This course provides a working knowledge of college-level algebra and its applications. Emphasis is on solving linear and quadratic equations, word problems, and polynomial, rational and radical equations and applications.
Students perform operations on real numbers and polynomials, and simplify algebraic, rational, and radical expressions. Arithmetic and geometric sequences are examined, and linear equations and inequalities are discussed.
Students learn to graph linear, quadratic, absolute value, and piecewise-defined functions, and solve and graph exponential and logarithmic equations.
Other topics include solving applications using linear systems, and evaluating and finding partial sums of a series.
Includes 10 hours of 1-on-1 live, on demand instructional support from SMARTHINKING.
Introductory Algebra is a not-for-credit course which prepares students to successfully complete College Algebra.
Introductory Algebra takes the learner through topics that teach the basics of algebra. Real-life scenarios students can relate to are used to teach difficult concepts and topics. After a pre-algebra review, this course focuses on the basics of algebra and includes math vocabulary and notation, operations with numbers, fractions, decimals, percentages, and quadratic equations. Students also learn to read and interpret graphs.
Introductory Algebra is a not-for-credit course which prepares students to successfully complete College Algebra. For more information visit: http://straighterline.com/courses/descriptions/introductory-algebra/
The document provides an overview of math units for grades K-6. It lists the unit titles and brief descriptions of the key concepts and skills covered in each unit, organized by grade level. The units progress from foundational topics like numbers, counting, and basic operations in early grades to more advanced topics like fractions, decimals, geometry, and algebra in later grades.
- The document is an algebra 1 syllabus for the fall semester from September 7 to February 3 that outlines what topics will be covered each quarter, assignments, tests, and resources for extra help.
- The first quarter covers understanding the language of algebra, linear equations, and graphing linear equations. The second quarter covers analyzing and graphing linear equations, systems of linear equations, and linear inequalities. Tests will be every 2 weeks, quizzes weekly, and homework daily. Students can get extra help by asking the teacher before or after school or forming a study group.
This document appears to be the cover page and instructions for a GCSE mathematics exam. It provides information such as the exam date and time allotted, materials allowed, instructions for candidates, and a formulae page. Candidates are instructed to show all work, not spend too long on any single question, and attempt all 23 questions, writing their answers in the provided spaces. The formulae page lists various mathematical formulas that may be useful for the exam but on which candidates are not allowed to write.
This document provides instructions and information for a GCSE mathematics exam, including the exam paper reference number, candidate details to fill in, materials allowed, instructions to candidates, information about marking, and a formulae page. It specifies that the exam is 2 hours long and contains 23 questions covering a range of mathematics topics. Candidates are advised to show their working, work steadily, and attempt all questions.
This document contains a rubric for evaluating a student project on mathematical art. The rubric assesses the project across several criteria including academic content, communication, global awareness, work ethic, and oral communication. For the academic content criterion, the rubric evaluates whether the student drawing contains the correct number of lines, accurate slope calculations, and correct line equations. It also assesses whether multiple quadrants of the coordinate grid are used. The communication criterion examines whether all calculations and diagrams are shown and the process is clearly explained. It also evaluates the paragraph explaining the Asian theme of the drawing. The global awareness criterion assesses whether the drawing has an accurate Asian theme. The work ethic criterion rates whether all aspects of the project were
This document describes expressions in Verilog. It defines expressions as constructs that combine operands and operators to produce a result. Expressions can include numbers, nets, registers, operators, and functions. The document discusses the different types of operators available in Verilog, including arithmetic, relational, equality, logical, bit-wise, and reduction operators. It provides precedence rules and examples of using different operators in expressions.
1. The document provides instructions for a GCSE mathematics exam, including information about the structure, time allowed, materials permitted and formulas.
2. It instructs students to write their name, center number and candidate number in the boxes at the top of the page.
3. Students are advised to read questions carefully, try to answer every question, check answers at the end and use the time guide for each question.
Introductory Algebra takes the learner through topics that teach the basics of algebra. Real-life scenarios students can relate to are used to teach difficult concepts and topics. After a pre-algebra review, this course focuses on the basics of algebra and includes math vocabulary and notation, operations with numbers, fractions, decimals, percentages, and quadratic equations. Students also learn to read and interpret graphs.
