The mathematics curriculum is aligned with California Common Core State Standards for Mathematics. The goal of the mathematics curriculum is to develop mathematically powerful students. Mathematical power involves the ability to discern mathematical relationships, reason logically, and use mathematical techniques effectively. The focus of each course is a balance among understanding of basic skills, problem solving, and concept development.
This course DOES NOT meet the approved "C" requirement for UC A-G.
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This course DOES NOT meet the approved "C" requirement for UC A-G.
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This course DOES NOT meet the approved "C" requirement for UC A-G.
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This course DOES NOT meet the approved "C" requirement for UC A-G.
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This course DOES NOT meet the approved "C" requirement for UC A-G.
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This course DOES NOT meet the approved "C" requirement for UC A-G.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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This course is designed to promote an awareness of numbers and symbols in society. Students will learn mathematical functions, such as addition, subtraction, multiplication, division, and counting. Emphasis is placed on students' improvement of number awareness, money awareness, and measurement, as applied in real world scenarios.
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Integrated Math 1 continues the development of the students’ understanding, begun in grades K-8. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers of relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for functions in terms of the situation they model. They will experiment with transformations in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically, They will summarize, represent, and interpret data on a single count or measurement variable, and interpret data on two categorical and quantitative variables, and interpret linear models.
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Integrated Math 1 continues the development of the students’ understanding, begun in grades K-8. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers of relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for functions in terms of the situation they model. They will experiment with transformations in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically, They will summarize, represent, and interpret data on a single count or measurement variable, and interpret data on two categorical and quantitative variables, and interpret linear models.
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Integrated Math 1-2 Honors continues the development of the students’ understanding, begun in grades K-8 and is the first course in a two-year compaction of the three-year California Integrated Mathematics Pathway. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers or relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for in terms of the situation they model. They will experiment with transformation in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically. They will summarize, represent, and interpret data on a single count or measurement variable, summarize, represent, and interpret data on two categorical and quantitative variables, and interpret linear models. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will extend their understanding of similarity (from Grade 8) in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve problems involving right triangles. Students will understand and apply theorems about circle and find arc lengths and areas of sectors of circles. Students will use coordinates to prove simple geometric theorems algebraically.
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Integrated Math 1-2 Honors continues the development of the students’ understanding, begun in grades K-8 and is the first course in a two-year compaction of the three-year California Integrated Mathematics Pathway. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers or relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for in terms of the situation they model. They will experiment with transformation in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically. They will summarize, represent, and interpret data on a single count or measurement variable, summarize, represent, and interpret data on two categorical and quantitative variables, and interpret linear models. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will extend their understanding of similarity (from Grade 8) in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve problems involving right triangles. Students will understand and apply theorems about circle and find arc lengths and areas of sectors of circles. Students will use coordinates to prove simple geometric theorems algebraically.
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This course Integrated Math 1-2 Honors (Spanish) is taught
entirely in Spanish. Integrated Math 1-2 Honors continues the development of the students’ understanding, begun in grades K-8 and is the first course in a two-year compaction of the three-year California Integrated Mathematics Pathway. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers or relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for in terms of the situation they model. They will experiment with transformation in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically. They will summarize, represent, and interpret data on a single count or measurement variable, summarize, represent, and interpret data on two categorical and quantitative variables, and interpret linear models. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will extend their understanding of similarity (from Grade 8) in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve problems involving right triangles. Students will understand and apply theorems about circle and find arc lengths and areas of sectors of circles. Students will use coordinates to prove simple geometric theorems algebraically.
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This course Integrated Math 1-2 Honors (Spanish) is taught
entirely in Spanish. Integrated Math 1-2 Honors continues the development of the students’ understanding, begun in grades K-8 and is the first course in a two-year compaction of the three-year California Integrated Mathematics Pathway. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers or relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for in terms of the situation they model. They will experiment with transformation in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically. They will summarize, represent, and interpret data on a single count or measurement variable, summarize, represent, and interpret data on two categorical and quantitative variables, and interpret linear models. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will extend their understanding of similarity (from Grade 8) in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve problems involving right triangles. Students will understand and apply theorems about circle and find arc lengths and areas of sectors of circles. Students will use coordinates to prove simple geometric theorems algebraically.
