Mathematics Course: Algebra I Honors Overview: This course is a study of the algebraic language and concepts, together with the skills needed to master these concepts. Students will study the basics of arithmetic, real numbers, equations, inequalities, linear graphs and equations, systems of equations, rational exponents, polynomials, factoring, rational expressions and equations, radicals, quadratic equations and graphs. Algebra, Mathematical Models, and Problem Solving Alg1.1 Algebraic Expressions, Real Numbers, and Interval Notation Alg1.1a Translate English phrases into algebraic expressions Alg1.1b Evaluate algebraic expressions Alg1.1c Use mathematical models Alg1.1d Recognize the sets that make up the real numbers Alg 1.1e Use set‐builder notation Alg 1.1f Use the symbols “element of” and is “not an element of” Alg 1.1g Use inequality notation Alg 1.1h Use Interval notation Alg1.2 Operations with Real Numbers and Simplifying Algebraic Expressions Alg1.2a Find a number's absolute value Alg1.2b Add real numbers Alg1.2c Find opposites Alg 1.2d Subtract real numbers Alg1.2e Multiply real numbers Alg1.2f Evaluate exponential expressions Alg1.2g Divide real numbers Alg1.2h Use order of operations Alg1.2i Use commutative, associative, and distributive properties Alg1.2j Simplify algebraic expressions Alg1.3 Graphing equations Alg1.3a Plot points in the rectangular coordinate system Alg1.3b Graph equations in the rectangular coordinate system Alg1.3c Use the rectangular coordinate system to visualize relationships between variables. Alg1.3d Interpret information about a graphing utility’s viewing rectangle or table. Alg1.4 Solving Linear Equations Alg1.4a Solve linear equations Alg1.4b recognize identities, conditional equations, and inconsistent equations Alg1.4c Solve applied problems using mathematical models Alg1.5 Problem solving and Using Formulas Alg1.5a Solve algebraic word problems using linear equations Alg1.5b Solve a formula for a variable Alg1.6 Properties of Integral Exponents Alg1.6a Use the product rule Alg1.6b Use the quotient rule Alg1.6c Use the zero‐exponent rule Alg1.6d Use the negative‐exponent rule Alg1.6e Use the power rule Alg1.6f Find the power of a product Alg1.6g Find the power of a quotient Alg1.6h Simplify exponential expressions Alg1.7 Scientific Notation Alg1.7a Convert from scientific to decimal notation Alg1.7b Convert from decimal to scientific notation Alg1.7c Perform computations with scientific notation Alg1.7d Use scientific notation to solve problems Functions and Linear Functions Alg2.1 Introductions to Functions Alg2.1a Find the domain and range of a relation Alg2.1b Determine whether a relation is a function Alg2.1c Evaluate a function Alg2.2 Graphs of Functions Alg2.2a Graph functions by plotting points Alg2.2b Use the vertical line test to identify functions Alg2.2c Obtain information about a function from its graph Alg2.2d Identify the domain and range of a function from its graph Alg2.3 The Algebra of Functions Alg2.3a Find the domain of a function Alg2.3b Use the algebra of functions to combine functions and determine domains. Alg2.4 Linear Functions and Slope Alg2.4a Use intercepts to graph a linear function in standard form Alg2.4b Compute a line’s slope Alg2.4c Find a line’s slope and y‐intercept from its equation Alg2.4d Graph linear functions in slope‐intercept form Alg2.4d Graph horizontal or vertical lines Alg2.4e Interpret slope as rate of change Alg2.4f Find a function’s average rate of change Alg2.4g Use slope and y‐intercept to model data Alg2.5 The point‐slope from of the equation Alg2.5a Use the point‐slope form to write equations of a line Alg2.5b Model data with linear functions and make predictions Alg2.5c Find slopes and equations of parallel and perpendicular lines Systems of Linear Equations Alg3.1 Systems of Linear Equations in Two Variables. Alg3.1a Read bar and line graphs Alg3.1b Determine whether an ordered pair is a solution Alg3.1c Solve by graphing, substitution and addition Alg3.1d Select most efficient method Alg3.1e Identify systems with other solutions other than one ordered pair Alg3.2 Problem Solving and Business Applications using Systems of Equations Alg3.2a Solve problems using systems Alg3.2b Using functions to model revenue, cost and profit and break‐even point Alg3.2c Solve problems using systems of equations Alg3.3 Systems of Linear Equations in Three Variables Alg3.3a Verify the solution Alg3.3b Solve systems of equations in 3 variables Alg3.3c Identify inconsistent and dependent systems Alg3.3d Solve problems using a system in 3 variables Alg3.4 Matrix Solutions to Linear Systems Alg3.4a Write the augmented matrix Alg3.4b Perform matrix row operations Alg3.4c Use matrices to solve