Math 110 Final Exam Topics List – Summer II 2012
**The Final Exam is cumulative. Refer to the Exam 1 - 4 topic lists on the following pages and review
your past exams. Listed below are topics covered since Exam 4 followed by all of the topics lists for
Exam 1 – 4.**
Date covered in class
Topic
Jun 27 & 28
Polynomial Functions
Jul 02 & Jul 03
Quadratic Functions
Learning Objective
For any polynomial function, be able to identify and interpret the vertical
intercept, the horizontal intercepts, and the max/or min. value.
Find an appropriate window on your graphing calculator in order to find
key points on the graph of a polynomial function.
Be able to identify and/or interpret the characteristics of each family of
functions (Quadratic Functions) including: intercepts, rates of change,
asymptotes, end behavior, domain and range and max/min values.
For a quadratic function, be able to identify and interpret the vertical
intercept, the horizontal intercepts, and the vertex.
Find an appropriate window on your graphing calculator in order to find
key points on the graph of a quadratic function.
Perform a composition of two functions both with specific numbers and
with variables.
Jul 04 & Jul 05
Composition & Inverses
Find the inverse of a given function using proper inverse function
notation.
Given a context and a function such as t-1(4)=20, be able to interpret the
equation in context.
Jul 06
FINAL EXAM
Math 110 Exam 4 Topics List – Summer II 2012
Date covered in class
Topic
Learning Objective
Write the general form of a power function and identify the parts of the
equation.
Identify if a function is directly or indirectly proportional given context,
an equation, a table, or a graph.
Write the general equation for a power function from context, solve for
the constant of proportionality, and give the specific equation
Jun 27 & Jun 28
Power Functions
Jun 29
Regression
Jun 30
Polynomial Functions
Sketch the graph of a power function for different powers (even/odd and
neg/pos) as well as for functions with either a positive or a negative
constant of proportionality.
Be able to identify and/or interpret the characteristics of each family of
functions (Directly and Indirectly Proportional Power functions)
including: intercepts, rates of change, asymptotes, end behavior, and
domain and range.
Use your calculator to find a curve/ line of best fit. (Remember to
reinitialize the independent variable when appropriate)
Identify the most appropriate model based both on technology and the
context of the situation.
Be able to identify and/or interpret the characteristics of each family of
functions (Polynomial functions) including: intercepts, rates of change,
asymptotes, end behavior, domain and range and max/min values.
Given any polynomial function, be able to identify the leading term and
the degree and use this information to give the global behavior, the # of
turning points, and the # of horizontal intercepts.
For any polynomial function, be able to identify and interpret the vertical
intercept, the horizontal intercepts, and the max/or min. value.
Find an appropriate window on your graphing calculator in order to find
key points on the graph of a polynomial function.
Jul 01
EXAM 4
Math 110 Exam 3 Topics List – Summer II 2012
Date covered in class
Topic
Jun 17 and Jun 20
Rules of exponents
Learning Objective
Simply expressions using the rules of exponents.
Be able to write the general form of an exponential equation and identify
the parts of the equation.
Intro. to Exponential Equations
Given a list of equations, be able to identify which equations represent a
linear function, which equations represent an exponential function, and
which are neither.
From a table, be able to determine which functions are linear, which are
exponential, and which are neither. Be able to justify your choice.
From a table, be able to write a linear and exponential equation.
Jun 20
Given a verbal description with a calendar year such as 1995, be able to
reinitialize the variable to read: years after 1995.
Explain why a linear function better models a relationship.
Writing exponential equations from
two points
Explain why an exponential function better models a relationship.
Create an exponential equation from 2 points, one of which is the initial
value.
Create an exponential equation given the initial value and a rate in
Exponential Equations - A constant percentage form.
% change
Given an exponential equation, be able to determine the rate as a
percentage and interpret this value in the context of the situation.
Jun 21
Match equations with graphs of exponential functions (growth and
decay).
Visualizing exponential functions Identify the end behavior for a given function.
Identify the asymptotes of a given function.
Rewrite a logarithmic equation into exponential form and vice versa.
Logarithms
Jun 22
Jun 23
Jun 24
Be able to solve for a variable in the exponent using logarithms.
Be able to identify and/or interpret the characteristics of each family of
Linear, Exponential, and Logarithmic
functions (Linear, Exponential, and Logarithmic) including: intercepts,
Functions
rates of change, asymptotes, end behavior, and domain and range.
Identify the parts of the financial formulas:
𝑟 𝑛𝑡
𝑦 = 𝑃0 (1 + )
𝑂𝑅 𝑦 = 𝑃0 𝑒 𝑟𝑡
𝑛
Financial Formulas
Write the appropriate equation using the financial formulas:
𝑟 𝑛𝑡
𝑦 = 𝑃0 (1 + )
𝑂𝑅 𝑦 = 𝑃0 𝑒 𝑟𝑡
𝑛
Be able to complete all questions on this set of notes.
Review
EXAM 3
Math 110 Exam 2 Topics List – Summer II 2012
Date covered in class
Topic
Jun 13
Piecewise Functions
Jun 14 & 15
Jun 15 & 16
Linear Systems
Linear Programming
Learning Objective
Write the equation for a piecewise function (from a table, graph, or
situation)
Given context, define variables, write a linear system, solve a linear
system (algebraically (substitution or elimination) and graphically), and
interpret the solution.
Given context, define variables, write an equation for the objective
function, write a system of inequalities (constraints), graph the system of
inequalities and shade the feasible region, find all corner points (using
substitution or elimination when needed), determine the combination
needed to maximize or minimize the objective function, and write a
conclusion statement for the problem.
Explain what the feasible region represents.
Explain what the corner points represent.
Jun 17
EXAM 2
Math 110 Exam 1 Topics List – Summer II 2012
Date covered in class
Topic
Ind/Dep Variables
Learning Objective
Define independent and dependent variables (labeling with ind/dep,
meaning, units, and letter)
Identify if a relationship is a function and justify with the definition of a
function
Demonstrate proper use of function notation
Jun 06
Definition of a function, Function Differentiate between the following statements: Evaluate f(0) and Solve
f(x)=0.
Notation
Given input, find output AND interpret the results
Given output, find input AND interpret the results
Transformations (shifts and
reflections)
Given an expression or a graph, be able to identify and apply
transformations (hor/vert shifts, reflections)
Given a table, graph, equation, or situation, be able to identify the
domain and range
Jun 07
Domain and Range
Average Rate of Change
Be able to use either interval or inequality notation to define the domain
and range
Calculate AND interpret the average rate of change
Given a table, graph, equation, or situation, be able to identify if the
function is a linear function
Write the equation of a linear function from a table, graph, or situation
Jun 08
Linear Functions
Given an initial value and slope, write the equation for a linear function
Given a linear function, identify AND interpret the slope and vertical
intercept in the context of the problem
Given any two points , be able to calculate the slope and the vertical
intercept and then write the equation using this information (saucy soda
factory question)
Differentiate between the vertical and horizontal intercept
Linear Functions
Find the horizontal intercept and interpret it in the context of the
situation
Jun 09
Find the domain and range of any linear function
View Tubes Lab
Jun 10
Apply all concepts above to real data. Analyze data to determine if data
can be represented by a linear function.
EXAM 1