College Preparatory Math

College Preparatory Math Instructors: Name: John Fikes Room: L202 Phone: (469) 302­3824 Conference Time: 8:24AM ­ 9:12AM (2nd Period) E­mail: [email protected] Website ✓ Each teacher has a website for their class. Visiting this website on a regular basis will be instrumental to success in this course. “website” Text Beginning & Intermediate Algebra​, sixth edition by Elayn Marin­Gay. Course Description ​This is a high school course that provides a solid foundation in Algebra and relevant preparation for the student’s next mathematics course or for any non­mathematical courses that require an understanding of algebraic fundamentals. Student Learning Outcomes Upon successful completion of this course, students will: 1. Review all operation and properties of real numbers. 2. Understand algebraic reasoning and be able to apply that understanding to solve equations, inequalities and application problems. 3. Identify, graph, and evaluate a linear function including all linear attributes. 4. Solve a system of two linear equations and interpret the solution graphically and algebraically. 5. Review all operation and properties of polynomials and exponents. 6. Solve problems of quadratics by factoring in a variety of ways. 7. Review all operation and properties of rational and complex fractions. 8. Write and graph linear and nonlinear functions to solve problems involving combined variations. 9. Solve compound inequalities and absolute value problems. 10. Solve and simplify problems involving rational exponents, radicals and complex numbers. 11. Solve and graph quadratics using various methods. 12. Solve and simplify problems logarithms and exponential functions. Requirements ● Students should be in attendance each and every day. Because this curriculum is sequential and each lesson builds on from previous lessons, attendance is critical. ● Students are required to have class materials every day, including a ​composition or spiral notebook. Each teacher will be asking students to bring supplies to share with the class. Resources ✓ Assignments/practice problems will be available in class as well as online from the teacher’s College Math website and the textbook material. ‘website’ ✓ Graphing Calculator – It is imperative that students have a graphing calculator. Graphing calculators may be checked out from the school library with parental permission or purchased at most office supply stores. College Math classes use TI–84 Silver and TI–84 Silver Plus calculators. ✓ Online – There are online websites such as ​www.purplemath.com or ​www.brightstorm.com students may find helpful. ​www.desmos.com/calculator will provide students access to an online graphing calculator Tutoring Tutoring is available before and after school. Each teacher will have a tutoring schedule and will also make tutoring appointments when necessary. Students are encouraged to go to any available College Math teacher. Practice/ Homework Practice questions are given to enable the student to succeed on summative assessments. Practices that are not completed during the class period will be assigned for homework. Homework will be assigned at least twice per week. Projects Students will work on several individual and group projects throughout the year. These projects are intended to provide real­world applications of mathematical concepts. Evaluation Students’ work will be assessed on a regular basis. Assessments may include daily class work, quizzes, and chapter tests, as well as projects and performance­based assessments. Grade Categories Formative 30% of quarter grade Formative assessments (10 minimum per grading period) include​ ​class work and quizzes. Summative 70% of quarter grade Summative assessments (3 minimum per grading period) are cumulative. This category includes major tests, written assessments and project based assessments. No major tests are permitted to be sent home because many of them are developed for the entire district. Make­up/Retake Policy When a student is absent, it is his/her responsibility to obtain any missed notes or assignments upon returning to class. If a student misses a class for a planned extracurricular activity, it is preferred that the student comes in advance to get their classwork. Missed classwork and assessments must be made up before or after school. Most assignments will be online at mymathlabforschool.com and can be accessed at home. Each student has the right to retake a different form of a summative assessment one time for a maximum of an 80. Retakes of assessments in a unit must be retaken within two weeks of the first attempt. Before retaking a summative assessment, students must attend at least one College Math tutoring session and have completed all the homework assignments. Academic Honesty The department has realistically high expectations for academic honesty, academic behavior, effort, and attitude. ● Students are