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Integrated Math 2 continues the development of the students’ understanding, begun in Integrated Math 1. Students will extend the properties of exponents to rational exponents, use properties of rational, and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and be able to write quadratic and exponential expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials that simplify to quadratics and be able to create equations that describe numbers or relationships, solve quadratic equations with real coefficients and inequalities in one variable. They will be able to solve linear-quadratic systems of equations. Students will interpret quadratic functions that arise in applications in terms of the context and the situation they model. Students will analyze functions using different representations, build quadratic and exponential functions that model a relationship between two quantities and build new quadratic and absolute value functions from existing functions. They will construct and compare linear, quadratic, and exponential models and solve problems. Students will extend their understanding of similarity in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, and trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve circles and find arc lengths and areas of sectors of circles. Students will translate between the geometric description and the equation for a conic section, use coordinates to prove simple geometric theorems algebraically, and explain volume formulas and use them to solve problems. Students will understand independence and conditional probability and use them to interpret data, use the rules of probability to compute probabilities of compound events in a uniform probability and then use probability to evaluate outcomes of decisions, applying counting rules.
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Integrated Math 2 continues the development of the students’ understanding, begun in Integrated Math 1. Students will extend the properties of exponents to rational exponents, use properties of rational, and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and be able to write quadratic and exponential expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials that simplify to quadratics and be able to create equations that describe numbers or relationships, solve quadratic equations with real coefficients and inequalities in one variable. They will be able to solve linear-quadratic systems of equations. Students will interpret quadratic functions that arise in applications in terms of the context and the situation they model. Students will analyze functions using different representations, build quadratic and exponential functions that model a relationship between two quantities and build new quadratic and absolute value functions from existing functions. They will construct and compare linear, quadratic, and exponential models and solve problems. Students will extend their understanding of similarity in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, and trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve circles and find arc lengths and areas of sectors of circles. Students will translate between the geometric description and the equation for a conic section, use coordinates to prove simple geometric theorems algebraically, and explain volume formulas and use them to solve problems. Students will understand independence and conditional probability and use them to interpret data, use the rules of probability to compute probabilities of compound events in a uniform probability and then use probability to evaluate outcomes of decisions, applying counting rules.
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Integrated Math 2-3 Honors continues the development of the student’s understanding, begun in grades K-8 and is the second course in a two year compaction of the three year Integrated Mathematics Pathway as adopted by the State of California. Students will extend the properties of exponents to rational exponents, use properties of rational and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and write expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials, understand the relationship between zeros and factors of polynomials, and use polynomial identities to solve problems. Students will rewrite rational expressions with linear and quadratic denominators. Students will create and solve equations that describe numbers or relationships, using all available types of expressions including simple root functions and quadratic terms with real coefficients. They will solve systems of linear-quadratic systems understand solving equations as a process of reasoning and explain the reasoning. Students will represent and solve equations and inequalities graphically. They will combine polynomial, radical, absolute value, and exponential functions. Students will interpret quadratic functions that arise in applications in terms of a context. They will analyze linear, exponential, quadratic, absolute value, step, piecewise-defined functions using different representations. Students will build a function that models a relationship between two quantities and build new functions from existing functions. Students will construct and compare linear, quadratic, and exponential models and solve problems (including Logarithms as solutions for exponentials). Students will prove and apply trigonometric identities. They will extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. Students will prove geometric theorems, focusing on validity of underlying reasoning while using variety of ways of writing proofs.
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Integrated Math 2-3 Honors continues the development of the student’s understanding, begun in grades K-8 and is the second course in a two year compaction of the three year Integrated Mathematics Pathway as adopted by the State of California. Students will extend the properties of exponents to rational exponents, use properties of rational and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and write expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials, understand the relationship between zeros and factors of polynomials, and use polynomial identities to solve problems. Students will rewrite rational expressions with linear and quadratic denominators. Students will create and solve equations that describe numbers or relationships, using all available types of expressions including simple root functions and quadratic terms with real coefficients. They will solve systems of linear-quadratic systems understand solving equations as a process of reasoning and explain the reasoning. Students will represent and solve equations and inequalities graphically. They will combine polynomial, radical, absolute value, and exponential functions. Students will interpret quadratic functions that arise in applications in terms of a context. They will analyze linear, exponential, quadratic, absolute value, step, piecewise-defined functions using different representations. Students will build a function that models a relationship between two quantities and build new functions from existing functions. Students will construct and compare linear, quadratic, and exponential models and solve problems (including Logarithms as solutions for exponentials). Students will prove and apply trigonometric identities. They will extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. Students will prove geometric theorems, focusing on validity of underlying reasoning while using variety of ways of writing proofs.
