Test Topics
Test 4
12/02/05
Sec. 4.5, 5.1, 5.2, 5.3, 5.4
- Applications of exponential and logarithmic
functions (compound interest, doubling time, etc)
- See workbook pages 169-170
- Sequence definition and notation
- Find the nth term or a specific term of a
sequence
- Finite/infinite sequences
- Using recursively-defined sequence formulas
- Graphs of sequences
- Summation (Sigma) notation
- Expanding sums
- Writing a sum in sigma notation
- Properties of sums
- Factorials
- Summation formulas
- Definition of arithmetic sequence/series
- Identify arithmetic sequences and series
- Common difference
- Find the nth term or a specific
term of an arithmetic sequence
- Use formulas for arithmetic sequences
- Use formulas for arithmetic series
- Graph arithmetic sequences; relationship to
linear functions
- Definition of geometric sequence/series
- Identify geometric sequences and series
- Common ratio
- Find the nth term or a specific
term of a geometric sequence
- Use formulas for geometric sequences
- Use formulas for geometric series
- Graph geometric sequences; relationship to exponential
functions
Test 3
11/10/05
Sec. 3.3, 4.1, 4.2, 4.3, 4.4, 4.5
- Vertical, horizontal and slant asymptotes
- Zeors/intercepts
- Domain of rational functions
- Graphing rational functions (including
non-reduced rational functions)
- Given a graph, write an equation
for the rational function
- Shape/basic features of exponentials
- Compounded interest
- Don't need to know formulas for doubling time
or half-life
- Do need to know what doubling
time and half-life are
- Given a graph, write an equation in the form y=
k b^x
- Shape/basic features of y = e^x
- Continuously compounded interest formula
- Use of Newton's Law of Cooling
(formula will be provided)
- Understand what inverse relationship means
- Verify algebraically that two functions are inverses
- Graphical
relationship between inverse functions
- One-to-one functions
- Determine whether a function is one-to-one graphically
and/or
algebraically
- Find the inverse of a function in any representation
(equation, graph, table, words)
- Meaning of logarithm
- Inverse relationship between logs and exponentials
- Convert between log and exponential forms
- Evaluate simple logs
- Solve logarithmic and exponential equations
- Shape/basic features of logarithmic graphs
- Natural and common logs - meaning, notation, use on
calculator
- Properties of logs
- Expanding/condensing log expressions using log properties
- Change of base formula
- Solving exponential equations of all types
- Solve log equations of all types
- Applications of exponential and logarithmic functions
Test 2
10/11/05
Sec. 1.5, 1.6, 2.1, 2.2, 3.1, 3.2
- Transformations of graphs:
- translations (shifts)
- expansions/compressions
- reflections
- Use transformations on graphs, equations,
tables and/or
individual points
- Sum, difference, product, and quotient of
functions
- Composition of functions
- Apply operations to all representations of
functions
(tables/graphs/equations)
- "Decomposition" of functions
- Slope
- Equations of lines (3 different forms)
- Parallel and perpendicular lines
- Converting to standard form (completing the
square)
- Finding the vertex/finding the minimum or
maximum
- Given graph - write equation for parabola
- Behavior of polynomial graphs for extreme
values of x
- Properties of polynomial graphs (number of
turning points/ number
of intercept, etc)
- "Leading term property"
- Multiplicity
- Long division of polynomials
- Factor Theorem
- Equivalent statements about factors, zeros,
solutions and
intercepts
- Construction of polynomial with given zeros
Test 1
9/13/05
Sec. 1.1 - 1.4
- Definition of a function
- Domain
- Identifying functions
- Evaluating functions
- Finding the zeros of a function
- Identifying increasing/decreasing intervals
- Identifying negative/positive intervals
- Turning points
- Finding x
and y-intercepts
- Basic graphs
- Odd/even/neither functions
- Graphing piecewise defined functions
- "Complete graphs" - on calculator
- Window notation
- Setting up equations to model situations
- Using models to answer questions
- Wording i.e. what does "_____ is
a function of
_____" mean?