# Montgomery College algebra Equations & Problem Solving *Order of Operations & Simplifying Algebraic. Expressions

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1 Where to go for help with the lessons in the I textbook: Username: student id number followed by scpsfl Password: YYYYMMDDscpsfl Click Student Resource Choose the chapter Choose Homework View Tutors Chapter 1 Lesson Pearson Montgomery College prealgebra 1-1 Variables and Expressions 1-2 Order of Operations/ Evaluating Expressions *Writing algebraic from words *Writing an equation *Using the order of operations to simplify an expression *Evaluating algebraic with exponents Whole Numbers *Into to Variables /Problem Solving *Simplifying ic Expressions Whole Numbers *Exponents and Order of Operations Integers *Order of Operations with Integers Montgomery College algebra & Problem Solving *Order of Operations & Simplifying ic Expressions Khan Academy Other Lessons/vol7/.html Lessons/vol7/ order_operations.html Lessons/vol7/ operations_ exponents.html Lessons/vol7/ operations_

2 1-3 Real Numbers 1-4 Properties of Real Numbers 1-5 Add/Sub Real Numbers *Ordering positive and negative fractions *Classifying numbers *Simplifying square roots of numbers *Estimating square roots of numbers *Identifying properties of real numbers *Using properties of real numbers *Adding numbers *Adding numbers to solve problems *Subtracting numbers *Evaluating algebraic with numbers *Finding absolute value Integers *Intro to Integers Integers *Adding Integers *Subtracting Integers *Number Sets 1 *Number Sets 2 *Number Sets 3 *Absolute Value 1 *Absolute Value and Number Lines integers.html Lessons/vol5/ intro_integers.html Lessons/vol5/ compare_order.html Lessons/vol5/ absolute_value.html Lessons/vol5/ addition.html Lessons/vol5/ subtraction.html

3 1-6 Mult/Div Real Numbers 1-7 Distributive Property 1-8 Intro to 1-9 Patterns,, and Graphs *Multiplying numbers *Dividing numbers *Simplifying algebraic with exponents Integers *Multiplying & Dividing with Integers /Problem Solving *Using the Addition Property of Equality to Solve *Using the Multiplication Property of Equality to Solve *Using Multiple Properties of Equality to Solve Decimals Containing Decimals Struggling with other concepts: Whole Numbers *Rounding & Estimating *Multiply Whole Numbers *Divide Whole Numbers *General Steps for Solving Word Problems Fractions Decimals & Problem Solving *Using the Properties of Equality to Solve Struggling with other concepts: & Problem Solving *General Steps for Solving Word Problems Lessons/vol5/ multiplication.html Lessons/vol5/ division.html Lessons/vol7/ equations.html

4 Percents Graphing *Mean, Medians, & Modes Chapter 2 Lesson Pearson Montgomery College prealgebra 2-1 One-Step /Problem Solving *Using the Addition Property of Equality to Solve *Using the Multiplication Property of Equality to Solve Montgomery College algebra & Problem Solving *Using the Properties of Equality to Solve Khan Academy *Simple Other 2-2 Two-Step 2-3 Multi-Step 2-4 with Variables on Both Sides a twostep equation *Writing and solving twostep equations multistep equations multistep equations by combining like terms equations with variables on both sides /Problem Solving *Using Multiple Properties of Equality to Solve * 2 *: 4 1 * 3 2 with the Distributive Property Solving with the Distributive Property 2

5 2-5 Literal and Formulas 2-6 Ratios, Rates, Conversions 2-7 Solving Proportions 2-8 Similar Figures *Converting rates using unit or dimensional analysis proportions using cross products multistep proportions *Comparing unit rates *Using similar figures to find indirect measurement *Using proportion to find unknown length in similar figures *Finding distances on maps using scale *Example of Solving for a Variable for a Variable 2 *Introduction to Ratios *Ratio Problem with Basic *Writing Proportions Lessons/percent/ proportions.html 2-9 Percents Lessons/percent/