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This course Integrated Math 2-3 HP (Spanish) is taught entirely in Spanish. Integrated Math 2-3 Honors continues the development of the student’s understanding, begun in grades K-8 and is the second course in a two year compaction of the three year Integrated Mathematics Pathway as adopted by the State of California. Students will extend the properties of exponents to rational exponents, use properties of rational and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and write expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials, understand the relationship between zeros and factors of polynomials, and use polynomial identities to solve problems. Students will rewrite rational expressions with linear and quadratic denominators. Students will create and solve equations that describe numbers or relationships, using all available types of expressions including simple root functions and quadratic terms with real coefficients. They will solve systems of linear-quadratic systems understand solving equations as a process of reasoning and explain the reasoning. Students will represent and solve equations and inequalities graphically. They will combine polynomial, radical, absolute value, and exponential functions. Students will interpret quadratic functions that arise in applications in terms of a context. They will analyze linear, exponential, quadratic, absolute value, step, piecewise-defined functions using different representations. Students will build a function that models a relationship between two quantities and build new functions from existing functions. Students will construct and compare linear, quadratic, and exponential models and solve problems (including Logarithms as solutions for exponentials). Students will prove and apply trigonometric identities. They will extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. Students will prove geometric theorems, focusing on validity of underlying reasoning while using variety of ways of writing proofs.
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This course Integrated Math 2-3 HP (Spanish) is taught entirely in Spanish. Integrated Math 2-3 Honors continues the development of the student’s understanding, begun in grades K-8 and is the second course in a two year compaction of the three year Integrated Mathematics Pathway as adopted by the State of California. Students will extend the properties of exponents to rational exponents, use properties of rational and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and write expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials, understand the relationship between zeros and factors of polynomials, and use polynomial identities to solve problems. Students will rewrite rational expressions with linear and quadratic denominators. Students will create and solve equations that describe numbers or relationships, using all available types of expressions including simple root functions and quadratic terms with real coefficients. They will solve systems of linear-quadratic systems understand solving equations as a process of reasoning and explain the reasoning. Students will represent and solve equations and inequalities graphically. They will combine polynomial, radical, absolute value, and exponential functions. Students will interpret quadratic functions that arise in applications in terms of a context. They will analyze linear, exponential, quadratic, absolute value, step, piecewise-defined functions using different representations. Students will build a function that models a relationship between two quantities and build new functions from existing functions. Students will construct and compare linear, quadratic, and exponential models and solve problems (including Logarithms as solutions for exponentials). Students will prove and apply trigonometric identities. They will extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. Students will prove geometric theorems, focusing on validity of underlying reasoning while using variety of ways of writing proofs.
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Description: Integrated Math 3 continues the development of the students' understanding, begun in Integrated Math 2. Students use complex numbers in polynomial identities and equations, interpret the structure of polynomial and rational expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials. Student will build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems. They will extend the domain of trigonometric functions using the unit circle, model periodic phenomena with trigonometric functions and apply trigonometry to general triangles. Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments, make inferences and justify conclusions from sample surveys, experiments, and observational studies. Students will use probability to evaluate outcomes of decisions in more complex situations.
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Description: Integrated Math 3 continues the development of the students' understanding, begun in Integrated Math 2. Students use complex numbers in polynomial identities and equations, interpret the structure of polynomial and rational expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials. Student will build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems. They will extend the domain of trigonometric functions using the unit circle, model periodic phenomena with trigonometric functions and apply trigonometry to general triangles. Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments, make inferences and justify conclusions from sample surveys, experiments, and observational studies. Students will use probability to evaluate outcomes of decisions in more complex situations.