encouraged to collaborate on homework assignments. ● Students should never simply copy another’s assignment or misrepresent someone else’s work as their own. ● Students should not look on another’s paper during an assessment. ● Students should not have or use unauthorized materials during an assessment. ● Students should only write on an assessment while seated at their own desk. ● Students should not share information with others about an assessment after taking it, nor should they collect information about an assessment before taking it. This includes, but is not limited to, verbally sharing information, texting information and posting information on any social media site. Cheating and Plagiarism Following a complete investigation, any student caught cheating will receive a grade of "0”. If the assignment in question is copied from another student, both students will be penalized with a grade of “0”. Students caught cheating do not fall under the MISD Make­Up Policy and are not eligible to redo the assignment. Examples of CHEATING include, but are not limited to the below­mentioned items: • Copying by hand or copying with the aide of media sources (text messaging, faxing, emailing, photographing, tweeting, posting via media), or in any way duplicating assignments that are turned in, wholly or in part, as a student’s original work • Exchanging assignments, or portions of assignments, with other students and submitting for a grade, as one’s own work • Using books, notes, reviews, study guides, etc. during tests or quizzes without the permission of the teacher • Giving and/or receiving answers during tests or quizzes • Submitting material written by someone else or rephrasing the ideas of another without giving the author’s name or source • Submitting/presenting purchased papers/projects/assignments, in their entirety, or in portions, as your own form the Internet or other sources, including but not limited to tutors, parents, siblings, or friends • Assisting in plagiarism by providing your work to others. College Preparatory Objectives Upon successful completion of this course students will: 1. Review of Real Numbers 1.1 Study Skill Tips for Success in Mathematics. 1.2 Symbols and Sets of Numbers: (i) Use a number line to order numbers. (ii) Translate Sentences into mathematical statements. (iii) Identify natural Numbers, whole Numbers, integers, rational numbers, irrational numbers, and real numbers. (iv) Find the absolute value of a real number. 1.3 Fractions and Mixed Numbers: (i) Write fractions in simplest form. (ii) Multiply and divide fractions. (iii) Add and subtract fractions. (iv) Perform operations on mixed numbers. 1.4 Exponents, Order of Operations, Variable Expressions, and Equations: (i) Define and Use Exponents and the order of operations. (ii) Evaluate algebraic expressions, given replacement values for variables. (iii) Determine whether a number is a solution of a given equation. (iv) Translate phrases into expressions and sentences into statements. 1.5 Adding Real Numbers: (i) Add real numbers. (ii) Solve applications that involve addition of real numbers. (iii) Find the opposite of a number. 1.6 Subtracting Real Numbers: (i) Subtract real number. (ii) Add and subtract real numbers. (iii) Evaluate algebraic expressions using real number. (iv) Solve applications that involve subtraction of real numbers. (v) Find complementary and supplementary angles. 1.7 Multiplying and Dividing Real Numbers: (i) Multiplying real numbers. (ii) Find the reciprocal of a real number. (iii) Divide real numbers. (iv) Evaluate expressions using real numbers. (v) Solve applications that involve multiplication or division of real numbers. 1.8 Properties of Real Numbers: (i) Use the commutative and associative properties. (ii) Use the distributive property. (iii) Use the identify and inverse properties. 2. Equations, Inequalities, and Problem Solving 2.1 Simplifying Algebraic Expressions: (i) Identify terms, like terms, and unlike terms. (ii) Combine like terms. (iii) Use the distributive property to remove parentheses. (iv) Write word phrases as algebraic expressions. 2.2 The Addition and Multiplication Property of Equality: (i) Define linear equations and use the addition property of equality to solve linear equations. (ii) Use the multiplication property of equality to solve linear equations. (iii) Use both properties of equality to solve linear equations. (iv) Write word phrases as algebraic expressions. 2.3 Solving Linear Equations: (i) Apply a general strategy for solving a linear equation. (ii) Solve equations containing fractions. (iii) Solve equations containing decimals. (iv) Recognize identities and equations with no solution. 2.4 An Introduction to Problem Solving: (i) Solve problems involving direct translations. (ii) Solve problems involving relationships among unknown quantities. (iii) Solve problems involving consecutive integers. 