Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Number
of Days
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Topic and Essential Questions
Additional Instructional
Resources
Matrices
5
Writing a matrix
AA1
 Dimensions
Websites –
www.kutasoftware.com for free
worksheets
Operations:
 Addition
AA1
 Subtraction
www.edhelper.com for free
worksheets
www.math.about.com for free
worksheets
 Scalar Multiplication
Matrix Multiplication
AA1
 Larger than a 3 X 3 on calculator only, all others
without the aid of a calculator
Determinants
 Larger than a 3 X 3 on calculator only, all others
without the aid of a calculator
AA2
 Meaning of a determinant of zero
Solving systems
 Write the system as a matrix
AA2
 Solve using an inverse matrix
 Larger than a 3 X 3 on calculator only, but write the
matrix equation
Applications involving matrices
 Area of a triangle
 Determine if points are collinear
AA2
 Cryptography
1
http://people.richland.edu/james
/lecture/m116/matrices/applicati
ons.html for applications
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Number
of Days
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Topic and Essential Questions
Conics
Additional Instructional
Resources
Websites –
Circle
10

Graph the Standard Form

Write the equation of a circle given information about
its center, radius, or diameter

Graph a circle from General Form

Find the x and y intercepts of the circle

Convert between Standard Form and General Form
AA3
Parabola
 Define a parabola using the focus and the directrix

Identify whether the parabola is horizontal or vertical
and how it opens

Graph A parabola – identify the vertex, focus, directrix
and latus rectum

Write the equation of a graph given the vertex, focus,
directrix or latus rectum
AA3
Ellipse

Define an ellipse using the foci

Identify whether the ellipse is horizontal or vertical

Graph the ellipse – identify the major/minor axes, the
center, the vertices, and the foci

Write the equation of the ellipse given the center, foci,
vertices, or axes

Find the x and y intercepts of the ellipse

Convert between Standard Form and General Form
2
AA3
http://math2.org/math/algebr
a/conics.htm to see pictures
of how the conic sections are
formed when a plane cuts
through a cone. This website
will also have the equations
for the conic sections.
To see some awesome pictures
of conics and to read about the
history of conics , visit
http://xahlee.org/SpecialPlane
Curves_dir/ConicSections_dir/
conicSections.html
This website has links to real
life applications of conic
sections including engineering,
physics, navigation, and roller
coaster design.
http://www.k12.hi.us/~mathap
pl/MAch3Curves.html
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Hyperbola

Define a hyperbola using the foci

Identify whether the hyperbola is horizontal or vertical

Graph the hyperbola –identify the center, vertices, foci
and the equations of the asymptotes

Write the equation of the hyperbola given information
about the center, vertices, foci or the equations of the
asymptotes

Find the x and y intercepts of the hyperbola

Convert between Standard Form and General Form
AA3
Sullivan Sec 1.2
Applications of conics

Solving systems of conics

Satellite dishes (parabola)

Orbits, whispering galleries (ellipses)
Visit this website for further
lessons on how to work conic
section problems. There are
also some real life applications
to be found here.
http://jwilson.coe.uga.edu/emt
669/student.Folders/Jones.Ju
ne/conics/conics.html
Sullivan Sec 9.2
Sullivan Sec 9.3
LOng RAnge Navigation system (LORAN) (hyperbola)
3
AA4
Sullivan Sec 9.4
Sullivan at the end of each
section
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Introduction to trigonometry
Angles
2

Define angle, including its initial and terminal sides

Identify the direction of rotation for angles to be
positive and negative

Define standard position of an angle, direction of
rotation, quadrant in which an angle lies, and
quadrantal angles

Draw angles of varying measures
Sullivan Sec 5.1
Sullivan Sec 5.1
AA5
Sullivan Sec 5.1
Sullivan Sec 5.2
Sullivan Sec 5.3
Sullivan Sec 5.4 – 5.6
4
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Quarter 2
Number
of Days
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Topic and Essential Questions
Angle Measurements
Additional Instructional
Resources
Websites –

Define radian
AA5
www.funmaths.com/worksheets

Use the Arc Length and Area of a Sector Theorems
to solve problems
AA7
www.analyzemath.com/trigonometry

Convert from radians to degrees and back
AA5

Use unit analysis to solve problems involving linear
speed, rotational speed and angular speed
AA6
3
Unit Circle

10
Use the concepts of the special right triangles to
create the Unit Circle
AA5
a. Reproduce the Unit Circle without aid of a
calculator

Define the six trigonometric functions

Find the six trigonometric functions
AA8
AA8, AA9
a. in terms of the coordinates of any point on the
Unit Circle
b. using a calculator
c. in terms of the coordinates of any point on a
circle of radius r
d. given the coordinates of any point on the
terminal side of an angle

Write the following fundamental identities:
AA11
a. reciprocal identities
5
www.onlinemathlearning.com/tri
gonometry
www.kutasoftware.com
www.ti.com
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
b. quotient identities
c. Pythagorean identities