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This Precalculus Honors course is a UC weighted course. It prepares the student to succeed in AP Calculus BC or in a second course of Calculus at the college level. Students will continue developing their understanding of Number and Quantity in the study of the Complex Number System and Vector and Matrix Quantities as they perform arithmetic operations with complex numbers, representing them on the complex plane and represent and model with and perform operations on vectors and matrices. Students will also use matrices in applications. Continuing their study of algebra, students will interpret the structure of expressions, rewrite rational expressions, create equations that describe numbers or relationships, and solve systems of equations. The student’s understanding of functions will enable her to interpret functions (in context and through different representations), build new functions from existing functions, expand the domain of Trigonometry functions using the unit circle and use the trigonometry functions to model periodic phenomena. Students will prove and apply trigonometry identities. They will apply trigonometry to general triangles and translate between the geometric description and the equation for a conic section. In addition, the students will study traditional introductory Calculus topics such as Limits, Continuity, and Derivatives.
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This Precalculus Honors course is a UC weighted course. It prepares the student to succeed in AP Calculus BC or in a second course of Calculus at the college level. Students will continue developing their understanding of Number and Quantity in the study of the Complex Number System and Vector and Matrix Quantities as they perform arithmetic operations with complex numbers, representing them on the complex plane and represent and model with and perform operations on vectors and matrices. Students will also use matrices in applications. Continuing their study of algebra, students will interpret the structure of expressions, rewrite rational expressions, create equations that describe numbers or relationships, and solve systems of equations. The student’s understanding of functions will enable her to interpret functions (in context and through different representations), build new functions from existing functions, expand the domain of Trigonometry functions using the unit circle and use the trigonometry functions to model periodic phenomena. Students will prove and apply trigonometry identities. They will apply trigonometry to general triangles and translate between the geometric description and the equation for a conic section. In addition, the students will study traditional introductory Calculus topics such as Limits, Continuity, and Derivatives.
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Application of Functions 1 continues the development of the students’ understanding, begun in Integrated Math 2 (CA Integrated Mathematics II). Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments and make inferences and justify conclusions from sample surveys, experiments and observational studies. Students will use complex numbers in polynomial identities and equations, interpret the structure of Polynomial expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials, use polynomial identities to solve problems. They will create equations that describe numbers or relationships, understand and explain the solving linear, quadratic and polynomial equations as a process of reasoning, and represent and solve equations and inequalities graphically. Students will be able interpret Linear, Quadratic and Polynomial functions that arise in applications in terms of the context, and analyze functions using different representations. They will build a function that models a relationship between two quantities, build new functions from existing Linear, Quadratic and Polynomial functions, construct and compare linear and quadratic models and solve problems.
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Application of Functions 1 continues the development of the students’ understanding, begun in Integrated Math 2 (CA Integrated Mathematics II). Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments and make inferences and justify conclusions from sample surveys, experiments and observational studies. Students will use complex numbers in polynomial identities and equations, interpret the structure of Polynomial expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials, use polynomial identities to solve problems. They will create equations that describe numbers or relationships, understand and explain the solving linear, quadratic and polynomial equations as a process of reasoning, and represent and solve equations and inequalities graphically. Students will be able interpret Linear, Quadratic and Polynomial functions that arise in applications in terms of the context, and analyze functions using different representations. They will build a function that models a relationship between two quantities, build new functions from existing Linear, Quadratic and Polynomial functions, construct and compare linear and quadratic models and solve problems.
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The Introduction to Data Science course will emphasize the use of statistics and computation as tools for creative work, as a means of telling stories with data. Its content will prepare students to "read" and think critically about existing data stories. It will present a process that is iterative and authentically inquiry-based, comparing multiple "views" of one or more data sets. The student's interpretation relies on a special kind of computation, simulation, and modeling to describe the uncertainty in each view. This kind of reasoning is exploratory and investigatory, sometimes framed as hypothesis evaluation and sometimes as hypothesis generation. The statistical programming language used by academics and industry will be used to bring data science to life.
The main goal of the Introduction to Data Science course is to teach students to think critically about and with data. This new and innovative curriculum will meet the Common Core State Standards (CCSS) for High School Statistics and Probability, relevant second-year Algebra probability and statistics standards, the Modeling standard, and relevant mathematics standards. This course emphasizes the CCSS High School — Statistics and Probability Standards that involve the study of data science. Students authentically apply the Standards for Mathematical Practice throughout the course.
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The Introduction to Data Science course will emphasize the use of statistics and computation as tools for creative work, as a means of telling stories with data. Its content will prepare students to "read" and think critically about existing data stories. It will present a process that is iterative and authentically inquiry-based, comparing multiple "views" of one or more data sets. The student's interpretation relies on a special kind of computation, simulation, and modeling to describe the uncertainty in each view. This kind of reasoning is exploratory and investigatory, sometimes framed as hypothesis evaluation and sometimes as hypothesis generation. The statistical programming language used by academics and industry will be used to bring data science to life.