Introductory Algebra is a not-for-credit course which prepares students to successfully complete College Algebra. For more information visit: http://straighterline.com/courses/descriptions/introductory-algebra/
The document provides an overview of math units for grades K-6. It lists the unit titles and brief descriptions of the key concepts and skills covered in each unit, organized by grade level. The units progress from foundational topics like numbers, counting, and basic operations in early grades to more advanced topics like fractions, decimals, geometry, and algebra in later grades.
- The document is an algebra 1 syllabus for the fall semester from September 7 to February 3 that outlines what topics will be covered each quarter, assignments, tests, and resources for extra help.
- The first quarter covers understanding the language of algebra, linear equations, and graphing linear equations. The second quarter covers analyzing and graphing linear equations, systems of linear equations, and linear inequalities. Tests will be every 2 weeks, quizzes weekly, and homework daily. Students can get extra help by asking the teacher before or after school or forming a study group.
This document appears to be the cover page and instructions for a GCSE mathematics exam. It provides information such as the exam date and time allotted, materials allowed, instructions for candidates, and a formulae page. Candidates are instructed to show all work, not spend too long on any single question, and attempt all 23 questions, writing their answers in the provided spaces. The formulae page lists various mathematical formulas that may be useful for the exam but on which candidates are not allowed to write.
This document provides instructions and information for a GCSE mathematics exam, including the exam paper reference number, candidate details to fill in, materials allowed, instructions to candidates, information about marking, and a formulae page. It specifies that the exam is 2 hours long and contains 23 questions covering a range of mathematics topics. Candidates are advised to show their working, work steadily, and attempt all questions.
This document contains a rubric for evaluating a student project on mathematical art. The rubric assesses the project across several criteria including academic content, communication, global awareness, work ethic, and oral communication. For the academic content criterion, the rubric evaluates whether the student drawing contains the correct number of lines, accurate slope calculations, and correct line equations. It also assesses whether multiple quadrants of the coordinate grid are used. The communication criterion examines whether all calculations and diagrams are shown and the process is clearly explained. It also evaluates the paragraph explaining the Asian theme of the drawing. The global awareness criterion assesses whether the drawing has an accurate Asian theme. The work ethic criterion rates whether all aspects of the project were
This document describes expressions in Verilog. It defines expressions as constructs that combine operands and operators to produce a result. Expressions can include numbers, nets, registers, operators, and functions. The document discusses the different types of operators available in Verilog, including arithmetic, relational, equality, logical, bit-wise, and reduction operators. It provides precedence rules and examples of using different operators in expressions.
1. The document provides instructions for a GCSE mathematics exam, including information about the structure, time allowed, materials permitted and formulas.
2. It instructs students to write their name, center number and candidate number in the boxes at the top of the page.
3. Students are advised to read questions carefully, try to answer every question, check answers at the end and use the time guide for each question.
The document provides an overview of math topics that readers should already know, including properties of exponents, factoring polynomials, operations on rational expressions, operations on radicals, and linear functions. It lists specific skills under each topic, such as multiplying and dividing powers for exponents or factoring out a monomial. The document concludes by assigning practice problems from different books to reinforce these math concepts.
This unit template from the Hempfield School District covers tools of algebra. It includes the unit title, teachers who developed it, dates, and topics to be covered such as the real number system, order of operations, algebraic expressions, equations, inequalities, and probability. Students will understand properties of real numbers and how to use them to simplify expressions and solve equations and inequalities. They will also learn about experimental and theoretical probability. The unit will be assessed through benchmarks, self-assessments, and performance tasks.
This two semester algebra 1 course covers linear, quadratic, and other foundational algebraic concepts. Students will learn to perform operations with real numbers, simplify expressions, graph and solve equations and inequalities, work with functions and polynomials, and apply algebraic skills to probability and data problems. Assessment is based on completing homework, projects for each unit, and passing unit tests with a proficiency of 70% or higher. The course addresses state standards for algebra 1.
Derivative Free Optimization and Robust OptimizationSSA KPI
The document summarizes presentations on nonsmooth optimization, robust optimization, and derivative-free optimization given at the 4th International Summer School in Kiev, Ukraine. Gerhard Weber and Basak Akteke-Ozturk presented on nonsmooth optimization and its applications in clustering problems. Robust optimization approaches were discussed for problems with uncertain parameters. Methods for minimizing functions without computing derivatives, known as derivative-free optimization, were also covered. Examples included trust-region algorithms and using models based on interpolation. Semidefinite programming relaxations for support vector clustering were mentioned.
