MATHEMATICS
C. REQUIREMENT
The PCHS Mathematics department prides itself on its wide array of diverse math courses. To continue a PCHS math course sequence, students must pass each course with a C or better. Only classes passed with a C or better will count towards meeting college entrance requirements. If students earn a “D”, they will receive high school credits towards graduation. However, a grade of "C" or higher will meet college entrance (A-G) requirements. Math courses offered at an Honors level are denoted with an H. Students in Honors classes investigate the same course content and standards in greater depth and will demonstrate proficiency in computing, applying processes, problem-solving, and analyzing complex mathematical concepts. Assignments and assessments are more rigorous and an Honors project may be required. Math students at all levels are expected to spend 45-90 minutes on average outside of class per class meeting to complete assignments and study for the class. Students in Honors or AP classes should expect to spend 30-60 minutes more outside of class per class meeting than their peers in regular courses. Incoming nine-grade students will take a placement test to ensure proper placement in the math sequence. For any student taking an Algebra 1, Geometry, and/or Algebra 2 class, such classes must be taken in person at PCHS for the first time.
ALGEBRA 1A/B
FALL 310301 SPRING 310302
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: Pre-algebra or middle school math course
Algebra is a first-year course in the study of algebraic expressions, equations, inequalities, and functions. Algebra focuses on developing proficiency in operations with polynomials, exponents, and radicals, mastering the solving equations and inequalities, and providing an in-depth study of linear functions. Algebra 1B requires students to apply and extend the skills from Algebra 1A through solving systems of equations and inequalities, studying nonlinear functions, evaluating descriptive statistics, and making connections to geometry through conditional statements and logical reasoning.
Prerequisite Skills:
Operations with fractions and decimals, percents, integers, order of operations, locating points on a number line and a coordinate plane, evaluating and simplifying algebraic expressions, operations with real numbers
ALGEBRA SUPPORT 1A/B
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: Pre-algebra or middle school math course
Algebra Support is a first-year course in the study of algebraic expressions, equations, inequalities, and functions. Algebra focuses on developing proficiency in operations with polynomials, exponents, and radicals, mastering the solving equations and inequalities, and providing an in-depth study of linear functions. Algebra 1B requires students to apply and extend the skills from Algebra 1A through solving systems of equations and inequalities, studying nonlinear functions, evaluating descriptive statistics, and making connections to geometry through conditional statements and logical reasoning.
CP/HONORS GEOMETRY A/B
FALL 310401H SPRING 310402H
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: Algebra 1 AND students must meet the department criteria for honors in order to enroll in the honors course or submit a parent waiver to the Counseling Office.
Geometry is a course in logic, proof, and measurement. Students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. Some of the topics covered include definitions, postulates, and theorems regarding angles, segments and lines, arcs, congruent triangles, similar triangles, special quadrilaterals, parallel lines, circles, coordinate geometry, area and volume formulas, transformations, constructions, and right triangle trigonometry.
Prerequisite Skills:
Simplifying algebraic and numeric expressions, solving linear and quadratic equations and systems, writing and solving proportions, graphing coordinates, finding slopes, simplifying radicals, perimeter/area of basic geometric figures
CP/HONORS ALGEBRA II A/B
FALL 310303H SPRING 310304H
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: Geometry AND students must meet the department criteria for Honors in order to enroll in the Honors course or submit a parent waiver to the Counseling Office.
Algebra 2 is a math course in the study of algebraic expressions, equations, inequalities, and functions. This course complements and expands the mathematical content and concepts of Algebra 1 and Geometry. Some of the topics covered include complex numbers, exponents, radicals, matrices, systems of linear equations, functions (absolute value, exponential, logarithmic, quadratic, radical, polynomial, and rational) and their behavior, solving nonlinear equations, conic sections, combinatorics, probability, and sequences/series.
Prerequisite Skills: Solving, graphing and writing linear equations/inequalities, solving linear systems in two variables, simplifying exponents and radicals, operations with polynomial expressions, factoring, solving/graphing quadratic equations, distance, slope, and midpoint formulas.
ADVANCE MATHEMATICAL CONCEPTS & SKILLS AB
FALL 310501 SPRING 310502
Length: 1-2 semesters
Credit: 5.0 per semester
Grade Level: 10-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: Algebra 2
This course is a year-long survey course of advanced mathematics concepts and skills consisting of two independent semesters. The first semester introduces students to properties and applications of matrices in linear algebra and reasoning and rules that govern basic principles of logic and set theory. Students will also further investigate and study the behavior and characteristics of non-linear functions first introduced in Algebra 2. The second semester will include basic trigonometric concepts involving the unit circle, graphs of trigonometric functions, trigonometric equations, and trigonometric identities. Lastly, students will explore data collection and analysis in a unit on statistics and probability. In short, this course will expose students to advanced math concepts and skills in Functions, Algebra, Statistics, and Trigonometry. Upon successful completion of the course, students will be eligible to take Math Analysis or AP Statistics.