The main goal of the Introduction to Data Science course is to teach students to think critically about and with data. This new and innovative curriculum will meet the Common Core State Standards (CCSS) for High School Statistics and Probability, relevant second-year Algebra probability and statistics standards, the Modeling standard, and relevant mathematics standards. This course emphasizes the CCSS High School — Statistics and Probability Standards that involve the study of data science. Students authentically apply the Standards for Mathematical Practice throughout the course.
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In PreCalculus (P), students extend their work with complex numbers begun in AUHSD Integrated Math 3, or equivalent, to see that the complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors, representing them geometrically and performing operations with them. They connect the notion of vectors to the complex numbers. Students also work with matrices and their operations, experiencing for the first time an algebraic system in which multiplication is not commutative. Finally, they see the connection between matrices and transformations of the plane, namely that a vector in the plane can be multiplied by a 2×2 matrix to produce another vector, and they work with matrices from the point of view of transformations. They also find inverse matrices and use matrices to represent and solve linear systems. Students extend their work with trigonometric functions, investigating the reciprocal functions secant, co-secant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts. While students have worked previously with parabolas and circles, they now work with ellipses and hyperbolas. They also work with polar coordinates and curves defined parametrically, and connect these to their other work with trigonometry and complex numbers. Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Students who successfully complete this course are prepared to take an introductory college-level Calculus course.
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In PreCalculus (P), students extend their work with complex numbers begun in AUHSD Integrated Math 3, or equivalent, to see that the complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors, representing them geometrically and performing operations with them. They connect the notion of vectors to the complex numbers. Students also work with matrices and their operations, experiencing for the first time an algebraic system in which multiplication is not commutative. Finally, they see the connection between matrices and transformations of the plane, namely that a vector in the plane can be multiplied by a 2×2 matrix to produce another vector, and they work with matrices from the point of view of transformations. They also find inverse matrices and use matrices to represent and solve linear systems. Students extend their work with trigonometric functions, investigating the reciprocal functions secant, co-secant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts. While students have worked previously with parabolas and circles, they now work with ellipses and hyperbolas. They also work with polar coordinates and curves defined parametrically, and connect these to their other work with trigonometry and complex numbers. Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Students who successfully complete this course are prepared to take an introductory college-level Calculus course.
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Students will work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. Understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems. Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems. Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. Communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems. Model a written description of a physical situation with a function, a differential equation, or an integral. Use technology to help solve problems, experiment, interpret results, and verify conclusions. Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
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Students will work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. Understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems. Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems. Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. Communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems. Model a written description of a physical situation with a function, a differential equation, or an integral. Use technology to help solve problems, experiment, interpret results, and verify conclusions. Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
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Application of Functions 2 continues the development of the students’ understanding, begun in Integrated Math 2 (CA Integrated Mathematics II) and Introduction to Functions I.
Students will rewrite rational expressions with linear and quadratic denominators. Students will be able interpret Rational, Radical, Exponential and Logarithmic functions that arise in applications in terms of the context. Students will be analyzing Rational, Radical, Exponential and Logarithmic functions using different representations. They will build a function that models a relationship between two quantities with any type of function studied, build new functions from existing Rational, Radical, Exponential and Logarithmic functions, construct and compare linear and quadratic and exponential models and solve problems.
Students will be able to extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. They will apply trigonometry to general triangle, translate between the geometric description and the equation for a conic section, and visualize relationships between two- and three-dimensional objects. Students will be able to apply geometric concepts in modeling situations.
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Applications of Functions 2 continues the development of the students’ understanding, begun in Integrated Math 2 (CA Integrated Mathematics II) and Introduction to Functions I.
Students will rewrite rational expressions with linear and quadratic denominators. Students will be able interpret Rational, Radical, Exponential and Logarithmic functions that arise in applications in terms of the context. Students will be analyzing Rational, Radical, Exponential and Logarithmic functions using different representations. They will build a function that models a relationship between two quantities with any type of function studied, build new functions from existing Rational, Radical, Exponential and Logarithmic functions, construct and compare linear and quadratic and exponential models and solve problems.
