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.

3725 MATH 3 P 9th - 12th 10.0 credits Recommendation: Completion of Junior High Course, Math 2. UC - "C" Approved Math 3 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. |

3726 MATH 3-4 HONORS HP 9th - 12th 10.0 credits Recommendation: Completion of Math 2 with a "B" or higher, and/or teacher recommendation. UC - "C" Approved Math 3-4 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. |

3733 MATH 4A P 11th - 12th 10.0 credits Prerequisite: Completion of Math 3A and Math 3B or equivalent. For Mild/Moderate only. UC - "C" Approved (Mild Moderate students only.) Note: Students must complete both Math 4A and Math 4B to receive CA Integrated Mathematics II credit. Building on the work done in Grade 8 and Math 3A, students in Math 4A will extend their understanding of similarity in terms of similarity transformations. They will develop understanding of the concept of proof and then prove geometric theorems, including those involving similarity, and trigonometric identities as they apply to the Pythagorean Theorem. They will continue to explore and then define trigonometric ratios and solve problems involving right triangles. Students will explore, understand and apply theorems about circles and find arc lengths and areas of sectors of circles. Students will translate between the geometric description and the equation for circles and parabolas, use coordinates to prove simple geometric theorems algebraically, and explain volume formulas and use them to solve problems. Students will explore independence and conditional probability and use them to interpret data; they will 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. |

3734 MATH 4B P 11th - 12th 10.0 credits Prerequisite: Completion of Math 4A, still needing a slower pace for math concept and skill acquisition. For Mild/Moderate only. UC - "C" Approved (Mild Moderate students only.) Note: Completion of Math 4A/Math 4B sequence is equivalent to one year of CA Integrated Math 2). Students in Math 4B will extend the properties of exponents to rational exponents and use properties of rational and irrational numbers. They will perform arithmetic operations with complex numbers and when a quadratic equation will have complex solutions. Students will interpret the structure of quadratic and exponential expressions and be able to write quadratic and exponential expressions in equivalent forms, including factored form, 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 (Linear, exponential, quadratic, absolute value, step, piecewise) 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. |

3735 MATH 4 P 10th - 12th 10.0 credits Recommendation: Completion of a Math 3 or equivalent course. UC - "C" Approved Math 4 continues the development of the students’ understanding, begun in Math 3. 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. |

3753 INTRODUCTION TO FUNCTIONS 1 11th - 12th 10.0 credits Recommendation: Math 4 completion with a low "C" or "D", or failed one semester. Students must pass both Functions 1 and Functions 2 with a "C" or higher to receive the UC "C" credit. UC - "C" Approved Introduction to Functions I continues the development of the students’ understanding, begun in Math 4 (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. |

3754 INTRODUCTION TO FUNCTIONS 2 12th 10.0 credits Second of a two year course sequence. Students must pass both Functions 1 and Functions 2 with a "C" or higher to receive the UC "C" credit. UC - "C" Approved Introduction to Functions II continues the development of the students’ understanding, begun in Math 4 (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. |

3755 MATH 5 P 9th - 12th 10.0 credits Recommendation: Completion of Math 4 or equivalent course. UC - "C" Approved Description: Math 5 continues the development of the students' understanding, begun in Math 4. 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. |

3756 MATH 4-5 HONORS HP 9th - 12th 10.0 credits Recommendation: Completion of a Math 3-4 Honors or equivalent course with a "B" or higher. UC - "C" Approved Math 4-5 Honors continues the development of the student’s understanding, beguin 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. |

3795 PRECALCULUS P 10th - 12th 10.0 credits Recommendation: Completion of Math 5 or equivalent course. UC - "C" Approved In PreCalculus (P), students extend their work with complex numbers begun in AUHSD Math 5, 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. |

3796 PRECALCULUS HP 10th - 12th 10.0 credits Recommendation: Completion of Math 4-5 HP or equivalent course. UC - "C" Approved 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. |

3800 AP CALCULUS AB 9th - 12th 10.0 credits Recommendation: A grade of "B" or better in Pre-Calculus HP. UC - "C" Approved 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. |

3802 AP CALCULUS BC 11th - 12th 10.0 credits Recommendation: A grade of "B" or better in Calculus AB, or Pre-Calculus HP. UC - "C" Approved 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. |

3870 or 3870E (eLearning) AP STATISTICS 9th - 12th 10.0 credits Recommendation: None. UC - "C" Approved 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. |

3875 STATISTICS & PROBABILITY P 12th 10.0 credits This course is intended to be an alternative fourth year math course for college-ready students. UC - "C" Approved 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. |

3990 MATH ELECTIVE CREDIT 9th - 12th 10.0 credits Recommendation: None. 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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