Math
Precalculus
Unit One
Length of
Unit
4 Weeks
Core Content
A-CED 1
A-CED 2
A-REI 3
F-IF 1
F-IF 2
F-IF 3
F-IF 4
F-IF 5
F-IF 7
F-LE 1
F-EL 5
Rowan County Senior High School 2010-2011
2011-2012
Linear Relations and Functions
Key Concepts/Skills/Guiding Questions
Activities/Assessments/
Resources
Terms:
Abscissa, absolute value function, boundary, coinciding lines,
composite, composition of functions, constant function, domain,
family of graphs, function, function notation, greatest integer
function, half plane, iterate, iteration, linear equation, linear
function, linear inequality, ordinate, parallel lines, perpendicular
lines, piecewise function, point-slope form, range, relation,
slope, slope-intercept form, standard form, step function, vertical
line test, x-intercept, y-intercept, zero of a function, best-fit line,
correlation coefficient, goodness of fit, model, pearson-product
moment correlation, prediction equation, regression line, scatter
plot
Students will:
 Determine whether a given relation is a function
 Identify the domain and range of a relation or function
 Evaluate functions
 Perform operations with functions
 Find composite functions
 Iterate functions using real numbers
 Graph linear equations
 Find the x- and y-intercepts of a line
 Find the slope of a line through two points
 Find zeros of linear functions
 Investigate the effect of changing the value of m or b in
y = mx + b
 Write linear equations
 Write equations of parallel and perpendicular lines
 Draw and analyze scatter plots
 Write a prediction equation and draw best-fit lines
 Use a graphing calculator to compute correlation
coefficients to determine goodness of fit
 Solve problems using prediction equation models
 Identify and graph piecewise functions including
greatest integer, step, and absolute value functions
 Graph linear inequalities
Pre-test
Intentional Review with Bell Ringers
Word Wall
Think-Pair Share
Anticipation Guides
Admit/exit slips
Jigsaw
Double entry organizer
Note-taking Guide
Win-plot
TI-84 graphing calculator
Power point presentations
Post-test
Page 1
Math
Precalculus
2011-2012
Guiding Questions
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Rowan County Senior High School 2010-2011
How can I determine whether a given relation is a
function?
How can I identify the domain and range of a relation or
function?
How can I evaluate functions?
How can I perform operations with functions?
How do I find composite functions?
How can I iterate functions using real numbers?
How do I graph linear equations?
How can I find the x- and y-intercepts of a line?
How can I find the slope of a line through two points?
How can I find zeros of linear functions?
How can I investigate the effect of changing the value of
m or b in y = mx + b?
How can I write linear equations?
How can I write equations of parallel and perpendicular
lines?
How can I draw and analyze scatter plots?
How can I write a prediction equation and draw best-fit
lines?
How can I use a graphing calculator to compute
correlation coefficients to determine goodness of fit?
How can I solve problems using prediction equation
models?
How can I identify and graph piecewise functions
including greatest integer, step, and absolute value
functions?
How can I graph linear inequalities?
Page 2
Math
Precalculus
Unit Two
Length of
Unit
Core Content
4 Weeks
F-IF 4
F-IF 7
F-IF 8
F-IF 9
F-BF 3
F-BF 4
Rowan County Senior High School 2010-2011
2011-2012
The Nature of Graphs
Key Concepts/Skills/Guiding Questions
Terms:
Absolute maximum, absolute minimum, asymptotes, constant
function, constant of variation, continuous, critical point,
decreasing function, direct variation, discontinuous, end behavior,
even function, everywhere discontinuous, extremum, horizontal
asymptote, horizontal line test, image point, increasing function,
infinite discontinuity , inverse function, inverse process, inversely
proportional, inverse relations, joint variation, jump discontinuity,
line symmetry, maximum, minimum, monotonicity, off function,
parent graph, point discontinuity, point of inflection, point
symmetry, rational function, relative extremum, relative maximum,
relative minimum, slant asymptote, symmetry with respect to the
origin, vertical asymptote
Students will
 Use algebraic tests to determine whether the graph of a
relation is symmetrical
 Classify functions as even or odd
 Identify transformations of simple graphs
 Sketch graphs of related functions
 Graph polynomial, absolute value, and radical inequalities
in two variables
 Solve absolute value inequalities
 Determine inverses of relations and functions
 Graph functions and their inverses
 Determine whether a function is continuous or
discontinuous
 Identify the end behavior of functions
 Determine whether a function is increasing or decreasing
on an interval
 Construct and graph functions with gap discontinuities
 Find the extrema of a function
 Graph rational functions
 Determine vertical, horizontal, and slant asymptotes
 Solve problems involving direct, inverse, and joint
variation
Activities/Assessments/
Resources
Pre-test
Intentional Review with Bell Ringers
Word Wall
Think-Pair Share
Anticipation Guides
Admit/exit slips
Jigsaw
Double entry organizer
Note-taking Guide
Win-plot
TI-84 graphing calculator
Power point presentations
Post-test
Page 3
Math
Precalculus
2011-2012
Guiding Questions
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Rowan County Senior High School 2010-2011
How will I use algebraic tests to determine whether the
graph of a relation is symmetrical?
How will I classify functions as even or odd?
How will I identify transformations of simple graphs?
How will I sketch graphs of related functions?