Students will be able to extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. They will apply trigonometry to general triangle, translate between the geometric description and the equation for a conic section, and visualize relationships between two- and three-dimensional objects. Students will be able to apply geometric concepts in modeling situations.
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AP Calculus BC is equivalent to a 2 semester college level Calculus course. Calculus BC is an extension of Calculus AB rather than an enhancement. The courses emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The course includes all the topics covered in AP Calculus AB along with advanced methods of integration, logistic differential equations, methods of approximating solutions, polar and parametric curves and applications, Taylor series and polynomials, and vector functions.
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AP Calculus BC is equivalent to a 2 semester college level Calculus course. Calculus BC is an extension of Calculus AB rather than an enhancement. The courses emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The course includes all the topics covered in AP Calculus AB along with advanced methods of integration, logistic differential equations, methods of approximating solutions, polar and parametric curves and applications, Taylor series and polynomials, and vector functions.
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The exploratory analysis of data uses graphical and numerical techniques to study patterns and departures forming the patterns. Data is collected according to a well-developed plan of valid information and a conjecture is obtained.
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The exploratory analysis of data uses graphical and numerical techniques to study patterns and departures forming the patterns. Data is collected according to a well-developed plan of valid information and a conjecture is obtained.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives. Topics covered include: One-and Two variable data, elementary probability and modeling, data collection, sample spaces, distributions, making decisions, and probability models.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives. Topics covered include: One-and Two variable data, elementary probability and modeling, data collection, sample spaces, distributions, making decisions, and probability models.
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Advanced Algebra with Financial Applications is a mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Pre calculus, and Calculus under seven financial umbrellas: Banking, Investing, Credit, Employment and IncomeTaxes, Automobile Ownership, Independent Living, and Retirement Planning and Household Budgeting. The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. The mathematics topics contained in this course are introduced, developed, and applied in an as-
needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future, and is aligned with the recommendations of the Common Core State Standards.
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Advanced Algebra with Financial Applications is a mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Pre calculus, and Calculus under seven financial umbrellas: Banking, Investing, Credit, Employment and IncomeTaxes, Automobile Ownership, Independent Living, and Retirement Planning and Household Budgeting. The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. The mathematics topics contained in this course are introduced, developed, and applied in an as-
needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future, and is aligned with the recommendations of the Common Core State Standards.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives through the lens of Data Analytics. This course will include enrollment in the Google Certificate in Data Analytics.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives through the lens of Data Analytics. This course will include enrollment in the Google Certificate in Data Analytics.
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(eLearning) Integrated Math 1-2 Honors continues the development of the students’ understanding, begun in grades K-8 and is the first course in a two-year compaction of the three-year California Integrated Mathematics Pathway. Students will reason quantitatively and use units to solve problems, interpret the structure of expressions, create equations that describe numbers or relationships, understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. Students will understand the concept of a function and use function notation, interpret functions that arise in applications in terms of the context, analyze functions using different representations, build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems, and interpret expressions for in terms of the situation they model. They will experiment with transformation in the plane, understand congruence in terms of rigid motions, make geometric constructions, and use coordinates to prove simple geometric theorems algebraically. They will summarize, represent, and interpret data on a single count or measurement variable, summarize, represent, and interpret data on two categorical and quantitative variables, and interpret linear models. The students go beyond the simple application of previously constructed mathematics to real-world problems. Students will extend their understanding of similarity (from Grade 8) in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve problems involving right triangles. Students will understand and apply theorems about circle and find arc lengths and areas of sectors of circles. Students will use coordinates to prove simple geometric theorems algebraically.
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(eLearning) Integrated Math 2 continues the development of the students’ understanding, begun in Integrated Math 1. Students will extend the properties of exponents to rational exponents, use properties of rational, and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and be able to write quadratic and exponential expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials that simplify to quadratics and be able to create equations that describe numbers or relationships, solve quadratic equations with real coefficients and inequalities in one variable. They will be able to solve linear-quadratic systems of equations. Students will interpret quadratic functions that arise in applications in terms of the context and the situation they model. Students will analyze functions using different representations, build quadratic and exponential functions that model a relationship between two quantities and build new quadratic and absolute value functions from existing functions. They will construct and compare linear, quadratic, and exponential models and solve problems. Students will extend their understanding of similarity in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, and trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve circles and find arc lengths and areas of sectors of circles. Students will translate between the geometric description and the equation for a conic section, use coordinates to prove simple geometric theorems algebraically, and explain volume formulas and use them to solve problems. Students will understand independence and conditional probability and use them to interpret data, use the rules of probability to compute probabilities of compound events in a uniform probability and then use probability to evaluate outcomes of decisions, applying counting rules.