linear systems in 2 variables Alg3.4d Use matrices to solve linear systems in 3 variables Alg3.4e Use matrices to identify inconsistent and dependent systems Alg3.5 Determinants and Cramer's Rule Alg3.5a Evaluate a second order determinant Alg3.5b Solve a system of 2 variables using Cramer's rule Alg3.5c Evaluate a third order determinant Alg3.5d Solve a system in 3 variables using Cramer's rule Inequalities and Problem Solving Alg4.1 Solving Linear Inequalities Alg4.1a Solve linear inequalities Alg4.1b Recognize inequalities with no solution or all real numbers as solutions Alg4.1c Solve applied problems using linear inequalities Alg4.2 Compound Inequalities Alg4.2a Find the intersection of two sets and the union of two sets Alg4.2b Solve compound inequalities containing And, Or Alg4.3 Absolute Value Equations and Inequalities Alg4.3a Solve absolute value equations Alg4.3b Solve absolute value inequalities in the form lxl <a Alg4.3c Solve absolute value inequalities in the form lxl>a Alg4.4d Recognize absolute value inequalities with no solution or all real numbers Alg4.5e Solve problems using absolute value inequalities Alg4.4 Linear Inequalities in Two Variables Alg4.4a Graph a linear inequality in two variables Alg4.4b Graph a system of inequalities Alg4.5 Linear Programming Alg4.5a Write objective functions Alg4.5b Use inequalities to model the limitations Alg4.5c Use linear programming to solve problems Polynomials, Polynomial Functions, and Factoring Systems of Linear Equations and Inequalities Alg5.1 Introduction to Polynomials and Polynomial Functions Alg5.1a Use vocabulary of polynomials Alg5.1b Evaluate polynomial functions Alg5.1c Determine end behavior Alg5.1d Add and subtract polynomials Alg5.2 Multiplication of Polynomials Alg5.2a Multiply monomials, monomials to polynomials Alg5.2b Multiply all forms of polynomials Alg5.2c Use FOIL Alg5.2d Square binomial, multiply sum and difference Alg5.2e Find the product of functions Alg5.2f Use polynomial functions to evaluate functions Alg5.3 Greatest Common Factors and Factoring by Grouping Alg5.3a Factor out the GCF of a polynomial Alg5.3b Factor out a common factor and a negative coefficient Alg5.3c Factor by grouping Alg5.4 Factoring Trinomials Alg5.4a Factor a trinomial with leading coefficient is 1 Alg5.4b Factor using substitution Alg5.4c Factor a trinomial with leading coefficient other than 1 Algd5.4d Factor trinomials by grouping Alg5.5 Factoring Special Forms Alg5.5a Factor the difference of two square Alg5.5b Factor perfect square trinomials Alg5.5c Use grouping to obtain the difference of two squares Alg5.5d Factor the sum or difference of two cubes Alg5.6 A General Factoring Strategy Alg5.6a Use a general factoring strategy for polynomials Alg5.7 Polynomial Equations and Their Applications Alg5.7a Solve quadratic equations by factoring Alg5.7b Solve higher degree polynomial equations by factoring Alg5.7c Solve problems using polynomial equations Rational Expressions, Functions, and Equations and Polynomials Alg6.1 Multiplying and Dividing Rational Expressions and Functions Alg6.1a Evaluate rational functions Alg6.1b Find the domain of a rational function Alg6.1c Interpret the information given by the graph of a rational function Alg6.1d Simplify rational expressions Alg6.1e Multiply and Divide rational expressions Alg6.2 Adding and Subtracting Rational Expressions Alg6.2a Add and Subtract expressions with the same denominator Alg6.2b Find the LCD Alg6.2c Add and Subtract expressions with different denominators Alg6.3 Complex Rational Expressions Alg6.3a Simplify complex rational expressions by multiplying by 1 Alg6.3b Simplify complex rational expressions by dividing 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 Synthetic Division and the Remainder Theorem Alg6.5a Divide using synthetic division Alg6.5b Evaluate a polynomial function using the Remainder Theorem Alg6.5c Show a number is a solution using the Remainder Theorem Alg6.6 Rational Equations Alg6.5a Solve rational equations Alg6.5b Solve problems involving rational functions that model applied situations Alg6.7 Formulas and Applications of Rational Equations Alg6.7a Solve a formula with a rational expression for a variable Alg6.7b Solve business problems involving average cost Alg6.7c Solve problems involving time in motion Alg6.7d Solve problems involving work Alg6.8 Modeling Using Variation Alg6.8a Solve direct variation Alg6.8b Solve inverse variation Alg6.8c Solve combined variation Alg6.8d Solve joint variation Radicals, Radical Functions, and Rational Exponents and Polynomials Alg7.1 Radical Expressions and Functions Alg7.1a Evaluate square roots and functions Alg7.1b Find the domain of the square root function Alg7.1c Model