2.5 Formulas and Problem Solving: (i) Use formulas to solve problems. (ii) Solve a formula or equation for one of its variables 2.6 Percent and Mixture Problem Solving: (i) Solve percent equations. (ii) Solve discount and mark­up problems. (iii) Solve percent of increase and percent of decrease problems. (iv) Solve mixture problems. 2.7 Further Problem Solving: (i) Solve problems involving distance. (ii) Solve problems involving money. (iii) Solve problems involving interest. 2.8 Solving Linear Inequalities: (i) Define linear inequality in one variable, graph solution sets on a number line, and use interval notation. (ii) Solve linear inequalities. (iii) Solve compound inequalities. (iv) Solve inequality applications. 3. Graphing 3.1 Reading Graphs and the Rectangular Coordinate System: (i) Read bar and line graphs. (ii) Define the rectangular coordinate system and plot ordered pairs of numbers. (iii) Graph paired data to create a scatter diagram. (iv) Determine whether an ordered pair is a solution of an equation in two variables. (v) Find the missing coordinate of an ordered pair solution, given one coordinate of the pair. 3.2 Graphing Linear Equations: (i) Identify linear equations. (ii) Graph a linear equation by finding and plotting ordered pair solutions. 3.3 Intercepts: (i) Identify intercepts of a graph. (ii) Graph a linear equation by finding and plotting intercepts. (iii) Identify and graph vertical and horizontal lines. 3.4 Slope and Rate of Change: (i) Find the slope of a line given two points of the line. (ii) Find the slope of line given its equation. (iii) Find the slopes of horizontal and vertical lines. (iv) Compare the slopes of parallel and perpendicular lines. (v) Interpret slope as a rate of change. 3.5 Equations of Lines: (i) Use the slope­intercept form to graph a linear equation. (ii) Use the slope­intercept form to write an equation of a line. (iii) Use the point­slope form to find an equation of a line given its slope and a point of the line. (iv) Use the point­slope form to find an equation of a line given two points of the line. (v) Find equations of vertical and horizontal lines. (vi) Use the point­slope form to solve problems. 3.6 Functions: (i) Identify relations, domains, and ranges. (ii) Identify functions. (iii) Use the vertical line test. (iv) Use function notation. 4. Solving Systems of Linear Equations 4.1 Solving Systems of Linear Equations by Graphing: (i)Determine if an ordered pair is a solution of a system of equation in two variables. (ii) Solve a system of linear equation by graphing. (iii) Without graphing, determine the number of solutions of a system. 4.2 Solving Systems of Linear Equations by Substitution: (i) Use the substitution method to solve a system of linear equations. 4.3 Solving Systems of Linear Equations by Addition: (i) Use the addition method to solve a system of linear equations. 4.4 Solving Systems of Linear Equations in Three Variables: (i) Solve a system of three linear equations in three variables. 4.5 Systems of Linear Equations and Problem Solving: (i) Solve problems that can be modeled by a system of two linear equations. (ii) Solve problems with cost and revenue functions. (iii) Solve problems that can be modeled by a system of three equations. 5. Exponents and Polynomials 5.1 Exponents: (i) Evaluate exponential expressions. (ii) Use the product rule for exponents. (iii) Use the power rule for exponents. (iv) Use the power rules for products and quotients. (v) Use the quotient rule for exponents, and define a number raised to the 0 power. (vi) Decide which rule(s) to use to simplify an expression. 5.2 Polynomial Functions and Adding and Subtracting Polynomials: (i) Define polynomial, monomial, binomial, trinomial, and degree. (ii) Define polynomial functions. (iii) Simplify a polynomial by combining like terms. (iv) Add and subtract polynomials. 5.3 Multiplying Polynomials: (i) Multiplying monomials. (ii) Use the distributive property to multiply polynomials. (iii) Multiply polynomials vertically 5.4 Specials Products: (i) Multiply two binomials using the FOIL method. (ii) Square a binomial. (iii) Multiply the sum and difference of two terms. (iv) Use special products to multiply binomials. 5.5 Negative Exponents and Scientific Notation: (i) Simplify expressions containing negative exponents. (ii) Use all the rules and definitions for exponents to simplify exponential expression. (iii) Write numbers in scientific notation. (iv) Convert numbers from scientific notation to standard form. (v) Perform operations on numbers written in scientific notation. 5.6 Dividing Polynomials: (i) Divide a polynomial by a monomial. (ii) Use long division to divide a polynomial by another polynomial. 5.7 Synthetic Division and the Remainder Theorem: (i) Use synthetic division to divide a polynomial by a monomial. (ii) Use the remainder theorem to evaluate polynomials. 6. Factoring Polynomials. 