### IA-2: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

#### IA-2.2: Carry out a procedure to solve a system of linear inequalities graphically.

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

#### IA-2.3: Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

#### IA-2.4: Use linear programming to solve contextual problems involving a system of linear inequalities.

Linear Programming

#### IA-2.7: Carry out a procedure to graph translations of parent functions (including y = x, y = x², y = square root of x, y = absolute value of x, and y = 1/x).

Absolute Value with Linear Functions

General Form of a Rational Function

Quadratics in Vertex Form

Rational Functions

Translating and Scaling Functions

Translations

Zap It! Game

#### IA-2.8: Carry out a procedure to graph transformations of parent functions (including y = x, y = x², and y = absolute value of x).

Absolute Value with Linear Functions

Exponential Functions

Quadratics in Vertex Form

Translating and Scaling Functions

Translations

Zap It! Game

#### IA-2.9: Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

Absolute Value with Linear Functions

#### IA-2.11: Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

### IA-3: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

#### IA-3.1: Carry out a procedure to simplify expressions involving powers of i.

Points in the Complex Plane

#### IA-3.2: Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

Points in the Complex Plane

#### IA-3.3: Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Roots of a Quadratic

#### IA-3.4: Use the discriminant to determine the number and type of solutions of a quadratic equation.

Roots of a Quadratic

#### IA-3.5: Analyze given information (including quadratic models) to solve contextual problems.

Addition and Subtraction of Functions

Quadratics in Polynomial Form

#### IA-3.6: Carry out a procedure to write an equation of a quadratic function when given its roots.

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

### IA-4: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

#### IA-4.1: Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

Addition and Subtraction of Functions

Addition of Polynomials

Dividing Exponential Expressions

Dividing Polynomials Using Synthetic Division

Exponents and Power Rules

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

#### IA-4.2: Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

#### IA-4.9: Carry out a procedure to solve radical equations algebraically.

Operations with Radical Expressions

Radical Functions

#### IA-4.13: Carry out a procedure to graph logarithmic functions.

Logarithmic Functions

#### IA-4.14: Carry out a procedure to graph exponential functions.

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

### IA-5: The student will demonstrate through the mathematical processes an understanding of conic sections.

#### IA-5.1: Carry out a procedure to graph the circle whose equation is the form x² + y² = r².

Circles

#### IA-5.2: Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

Circles

#### IA-5.3: Carry out a procedure to graph the ellipse whose equation is the form (x²/a²) + (y²/b²) = 1.

Ellipses

#### IA-5.4: Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

Ellipses

#### IA-5.5: Carry out a procedure to graph the hyperbola whose equation is the form (x²/a²) - (y²/b²) = 1.

Hyperbolas

#### IA-5.6: Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

Hyperbolas

#### IA-5.7: Match the equation of a conic section with its graph.

Circles

Ellipses

Hyperbolas

Parabolas

### IA-6: The student will demonstrate through the mathematical processes an understanding of sequences and series.

#### IA-6.1: Categorize a sequence as arithmetic, geometric, or neither.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

#### IA-6.2: Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

#### IA-6.3: Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

Arithmetic Sequences

Geometric Sequences

#### IA-6.4: Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

Arithmetic Sequences

Geometric Sequences

#### IA-6.7: Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

Arithmetic Sequences

Geometric Sequences

#### IA-6.8: Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

Arithmetic Sequences

Geometric Sequences

#### IA-6.9: Translate between the explicit form and the recursive form of sequences.

Arithmetic Sequences

Geometric Sequences

Correlation last revised: 4/4/2018