AA12
Solve problems by finding values of the six
trigonometric functions
a. using even-odd properties to find the exact
values of the trigonometric functions
b. using fundamental trigonometric identities
c. given one of the functions and the quadrant of
the angle

AA8
Determine the signs of the trigonometric functions
in each quadrant
Graphing Trigonometric Functions
5

State the domain, range, and periodicity of the
trigonometric functions

Graph the sine and cosine functions as parent
functions
a. identify the properties of the sine and cosine
graphs
b. use the sine and cosine graphs to develop and
explain the graphs of the remaining
trigonometric functions

AA10
Use knowledge of transformations to graph general
form of trigonometric equations in the form
y  A sin( Bx  C )  D
a. describe how changes in amplitude, period, phase
shifts, and vertical shifts affect sine and cosine
graphs from a practical application standpoint
b. determine the amplitude, period, phase shift, and
vertical shift of trigonometric functions and
6
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
their graphs
c. write a sine or cosine function that satisfies a
given data set allowing for amplitude, period,
phase shift, and vertical shift
End material for Semester Exam
Quarter 3
Inverse Trigonometric Functions
7

Define the inverse of each of the six trigonometric
functions, to include restricted domain and range

Find the exact value of the inverse trigonometric
functions using

graphing calculators

unit circle

composite trigonometric functions

Establish/verify trigonometric identities

Solve trigonometric equations using
AA11
a. Sum and Difference Formulas
b. Double and half Angle Formulas
c. Graphing on calculators
d. Factoring
7
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Number
of Days
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Topic and Essential Questions
Applications of Trigonometric Functions

Solve right triangles

Solve oblique triangles using
a. Law of Sines
5
AA13
b. Law of Cosines

Find the area of triangles using
a. Heron’s formula

Two sides and the sine of the included angle
8
Additional Instructional
Resources
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Number
of Days
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Topic and Essential Questions
Websites –
Exponential and Logarithmic Functions
8

Rewrite exponential expressions as logarithmic
expressions and vice versa

Evaluate exponential and logarithmic
expressions

Apply properties of logarithms to express in
expanded/condensed form

Use the change of base formula to evaluate
logarithms whose base in neither 10 nor e
www.kutasoftware.com
AA14
By comparing exponents when the bases match

Rewriting equations so that the bases match

Rewriting as a logarithmic equation

Taking the logarithms of both sides
www.ti.com
Sullivan Sec 4.2
AA14
Comparing arguments when the bases match

Rewriting as an exponential equation

Using the change of base formula

Solve literal logarithmic equations
Sullivan Sec 4.6
Sullivan Sec 4.7
Solving Logarithmic Equations

www.onlinemathlearning.com/ex
ponential-logarithmic.html
www.analyzemath.com
Solving Exponential Functions

Additional Instructional
Resources
Sullivan Sec 4.8
AA14
(Emphasis is to be given to checking solutions for
extraneous solutions in the domain)
9
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Using the graphing calculator

Use a graphing calculator to approximate the
value of non-rational solutions to exponential
and logarithmic equations

Use a graphing utility to fit data to an
exponential function

Use a graphing utility to fit data to a
logarithmic function
6
AA14
Applications

Determine the future value or present value of a
lump sum of money

Determine the time required for a lump sum of
money to double or triple

Find equations of populations that obey the law
of decay/growth

Use Newton’s Law of Cooling

Logistic Growth Models
10
AA14
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Number
of Days
Topic and Essential Questions
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Sequences and Series:
5

Sigma Notation
AA15

Applications
AA15

*Mathematical Induction
AA16

*The Binomial Theorem
AA17
(*May be moved until after Trigonometry)
11
Additional Instructional
Resources
Sullivan Sec 11.1
Sullivan Sec 11.1 – 11.3
Sullivan Sec 11.4
Sullivan Sec 11.5
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
Number
of Days
Topic and Essential Questions
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
LIMITS
Additional Instructional
Resources
Websites –
Finding Limits by Inspection
8

Find a limit numerically (using a table of values)

Find a limit graphically

Find the limit of a polynomial

Find the limit of a power or root
http://www.coolmath.com/lesso
n-whats-a-limit-1.htm
http://www.analyzemath.com/c
alculus/limits/introduction.html
Finding Limits Analytically

Find a limit by simplifying rational expressions, adding
fractions, multiplying numerator and denominator by a
conjugate

Find one-sided limits of a function (numerically,
graphically, analytically)

Find limits at infinity (numerically, graphically,
analytically)
http://www.analyzemath.com/c
alculus_worksheets/limits/limit
_1.pdf
http://www.themathpage.com/a
Calc/limits.htm
Application of Limits

Use limits to determine if a function is continuous at a
point

Find the limit of an average rate of change

Write the equation of the tangent line to a graph at a
point
Using Graphing Utilities

Use a graphing utility to find a limit numerically and
graphically

Use a graphing utility to verify the equation of the
tangent line to a graph at a point
12
http://www.sosmath.com/calcul
us/limcon/limcon04/limcon04.h
tml
Advanced Algebra (Precalculus) Scope and Sequence (Proposed)
13