6.1 The Greatest Common Factor and Factoring by Grouping: (i) Find the greatest common factor of a list of integers. (ii) Find the greatest common factor of a list of terms. (iii) Factor out the greatest common factor from a polynomial. (iv) factor a polynomial by grouping. 6.2 Factoring Trinomials of the Form ​x2​ + ​bx + ​c: (i) Factor trinomials of the form ​x2​ + bx + ​c. (ii) Factor out the greatest common factor and then factor a trinomial of the form x2​ + ​bx + ​c. 6.3 Factoring Trinomials of the Form ​ax2​ + ​bx + ​c and Perfect Square Trinomials: (i) Factor trinomials of the form ​ax​2​ + ​bx + ​c, where a ≠ 1. (ii) Factor out a GCF before factoring a trinomial of the form ​ax​2​ + ​bx + ​c. (iii) Factor perfect square trinomials. 6.4 Factoring Trinomials of the Form ​ax​2​ + ​bx + ​c by Grouping: (i) Use the grouping method to factor trinomials of the form ​ax​2​ + ​bx + ​c. 6.5 Factoring Binomials: (i) Factor the difference of two squares. (ii) Factor the sum or difference of two cubes. 6.6 Solving Quadratic Equations by Factoring: (i) Solve quadratic equations by factoring. (ii) solve equations with degree greater than 2 by factoring. (iii) Find the x­intercepts of the graph of a quadratic equation in two variables. 6.7 Quadratic Equations and Problem Solving: (i) Solve problems that can be modeled by quadratic equations. 7. Rational Expressions 7.1 Rational Functions and Simplifying Rational Expressions: (i) Find the domain of a rational function. (ii) Simplify or write rational expressions in lowest terms. (iii) a
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Write equivalent rational expressions of the form − b = b = −b . ​(iv) Use rational functions in applications. 7.2 Multiplying and Dividing Rational Expressions: (i) Multiply rational expressions. (ii) Divide rational expressions. (iii) Multiply or divide rational expressions. (iv) Convert between units of measure. 7.3 Adding and Subtracting rational Expressions with Common Denominators and least Common Denominator: (i) Add or subtract rational expressions with the same denominator. (ii) Find the least common denominator of list of rational expressions. (iii) Write a rational expression as an equivalent expression whose denominator is given. 7.4 Adding and Subtracting Rational Expressions with Unlike Denominators: (i) Add and subtract rational expressions with unlike denominators. 7.5 Solving Equations Containing Rational Expressions: (i) Solve equations containing rational expressions. (ii) Solve equations containing rational expressions for a specified variable. 7.6 Proportion and Problems Solving with Rational Equations: (i) Solve proportions. (ii) Use proportions to solve problems. (iii) Solve problems about numbers. (iv) Solve problems about work. (v) Solve problems about distance. 7.7 Simplifying Complex Fractions: (i) Simplify complex fractions by simplifying the numerator and denominator and then divide. (ii) Simplify complex fractions by multiplying by a common denominator. (iii) Simplify expressions with negative exponents. 8. More on Functions and Graphs 8.1 Graphing and Writing Linear Functions: (i) Graph linear functions. (ii) Write an equation of a line using function notation. (iii) Find equations of parallel and perpendicular lines. 8.2 Reviewing Function Notation and Graphing Nonlinear Functions: (i) Review function notation. (ii) Find square roots of numbers. (iii) Graph nonlinear functions. 8.3 Graphing Piecewise­Defined Functions and Shifting and Reflecting Graphs of Functions: (i) Graph piecewise­defined functions. (ii) Vertical and horizontal shifts. (iii) Reflect graphs. 8.4 Variation and Problem Solving: (i) Solve problems involving direct variation. (ii) Solve problems involving inverse variation. (iii) Solve problems involving joint variation. (iv) Solve problems involving combined variation. 9. Inequalities and Absolute Valve 9.1 Compound Inequalities: (i) Find the intersection of two sets. (ii) Solve compound inequalities containing ​and.​ (iii) Find the union of two sets. (iv) Solve compound inequalities containing ​or. 9.2 Absolute Value Equations: (i) Solve absolute value equations. 9.3 Absolute Value Equation: (i) Solve absolute value inequalities of the form |X | < a . (ii) Solve absolute value inequalities of the form |X | > a . 9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities: (i) Graph a linear inequality in two variables. (ii) Solve a system of linear inequalities. 10. Rational Exponents, Radicals, and Complex Numbers 10.1 Radicals and Radical Functions: (i) Find square roots. (ii) Approximate roots. (iii) Find cube roots. (iv) Find ​nth roots. (v) Find​ √an ​where ​a is a real number. (vi) Graph n
square and cube root functions. 1
10.2 Rational Exponents: (i) Understand the meaning of​ a n . ​ (ii) Understand the m
meaning of a n . ​ (iii) Understand the meaning of a
