ARKANSAS
ALGEBRA II MATHEMATICS
CURRICULUM FRAMEWORK
Correlated to
ALGEBRA 2
© 2004
4201 Woodland Road • Circle Pines, Minnesota 55014-1796 • Telephone (651) 287-7220 or (800) 328-2560 • www.agsnet.com
ARKANSAS: ALGEBRA II
STRAND: Relations and Functions
Content Standard 1: Students will represent and analyze mathematical situations and properties using
patterns, relations, functions and algebraic symbols.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
RF.1.AII.1
Determine, with or without
technology, the domain and range of
a relation defined by a graph, a table
of values, or a symbolic equation
including those with restricted
domains and whether a relation is a
function
Pages 37-38, 45, 460-462
RF.1.AII.2
Evaluate, add, subtract, multiply,
divide and compose functions and
give appropriate domain and range
restrictions
Pages 36-38, 39-42, 43-44, 45-47,
417-419, 420-422, 423-425, 426-429
RF.1.AII.3
Determine the inverse of a function
(Graph, with and without appropriate
technology, functions and their
inverses)
Pages 243-245, 248-251
RF.1.AII.4
Analyze and report, with and without
appropriate technology, the effect of
changing coefficients, exponents,
and other parameters on functions
and their graphs (linear, quadratic,
and higher degree polynomial)
Pages 45-48, 49-51, 52-53, 92-96,
110-112, 113-117, 118-121
RF.1.AII.5
Determine, with and without
appropriate technology, whether a
function is even, odd or neither to
analyze the behavior of a graph
Pages 113-117, 118-121, 122-126
RF.1.AII.6
Graph, with and without appropriate
technology, functions defined as
piece-wise and step
RF.1.AII.7
Apply the concepts of functions to
real world situations
1
Pages 42, 234, 251, 429
(Arkansas, Algebra II/AGS Algebra 2, Cont.)
STRAND: Linear and Absolute Value Equations and Inequalities
Content Standard 2: Students will analyze and apply various methods to model, graph and solve linear
and absolute value equations and inequalities.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
LEI.2.AII.1
Translate linear equations from one
form (slope-intercept, point-slope,
and standard) to another
Pages 48-51, 52-53, 59-60
LEI.2.AII.2
Develop, write, and graph, with and
without appropriate technology,
equations of lines in slope-intercept,
point-slope, and standard forms
given
• a point and the slope
• two points
• real world data
Pages 48-51, 52-53, 54-58, 59-60,
61-63
LEI.2.AII.3
Develop, write and graph (given the
point and the slope, two points, or a
point and a line) equations of
• a parallel line
• a perpendicular line
• a perpendicular bisector of a
segment
Pages 45, 49-51, 64-65
LEI.2.AII.4
Solve, with and without appropriate
Pages 24-25, 26-27
technology, absolute value equations
and inequalities written in one or two
variables, and graph solutions
LEI.2.AII.5
Solve, with and without appropriate
technology, systems of linear
equations and systems of linear
inequalities with two or more
variables through the use of graphs,
tables, matrices, and other algebraic
methods
2
Pages 135-138, 139-141
(Arkansas, Algebra II/AGS Algebra 2, Cont.)
STRAND: Linear and Absolute Value Equations and Inequalities
Content Standard 2, Cont.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
LEI.2.AII.6
Develop and apply, with and without
appropriate technology, the basic
operations and properties of matrices
(associative, commutative, identity,
and inverse)
See instruction on the identity
function on pages 428-429, and on
inverse functions on pages 243-245,
336-339. Basic matrices are covered
in AGS Algebra.
LEI.2.AII.7
Apply, with or without technology,
the concepts of linear and absolute
value equations and inequalities and
systems of linear equations and
inequalities to model real world
situations including linear
programming
Pages 25, 27, 41, 42, 51, 58, 66, 139141, 144
STRAND: Quadratic Equations and Functions
Content Standard 3: Students will use algebraic, graphical, and numerical methods to analyze,
compare, translate, and solve quadratic equations.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
QEF.3.AII.1
Perform computations with radicals
• simplify radicals with
different indices
• add, subtract, multiply and
divide radicals
• rationalize denominators
• solve equations that contain
radicals or radical
expressions
Pages 207-209, 210-211, 212-214,
215-218, 224-225
QEF.3.AII.2
Extend the number system to include
the complex numbers
• evaluate powers of I
• add, subtract, multiply, and
divide complex numbers
• rationalize denominators
Pages 97-100, 212, 404-407, 408410, 411-412
(Arkansas, Algebra II/AGS Algebra 2, Cont.)
