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Algebra II

Idaho Department of Education Objective Sub Objectives Task Analysis Essential Vocabulary
Content Standards
Cognitive level codes:
• B: Memorize
• C: Perform procedures
• D: Demonstrate understanding
• E: Conjecture, generalize, prove
• F: Solve non-routine problems, make connections
Bloom's Equivalent
• B = Knowledge
• C = Comprehension
• D = Comprehension
• E = Application and Analysis
• F = Synthesis
Calculator codes:
• NO: student MUST NOT have a calculator while
completing this item in order to assess this objective.
Standard 1: Number and Operation
Goal 1.1: Understand numbers, ways
of representing numbers, relationships
among numbers, and number systems.
AII.1.1.1 Compare and contrast the properties of
numbers and number systems within the complex
number system to include rational, irrational, and
imaginary numbers and factorials.
• Compare and contrast the properties of numbers and
number systems within the complex number system to
include rational, irrational, and imaginary numbers and
factorials.
• Define and explain the meaning of i s a solution to

the equation x² = -1.
- The square root of -1 is the basis of the imaginary
number system.
• Identify expressions of the form a + bi as complex
numbers.
- Every real number, a, is a complex number
expressed as a + 0i.
- Identify the real element and the imaginary
element of a complex number.
• Divide complex numbers using conjugates.
• Demonstrate the meaning of x!
- Evaluate factorials with and without calculators.
• real number • imaginary number • complex number •
conjugates • factorial
AII.1.1.2 Demonstrate meaning of complex numbers as
solutions to polynomial equations that do not have real
solutions.
• Demonstrate meaning of complex numbers as
solutions to polynomial equations that do not have real
solutions.
• Identify real and imaginary roots for polynomial
equations.
- Simplify those roots with negative radicands
• radicand • roots
AII.1.1.3 Recognize matrices as a method of arranging
data.
• Recognize matrices as a method of arranging data. • Identify the dimensions of a matrix. • matrix • row • column
AII 1.1.4 Develop an understanding of the properties of
logarithmic expressions and expressions with rational
exponents.
• Develop an understanding of the properties of
logarithmic expressions and expressions with rational
exponents.
• Identify a logarithmic function as the inverse of an
exponential function.
- Identify logarithmic and exponential functions
graphically.
- Define e.
• Apply the laws of exponents to algebraic expressions,
including those involving rational and negative
exponents, to order and rewrite them in alternative
forms.
- i.e.
• inverse function • logarithmic function • exponential
function • logarithm base • rational exponent
Goal 1.2: Understand meanings of
operations and how they relate to one
another.
AII 1.2.1 Develop an understanding of the properties
of, and representations for, the addition, subtraction,
and multiplication of matrices.
• Develop an understanding of the properties of, and
representations for, the addition, subtraction, and
multiplication of matrices.
• Identify which properties of real numbers apply to
matrices.
Goal 1.3: Compute fluently and make
reasonable estimates.
AII.1.3.1 Simplify expressions within the complex
number system.
• Simplify expressions within the complex number
system.
• Simplify rational expressions, expressions with
rational exponents, and logarithmic expressions.
- Simplify rational expressions containing monomials
in the numerator and denominator.
- Simplify rational expressions that contain
polynomials in the numerator and denominator that
require factoring.
- Simplify complex fractions.
• Simplify and estimate radical expressions having
various indices.
• Express the square root of a negative number in the
form bi, where b is real.
• Simplify rational expressions containing complex
numbers.
• Use properties of logarithms to simplify logarithmic
expressions.
- Expand single logarithmic expressions.
- Write expanded logarithmic expressions as single
logarithmic expressions.
- Apply change of base formula to convert a
logarithmic expression to an appropriate base.
• indices • rational exponent • rational expression •
logarithm • complex fraction
AII 1.3.2 Perform computations on expressions within
the complex number system.
• Perform computations on expressions within the
complex number system.
• Perform operations with matrices to include scalar
multiplication, addition, subtraction, and matrix
multiplication (2 by 2).
• Add, subtract, and multiply radical expressions and
expressions containing rational exponents.
• Use long division or synthetic division to divide a
polynomial by a lower degree polynomial.
• Add and subtract rational expressions with and
without common denominators.
• Multiply and divide rational expressions.
- Recognize the difference between a factor and
a term when simplifying rational expressions.
• scalar • radical expression • synthetic division • degree
of a polynomial • factors • terms • like radical
expressions
Standard 2: Concepts and Principles of Measurement
Goal 2.1: Understand measurable
attributes of objects and the units,
systems, and processes of
measurement.
AII.2.1.1 Recognize the relationship between radian
and degree measures.
• Recognize the relationship between radian and degree
measures.
• Convert between degree and radian measures. • degree • radian
Goal 2.2: Apply appropriate
techniques, tools,, and formulas to
determine measurements.
No objectives at this course level.
Standard 3: Concepts and Language of Algebra and Functions
Goal 3.1: Understand patterns,
relations, and functions.
