Mathematics

Welcome to the State College High School Mathematics Program!

The State College Area School District has a comprehensive mathematics program for all students. Each course sequence includes experiences with Common Core Mathematics strands of Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability. 

The Math Department offers Advanced and College-Prep course sequences. All course sequences are designed to prepare students for continuing education after high school. All math courses attend to the three components of mathematical rigor: conceptual understanding, procedural fluency, and application. Advanced courses often feature an increase in depth and breadth of study, including the pace of content explored, as well as the difficulty of content and time required outside of class. Math courses require prerequisite knowledge since the content builds on previously-learned concepts. As such, it is essential to select courses in keeping with the prerequisites listed below so that students may have the necessary foundation on which to build additional knowledge and understanding.

All students are required to take three years of high school mathematics to graduate, but it is strongly recommended that students study mathematics in every year of high school. Students will take the Algebra 1 Keystone Exam toward the end of the course when enrolled in CP Algebra 1 or Algebra 1 AB. 

Math Course Sequences

CP Algebra 1 

Linear equations, functions, and inequalities are the primary focus of the first half of the course, with emphasis on solving equations and inequalities graphically and algebraically. The concepts of linear equations and inequalities are extended to systems of linear equations and inequalities. A study of absolute value equations and inequalities extends the concepts and skills related to linear equations and inequalities. Equivalent expressions involving exponents, polynomials, rationals, and radicals are the primary focus of the second half of the course, with an emphasis on creating simplified equivalent forms using properties of real numbers. The course concludes with a statistical unit focused on analyzing data using plots and graphs. After the Keystone Algebra 1 Exam, the concept of solving quadratic equations by factoring is introduced.

CP Geometry

The general goals of this course are to develop an understanding of geometric concepts and use logical reasoning skills. The topics to be covered include logic, properties of angles, lines, polygons and congruence, similarity, coordinate geometry, justification and proof, right triangles, circles, two-dimensional and three-dimensional shapes and figures. 

CP Algebra 1 is a prerequisite for this course.

CP Algebra 2

The primary focus of this course is to further develop algebraic skills and apply them to contextual problems. This course extends Algebra 1 concepts and includes a study of the following topics: quadratic functions, polynomial functions, radical functions and rational exponents, exponential and logarithmic functions, rational functions, and probability.

Completion of or concurrent enrollment in CP Geometry is a prerequisite for this course.

Precalculus

This course consists of the study of topics in mathematics that prepare students for Calculus. These topics include: families of functions, sequences and series, and trigonometry. The analysis of quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions connects symbolic, graphical, and contextualized representations of functions. An abstract and contextual understanding of right and oblique triangle trigonometry, radian measure, and the unit circle will be developed. Identities and properties of trigonometric functions will be explored and applied to solve problems.

CP Geometry and CP Algebra 2 are prerequisites for this course.

Functions and Trigonometry

This course focuses on applying and expanding upon previously acquired knowledge of functions to analyze data, make predictions, and solve contextual problems. The analysis of linear, quadratic, exponential, logarithmic, and trigonometric functions connects symbolic and graphical representations to applied problems. Emphasis is placed on using technology to create, use, and analyze results from models. Additionally, the course will extend previous trigonometry concepts from geometry to radian measure and the unit circle. Problems involving the use of both right and oblique triangle trigonometry will be explored in context.

CP Algebra 2 or Algebra 2 is a prerequisite for this course.

Introductory Calculus

Introductory Calculus is a full-year course covering differentiation and integration of functions of a single variable, with applications. The concept of a limit will be introduced as a means for evaluating derivatives and integrals. Students will apply skills of differentiation to measure instantaneous rates of change and determine optimal solutions to contextual problems. Students will evaluate integrals using both Riemann Sums and antiderivative techniques and apply these skills in calculating total change. Students will create and solve differential equations to model real-world change. A graphing approach to the subject will be employed and graphing calculators will be used for various topics in the class. 

Precalculus or Advanced Precalculus is a prerequisite for this course.

Statistics

The topics of this course will include exploration of categorical and quantitative data and comparison of data distributions. Students will learn to produce meaningful data by sample, surveys, and experiment. Probability, normal distributions, and sampling distributions of random variables are included. Students will learn to use confidence intervals and significance tests for means and proportions. This is not a lecture course, but rather one of active learning with an investigative approach to statistics.

CP Algebra 2 or Algebra 2 is a prerequisite for this course.

College-Prep Math Courses with Additional Supports and a Slower Pace

Algebra 1 AB

Linear equations, inequalities, and functions are the primary focus of this course, with emphasis on solving equations and inequalities graphically and algebraically. The concepts of linear equations and inequalities are extended to systems of linear equations and inequalities. A study of absolute value equations and inequalities extends the concepts and skills related to linear equations and inequalities. Expressions involving exponents, polynomials, rationals, and radicals are simplified to equivalent forms using properties of real numbers. A statistical unit focusing on analyzing data using plots, graphs, and measures of central tendencies is also explored. To prepare for Geometry, students learn to solve polynomials by factoring.

This two-credit Algebra 1 course meets everyday for the full year.

Geometry

The general goals of this course are to develop a working knowledge of geometric principles and use logical thinking skills. Students will apply definitions, postulates, and theorems to situations in order to develop problem-solving skills. The topics to be covered include logic, properties of angles, lines, polygons and congruence, similarity, coordinate geometry, justification and proof, right triangles, circles, two-dimensional and three-dimensional shapes and figures.

Algebra 1 AB is a prerequisite for this course.

