Advanced Algebra II
Scope and Sequence
NCTM Standards covered in this course:
 Understand numbers, ways of representing numbers, relationships among numbers,
and number systems
 Understand meanings of operations and how they relate to one another
 Compute fluently and make reasonable estimates
 Understand patterns, relations, and functions
 Represent and analyze mathematical situations and structures using algebraic symbols
 Use mathematical models to represent and understand quantitative relationships
 Analyze change in various contexts
 Understand measurable attributes of objects and the units, systems, and processes of
measurement
 Problem solving, reasoning and proof, communication, connections, and representation
are also addressed in this course
Kentucky Standards covered in this course:
 Linear equations, inequalities, and functions
 Non-linear functions: quadratic and absolute value
 Proportional reasoning
 Sequences
Unit 1: Solving Equations and Inequalities (3-4 days)*
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Solve an equation for a specific variable.
Solve an absolute value equation.
Set up and solve an absolute value equation from a word description.
Solve an inequality using the addition, subtraction, multiplication and division
rules for inequalities.
Solve an inequality and graph the solution on a number line.
Solve an inequality and write the solution in interval notation and set-builder
notation.
Set up and solve a simple word problem involving a linear equation, absolute
value equation, and inequalities, and absolute value inequalities from a word
description.
Solve a compound inequality which uses the “and” connector; solve a
compound inequality which uses the “or” connector.
Write an “and” type inequality as a three-way inequality.
Solve an absolute value inequality using <, >, ≤, 𝑜𝑟 ≥ inequalities and graph the
solution set of an absolute value inequality.
Unit 2: Linear Relations and Functions (9-10 days)
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Find the domain and range of a function from a set of points.
Evaluate a function written in function notation.
Determine whether a graph represents a relation or a function.
Set up and solve equations involving direct variation
State whether the equation of a given function is linear or not.
Find the x- and y-intercepts of a linear function.
Write and graph a linear function in Standard Form.
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Determine whether a line is perpendicular to a given line, parallel to a given
line, or neither by comparing slopes of the two lines.
Use slope to model a “rate of change” between two variables.
Write the equation of a line in Slope-Intercept Form given various combinations
of information (i.e. a point and slope or two points).
Graph the equation of a line written in Slope-Intercept Form.
Identify and graph the step function, piecewise-defined function, and absolute
value function.
Identify the domain and the range of a function from its graph.
Unit 3 – Systems of Linear Equations and Inequalities (7-8 days)
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Graph a system of linear equations.
Solve a system of linear equations from its graph.
Solve a system of linear equations by the Substitution Method.
Solve a system of linear equations by the Elimination Method.
Determine whether a system is consistent or inconsistent when using the
Graphing, Substitution or Elimination Methods.
Graph a system of linear inequalities and shade the solution region.
Find the coordinates of the corners of the solution region of a system of linear
inequalities.
Write a system of linear inequalities from a word description.
Set up and solve a linear program. (Financial Literacy)
Solve a system of three linear equations in three variables by using successive
elimination of variables.
Unit 4 – Quadratic Functions (10-12 days)
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Find the vertex of a quadratic function in standard form by using x = -b/2a.
Write the axis of symmetry for a quadratic function.
Find the y-intercept of a quadratic function in standard form.
Graph a quadratic function (parabola) from standard form.
Find the maximum or minimum value of a quadratic function.
Solve a quadratic equation by factoring by using the Zero Product Property.
Find the x-intercepts of a quadratic function by factoring.
Factor a standard trinomial of the form ax2 + bx + c by the Method of
Grouping.
Solve a quadratic equation by the Square Root Method.
Solve a quadratic equation by completing the square.
Solve a radical inequality and graph the solution on a number line and also
write the solution in interval notation.
Write the square root of a negative number as an imaginary number (i).
Simplify powers of i.
Add and subtract complex numbers.
Multiply complex numbers and simplify the result.
Solve a quadratic equation by using the Quadratic Formula.