AII.3.1.1. Represent patterns and functional
relationships in a table and as a graph.
• Represent patterns and functional relationships in a
table and as a graph.
• Graph absolute value functions.
• Graph quadratic equations and inequalities.
• Graph polynomial functions.
- Determine end behavior and x- and y-intercepts.
• Graph exponential functions.
• Graph circles.
- Identify the coordinates of the center and
determine the length of the radius.
• Graph functions by plotting points.
• Determine domain and range using algebraic and
graphing techniques.
• absolute value function • quadratic function • domain •
range • end behavior
AII.3.1.2. Describe the graphs of polynomial and
absolute value functions and discuss their attributes in
terms of the basic concepts of maximum, minimum,
intercepts, and roots.
• Describe the graphs of polynomial and absolute value
functions and discuss their attributes in terms of the
basic concepts of maximum, minimum, intercepts, and
roots.
• Determine the nature of the roots of an equation by
using the discriminant.
• Recognize contexts in which quadratic models are
appropriate.
- i.e. height as a function of time; the relationship
between the length of a side of a cube and its
surface area.
• Identify the graphs of absolute value functions and
identify their key characteristics.
• Determine the degree of a polynomial function.
• Determine the vertex and axis of symmetry of a
quadratic function.
• Identify the graphs of polynomial functions.
-i.e. parent graphs
• Find the x- and y-intercepts for applicable functions.
• x- and y-intercepts • zeros • discriminant • polynomial
function • parent graph • vertex • axis of symmetry
AII 3.1.3. Perform operations on functions including
composition of functions and finding inverse functions.
• Perform operations on functions including
composition of functions and finding inverse functions.
A. Combine functions by addition, subtraction,
multiplication, and division.
B. Determine the composition of two functions,
including any necessary restrictions on the domain.
C. Determine and graph the inverse relation of a
function.
- Determine if the inverse relation is a function.
• composition of functions • inverse relation • inverse
function
Goal 3.2: Represent and analyze
mathematical situations and structures
using algebraic symbols.
AII.3.2.1. Write equations and inequalities in multiple
forms.
• Write equations and inequalities in multiple forms. • Rewrite equations of parabolas and circles in standard
form by completing the square as necessary.
- i.e. Use different forms of the function to extract
information For parabolas:
y = x² - 6x + 8 makes the y-intercept obvious,
y = (x - 2)(x - 4) provides access to the zeros,
and y = (x - 3)² - 1 makes it easy to find the vertex
and sketch the graph.
• perfect square trinomial • complete the square
AII.3.2.2. Recognize and generate equivalent forms of
algebraic expressions and solve equations, inequalities,
and systems of equations and inequalities.
• Recognize and generate equivalent forms of algebraic
expressions and solve equations, inequalities, and
systems of equations and inequalities.
• Solve systems of linear equations by graphing and
algebraic processes.
- Determine the number of solutions for a system of
equations.
• Solve systems of linear inequalities by graphing.
• Determine if an ordered pair satisfies a system of
linear equations or inequalities.
• Solve radical equations and inequalities.
- Determine the domain and range of radical
equations.
- Determine if extraneous solutions exist.
• Solve rational equations.
- Determine the domain and range of rational
equations.
- Determine if extraneous solutions exist.
• Solve logarithmic equations.
• Solve equations containing a variable in the exponent.
• Use the quadratic formula, factoring, and completing
the square to solve quadratic equations.
• Determine a single variable quadratic equation given
its solutions.
• systems of equations • radical equations • extraneous
solutions • quadratic formula
Goal 3.3: Use mathematical models to
represent and understand quantitative
relationships.
No objectives at this course level.
Goal 3.4: Analyze change in various
contexts.
AII.3.4.1. Interpret how changes to an equation effect
the parent graph of the equation.
• Interpret how changes to an equation effect the parent
graph of the equation.
• Compare and contrast the graphs of
f(x) = x² to f(x) = a(x-h)² + k.
• Recognize graphs of the following:

• Identify vertical and horizontal translations and
reflections about the x-axis.
• translation • reflection
Standard 4: Concepts and Principles of Geometry
Goal 4.1 Analyze characteristics and
properties of two- and threedimensional
geometric shapes and
develop mathematical arguments about
geometric relationships.
AII.4.1.1 Use trigonometric relationships to determine
lengths and angle measures.
• Use trigonometric relationships to determine lengths
and angle measures.
• Solve right triangles using the Pythagorean theorem
and trigonometric ratios.
• Demonstrate the proper use of the Law of Sines and
the Law of Cosines to solve triangles.
Goal 4.2 Specify locations and
describe spatial relationships using
coordinate geometry and other
representational systems.
AII.4.2.1. Analyze the graphs of circles and parabolas. • Analyze the graphs of circles and parabolas. • Graph circles and parabolas and their transformations.
Goal 4.3 Apply transformations and
use symme
No objectives at this course level.
Goal 4.4 Use visualization, spatial
reasoning, and geometric models to
solve problems.
No objectives at this course level.
Standard 5: Data Analysis, Probability, and Statistics
No objectives at this course level.