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 Alg4.4d 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 square root functions Alg7.1d Simplify all types of roots Alg7.1e Find even and odd roots
Alg7.2 Rational Exponents Alg7.2a Using the definitions of rational exponents Alg7.2b Simplify expressions with rational exponents and radical expressions using rational exponents
Alg7.3 Multiplying and Simplifying Radical Expressions Alg7.3a Use the product rule to multiply radicals Alg7.3b Use factoring and the product rule to simplify radicals Alg7.3c Multiply radicals and simplify
Alg7.4 Adding, Subtracting and Dividing Radical Expressions Alg7.4a Add, subtract and divide radicals
Alg7.5 Multiply with More Than One Term and Rationalizing Denominators Alg7.5a Multiply radicals Alg7.5b Rationalize the denominators with one or more terms Alg7.5c Rationalize numerators
Alg7.6 Radical Equations Alg7.6a Solve radical equations Alg7.6b Use models that are radical functions to solve problems
Alg7.7 Complex Numbers Alg7.7a Express square roots of negative numbers in terms of i Alg7.7b Add, subtract, multiply, divide complex numbers Alg7.7c Simplify powers of i
Quadratic Equations and Functions
Alg8.1 The Square Root Property and Completing the Square Alg8.1a Solve quadratic equations using the square root property Alg8.1b Complete the square and solve quadratic equations by completing the square Alg8.1c Solve problems using the above strategies
Alg8.2 The Quadratic Formula Alg8.2a Solve quadratic equations using the quadratic formula Alg8.2b Use the discriminant to determine the number and type of solutions Alg8.2c Determine the best method to solve a quadratic equation Alg8.2d Write quadratic equations from solutions Alg8.2e Use the quadratic formula to solve problems
Alg8.3 Quadratic Functions and Their Graphs Alg8.3a Recognize characteristics of parabolas Alg8.3b Graph parabolas in form of 𝑓 𝑥 𝑎 𝑥 ℎ + k Alg8.3c Graph parabolas in form of 𝑓 𝑥 𝑎𝑥 + bx + c Alg8.3d Determine minimum or maximum value and solve problems involving functions minimum or maximum value
Alg8.4 Equations Quadratic in Form Alg8.4a Solve equations quadratic in form
Alg8.5 Polynomial and Rational Inequalities Alg8.5a Solve polynomial inequalities Alg8.5b Solve rational inequalities Alg8.5c Solve problems using inequalities of both types
Exponential and Logarithmic Functions
Alg9.1 Exponential Functions Alg9.1a Evaluate the functions Alg9.1b Graph the functions Alg9.1c Evaluate with base e Alg9.1d Use compound interest formulas
Alg9.2 Composite and Inverse Functions Alg9.2a Form composite functions Alg9.2b Verify inverse functions Alg9.2c Find the inverse of a function Alg9.2d Use horizontal line test to determine if a function has an inverse Alg9.2e Use the graph of a one to one function to graph its inverse
Alg9.3 Logarithmic Functions Alg9.3a Change from logarithmic to exponential form and back Alg9.3b Evaluate logarithms Alg9.3c Use basic logarithm properties Alg9.4d Graph logarithmic functions Alg9.4e Find the domain of a logarithmic functions Alg9.4f Use common and natural logarithms
Alg9.4 Properties of Logarithms Alg9.4a Use the product, quotient and power rule Alg9.4b Expand logarithmic expressions Alg9.4c Condense logarithmic expressions Alg9.4d Use the change of base property
Alg9.5 Exponential and Logarithmic Equations Alg9.5a Use like bases to solve exponential equations Alg9.5b Use logarithms to solve exponential equations Alg9.5c Use exponential form to solve logarithmic equations Alg9.5d Use the one to one property to solve Alg9.5e Solve applied problems using exponential and logarithmic equations
Alg9.6 Exponential Growth and Decay Alg9.6a Model exponential growth and decay Alg9.6b Choose an appropriate model for data Alg9.6c Express and exponential model in base e