6 2-10 Change Expressed as a Percent *Finding percent increase *Finding percent decrease *Finding the greatest possible error *Finding percent errors interest.html Lessons/percent/ change.html Chapter 3 Lesson Pearson Montgomery College prealgebra 3-1 Inequalities and the Graphs 3-2 Solving Inequalities (+,-) 3-3 Solving Inequalities (x,/) *Graphing solutions to one variable inequalities *Writing an inequality from a graph *Writing inequalities onestep whole number inequalities by adding onestep inequalities by subtracting onestep inequalities by multiplying onestep inequalities Montgomery College algebra & Problem Solving and Graphing Inequality Khan Academy *: Solving Inequalities Inequalities *Inequalities *Writing and Using Inequalities 2 *Writing and Using Inequalities 3 Other

7 3-4 Solving Multi-Step Inequalities 3-5 Working with Sets by dividing twostep inequalities multistep inequalities using the distributive property multistep inequalities with variables on both sides lessons/sets 3-6 Compound Inequalities 3-7 Absolute Value *Writing and solving a compound inequality containing And *Writing and solving a compound inequality containing Or Solving an absolute value equation an absolute value inequality *Absolute Value *Absolute Value 2 *Absolute Value Inequalities Example 1 Read the lesson, work the problems then do the additional lessons at the bottom

8 *Absolute Inequalities 2 *Writing and Using Inequalities 3-8 Unions and Intersections Chapter 4 Lesson Pearson Montgomery College prealgebra 4-1 Graphs to Relate 2 Quantities 4-2 Patterns and Linear Functions 4-3 Patterns and Nonlinear Functions 4-4 Graphing a Function Rule *Interpreting a graph that is related to events *Sketching a graph that is related to events *Identifying independent and dependent quantities *Writing a rule from a table *Making a table from a function rule *Finding the range of a function given Graphing *Graphing Linear Montgomery College algebra Graphs of Linear *Graphing Linear Khan Academy *: Graphing Lines 1 *Patterns in Sequences *Patterns in Sequences 2 * of Sequence Patterns *Finding the 100 th Term in a Sequence Other

9 4-5 Writing a Function Rule 4-6 Formalizing Relations and Functions 4-7 Sequences and Functions the domain *Modeling a function using three views *Discrete vs. continuous data *Graphing a nonlinear function *Writing a function from words *Determining a reasonable domain and range for a situation *Identifying functions using a mapping diagram *Identifying functions using the vertical line test *Finding the common difference of an arithmetic sequence *Finding the value of the nth term of an arithmetic *Introduction to Functions *Functions Part 2 *Functions (Part III) *Functions (part 4) *Domain of a Function *Functional Relationships *Testing if a Relationship is a Function *Domain and Range 1 *Domain and Range 2

10 sequence Struggling with other concepts: Graphing *The Rectangular Coordinate System Struggling with other concepts: Graphs of Linear *The Rectangular Coordinate System Chapter 5 Lesson Pearson Montgomery College prealgebra 5-1 Slope *Finding slope using rise/run *Finding the rate of change using a table *Finding the rate of change using a graph *Finding slope using coordinates *Finding the slope of horizontal or 5-2 Direct Variation vertical lines *Using a direct variation to describe a situation *Using a proportion as an equation of direct variation *Using a proportion to solve a direct variation Montgomery College algebra Graphs of Linear *Slope Khan Academy *Slope *slope 2 *Recognizing Linear Functions *Slope of a Line *Slope Example *Direct and Inverse Variation *Recognizing Direct and Inverse Variation *Direct Variation Other

11 5-3 Slope- Intercept Form 5-4 Point- Slope Form 5-5 Standard Form problem *Graphing a linear equation using slopeintercept form *Writing and equation given the slope/yintercept *Writing an equation from a graph *Analyzing linear graphs *Graphing linear equations using pointslope form *Writing an equation in point-slope form using a point and the slope *Writing an equation in point-slope form from a graph *Writing a linear equation using a table *Modeling real world situations using linear Graphs of Linear *Slope Intercept Form *slope 2 *slope 3 : Equation of a Line *Graphing a Line in Slope-Intercept Form *Equation of a Line 2 *Converting to Slope- Intercept Form *Point-Slope and Standard Form *X and Y Intercepts *X and Y Intercepts 2