How will I graph polynomial, absolute value, and radical
inequalities in two variables?
How will I solve absolute value inequalities?
How will I determine inverses of relations and functions?
How will I graph functions and their inverses?
How will I determine whether a function is continuous or
discontinuous?
How will I identify the end behavior of functions?
How will I determine whether a function is increasing or
decreasing on an interval?
How will I construct and graph functions with gap
discontinuities?
How do I find the extrema of a function?
How can I graph rational functions
How can I determine vertical, horizontal, and slant
asymptotes?
How can I solve problems involving direct, inverse, and
joint variation?
Page 4
Math
Precalculus
Unit Three
Length of
Unit
4 Weeks
Core Content
F-IF 7
F-IF 8
F-BF 5
F-LE 2
F-LE 3
F-LE 4
F-LE 5
Rowan County Senior High School 2010-2011
2011-2012
Exponential and Logarithmic Functions (ch 11)
Key Concepts/Skills/Guiding Questions
Terms:
Antiln x, antilogarithm, characteristic, common logarithm,
doubling time, exponential decay, exponential function,
exponential growth, ln x, logarithm, logarithmic function,
mantissa, natural logarithm, power function, scientific notation,
linearizing data, nonlinear regression
Students will
 Use the properties of exponents
 Evaluate and simplify expressions containing rational
exponents
 Solve equations containing rational exponents
 Graph exponential functions and inequalities
 Solve problems involving exponential growth and decay
 Use the exponential function y = ex
 Evaluate expressions involving logarithms
 Solve equations and inequalities involving logarithms
 Graph logarithmic functions and inequalities
 Find common logarithms and antilogarithms of numbers
 Solve equations and inequalities using common
logarithms
 Solve real-world applications with common logarithmic
functions
 Graph logarithmic functions and inequalities
 Find common logarithms and antilogarithms of numbers
 Solve equations and inequalities using natural
logarithms
 Solve real-world applications with natural logarithmic
functions
 Investigate the relationship between area of regions
below the graph of y=1/x
 Find the doubling time of an exponential quantity
 Find exponential and logarithmic functions to model
real-world data
 Linearize data
Activities/Assessments/
Resources
Pre-test
Intentional Review with Bell Ringers
Word Wall
Think-Pair Share
Anticipation Guides
Admit/exit slips
Jigsaw
Double entry organizer
Note-taking Guide
Win-plot
TI-84 graphing calculator
Power point presentations
Post-test
Page 5
Math
Precalculus
2011-2012
Guiding Questions
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Rowan County Senior High School 2010-2011
How can I use the properties of exponents?
How can I evaluate and simplify expressions containing
rational exponents?
How can I solve equations containing rational
exponents?
How can I graph exponential functions and inequalities?
How can I solve problems involving exponential growth
and decay?
How can I use the exponential function y = e x?
How can I evaluate expressions involving logarithms?
How can I solve equations and inequalities involving
logarithms?
How can I graph logarithmic functions and inequalities?
How can I find common logarithms and antilogarithms of
numbers?
How can I solve equations and inequalities using
common logarithms?
How can I solve real-world applications with common
logarithmic functions?
How can I graph logarithmic functions and inequalities?
How can I find common logarithms and antilogarithms of
numbers?
How can I solve equations and inequalities using natural
logarithms?
How can I solve real-world applications with natural
logarithmic functions?
How can I investigate the relationship between area of
regions below the graph of y=1/x?
How can I find the doubling time of an exponential
quantity?
How can I find exponential and logarithmic functions to
model real-world data?
How can I linearize data?
Page 6
Math
Precalculus
Unit Six
Length of
Unit
2 Weeks
Core Content
F-IF 6
2011-2012
Introduction to Calculus (ch 15)
Key Concepts/Skills/Guiding Questions
Terms:
Antiderivative, definite integral, derivative, differentiation,
Fundamental Theorem of Calculus, indefinite integral, integral,
integration, limit, rate of change, secant line, slope of a curve,
tangent line
Students will
 Calculate limits of polynomial and rational functions
algebraically
 Evaluate limits of functions using a calculator
 Approximate the slope of a curve
 Find derivatives and antiderivatives of polynomial
functions
 Use derivatives and antiderivatives in applications
 Find values of integrals of polynomial functions
 Find areas under graphs of polynomial functions
 Use the Fundamental Theorem of Calculus to evaluate
definite integrals of polynomial functions
Activities/Assessments/
Resources
Pre-test
Intentional Review with Bell Ringers
Word Wall
Think-Pair Share
Anticipation Guides
Admit/exit slips
Jigsaw
Double entry organizer
Note-taking Guide
Win-plot
TI-84 graphing calculator
Power point presentations
Post-test
Guiding Questions
 How can I calculate limits of polynomial and rational
functions algebraically?
 How can I evaluate limits of functions using a
calculator?
 How can I approximate the slope of a curve?
 How can I find derivatives and antiderivatives of
polynomial functions?
 How can I use derivatives and antiderivatives in
applications?
 How can I find values of integrals of polynomial
functions?
 How can I find areas under graphs of polynomial
functions?
 How can I use the Fundamental Theorem of Calculus to
evaluate definite integrals of polynomial functions?
Rowan County Senior High School 2010-2011
Page 7
Math
Rowan County Senior High School 2010-2011
Precalculus
2011-2012
Page 8