3
STRAND: Quadratic Equations and Functions
Content Standard 3, Cont.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
QEF.3.AII.3
Solve quadratic equations with and
without appropriate technology by
• extracting the square root
• graphing
• factoring
• completing the square
• using the quadratic formula
Pages 72-74, 75-78, 79-80, 81-82,
83-85, 86-88, 89-91, 92-96, 97-100,
210-211, 212-214, 215-218, 295299, 300-305
QEF.3.AII.4
Develop and analyze, with and
without appropriate technology,
quadratic relations
• graph a parabolic
relationship when given its
equation
• write an equation when given
its roots (zeros or solutions)
or graph
• determine the nature of the
solutions graphically and by
evaluating the discriminant
• determine the maximum or
minimum values and the axis
of symmetry both graphically
and algebraically
Pages 97-100, 113-117, 118-121,
122-126, 130-134, 142-143, 207209, 210-211, 215-218, 295-299,
300-305
QEF.3.AII.5
Apply the concepts of quadratic
equations and functions to model
real world situations by using
appropriate technology when needed
Pages 78, 88, 92, 95, 139-140, 144
4
(Arkansas, Algebra II/AGS Algebra 2, Cont.)
STRAND: Polynomial and Rational Functions
Content Standard 4: Students will use algebraic, graphical, and numerical methods to analyze,
compare, translate, and solve polynomial and rational equations.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
PRF.4.AII.1
Determine the factors of polynomials
by
• using factoring techniques
including grouping and the
sum or difference of two
cubes
• using long division
• using synthetic division
Pages 157-159, 162-163, 164-168
PRF.4.AII.2
Develop and analyze, with and
without appropriate technology,
polynomial functions from their
roots, graphs, or equations
• write an equation when given
its factors or roots (zeros or
solutions)
• determine the x- and yintercepts
• describe the end behaviors
• sketch the graph
Pages 39-42, 43-44, 45-47, 54-58,
59-60, 61-63, 86-88, 89-91, 92-95,
97-100, 110-112, 113-117, 118-121,
122-126, 127-129, 130-134
PRF.4.AII.3
Solve, with and without appropriate
technology, polynomial equations,
including real world situations,
graphically, numerically (using
tables), and algebraically
Pages 150-152, 153-156, 160-161,
162-163, 164-168
PRF.4.AII.4
Simplify, add, subtract, multiply, and
divide with rational expressions
Pages 180-182, 183-185, 186, 187188
PRF.4.AII.5
Graph, with and without appropriate
technology, rational functions of the
form y = 1/x and y = 1/x2 and their
transformations and identify x- and
y- intercepts, domain restrictions,
and vertical asymptotes
Pages 285-289, 293-294
5
(Arkansas, Algebra II/AGS Algebra 2, Cont.)
STRAND: Polynomial and Rational Functions
Content Standard 4, Cont.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
PRF.4.AII.6
Solve, with and without appropriate
technology, problems using rational
equations, including proportions,
rate, and variation (direct,
inverse(indirect), or joint) and real
world problems
Pages 66, 183-185, 186, 187-188,
189-191, 454-456
PRF.4.AII.7
Establish the relationship between
radical expressions and expressions
containing rational exponents
Pages 212-214, 215-218
PRF.4.AII.8
Simplify variable expressions
containing rational exponents using
the laws of exponents
Pages 213-214
STRAND: Exponential and Logarithmic Functions
Content Standard 5: Students will graph exponential functions and relate them to logarithms. They
will solve real world problems using exponential functions.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
ELF.5.AII.1
Interpret and graph, with and without
appropriate technology, exponential
functions
Pages 232-234, 235-236, 241-242
ELF.5.AII.2
Solve, with and without appropriate
technology, exponential equations,
including real world problems
Pages 239-240
ELF.5.AII.3
Establish the relationship between
exponential and logarithmic
functions
Pages 246-247, 248-251
ELF.5.AII.4
Evaluate simple logarithms using the
definition (Ex. log 3 81)
Pages 248-251, 252-253
6
(Arkansas, Algebra II/AGS Algebra 2, Cont.)
STRAND: Data Analysis and Probability
Content Standard 5: Students will evaluate and interpret data, make predictions based on data, and
apply basic understanding of probability to solve real world problems.
STUDENT LEARNING EXPECTATIONS:
AGS ALGEBRA 2
DAP.6.AII.1
Interpret and evaluate, with and
without appropriate technology,
graphical and tabular data displays
for
• consistency with the data
• appropriateness of type of
graph or data display
• scale
• overall message
Pages 457-459, 460-461
DAP.6.AII.2
Calculate, with and without
appropriate technology, probabilities
of events using the laws of
probability
• apply the Fundamental
Counting Principle
• distinguish between and use
permutations and
combinations
• calculate conditional
probability
• calculate probabilities of
mutually exclusive events,
independent events, and
dependent events
Pages 376-379
7