This document outlines the learning outcomes for Montana State University Billings' M098 math course. It lists 22 math skills that students are expected to gain proficiency in, organized under the topics of arithmetic, algebra, functions, geometry, trigonometry, and calculus. For each outcome, it indicates if it will be assessed at a basic (B), competent (C), distinguished (D), or exemplary (E) level.
This document appears to be a rubric for evaluating a student project on mathematical art. It provides criteria for evaluating the project on academic content, communication, global awareness, work ethic, and oral communication. For each criteria, it lists the requirements to meet an unsatisfactory, proficient, or advanced level of achievement. Requirements for proficient level include using at least 15 lines in the drawing with correct coordinates and slopes, showing all calculations, explaining the Asian theme in writing, and completing all aspects of the project on time. Requirements for advanced level include additional details like using over 15 lines and fractional slopes in the drawing, clearly explaining the process, and completing all aspects of the project before the due time.
This course helps students develop quality writing skills by explaining and identifying the steps involved in the writing process.
Five types of writing are examined-compare/contrast, argumentative, persuasive, narrative, and descriptive. The importance of proper grammar, punctuation, and spelling is highlighted.
Students also learn research techniques, as well as how to edit and revise their work.
SMARTHINKING writing professionals will carefully review and provide personal feedback to students for 5 graded essays and 7 essay drafts.
Samacheer kalvi syllabus for 10th mathsSeeucom Sara
This document provides the syllabus for Sets and Functions from the 10th standard Tamil Nadu state board curriculum. It outlines the key topics to be covered, including introduction to sets, operations on sets, properties of set operations, De Morgan's laws, functions, and cardinality of sets. The expected learning outcomes and number of periods allocated for each topic are also specified. Teaching strategies like using Venn diagrams, real-life examples, and pattern approaches are recommended to help students understand the concepts.
This course examines the fundamental process, theories, and methods that enhance a student's overall writing ability. It introduces various strategies for writing within multiple disciplines and professions. This course examines basic principles of effective college-level writing through drafting and revising sentences, paragraphs, and essays. Topics to improve sentence structure and clarity include grammar, punctuation, and word choice. In addition to learning proper research techniques, students explore various writing genres including narration, cause and effect, compare and contrast, definition, and argumentation.
Developmental Writing is a not-for-credit course which prepares students to successfully complete English Composition I.
The document discusses inequalities and their solutions. It defines absolute and conditional inequalities and explains how to represent solutions using interval, set, and graphical notation. Methods are presented for solving linear, polynomial, rational, and absolute value inequalities. Key steps include determining intervals where an expression is positive or negative, identifying valid intervals based on inequality signs, and expressing the solution in interval notation. Examples are provided throughout to demonstrate these techniques.
1) The document discusses the differences between linear equations and inequalities in two variables. Linear equations use the equal sign while inequalities use symbols like <, >, ≤, ≥, ≠.
2) The graph of a linear equation is a single line, while the graph of an inequality shows the shaded region that satisfies the inequality. For < or > the line is broken, and for ≤ or ≥ the line is solid.
3) The document provides steps for graphing a linear inequality in two variables: graph the line by changing the inequality to an equation, use a test point to determine which side to shade, and shade the area where the test point satisfies the inequality.
How to Manage Reception Report in Odoo 17Celine George
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
🔥🔥🔥🔥🔥🔥🔥🔥🔥
إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
The document provides an overview of math topics that readers should already know, including properties of exponents, factoring polynomials, operations on rational expressions, operations on radicals, and linear functions. It lists specific skills under each topic, such as multiplying and dividing powers for exponents or factoring out a monomial. The document concludes by assigning practice problems from different books to reinforce these math concepts.
This unit template from the Hempfield School District covers tools of algebra. It includes the unit title, teachers who developed it, dates, and topics to be covered such as the real number system, order of operations, algebraic expressions, equations, inequalities, and probability. Students will understand properties of real numbers and how to use them to simplify expressions and solve equations and inequalities. They will also learn about experimental and theoretical probability. The unit will be assessed through benchmarks, self-assessments, and performance tasks.