Prerequisite Skills:
Right triangle trigonometry, systems of equations, solving linear and nonlinear equations, graphing functions, complex numbers, matrix operations, parent functions, basic geometry properties, operations with polynomial and rational expressions, and properties of radicals/exponents/logarithms
CP/HONORS MATH ANALYSIS A/B
FALL 310601H SPRING 310602H
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: Algebra 2 AND teacher recommendation or submit a parent waiver to the Counseling Office.
Math Analysis is a pre-calculus course that emphasizes a better understanding of functions and their applications and strengthens students’ mathematical reasoning and problem-solving skills. Some of the topics covered include trigonometry, parametric equations, vectors, polar coordinates, complex numbers, matrices, polynomial functions, rational functions, exponential functions, logarithmic functions, sequences, series, and limits.
Prerequisite Skills:
Right triangle trigonometry, systems of equations, solving linear and nonlinear equations, graphing functions, complex numbers, matrix operations, parent functions, basic geometry properties, operations with polynomial and rational expressions, and properties of radicals/exponents/logarithms.
HIGH SCHOOL CALCULUS A/B
FALL 310707 SPRING 310708
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: C or better in Math Analysis
High School Calculus is a first year calculus course. Some of the topics covered include limits, continuity, derivatives, applications of derivatives (related rates, curve-sketching, optimization), integrals, applications of integrals (volumes, accumulation of change, differential equations), and techniques of integration.
Prerequisite Skills:
Right triangle trigonometry, systems of equations, solving linear and nonlinear equations, graphing functions, complex numbers, matrix operations, parent functions, basic geometry properties, operations with polynomial and rational expressions, and properties of radicals/exponents/logarithms.
AP CALCULUS AB/BC
FALL 310701 SPRING 310702
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 9-12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: C or better in Math Analysis AND teacher recommendation or submit a parent waiver to the Counseling Office
AP Calculus AB is a challenging, in-depth study of functions, graphs, limits, derivatives, definite integrals, antiderivatives, and real-world applications of differentiation and anti-differentiation. Students will work with functions graphically, numerically, analytically, and verbally and understand the connections among these representations. Some of the topics covered include limits, continuity, derivatives, applications of derivatives (rates of change, rectilinear motion, related rates, curve-sketching, optimization), integrals, applications of integrals (area, volumes, accumulation of change, differential equations), and techniques of integration. AP Calculus BC includes all of the AP Calculus AB topics as well as applications using parametric, polar and vector forms, the geometric, interpretation and numerical solution of differential equations, improper integrals, series, and Taylor polynomial approximations of functions.
Prerequisite Skills:
Trigonometry, linear and nonlinear equations and systems, piecewise functions, elementary functions (equations, graphs, and behavior), transformations of parent functions, basic geometry properties, operations with polynomial and rational expressions, properties of radicals/exponents/logarithms, parametric equations, polar equations, vectors, and sequences/series
Summer work is recommended.
Link to AP Calculus Summer Work
AP STATISTICS
FALL 310609 SPRING 310610
Length: 2 semesters
Credit: 5.0 per semester
Grade Level: 12
Postsecondary: Meets UC/CSU C requirement
Prerequisites: C or better in Algebra II or student submits a math department waiver to the Counseling Office with teacher signature. All students must take a prerequisite test upon entering the course; this test grade will count in student's course grade.
Recommended: AMS/AMC grade of C or above, Math Analysis grade of C or above, teacher recommendation, or student submits a parent waiver to the Counseling Office. Students planning to take AP Calculus and AP Statistics should take AP Calculus before AP Statistics.
AP Statistics is a college-level mathematics course. The purpose of the Advanced Placement course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Four major themes are covered in the course:
1) Exploring data – observing patterns and departures from patterns
2) Planning a study – deciding what and how to measure
3) Anticipating patterns in advance – producing models using probability and
simulation
4) Statistical inference – confirming models
While exploring these themes, some of the topics that will be covered include distributions of data, measures of center, standard deviation, linear regression, correlation, data collection, sampling, randomization, probability and discrete random variables, binomial distributions, Central Limit Theorem, confidence intervals, tests of significance using large samples, small samples, means, and proportions, and Chi-square test.
Prerequisite Skills: Data analysis (mean, median, mode, standard deviation, range, outliers), data displays (scatter plots, histograms, stem plots, box plots, frequency tables), regression, probability, combinatorics, and normal distributions.
Summer review work is provided through a Schoology summer course. Work will NOT be collected. All students must take a prerequisite test upon entering the course; this test grade will count in student's grade.