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(eLearning) Integrated Math 2-3 Honors continues the development of the student’s understanding, begun in grades K-8 and is the second course in a two year compaction of the three year Integrated Mathematics Pathway as adopted by the State of California. Students will extend the properties of exponents to rational exponents, use properties of rational and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and write expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials, understand the relationship between zeros and factors of polynomials, and use polynomial identities to solve problems. Students will rewrite rational expressions with linear and quadratic denominators. Students will create and solve equations that describe numbers or relationships, using all available types of expressions including simple root functions and quadratic terms with real coefficients. They will solve systems of linear-quadratic systems understand solving equations as a process of reasoning and explain the reasoning. Students will represent and solve equations and inequalities graphically. They will combine polynomial, radical, absolute value, and exponential functions. Students will interpret quadratic functions that arise in applications in terms of a context. They will analyze linear, exponential, quadratic, absolute value, step, piecewise-defined functions using different representations. Students will build a function that models a relationship between two quantities and build new functions from existing functions. Students will construct and compare linear, quadratic, and exponential models and solve problems (including Logarithms as solutions for exponentials). Students will prove and apply trigonometric identities. They will extend the domain of trigonometric functions using the unit circle and model periodic phenomena with trigonometric functions. Students will prove geometric theorems, focusing on validity of underlying reasoning while using variety of ways of writing proofs.
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(eLearning) Integrated Math 2 continues the development of the students’ understanding, begun in Integrated Math 1. Students will extend the properties of exponents to rational exponents, use properties of rational, and irrational numbers, perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations (specifically with quadratics with real coefficients). Students will interpret the structure of quadratic and exponential expressions and be able to write quadratic and exponential expressions in equivalent forms to solve problems. Students will perform arithmetic operations on polynomials that simplify to quadratics and be able to create equations that describe numbers or relationships, solve quadratic equations with real coefficients and inequalities in one variable. They will be able to solve linear-quadratic systems of equations. Students will interpret quadratic functions that arise in applications in terms of the context and the situation they model. Students will analyze functions using different representations, build quadratic and exponential functions that model a relationship between two quantities and build new quadratic and absolute value functions from existing functions. They will construct and compare linear, quadratic, and exponential models and solve problems. Students will extend their understanding of similarity in terms of similarity transformations. They will prove geometric theorems, including those involving similarity, and trigonometric identities as they apply to the Pythagorean Theorem. They will define trigonometric rations and solve circles and find arc lengths and areas of sectors of circles. Students will translate between the geometric description and the equation for a conic section, use coordinates to prove simple geometric theorems algebraically, and explain volume formulas and use them to solve problems. Students will understand independence and conditional probability and use them to interpret data, use the rules of probability to compute probabilities of compound events in a uniform probability and then use probability to evaluate outcomes of decisions, applying counting rules.
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Description: Integrated Math 3 continues the development of the students' understanding, begun in Integrated Math 2. Students use complex numbers in polynomial identities and equations, interpret the structure of polynomial and rational expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials. Student will build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems. They will extend the domain of trigonometric functions using the unit circle, model periodic phenomena with trigonometric functions and apply trigonometry to general triangles. Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments, make inferences and justify conclusions from sample surveys, experiments, and observational studies. Students will use probability to evaluate outcomes of decisions in more complex situations.
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Description: Integrated Math 3 continues the development of the students' understanding, begun in Integrated Math 2. Students use complex numbers in polynomial identities and equations, interpret the structure of polynomial and rational expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials. Student will build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems. They will extend the domain of trigonometric functions using the unit circle, model periodic phenomena with trigonometric functions and apply trigonometry to general triangles. Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments, make inferences and justify conclusions from sample surveys, experiments, and observational studies. Students will use probability to evaluate outcomes of decisions in more complex situations.