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. ​ (iv) Use rules for exponents to simplify expressions that contain rational exponents. (v) Use rational exponents to simplify radical expressions. 10.3 Simplifying Radical Expressions: (i) Use the product rule for radicals. (ii) Use the quotient rule for radicals. (iii) Simplify radicals. (iv) Use the distance and midpoint formulas. 10.4 Adding, Subtracting, and Multiplying Radicals Expressions: (i) Add or subtract radical expressions. (ii) Multiply radical expressions. 10.5 Rationalizing Denominators and Numerators of Radical Expressions: (i) Rationalize Denominators. (ii) Rationalize denominators having two terms. (iii) Rationalize numerators. 10.6 Radical Equations and Problem Solving: (i) Solve equations that contain radical expressions. (ii) Use the Pythagorean Theorem to model problems. 10.7 Complex Numbers: (i) Write square roots of negative numbers in the form b​i. (ii) Add or subtract complex numbers. (iii) Multiply complex numbers. (iv) Divide complex numbers. (v) Raise​ i to powers. 11. Quadratic Equations and Functions 11.1 Solving Quadratic Equations by Completing the Square: (i) Use the square root property to solve quadratic equations. (ii) Solve quadratic equations by completing the square. (iii) Use quadratic equations to solve problems. 11.2 Solving Quadratic Equations by the Quadratic Formula: (i) Solve quadratic equations by using the quadratic formula. (ii) Determine the number and type of solutions of a quadratic equation by using the discriminant. (iii) Solve problem modeled by quadratic equations. 11.3 Solving Equations by Using Quadratic Methods: (i) Solve various equations that are quadratic in form. (ii) Solve problems that lead to quadratic equations. 11.4 Nonlinear Inequalities: (i) Solve polynomial inequalities. (ii) Solve inequalities that contain rational expressions with variables in the denominator. 11.5 Quadratic Functions and Their Graphs: (i) Graph quadratic functions of the form f(​x) = ​x2​ + ​k. (ii) Graph quadratic functions of the form ​f(​x) = (​x ­ h)​2​. (iii) Graph quadratic functions of the form ​f(​x) = (​x ­ h)​2​ + ​k. (iv) Graph quadratic functions of the form ​f(​x) = ​ax2​. (v) Graph quadratic functions of the form ​f(​x) = ​a(​x ­ h)​2​ + ​k. 11.6 Further Graphing of Quadratic Functions: (i) Write quadratic functions in the form y = ​a(​x ­ h)​2​ + ​k. (ii) Derive a formula for finding the vertex of a parabola. (iii) Find the minimum or maximum value of a quadratic function. 12. Exponential and Logarithmic Functions 12.1 The Algebra of Functions; Composite Functions: (i) Add, subtract, multiply, and divide functions. (ii) Construct composite functions. 12.2 Inverse Functions: (i) Determine whether a function is a one­to­one function. (ii) Use the horizontal line test to decide whether a function is a one­to­one function. (iii) Find the inverse of a function. (iv) Find the equation of the inverse of a function. (v) Graph functions and their inverses. (vi) Determine whether two functions are inverses of each other. 12.3 Exponential Functions: (i) Graph exponential functions. (ii) Solve equation of the form bx = by. (iii) Solve problems modeled by exponential equations. 12.4 Exponential Growth and Decay Functions: (i) Model exponential growth. (ii) Model exponential decay. 12.5 Logarithmic Functions: (i) Write exponential equations with logarithmic notation and write logarithmic equations with exponential notation. (ii) Solve logarithmic equations by using exponential notation. (iii) Identify and graph logarithmic functions. 12.6 Properties of Logarithms: (i) Use the product property of logarithms. (ii) Use the quotient property of logarithms. (iii) Use the power property of logarithms. (iv) Use the properties of logarithms together. 12.7 Common logarithms, Natural Logarithms, and Change Base: (i) Identify common Logarithms and approximate them by calculator. (ii) Evaluate common logarithms of powers of 10. (iii) Identify natural logarithms and approximate them by calculator. (iv) Evaluate natural logarithms of powers of ​e. (v) Use the change of base formula. 12.8 Exponential and Logarithmic Equations and Problem Solving: (i) Solve exponential equations. (ii) Solve logarithmic equations. (iii) Solve problems that can be modeled by exponential and logarithmic equations. The student will demonstrate competency in the use of a graphing calculator by: Using the ROOT (ZERO) and INTERSECT features to solve an equation. Using the MATRIX feature to solve a system of equations. Checking solutions to an equation using the VARS, VALUE, STO or TABLE feature. Verify an ordered pair solution for a specified linear equation in two variables using the TABLE feature of a graphing calculator.​ Graph functions and use the result to answer questions about the function (​e.g.​, max, min, zeros). Using the features to verify the simplification of a radical expression, when appropriate. Find the decimal approximation of a square root using a calculator.