Exam reviews

(Note coverage of topics has moved a bit over the years)

Basics of differentiation

Spring 2020

Fall 2019

Fall 2018

Major topics include:

    • Average rate of change; instantaneous rate of change

    • Limits; limit rules; one-sided limits; limits involving infinity

    • Continuity; types of discontinuities (e.g. removable, jump, ...)

    • Limit definition of derivative

    • Derivative at a point; derivative as a function

    • Higher order derivatives; notation

    • Find tangent lines to curves

    • Sum, product, quotient rules for differentiation

    • Derivatives of x^k, e^x, sin(x), cos(x), tan(x), sec(x)

    • Differentiation and motion (velocity and acceleration)

    • Chain rule

Advanced differentiation

Fall 2019

Fall 2018

Major topics include:

    • Implicit differentiation; derivative of inverse function

    • Derivatives of ln(x), arctan(x), arcsin(x), arcsec(x)

    • Logarithmic differentiation

    • Linearization and approximating function

    • Related rates problems

    • Absolute and local maximums and minimums

    • Identify critical points; classify critical points by use of either the first or second derivative tests

    • Setting up and solving optimization problems

    • Identifying when functions are increasing/decreasing; identifying when functions are concave up/down

    • Sketching functions

    • L'Hospital's rule for working with indeterminant limits

    • Newton's method for finding roots

Basics of integration

Fall 2019

Spring 2019

Fall 2018

Major topics include:

    • L'Hospital's rule for working with indeterminant limits

    • Newton's method for finding roots

    • Mean Value Theorem

    • Finding antiderivatives of basic functions x^k, e^x, sin(x), cos(x), sec^2(x), sec(x)tan(x), 1/(1+x^2), sec(x), and tan(x). Know that antiderivatives are unique up to "+C"

    • Use Riemann sums to approximate totals; definite integrals

    • Using basic properties of definite integrals (constant multiple, sums, inequalities, breaking into multiple parts, reversing order)

    • Compute average of a function over an interval

    • State and use both variations of the Fundamental Theorem of Calculus

    • Use substitution for definite and indefinite integration

    • Find the net area under a curve or between two curves

    • Integration and motion

    • Solve separable differential equations

    • Hyperbolic functions

Final Exam (Comprehensive)

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Fall 2016

Final exam "unboxing"