Mathematics Course: Algebra 2

Overview: In addition to reviewing previous math topics, students will study rational exponents, polynomial and rational expressions, rational equations, complex numbers, functions and function notation, linear systems of equations, quadratic equations and functions. If time permits, students will get an introduction to non‐linear systems of equations and conic sections. Real Numbers and Algebraic Expressions

Alg1.2 Algebraic Expressions and Sets of Numbers Alg1.2a Identify and evaluate algebraic expressions Alg1.2b Identify natural numbers, whole numbers, integers, and rational and irrational real numbers Alg1.2c Find the absolute value of a number Alg1.2d Find the opposite of a number Alg1.2e Write phrases as algebraic expressions

Alg1.3 Operations on Real Numbers Alg1.3a Add and subtract real numbers Alg1.3b Multiply and divide real numbers Alg1.3c Evaluate expressions containing exponents Alg1.3d Find roots of numbers Alg1.3e Use the order of operations Alg1.3f Evaluate algebraic expressions

Alg1.4 Properties of Real Numbers Alg1.4a Use operations and order symbols to write mathematical sentences Alg1.4b Identify identity numbers and inverses Alg1.4c Identify and use the commutative, associative, and distributive properties Alg1.4d Write and simplify algebraic expressions

Equations, Inequalities, and Problem Solving

Alg2.1 Linear Equations in One Variable Alg2.1a Solve linear equations using properties of equality Alg2.1b Solve linear equations that can be simplified by combining like terms Alg2.1c Solve linear equations containing fractions or decimals Alg2.1d Recognize identities and equations with no solutions Alg2.2 An Introduction to Problem Solving Alg2.2a Write algebraic expressions that can be simplified Alg2.2b Apply the steps for problem solving

Alg2.3 Formulas and Problem Solving Alg2.3a Solve a formula for a specified variable Alg2.3b Use formulas to solve problems

Alg2.4 Linear Inequalities and Problem Solving Alg2.4a Use interval notation Alg2.4b Solve linear inequalities using the addition property of inequality Alg2.4c Solve linear inequalities using the multiplication and the addition properties of inequality Alg2.4d Solve problems that can be modeled by linear inequalities

Alg2.5 Compound Inequalities Alg2.5a Find the intersection of two sets Alg2.5b Solve compound inequalities containing and Alg2.5c Find the union of two sets Alg2.5d Solve compound inequalities containing or

Alg2.6 Absolute Value Equations Alg2.6a Solve absolute value equations

Alg2.7 Absolute Value Inequalities Alg2.7a Solve absolute value inequalities

Graphs and Functions

Alg3.1 Graphing Equations Alg3.1a Plot ordered pairs Alg3.1b Determine whether an ordered pair of numbers is a solution to an equation in two variables Alg3.1c Graph linear equations Alg3.1d Graph nonlinear equations

Alg3.2 Introduction to Functions Alg3.2a Define relation, domain, and range Alg3.3b Identify functions Alg3.3c Use the vertical line test for functions Alg3.3d Find the domain and range of a function Alg3.3e Use function notation

Alg3.3 Graphing Linear Functions Alg3.3a Graph linear functions Alg3.3b Graph linear functions by finding intercepts Alg3.3c Graph vertical and horizontal lines

Alg3.4 The Slope of a Line Alg3.4a Find the slope of a line given two points on the line Alg3.4b Find the slope of a line given the equation of a line Alg3.4c Interpret the slope‐intercept form in an application Alg3.4d Find the slopes of horizontal and vertical lines Alg3.4e Compare the slopes of parallel and perpendicular lines

Alg3.5 Equations of Lines Alg3.5a Use the slope‐intercept form to write the equation of a line Alg3.5b Graph a line using its slope and y‐intercept Alg3.5c Use the point‐slope form to write the equation of a line Alg3.5d Write equations of vertical and horizontal lines Alg3.5e Find equations of parallel and perpendicular lines

Alg3.7 Graphing Linear Inequalities Alg3.7a Graph linear inequalities Alg3.7b Graph the intersection or union of two linear inequalities

Systems of Equations

Alg4.1 Solving Systems of Linear Equations in Two Variables Alg4.1a Determine whether an ordered pair is a solution of a system of two linear equations Alg4.1b Solve a system by graphing Alg4.1c Solve a system by substitution Alg4.1d Solve a system by elimination

Alg4.2 Solving Systems of Linear Equations in Three Variables Alg4.2a Solve a system of three linear equations in three variables

