Lakewood City Schools
Course: Precalculus with trigonometry
Revised: July 2008
Full Year, one credit, 5 periods per week, 10th, 11th, & 12th grade
Precalculus with trigonometry is an elective mathematics course taken after algebra 2. It covers the
mathematical functions (polynomial, exponential, logarithmic, and trigonometric), systems of equations
and inequalities, sequences and series, limit and the derivative. These are all necessary for the
understanding of calculus. This course will integrate a graphing calculator in all topics.
Lakewood City Schools
Course: Precalculus with trigonometry
Revised: July 2008
Pacing Chart
First quarter:
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Chapter 1-Graphs [1-1 to 1-4]
Chapter 2-Functions and Their Graphs [2-1 to 2-7]
Chapter 3-Polynomial and Rational Functions [3-1 to 3-7]
Second quarter:
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

Chapter 4-Exponential and Logarithmic Functions [4-1 to 4-8]
Chapter 5-Trigonometric Functions [5-1 to 5-6]
Chapter 6-Analytical Trigonometry [6-1 to 6-4]
Third quarter:
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


Chapter 6-Analytical Trigonometry [6-5,6-7,6-8]
Chapter 7-Applications of Trigonometry [7-1 to 7-4]
Chapter 8-Polar Coordinates [8-1 to 8-3]
Chapter 10-Systems of Equations and Inequalities [10-1 to 10-4,10-6,10-7]
Fourth quarter:
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
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Chapter 10-Systems of Equations and Inequalities [10-8]
Chapter 11-Sequences, Inductions, and the Binomial Theorem [11-1 to 11-5]
Chapter 13- Limits and Derivatives [13-1 to 13-5]
Chapter 12-Counting and Probability [12-1 to 12-3]—if time
One week review for the final exam
Currently all teacher resources will refer to the book Precalculus by Michael Sullivan and Michael
Sullivan, III (copyright 2006), unless otherwise noted. The recommended graphing calculator is the TI84.
11-12 Benchmark
A. Create and analyze
tabular and graphical
displays of data using
appropriate tools,
including spreadsheets
and graphing calculators
Data Analysis Grade 11
Grade Level Indicator
11D4 Create a scatter plot of
bivariate data, identify trends,
and find a function to model the
data
11D5 Use technology to find the
Least Squares Regression Line,
the regression coefficient, and
the correlation coefficient for
bivariate data with a linear trend,
and interpret each of these
statistics in the context of the
problem situation
11D7 Describe the standard
normal curve and its general
properties, and answer questions
dealing with data assured to be
normal
11D8 Analyze and interpret
univariate and bivariate data to
identify patterns, note trends,
draw conclusions and make
predications
B. Use descriptive
statistics to analyze and
summarize data,
including measures of
center, dispersion,
11D10 Understand and use the
concept of random variable and
compute and interpret the
expected value for a random
variable in simple cases
11D3 Describe how a linear
transformation of univariate data
affects range, mean, mode, and
median
Teacher Resources
2-2,5-6
2-4
correlation and
variability
11D5 Use technology to find the
Least Squares Regression Line,
the regression coefficient, and
the correlation coefficient for
bivariate data with a linear trend,
and interpret each of these
statistics in the context of the
problem situation
11D6 Use technology to compute
the standard deviation for a set
of data and interpret standard
deviation in relation to the
context or problem situation
11D8 Analyze and interpret
univariate and bivariate data to
identify patterns, note trends,
draw conclusions, and make
predictions
C. Design and perform a
statistical experiment,
simulation or study;
collect and interpret
data; and use descriptive
statistics to
communicate and
support predications and
conclusions
11D1 Design a statistical
experiment, survey or study for a
problem; collect data for the
problem; interpret data with
appropriate graphical displays,
descriptive statistics, concepts of
variability, causation, correlation
and standard deviation
11D2 Describe the role of
randomization in a well-designed
study, especially as compared to
a convenience sample, and the
generalization of results from
each
D. Connect statistical
techniques to
applications and
consumer situations
11D9 Evaluate validity of results
of a study based on
characteristics of the study
design, including sampling
method, summary statistics and
data analysis techniques
11D1 Design a statistical
experiment, survey or study for a
problem; collect data for the
problem; interpret data with
2-4
appropriate graphical displays,
descriptive statistics, concepts of
variability, causation, correlation
and standard deviation
11D2 Describe the role of
randomization in a well-designed
study, especially as compared to
a convenience sample, and the
generalization of results from
each
11D9 Evaluate validity of results
of a study based on
characteristics of the study
design, including sampling
method, summary statistics and
data analysis techniques
11D11 Examine statements and
decisions involving risk; e.g.,
insurance rates and medical
decisions
11-12 Benchmark
A. Use trigonometric
relationships to verify and
determine solutions in
problem situations
B. Represent transformations
within a coordinate system
using vectors and matrices
Geometry and Spatial Sense Grade 11
Grade Level Indicator
Teacher Resources
11G4 Use trigonometric
7-1,7-2,7-3,7-4
relationships to determine
lengths and angle measures
11G1 Use polar coordinates to
specify locations on a plane