Determine the number and type of roots of a quadratic equation by using the
discriminant.
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Find the coordinates of the vertex, axis of symmetry and the x- and yintercepts of a quadratic function written in vertex form.
Convert quadratic functions from vertex to standard form.
Convert quadratic functions from standard to vertex form.
Graph quadratic function written from vertex form.
Write the equation of a quadratic function in vertex form when given the
coordinates of the vertex and one other point.
Graph a quadratic inequality (in both vertex and standard forms).
Find the solution set for a quadratic inequality and:
 Graph the solution set on a number line.
 Write the solution set in interval notation.
Solve a quadratic word problems (financial literacy)
Unit 5 – Polynomials (6-8 days)
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Determine the degree of a polynomial.
Identify monomials, binomials and trinomials.
Multiply polynomials using the appropriate property.
Divide polynomials by using the division algorithm.
Divide suitable polynomials using synthetic division.
Factor a polynomial with four terms by the Grouping Method.
Factor a difference of squares, cubes and fourths
Find the GCF of an algebraic expression and re-write the expression as a
product of the GCF.
Simplify a rational expression
Multiply and divide rational expressions and simplify the answers.
Add and subtract rational expressions and simplify the answers
Solve rational equations
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Simplify the square, cube and fourth roots of whole numbers.
Simplify the square, cube and fourth roots an algebraic expression.
Add, subtract, multiply and divide radical expressions and simplify the answers.
Rationalize the denominator of a radical expression (monomial and binomial).
Simplify an algebraic expression with rational exponents.
Write a radical expression as an expression with rational exponents.
Solve a radical equations and check for extraneous roots.
Perform basic function operations
Calculate the composition of two functions
Evaluate the composition of two functions
Solve for the inverse of a given functions
Solve challenging radical equations
Unit 6 – Radicals and Rational Exponents (6-7 days)
Unit 7 –
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Conic Sections (6 days)
Apply the Distance Formula
Apply the Midpoint Formula
Identify circles, parabolas, ellipses, and hyperbolas from the equation
Identify lines of symmetry for circles, parabolas, ellipses, and hyperbolas
Graph circles, parabolas, ellipses, and hyperbolas
Unit 8 – Matrices (6-7 days)
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Determine the dimensions of a matrix and the elements within a matrix.
Add and Subtract conformable matrices; determine when two matrices are not
conformable for addition or subtraction.
Multiply a matrix by a scalar.
Determine when two matrices are conformable for multiplication.
State the dimensions of the resultant matrix before two matrices are multiplied.
Multiply two conformable matrices.
Perform combined operations with matrices.
Perform translations, rotations and reflections of simple geometric figures with
matrix operations.
Graph the images of the above transformations on graph paper.
Find the determinant of a 2x2 matrix.
Determine if two matrices are inverses of each other.
Determine whether a matrix has an inverse.
Find the inverse of a 2x2 matrix by hand (shortcut using determinant).
Find the inverse of 3x3 and 4x4 matrices on a calculator with matrix functions.
Code and decode messages using matrix inverses.
Re-write a system of equations as a matrix equation.
Use the inverse of the constant matrix to solve the matrix equation. (X = A-1B).
Additional Topics as time permits
 Combinations and Permutations
 Sequences and Series
 Basic Exponential Equations
Calculator Skills
 Scatter Plots
 Line of Best Fit
 Using the Table Function
 Evaluate Roots
 Graphing Linear, Absolute Value, Quadratic, Polynomial, and Radical Functions
 Matrix Operations
 Conics
Outcomes for Advanced Algebra II
1. Students will be able to solve, graph, and apply linear equations, inequalities, and
systems.
2. Students will be able to perform matrix operations.
3. Students will be able to solve and perform operations with polynomials and complex
numbers
4. Students will be able to solve, graph, and apply quadratic functions.
5. Students will be able to solve and apply rational equations.
6. Students will be able to solve, graph, and apply radical equations.
7. Students will be able to solve, graph, and apply conic sections
Revised August 2015