Alg4.3 Systems of Linear Equations and Problem Solving Alg4.3a Solve problems that can be modeled by a system of two linear equations Alg4.3b Solve problems with cost and revenue functions Alg4.3c Solve problems that can be modeled by a system of three linear equations Alg4.5 Systems of Linear Inequalities Alg4.5a Graph a system of linear inequalities

Exponents, Polynomials, and Polynomial Functions

Alg5.1 Exponents and Scientific Notation Alg5.1a Use the product rule for exponents Alg5.1b Evaluate expressions raised to the 0 power Alg5.1c Use the quotient rule for exponents Alg5.1d Evaluate expressions raised to the negative nth power Alg5.1e Convert between scientific notation and standard notation

Alg5.2 More Work with Exponents and Scientific Notation Alg5.2a Use the power rules for exponents Alg5.2b Use exponent rules and definitions to simplify exponential expressions Alg5.2c Compute, using scientific notation

Alg5.3 Polynomials and Polynomial Functions Alg5.3a Identify term, constant, polynomial, monomial, binomial, trinomial, and the degree of a term of a polynomial Alg5.3b Define polynomial functions Alg5.3c Review combining like terms Alg5.3d Add polynomials Alg5.3e Subtract polynomials Alg5.3f Recognize the graph of a polynomial function from the degree of the polynomial

Alg5.4 Multiplying Polynomials Alg5.4a Multiplying two polynomials Alg5.4b Multiplying Binomials Alg5.4c Square Binomials Alg5.4d Multiply the sum and difference Alg5.4e Multiply three or more polynomials Alg5.4f Evaluate polynomial functions

Alg5.5 The Greatest Common Factor and Factoring by Grouping Alg5.5a Identify the GCF Alg5.5b Factor out the GCF of a polynomial’s term Alg5.5c Factor polynomials by grouping

Alg5.6 Factoring Trinomials Alg5.6a Factor trinomials with a lead coefficient of 1 Alg5.6b Factor trinomials with a lead coefficient not equal to 1 Alg5.6c Factor by substitution

Alg5.7 Factoring by Special Products Alg5.7a Factor a Perfect Square trinomial Alg5.7b Factor the difference of two squares Alg5.7c Factor the sum or difference of two cubes

Alg5.8 Solving Equations Alg5.8a Solve polynomial equations by factoring Alg5.8b Solve problems that can be modeled by polynomial equations Alg5.8c Find the x‐intercepts of a polynomial function

Rational Expressions

Alg6.1 Rational Functions and Multiplying and Dividing Rational Expressions Alg6.1a Find the domain of a rational expression Alg6.1b Simplify rational expressions Alg6.1c Multiply rational expressions Alg6.1d Divide rational expressions Alg6.1e Use rational functions in applications

Alg6.2 Adding and Subtracting Polynomials Alg6.2a Define polynomial, monomial, binomial, trinomial and degree Alg6.2b Find the value of a polynomial given replacement values for the variables Alg6.2c Simplify a polynomial by combining like terms Alg6.2d Add and subtract polynomials

Alg6.3 Multiplying Polynomials Alg6.3a Use the distributive property to multiply polynomials Alg6.3b Multiply polynomials vertically

Alg6.4 Dividing Polynomials Alg6.4a Divide a polynomial by a monomial Alg6.4b Use long division to divide a polynomial by another polynomial

Alg6.5 Special Products Alg6.5a Multiply two binomials using the FOIL method Alg6.5b Square a binomial Alg6.5c Multiply the sum and difference of two terms

Factoring Polynomials

Alg7.1 Greatest Common Factor and Factoring by Group Alg7.1a Find the greatest common factor of a list of integers Alg7.1b Find the greatest common factor of a list of terms Alg7.1c Factor out the greatest common factor from a polynomial Alg7.1d Factor a polynomial by grouping

Alg7.2 Factoring Trinomials of the Form x^2 + bx + c Alg7.2a Factor trinomials of the form x^2 + bx + c Alg7.2b Factor out the greatest common factor and then factor a trinomial of the form x^2 + bx + c

Alg7.3 Factoring Trinomials of the Form ax^2 + bx + c and Perfect Square Trinomials Alg7.3a Factor trinomials of the form ax^2 + bx + c, where a ≠ 1 Alg7.3b Factor out a GCF before factoring a trinomial of the form ax^2 + bx + c Alg7.3c Factor perfect square trinomials

Alg7.4 Factoring Trinomials of the Form ax^2 + bx + c by Grouping Alg7.4a Use the grouping method to factor trinomials of the form ax^2 + bx + c