12 5-6 Parallel and Perpendicular lines 5-7 Trend Lines equations *Finding the x- and y- intercepts from an equation in standard form *Graphing linear equations using intercepts *Determining whether lines are parallel *Writing equations of parallel lines *Determining whether lines are perpendicular *Writing equations of perpendicular lines *Making a scatter plot *Using scatter plots and trend lines to make predictions *Writing an equation for a trend line *Writing an equation for a line of best fit *Point-Slope and Standard Form *Parallel Lines *Parallel Lines 2 *Parallel Lines 3 *Perpendicular Lines *Perpendicular Lines 2 Other

13 *Slope and Y-Intercept Intuition Chapter 6 Lesson Pearson Montgomery College prealgebra 6-1 Solving Systems by Graphing 6-2 Solving Systems with Substitutions 6-3 Solving Systems using and interpreting as system of linear equations by graphing *Interpreting solutions of systems of linear equations *Analyzing special types of linear systems linear systems using substitutions linear systems for real-world situations using substitutions linear systems Montgomery College algebra Systems of Linear Linear Systems by Graphing Systems of Linear *The Substitution Method Systems of Linear *The Addition Khan Academy I Worked Systems by Graphing Systems by Graphing 2 Systems by Graphing 3 I Worked Systems by Substitution 1 Systems by Substitution 2 Systems by Substituion 3 *Systems of Other

14 Elimination 6-4 Applications of Linear Systems 6-5 Linear Inequalities using elimination, adding linear systems using elimination, multiplying first *Writing and solving linear systems *Finding a break even point *Modeling real world situations using linear inequalities Method Systems of Linear *Word Problems that Involve Systems Word Problems *Word Problems Involving Mixtures *Word Problems Involving Work *Word Problems Involving Rate, Time, & Distance Graphs of Linear *Graphing Linear Inequalities I Worked Systems by elimination Systems by Elimination 2 Systems by Elimination 3 I Worked *Systems and Rate Problems *Systems and Rate Problems 2 *Systems and Rate Problems 3 *Mixture Problems 1 *Mixture Problems 2 *Mixture Problems 3 I Worked and Graphing Linear Inequalities in Two Variables *Graphing Linear Inequalities in Two Variables 2 *Graphing Linear Inequalitities in Two Variables 3

15 6-6 Systems of Linear Inequalities *Graphing systems of linear inequalities *Writing a system of linear inequalities *Using a system of linear inequalities Word Problems *Word Problems Involving Systems Chapter 7 Lesson Pearson Montgomery College prealgebra 7-1 Zero and Negative Exponents 7-2 Scientific Notation *Simplifying exponential algebraic including negative values *Evaluating exponential *Writing a number in scientific notation *Writing a number in standard notation *Ordering numbers in scientific I Worked *Graphing Systems of Inequalities *Graphing Systems of Inequalities 2 *Graphing Systems of Inequalities 3 Montgomery College algebra Exponents & Polynomials * Negative Exponents Exponents & Polynomials * Scientific Notation Khan Academy *Scientific Notation 1 *Scientific Notation 2 *Scientific Notation 3 Other

16 7-3 Multiplying Powers with the Same Base 7-4 Multiplication Properties of Exponents 7-5 Division Properties of Exponents notation *Multiplying a number in scientific notation by a single number *Multiplying powers with the same base *Multiplying powers in an algebraic expression *Multiplying numbers in scientific notation *Simplifying a power raised to a power *Raising a product to a power *Raising a number in scientific notation to a power *Dividing numbers in scientific notation *Dividing algebraic containing exponents *Raising a Polynomials *Multiplication Properties of Exponents Exponents & Polynomials * Exponents Exponents & Polynomials * Rational Expressions & Exponents *Simplifying Expressions with Exponents *Exponent Rules 1 *Simplifying Expressions with Exponents 3 *Simplifying Expressions with Exponents 2

