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 nonroutine 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 yintercepts. • 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 yintercepts for applicable functions. 
• x and yintercepts • 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 yintercept 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(xh)² + k. • Recognize graphs of the following: • Identify vertical and horizontal translations and reflections about the xaxis. 
• 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.  