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Description: Integrated Math 3 continues the development of the students' understanding, begun in Integrated Math 2. Students use complex numbers in polynomial identities and equations, interpret the structure of polynomial and rational expressions, write expressions in equivalent forms to solve problems, understand the relationship between zeros and factors of polynomials. Student will build a function that models a relationship between two quantities, build new functions from existing functions, construct and compare linear, quadratic, and exponential models and solve problems. They will extend the domain of trigonometric functions using the unit circle, model periodic phenomena with trigonometric functions and apply trigonometry to general triangles. Students will summarize, represent, and interpret data on a single count or measurement variable, understand and evaluate random processes underlying statistical experiments, make inferences and justify conclusions from sample surveys, experiments, and observational studies. Students will use probability to evaluate outcomes of decisions in more complex situations.
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The exploratory analysis of data uses graphical and numerical techniques to study patterns and departures forming the patterns. Data is collected according to a well-developed plan of valid information and a conjecture is obtained. This course meets the approved "C" requirement for UC A-G.
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The exploratory analysis of data uses graphical and numerical techniques to study patterns and departures forming the patterns. Data is collected according to a well-developed plan of valid information and a conjecture is obtained. This course meets the approved "C" requirement for UC A-G.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives. Topics covered include: One-and Two variable data, elementary probability and modeling, data collection, sample spaces, distributions, making decisions, and probability models.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives. Topics covered include: One-and Two variable data, elementary probability and modeling, data collection, sample spaces, distributions, making decisions, and probability models.
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This course is student-centered and group-oriented with project-based learning and discovery. Students will collaborate on real-life situations, use technology, collect data, and do studies on an issue relevant to their own lives. Topics covered include: One-and Two variable data, elementary probability and modeling, data collection, sample spaces, distributions, making decisions, and probability models.
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Advanced Algebra with Financial Applications is a mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Pre calculus, and Calculus under seven financial umbrellas: Banking, Investing, Credit, Employment and IncomeTaxes, Automobile Ownership, Independent Living, and Retirement Planning and Household Budgeting. The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. The mathematics topics contained in this course are introduced, developed, and applied in an as-
needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future, and is aligned with the recommendations of the Common Core State Standards.
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Advanced Algebra with Financial Applications is a mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Pre calculus, and Calculus under seven financial umbrellas: Banking, Investing, Credit, Employment and IncomeTaxes, Automobile Ownership, Independent Living, and Retirement Planning and Household Budgeting. The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. The mathematics topics contained in this course are introduced, developed, and applied in an as-
needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future, and is aligned with the recommendations of the Common Core State Standards.
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(eLearning) In PreCalculus (P), students extend their work with complex numbers begun in AUHSD Integrated Math 3, or equivalent, to see that the complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors, representing them geometrically and performing operations with them. They connect the notion of vectors to the complex numbers. Students also work with matrices and their operations, experiencing for the first time an algebraic system in which multiplication is not commutative. Finally, they see the connection between matrices and transformations of the plane, namely that a vector in the plane can be multiplied by a 2×2 matrix to produce another vector, and they work with matrices from the point of view of transformations. They also find inverse matrices and use matrices to represent and solve linear systems. Students extend their work with trigonometric functions, investigating the reciprocal functions secant, co-secant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts. While students have worked previously with parabolas and circles, they now work with ellipses and hyperbolas. They also work with polar coordinates and curves defined parametrically, and connect these to their other work with trigonometry and complex numbers. Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Students who successfully complete this course are prepared to take an introductory college-level Calculus course.
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In PreCalculus (P), students extend their work with complex numbers begun in AUHSD Integrated Math 3, or equivalent, to see that the complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors, representing them geometrically and performing operations with them. They connect the notion of vectors to the complex numbers. Students also work with matrices and their operations, experiencing for the first time an algebraic system in which multiplication is not commutative. Finally, they see the connection between matrices and transformations of the plane, namely that a vector in the plane can be multiplied by a 2×2 matrix to produce another vector, and they work with matrices from the point of view of transformations. They also find inverse matrices and use matrices to represent and solve linear systems. Students extend their work with trigonometric functions, investigating the reciprocal functions secant, co-secant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts. While students have worked previously with parabolas and circles, they now work with ellipses and hyperbolas. They also work with polar coordinates and curves defined parametrically, and connect these to their other work with trigonometry and complex numbers. Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Students who successfully complete this course are prepared to take an introductory college-level Calculus course.
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This course code number will be used to designate credits for courses not offered in the Anaheim Union High School District.
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