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Math Exam 2 Review
Note: This is not a comprehensive list, but highlights the main topics
covered in
these sections. Your best source of review is previous team homework
assignments and individual daily homework problems.
Sections 3.3 – 3.5
• The definition of a horizontal asymptote
• The general shape of an exponential function
• How the growth factor , growth rate, and continuous rate (in exponential
functions) are related
• When it is appropriate to use Q = ab^{t} or Q = ae^{kt}
• The difference between annual and continuous growth rates
• The difference between nominal and effective interest rates
• What it means to compound interest n times per year
• How to find the balance of an account when interest is either compounded
annually, n times per year, or continuously
Sections 4.1 – 4.3
• All logarithmic rules (including those for base 10 and those for base e)
• How to simplify algebraic expressions using logarithm rules
• How to solve exponential functions using logarithms
• The definition of doubling time and halflife
• How to find the halflife and doubling time given an exponential function
• How to find exponential formulas given the doubling time and halflife
• The domain and range of log(x) and ln(x)
• The general shape of the graphs of log (x) and ln(x) and how these
compare to 10^{x} and e^{x} , respectively.
• The definition of a vertical asymptote
• Limit notation for asymptotes
• Using logarithms to compare quantities of different orders of magnitude
(such as pH, decibels, etc., though you do not need to memorize these
specific formulas)
Sections 5.1 – 5.5
• Vertical and horizontal shifts, stretches, compressions, and reflections,
and how to write these transformations in terms of the original function
• The definitions of even and odd functions
• How to algebraically show a function is even, odd, or neither
• How to practically interpret expressions such as f(A5) in practical terms
for the context of the problem.
• Given a graph, produce a new graph of another function that is a
transformation of the original
• Given table data for the original function, how to complete tables of
transformations of this function
• Given table data, how to complete the table if it is even or odd
• Completing the Square
• How to find the maximum or minimum of a parabola by completing the
square
• Vertex , factored, and standard forms for quadratic functions
• Given a graph of a quadratic function , how to find the appropriate formula
• How to find the zeros of a quadratic function
Sections 6.1 – 6.4
• The definition of a periodic function
• How to identify the period, midline, and amplitude of a periodic function
• Given a scenario that is periodic, sketch the graph that models the
situation and determine its period, midline, and amplitude
• Given a graph of a periodic function that models a situation, describe the
situation in words and relate the period, midline, and amplitude into real world
terms as is appropriate for the context of the problem
• How to find the coordinates of a point on a circle of radius r
• How to convert degrees into radians
• How to convert radians into degrees
• How to calculate arc length
• The general shapes of the graphs of sin(x) and cos(x)
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