acceleration of a particle (usually constant), plus some initial conditions on the velocity and position of the particle, answer questions about the motion of the particle by solving initial-value problems for its velocity and position functions. Section 5.2: 57-79. Section 5.MP: 31-38.

Separable differential equations (two problems): Solve a separable differential equation, with or without an initial-value condition. Translate a word problem into a separable differential equation. Section 8.3: 1-20, 21-30 (ignore the instructions), 31-41. Section 8.MP: 1-12, 31-37.


There will be two to four more problems, all material you've already been tested on. Expect at least one optimization problem of some kind (everybody loves those). Maybe a related rates problem, or an implicit differentiation problem, or a Mean Value Theorem/Rolle's Theorem problem, or a logarithmic differentiation problem...the possibilities are endless.