This two semester algebra 1 course covers linear, quadratic, and other foundational algebraic concepts. Students will learn to perform operations with real numbers, simplify expressions, graph and solve equations and inequalities, work with functions and polynomials, and apply algebraic skills to probability and data problems. Assessment is based on completing homework, projects for each unit, and passing unit tests with a proficiency of 70% or higher. The course addresses state standards for algebra 1.
Derivative Free Optimization and Robust OptimizationSSA KPI
The document summarizes presentations on nonsmooth optimization, robust optimization, and derivative-free optimization given at the 4th International Summer School in Kiev, Ukraine. Gerhard Weber and Basak Akteke-Ozturk presented on nonsmooth optimization and its applications in clustering problems. Robust optimization approaches were discussed for problems with uncertain parameters. Methods for minimizing functions without computing derivatives, known as derivative-free optimization, were also covered. Examples included trust-region algorithms and using models based on interpolation. Semidefinite programming relaxations for support vector clustering were mentioned.
This document outlines the learning outcomes for Montana State University Billings' M098 math course. It lists 22 math skills that students are expected to gain proficiency in, organized under the topics of arithmetic, algebra, functions, geometry, trigonometry, and calculus. For each outcome, it indicates if it will be assessed at a basic (B), competent (C), distinguished (D), or exemplary (E) level.
This document appears to be a rubric for evaluating a student project on mathematical art. It provides criteria for evaluating the project on academic content, communication, global awareness, work ethic, and oral communication. For each criteria, it lists the requirements to meet an unsatisfactory, proficient, or advanced level of achievement. Requirements for proficient level include using at least 15 lines in the drawing with correct coordinates and slopes, showing all calculations, explaining the Asian theme in writing, and completing all aspects of the project on time. Requirements for advanced level include additional details like using over 15 lines and fractional slopes in the drawing, clearly explaining the process, and completing all aspects of the project before the due time.
This course helps students develop quality writing skills by explaining and identifying the steps involved in the writing process.
Five types of writing are examined-compare/contrast, argumentative, persuasive, narrative, and descriptive. The importance of proper grammar, punctuation, and spelling is highlighted.
Students also learn research techniques, as well as how to edit and revise their work.
SMARTHINKING writing professionals will carefully review and provide personal feedback to students for 5 graded essays and 7 essay drafts.
Samacheer kalvi syllabus for 10th mathsSeeucom Sara
This document provides the syllabus for Sets and Functions from the 10th standard Tamil Nadu state board curriculum. It outlines the key topics to be covered, including introduction to sets, operations on sets, properties of set operations, De Morgan's laws, functions, and cardinality of sets. The expected learning outcomes and number of periods allocated for each topic are also specified. Teaching strategies like using Venn diagrams, real-life examples, and pattern approaches are recommended to help students understand the concepts.
This course examines the fundamental process, theories, and methods that enhance a student's overall writing ability. It introduces various strategies for writing within multiple disciplines and professions. This course examines basic principles of effective college-level writing through drafting and revising sentences, paragraphs, and essays. Topics to improve sentence structure and clarity include grammar, punctuation, and word choice. In addition to learning proper research techniques, students explore various writing genres including narration, cause and effect, compare and contrast, definition, and argumentation.
Developmental Writing is a not-for-credit course which prepares students to successfully complete English Composition I.
The document discusses inequalities and their solutions. It defines absolute and conditional inequalities and explains how to represent solutions using interval, set, and graphical notation. Methods are presented for solving linear, polynomial, rational, and absolute value inequalities. Key steps include determining intervals where an expression is positive or negative, identifying valid intervals based on inequality signs, and expressing the solution in interval notation. Examples are provided throughout to demonstrate these techniques.
1) The document discusses the differences between linear equations and inequalities in two variables. Linear equations use the equal sign while inequalities use symbols like <, >, ≤, ≥, ≠.
2) The graph of a linear equation is a single line, while the graph of an inequality shows the shaded region that satisfies the inequality. For < or > the line is broken, and for ≤ or ≥ the line is solid.
3) The document provides steps for graphing a linear inequality in two variables: graph the line by changing the inequality to an equation, use a test point to determine which side to shade, and shade the area where the test point satisfies the inequality.
How to Manage Reception Report in Odoo 17Celine George
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
🔥🔥🔥🔥🔥🔥🔥🔥🔥
إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Algebra Syllabus
1. College Algebra
Course Text
Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition,
McGraw-Hill, 2008, ISBN: 978-0-07-286738-1
Course Description
This course provides a working knowledge of college-level algebra and its applications.