11G2 Represent translations
using vectors
11G3 Describe multiplication of a
vector and a scalar graphically
and algebraically and apply to
problem situations
8-1,8-2
11-12 Benchmark
A. Explain differences
among accuracy , precision
and error, and describe
how each of those can
affect solutions in
measurement situations
B. Apply various
measurement scales to
describe phenomena and
solve problems
C. Estimate and compute
areas and volume in
increasingly complex
problem situations
D. Solve problem
situations involving derived
measurements
Measurement Grade 11
Grade Level Indicator
11M1 Determine the number
of significant digits in a
measurement
Teacher Resources
11M2 Use radian and degree
measures to solve problems
and perform conversions as
needed
11M3 Derive a formula for the
surface area of a cone as a
function of its slant height and
the circumference of its base
5-1,5-2,5-3,6-1,6-2,7-1,7-2,7-3,7-4
11M4 Calculate distances,
areas, surface areas and
volumes of composite threedimensional objects to a
specified number of significant
digits
11M5 Solve real-world
problems involving area,
surface area, volume and
density to a specified degree of
precision
1-1,1-2
1-1,1-2
Number, Number Sense and Operations Grade 11
11-12 Benchmark
Grade Level Indicator
Teacher Resources
A. Demonstrate that vectors 11N1 Determine what properties hold 10-2
and matrices are systems
for matrix addition and matrix
having some of the same
multiplication; e.g., use examples to
properties of the real
show addition is commutative and
number system
when multiplication is not
commutative
11N2 Determine what properties hold
for vector addition and multiplication,
and for scalar multiplication
B. Develop an
understanding of properties
of representations for
addition and multiplication
of vectors and matrices
11N1 Determine what properties hold
for matrix addition and matrix
multiplication; e.g., use examples to
show addition is commutative and
when multiplication is not
commutative
10-2
11N2 Determine what properties hold
for vector addition and multiplication,
and for scalar multiplication
C. Apply factorials and
exponents, including
fractional exponents, to
solve practical problems
D. Demonstrate fluency in
operations with real
numbers, vectors and
matrices, using mental
computation or paper and
pencil calculations for simple
cases and technology for
more complicated cases
11N5 Model, using the coordinate
plane, vector addition and scalar
multiplication
10-4
11N8 Use fractional and negative
exponents as optional ways of
representing and finding solutions for
problem situations
11N4 Use matrices to represent given
information in a problem situation
4-3,4-7,4-8
11N6 Compute sums, differences, and
products and quotients of matrices
using paper and pencil calculations for
simple cases and technology for more
complicated cases
10-4
11N9 Use vector addition and scalar
multiplication to solve problems
10-2,10-4
E. Represent and compute
with complex numbers
11N3 Represent complex numbers in
the complex plane
1N7 Compute sums, differences,
products and quotients of complex
numbers
8-3
8-3
11-12 Benchmark
A. Analyze functions by
investigating rates of
change, intercepts, zeros,
asymptotes and local and
global behavior
Patterns Functions and Algebra Grade 11
Grade Level Indicator
11P3 Describe and compare the
characteristics of the following families of
functions: quadratics with complex roots,
polynomials of any degree, logarithms, and
rational functions; e.g, general shape,
number of roots, domain and range,
asymptote behavior
Teacher Resources
2-1,2-2,2-3,2-4,2-5,3-1,32,3-3,3-4,3-6,3-7,4-3,4-4,4-5
11P4 Identify the maximum and minimum
points of a polynomial, rational and
trigonometric functions graphically and
with technology
2-3,3-1,3-2,3-3,3-4,5-4,55,5-6,6-1,6-2
11P5 Identify families of functions with
graphs that have rotation symmetry or
reflection symmetry about the y-axis, xaxis or y = x
1-1,3-1,8-2
11P6 Represent the inverse of a function
symbolically and graphically as a reflection
about y=x
4-2,4-4,6-1,6-2
11P10 Describe the characteristics of the
graphs of conic sections
1-5,10-6
11P11 Describe how a change in the value
of a constant in an exponential,
logarithmic or radical equation affects the
graph of the equation
3-4,4-3,4-4,4-6
12P1 Analyze the behavior of arithmetic
and geometric sequences and series as the
number of terms increases.
11-2,11-3
B. Use the quadratic
formula to solve quadratic
equations that have
complex roots
C. Use recursive functions
to model and solve
problems
D. Apply algebraic
methods to represent and
generalize problem
situations involving vectors
and matrices
12P2 Translate between the numeric and
symbolic form of a sequence or series
11-1,11-2,11-3
12P7 Make arguments using the concepts
of limit.
13-1,13-2
12P9 Translate freely between polar and
Cartesian coordinate systems.
8-1
12P10 Use the concept of limit to find
instantaneous rate of change for a point
on a graph as the slope of a tangent point.
13-2,13-3
11P8 Solve equations involving radical
expressions and complex roots
1-3,4-6,6-7,6-8,10-6
11P1 Identify and describe problem
situations involving an iterative process
that can be represented as a recursive
formula; e.g., compound interest
4-7,11-1
11P2 Translate a recursive function into a
closed form expression or formula for the
nth term to solve a problem situation
involving an iterative process
11-1,11-2,11-3
11P7 Model and solve problems with
matrices
10-2,10-3,10-4
11P9 Solve 3x3 systems of linear equations
by elimination and using technology and
interpret graphically what the solution
means
10-1