# 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 half-life

• How to find the half-life and doubling time given an exponential function

• How to find exponential formulas given the doubling time and half-life

• 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(A-5) 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)

Prev | Next |