Alg7.5 Factoring Binomials Alg7.5a Factor the difference of two squares Alg7.5b Factor the sum or difference of two cubes

Alg7.6 Solving Quadratic Equations by Factoring Alg7.6a Solve quadratic equations by factoring Alg7.6b Solve equations with degree greater than 2 by factoring Alg7.6c Find the x‐intercepts of the graph of a quadratic equation in two variables

Alg7.7 Quadratic Equations and Problem Solving Alg7.7a Solve Problems that can be Modeled by Quadratic Equations

Rational Expressions

Alg8.1 Simplify Rational Expressions Alg8.1a Find the value of a rational expression given a replacement number. Alg8.1b Identify values for which a rational expression is undefined Alg8.1c Simplify or write rational expressions in lowest terms. Alg8.1d Write equivalent rational expressions of the form ‐ = =

Alg8.2 Multiply and Divide Rational Expressions Alg8.2a Multiply Rational Expressions Alg8.2b Divide Rational Expressions

Alg8.3 Adding and Subtracting Rational Expressions Alg8.3a Add and Subtract Rational Expressions with the Same Denominator Alg8.3b Find the Least Common Denominator of a list of Rational Expressions Alg8.3c Write a Rational Expression as an Equivalent Expression whose Denominator is given

Alg8.4 Adding and Subtracting Rational Expressions Alg8.4a Add and Subtract Rational Expressions with Unlike Denominators

Alg8.5 Solve Equations Containing Rational Expressions Alg8.5a Solve Equations Containing Rational Expressions Alg8.5b Solve Equations Containing Rational Expressions for a Specified Variable

Alg8.6 Proportion and Problem Solving with Rational Equations Alg8.6a Solve Proportions Alg8.6b Use Proportions to Solve Problems Alg8.6c Solve Problems about Numbers Alg8.6d Solve Problems about Work Alg8.6e Solve Problems about Distance

Alg8.7 Variation and Problem Solving Alg8.7a Solve problems involving direct variation Alg8.7b Solve problems involving inverse variation Alg8.7c Other types of direct and inverse variation Alg8.8d Variation and problem Solving

Roots and Radicals

Alg9.1 Radicals and Radical Functions Alg9.1a Find square roots Alg9.1b Find cube roots Alg9.1c Find nth roots Alg9.1d Approximate square roots Alg9.1e Simplify radicals containing variables

Alg9.2 Simplifying Radicals Alg9.2a Use the product rule to simplify square roots Alg9.2b Use the quotient rule to simplify square roots Alg9.2c Simplify radicals containing variables Alg9.2d Simplify higher roots

Alg9.3 Adding and Subtracting Radicals Alg9.3a Add or subtract like radicals Alg9.3b Simplify radical expressions, and then add/subtract any like radicals

Alg9.4 Multiplying and Dividing Radicals Alg9.4a Multiply radicals Alg9.4b Divide radicals Alg9.4c Rationalize denominators

Alg9.5 Solving Equations Containing Radicals Alg9.5a Solve radical equations by using the squaring property of equality once. Alg9.5b Solve radical equations by using the squaring property of equality twice.

Alg9.6 Radical Equations and Problem Solving Alg9.6a Use the Pythagorean formula to solve problems Alg9.6b Use the converse of the Pythagorean theorem Alg9.6c Use the distance formula Alg9.6d Use the midpoint formula Alg9.6e Solve problems using formulas containing radicals

Quadratic Equations

Alg10.1 Solving Quadratic Equations by the Square Root Property Alg10.1a Use the square root property to solve quadratic equations Alg10.1b Solve problems modeled by quadratic equations

Alg10.2 Solving Quadratic Equations by Completing the Square Alg10.2a Write Perfect Square Trinomials Alg10.2b Solve Quadratic Equations of the form x^2+bx+c=0 by completing the square Alg10.2c Solve Quadratic Equations of the form ax^2+bx +c=0 by completing the square

Alg10.3 Solving Quadratic Equations by the Quadratic Formula Alg10.3a Use the quadratic formula to solve quadratic equations Alg10.3b Approximate solutions to quadratic equations Alg10.3c Determine the number of solutions of a quadratic equation by using the discriminant

Alg10.4 Graphing Quadratic Equations Alg10.4a Graph quadratic equations of the form y=ax^2 Alg10.4b Graph quadratic equations of the form y=ax^2+bx+c Alg10.4c Use the vertex formula to determine the vertex of a parabola