Emphasis is placed upon the solution and the application of linear and quadratic equations,
word problems, polynomials, and rational and radical equations. Students perform operations
on real numbers and polynomials and simplify algebraic, rational, and radical expressions.
Arithmetic and geometric sequences are examined, and linear equations and inequalities are
discussed. Students learn to graph linear, quadratic, absolute value, and piecewise-defined
functions and solve and graph exponential and logarithmic equations. Other topics include
solving applications using linear systems as well as evaluating and finding partial sums of a
series.
Course Objectives
After completing this course, students will be able to:
• Perform operations on real numbers and polynomials.
• Simplify algebraic, rational, and radical expressions.
• Solve both linear and quadratic equations and inequalities.
• Solve word problems involving linear and quadratic equations and inequalities.
• Solve polynomial, rational, and radical equations and applications.
• Solve and graph linear, quadratic, absolute value, and piecewise-defined functions.
• Perform operations with functions as well as find composition and inverse functions.
• Graph quadratic, square root, cubic, and cube root functions.
• Graph and find zeroes of polynomial functions.
• Perform vertical and horizontal shifts and reflections of a basic graph.
• Perform stretches and compressions on a basic graph.
• Transform the graph of a general function.
• Graph quadratic functions by completing the square, using the vertex formula, and
using transformations.
• Solve and graph exponential and logarithmic equations.
2. • Solve systems of linear equations and inequalities.
• Model and solve applications using linear systems.
• Evaluate and find partial sums of a series.
• Evaluate and find sums of arithmetic and geometric sequences.
• Solve application problems involving arithmetic and geometric sequences and series.
• Solve applications involving the various types of equations and inequalities.
Course Prerequisites
There are no prerequisites to take College Algebra.
Important Terms
In this course, different terms are used to designate tasks:
• Exercise: A non-graded assignment to assist you in practicing the skills discussed in a
topic.
• Exam: A graded online test.
Course Evaluation Criteria
There are a total of 500 points in the course:
Exam #1 100 points
Exam #2 100 points
Exam #3 100 points
Exam #4 100 points
Final Exam 100 points
At the end of the course, each student will receive the number of points earned. The student’s
final letter grade is determined by the corresponding institution’s grading scale.
Course Topics and Objectives
Topic Lesson Topic Subtopics Objectives
1 Basic Algebraic • Real Numbers and • Identify and use properties of real
Operations Polynomials numbers.
• Rational Expressions • Simplify algebraic expressions.
• Rational Exponents • Identify and classify polynomial
and Radicals expressions.
• Perform operations on polynomials.
• Factor polynomials.
• Write a rational expression in simplest
form.
• Compute rational expressions.
• Simplify radical expressions.
3. • Multiply and divide radical expressions.
2 Linear Equations and • Linear Equations and • Use the notation of inequalities.
Inequalities in One Applications • Solve linear equations by using all
Variable • Linear Inequalities properties of equality and the rules.
and Applications • Solve word problems using linear
• Absolute Value in equations.
Equations and • Solve and graph linear inequalities.
Inequalities • Solve an application using inequalities.
• Solve absolute value equalities and
inequalities.
3 Quadratic Equations • Factoring and • Write a quadratic equation in the
Solving Quadratic standard form.
Equations Using • Solve quadratic equations by factoring.
Factoring • Solve quadratic equations by the
• Completing the square root property.
Square • Solve quadratic equations by
• Quadratic Formula completing the square.
and Applications of • Solve quadratic equations by using the
the Quadratic quadratic formula.
Equations • Solve word problems involving
quadratic equations.
• Use the discriminant to identify the
number of solutions.
4 Polynomial and Other • Polynomial Equations • Solve polynomial equations using the
Equations and Applications zero factor property.
• Equations Involving • Solve rational equations.
Radicals and Rational • Solve radical equations.
Exponents • Identify and simplify complex numbers.
• Complex Numbers • Add and subtract complex numbers.
• Multiply and divide complex numbers.
5 Functions and Graphs • Rectangular • Use a table of values to graph linear
Coordinates and the equations.
Graph of a Line • Determine when lines are parallel or
perpendicular.
• Use linear graphs in an applied
context.
• Identify functions and state their
domain and range.
• Use function notation.
• Write a linear equation in function
form.