17 7-6 Exponential Functions quotient to a power *Evaluating an exponential function *Graphing an exponential function *Using an exponential function to model realworld situations *Finding the value of the nth term of geometric sequence Chapter 8 Lesson Pearson Montgomery College prealgebra 8-1 Add and Subtract Polynomials 8-2 Multiplying and Factoring *Classifying polynomials using the degree and number of terms *Adding polynomials *Subtracting polynomials *Multiplying a polynomial by a monomial *Finding the Polynomials *Adding & Subtracting Polynomials Polynomials *Multiplying Polynomials Montgomery College algebra Exponents & Polynomials * Adding & Subtracting Polynomials Exponents & Polynomials * Multiplying Polynomials Khan Academy *Adding and Subtracting Polynomials 1 *Adding and Subtracting Polynomials 2 *Adding and Subtracting Polynomials 3 *Factoring and the Distributive Property 2 Other

18 8-3 Multiplying Binomials 8-4 Multiplying Special Cases 8-5 Factoring x 2 + bx + c GCF of a polynomial *Factoring out a monomial using the GCF *Multiplying two binomials using the distributive property *Multiplying two binomials using FOIL *Applying the multiplication of polynomials *Multiplying a trinomial and binomial *Squaring a binomial *Squaring a binomial to find probability *Finding the difference of squares *Factoring trinomials of the type x 2 + bx + c where b is positive *Factoring trinomials of the type x 2 + bx + c where b is negative *Factoring *Factoring and the Distributive Property 3 *Level 1 Multiplying Expressions *Multiplying Polynomials 1 *Multiplying Polynomials 2 *Multiplying Polynomials 3 *Special Products of Polynomials *Special Products of Polynomials 2 *Special Products of Polynomials 3 a Quadratic by Factoring Quadratic by Factoring Quadratic by Factoring 2 Quadratic

19 8-6 Factoring ax 2 + bx + c 8-7 Factoring Special Cases 8-8 Factoring by Grouping trinomials of the type x 2 + bx c *Factoring trinomials with two variables *Factoring trinomials of the type ax 2 + bx + c where b is positive *Factoring trinomials of the type ax 2 + bx + c where b is negative *Factoring perfect square trinomials with a = 1 *Factoring perfect square trinomials with a not equal to 1 *Factoring the difference of two squares *Factoring a four-term polynomial by grouping *Factoring a trinomial by grouping *Using factoring of trinomials in real-world Factoring Polynomials *Factoring Trinomials in the Form ax 2 + bx + c by Factoring 3 *Factoring Special Products 1 *Factoring Special Products 2 *Factoring Trinomials by Grouping 1 *Factoring Trinomials by Grouping 2 *Factoring Trinomials by Grouping 3 *Factoring Trinomials by Grouping 4 *Factoring Trinomials

20 situations by Grouping 5 *Factoring Trinomials by Grouping 6 Chapter 9 Lesson Pearson Montgomery College prealgebra 9-1 Quadratic Graphs and their Properties 9-2 Quadratic Functions *Graphing a quadratic function using a table, y = ax 2 *Graphing a quadratic function using a table, y = ax 2 + c *Using the quadratic function to model the height of an object Example 1 Graphing a quadratic function, y = ax 2 + bx +c Struggling with the Basics? Factoring Polynomials *Greatest Common Factors Montgomery College algebra Quadratic *Graphing Quadratic Functions Struggling with the Basics? *Multiplying and Dividing Monomials 1 *Multiplying and Dividing Monomials 2 *Multiplying and Dividing Monomials 3 *Factoring and the Distributive Property Khan Academy *Quadratic Functions 1 *Quadratic Functions 2 *Quadratice Functions 3 Other

21 9-3 Solving Quadratic 9-4 Factoring to Solve Quadratic 9-5 Completing the Square 9-6 Quadratic Formula and Discriminant *Using the quadratic function to model the height of an object Example 2 quadratic equations by graphing quadratic equations by using square roots quadratic equations by factoring quadratic equations using completing the square quadratic equations using completing the square when a does not equal 1 quadratic equations using the Factoring Polynomials Using the Zero Property Quadratic *The Quadratic Formula *Introduction to the Quadratic Equation *Completing the Square *Completing the Square 1 *Completing the Square 2 *Completing the Square 3 *Completing the Square 4 *Quadratic Equation part 2