• Use function form to identify the slope.
• Use slope-intercept form to graph
linear functions.
• Write a linear equation in point-
intercept form.
• Use the function form, the slope-
intercept form, and the point-intercept
form to solve applications.
6 Operations on • The Algebra and • Compute a sum or difference of
Functions Composition functions and determine the domain of
Functions the result.
• One-to-One and • Compose two functions and find the
Inverse Functions domain.
• Identify one-to-one functions.
• Find inverse functions using an
algebraic method.
• Graph a function and its inverse.
• Graph factorable quadratic equations.
• Graph the square root, cubic, and cube
root functions.
• Compute a product or quotient of
functions and determine the domain of
the result.
4. 7 Analyzing Graphs • Piecewise-Defined • State the domain of a piecewise-
Functions defined function.
• Graphs and • Evaluate piecewise-defined functions.
Symmetry • Graph functions that are piece-wise
• Transformations defined.
• Identify different symmetry types.
• Use symmetry as an aid to graphing.
• Perform vertical and horizontal shifts of
a basic graph.
• Perform vertical and horizontal
reflections of a basic graph.
• Perform stretches and compressions on
a basic graph.
• Transform the graph of a general
function.
8 Graphing Polynomial • Graphing General • Graph quadratic functions by
Functions Quadratic Functions completing the square and using
• Graphing Polynomial transformations.
Functions • Graph a general quadratic function
• Applications of using the vertex formula.
Polynomial Functions • Solve applications involving quadratic
functions.
• Graph polynomial functions.
• Describe the end behavior of a
polynomial graph.
9 Graphing Rational • Asymptotes and • Graph the reciprocal and reciprocal
Functions Rational Functions quadratic functions.
• Graphing Rational • Identify horizontal and vertical
Functions asymptotes.
• Applications of • Use asymptotes to graph
Rational Functions transformations.
• Use asymptotes to determine the
equation of a rational function from its
graph.
• Find the domain of a rational function.
• Find the intercepts of a rational
function.
• Graph general rational functions.
• Solve applications involving rational
functions.
10 Exponential and • Exponential • Evaluate an exponential function.
Logarithmic Functions Functions • Graph exponential functions.
• Logarithms and • Solve certain exponential equations.
Logarithmic • Solve applications of exponential
Functions equations.
• The Exponential • Write exponential equations in
Function and Natural logarithmic form.
Logarithm • Graph logarithmic functions and find
their domains.
• Solve applications of logarithmic
functions.
• Evaluate and graph base exponential
functions.
• Evaluate and graph the natural
logarithm functions.
• Apply the properties of logarithms.
• Use the change-of-base formula.
11 Exponential and • Exponential • Write logarithmic and exponential
Logarithmic Equations Equations equations in simplified form.
• Logarithmic • Solve exponential equations.
Equations • Solve logarithmic equations.
• Applications of • Solve applications involving
Exponential and exponential and logarithmic equations.
Logarithmic • Use exponential equations to find the
Equations interest compounded in times per year.
5. • Use exponential equations to find the
interest compounded continuously.
• Solve exponential growth and decay
problems.
12 Systems of Linear • Solving Systems • Verify ordered pair solutions.
Equations in Two Graphically and by • Solve linear systems by graphing.
Variables Substitution • Solve linear systems by substitution.
• Solving Systems • Solve linear systems by elimination.
Using Elimination • Recognize inconsistent systems (no
• Applications of Linear solutions) and dependent systems
Systems (infinitely many solutions).
• Use a system of equations to
mathematically model and solve
applications.
13 Solving Linear • Matrices • State the size of a matrix and identify
Systems Using • Solving Linear entries in a specified row and column.
Augmented Matrices Systems Using • Form the augmented matrix of a
Matrix Equations system of equations.
• More Applications of • Recognize inconsistent and dependent
Linear Systems systems.
• Model and solve applications using
linear systems.
• Solve a system of equations using row
operations.
14 Sequences and Series • Sequences and • Write out the terms of a sequence
Series given the general term.
• Arithmetic • Determine the general term of a
Sequences sequence.
• Geometric • Find the partial sum of a series.
Sequences • Use summation notation to write and
evaluate the series.
• Solve applications using mathematical
sequences.
• Find the sum of a geometric series.
• Solve application problems involving
geometric sequences and series.
15 Review and Graded • Course Review • None
Final Exam