22 9-7 Linear, Quadratic, and Exponential Models quadratic formula realworld problems using the quadratic furmula *Choosing the appropriate method to solve quadratic equations *Using the discriminant to find the number of solutions and solve problems *Modeling data using a linear, quadratic, or exponential model example 1 *Modeling data using a linear, quadratic, or exponential model example 2 Word Problems *Word Problems Modeled by Quadratic *Quadratic Formula 1 *Quadratic Formula 2 *Quadratic Formula 3 *Applying Quadratic Functions 1 *Applying Quadratic Functions 2 *Applying Quadratic Functions 3

23 Chapter 10 Lesson Pearson Montgomery College prealgebra 10-1 Pythagorean Theorem 10-2 Simplifying Radicals 10-3 Operations with Radical *Using the Pythagorean Theorem to find the hypotenuse *Using the Pythagorean Theorem to find the leg *Using the converse of the Pythagorean Theorem *Simplifying radical involving products *Multiplying two radical *Simplifying radicals by dividing *Simplifying radical involving quotients, ize denominator *Simplifying radical sums and differences Montgomery College algebra Word Problems *Pythagorean Theorem Roots & Radicals *Simplifying Radical Expressions Roots & Radicals *Adding & Subtracting Radical Expressions Khan Academy *Pythagorean Theorem 1 *Pythagorean Theorem 2 *Pythagorean Theorem 3 *Simplifying Radical Expressions 1 *Simplifying Radical Expressions 2 *Simplifying Radical Expressions 3 Other

24 Expressions 10-4 Solving Radical 10-5 Graphing Square Root Functions *Simplifying radical products and quotients using the distributive property *Simplifying radical products and quotients using FOIL *Simplifying radical using conjugates proportions involving radical radical equations by isolating the radical *Using radical equations to solve problems *Identifying extraneous solutions *Identifying no solutions *Finding the domain and range of radical Radical 1 Radical 2 Radical 3 *Applying Radical 1 *Applying Radical 2 *Applying Radical 3

25 functions *Graphing radical functions *Graphing radical functions using a vertical translation *Graphing radical functions using a horizontal translation Struggling with the Basics? Roots & Radicals *Int roduction to Roots & Radicals Chapter 11 Lesson Pearson Montgomery College prealgebra 11-1 Simplifying Rational Expressions 11-2 x, / Rational Expressions *Simplifying a expression *Simplifying a expression by recognizing opposite factors *Multiplying using factoring *Multiplying Montgomery College algebra Rational Expressions *Simplifying Rational Expressions Rational Expressions *Multiplying & Dividing Rational Expressions Khan Academy *Simplifying Rational Expressions 1 *Simplifying Rational Expressions 2 *Simplifying Rational Expressions 3 *Multiplying and Dividing Rational Expressions 1 *Multiplying and Other

26 11-3 Divide Polynomials , - Rational Expressions by polynomials *Dividing by and polynomials *Dividing a polynomial by a monomial *Dividing a polynomial by a binomial *Dividing polynomials with a zero coefficient *Adding with like denominators *Subtracting with like denominators *Adding with unlike monomial denominators *Adding Rational Expressions *ic Least Common Denominators *Adding & Subtracting Rational Expressions Dividing Rational Expressions 2 *Multiplying and Dividing Rational Expressions 3 *ic Long Division *Adding and Subtracting Rational Expressions 1 *Adding and Subtracting Rational Expressions 2 *Adding and Subtracting Rational Expressions 3

27 with unlike polynomial denominators 11-5 Solving Rational equations equations using factoring a proportion a proportion, checking for extraneous solutions 11-6 Inverse *Writing the Variation equation of an inverse variation inverse variations *Determining direct or inverse variation *Determining whether realworld situations involve direct or inverse variation 11-7 Graphing *Graphing a Rational Expressions Containing Rational Expressions Rational 1 Rational 2 Rational 3 *Applying Rational 1 *Applying Rational 2 *Applying Rational 2

28 Rational Functions function using a vertical asymptote *Graphing a function using vertical and horizontal asymptotes *Describing the graph of different types of functions Struggling with the Basics *Domain Restrictions on ic Fractions

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