Algebra 2

The primary focus of this course is to further develop algebraic skills and apply them to contextual problems. The course includes a study of the following topics: linear functions, quadratic functions, polynomial functions, radical functions and rational exponents, exponential and logarithmic functions, and probability. This course emphasizes a graphical understanding of concepts utilizing available technology. This course emphasizes a graphical understanding of concepts utilizing available technology.

Geometry is a prerequisite for this course.

Advanced Geometry

The general goals of this course are to develop an in-depth understanding of geometric concepts and use logical reasoning skills. The topics to be covered include properties of angles, lines, polygons and congruence, similarity, coordinate geometry, justification and proof, right triangles, vectors, circles, two-dimensional and three-dimensional shapes and figures. There is a substantial emphasis on independent proof writing. Problems often require prerequisite algebra skills including: factoring quadratic equations, systems of equations, and literal equations.

Advanced Algebra 1 is a prerequisite for this course.

Advanced Algebra 2

The primary focus of this course is to develop algebraic skills and apply them to non-linear contextual problems. This course is an in-depth study of the properties and sets of real numbers through abstract algebra, linear equations of one and two variables, systems of equations, polynomial, rational, quadratic, exponential, logarithmic, and radical functions, radicals and rational exponents, and conic sections.

Completion of or concurrent enrollment in Advanced Geometry or CP Geometry is a prerequisite for this course.

Advanced Honors Precalculus

A rigorous treatment of different families of functions forms the basis of study for the course. An in-depth study of polynomial, rational, exponential, logarithmic, and trigonometric functions consists of connecting symbolic, graphical, and contextualized representations of functions. The concept of function is extended to sequences and series, and counting and probability. The second half of the course focuses on trigonometric functions, including the unit circle, triangle trigonometry, and analytical trigonometric identities. Trigonometric functions are conceptualized in the rectangular coordinate system, polar coordinate system, and complex coordinate system. Trigonometric functions are extended and applied to a study of parametric equations. Properties of functions and expressions will be derived and proved throughout the course. 

Advanced Geometry and Advanced Algebra 2 are prerequisites for this course.

Advanced Precalculus

This course consists of the study of topics in mathematics that prepare students for Calculus. These topics include: families of functions, sequences and series, and trigonometry. The analysis of quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions connects symbolic, graphical, and contextualized representations of functions. An abstract and contextual understanding of right and oblique triangle trigonometry, radian measure, and the unit circle will be developed. Identities and properties of trigonometric functions will be explored and applied to solve problems. In addition to an algorithmic understanding of concepts, there is an emphasis on analysis and synthesis of learned concepts.

Advanced Geometry and Advanced Algebra 2 are prerequisites for this course.

AP Calculus BC

The BC Calculus course is an intensive full-year course in the differential and integral calculus of functions of a single variable. It is a college-level mathematics course for which most colleges grant advanced placement and as many as eight credits. All students will be encouraged to take the Advanced Placement Mathematics examination in May. The course includes the study of limits using multiple approaches, how to apply limits to graphs, and the study of rates of change in context. The course also includes the study of differentiation including the derivative rules, approximating a derivative, and applying the derivative in real-world problem situations. The course also includes integration including accumulated change as well as application problems with area, volume and motion. The course also includes infinite series including convergence, divergence, Maclaurin and Taylor series and using series to make approximations. Lastly, the course includes vectors, parametrics, polar graphs and some elementary differential equations. A graphics approach to the subject will be employed, and graphing calculators will be used for various topics in the class.

Advanced Honors Precalculus or the recommendation of the Advanced Precalculus teacher is a prerequisite for this course.

AP Calculus AB

The AB Calculus course is a full-year course in the calculus of functions of a single variable. It is a college-level mathematics course for which many colleges grant advanced placement credit. All students will be encouraged to take the Advanced Placement Mathematics examination in May. The course includes the study of limits using multiple approaches, how to apply limits to graphs, and the study of rates of change in context. The course also includes the study of differentiation including the derivative rules, approximating a derivative, and applying the derivative in real-world problem situations. The course also includes integration including accumulated change as well as application problems with area, volume, and motion. Lastly, the course includes some elementary differential equations. A graphics approach to the subject will be employed, and graphing calculators will be used for various topics in the class.

Advanced Precalculus or the recommendation of the Precalculus teacher is a prerequisite for this course.

AP Statistics

The purpose of Advanced Placement Statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes:

1. Exploring data: exploring patterns and departures from patterns.

2. Planning a study: deciding what and how to measure.

3. Anticipating patterns: predicting models using probability and simulation.

4. Statistical inference: confirming models.

Students who successfully complete the course and the Advanced Placement examination may receive credit and/or advanced placement for a one-semester introductory college statistics course. At least one statistics course is typically required for majors such as engineering, psychology, sociology, health science, and business.

Advanced Algebra 2 or a very strong performance in CP Algebra 2 is a prerequisite for this course.

AP Computer Science A

AP Computer Science A is a full-year programming course using the Java language. It is a college-level course for which many universities grant advanced placement credit dependent on the results of an AP Exam given in May. The course will begin with an introduction to Java syntax and style conventions and basic programming constructs such as data types, variables, control statements, iteration, and recursion. Well-known algorithms will be applied to solve problems, especially when working with structures like Strings and Arrays. Object Oriented Programming Design will be employed throughout the course. The use of classes will be fundamental. Searching and sorting algorithms and their efficiencies will be discussed. Managing and manipulating larger data sets will be explored, with a focus on selecting appropriate data structures, writing algorithms to extract meaningful knowledge, and developing code to handle input and output, reading from and writing to a console or an external text file. At the end of the course, students will explore components that make programs more viable. Topics may include streams and files, graphics, GUI components, mouse, keyboard, sound, and images. A culminating final project will give students the opportunity to showcase learned skills and concepts and to research new skills to create and present a program of their choice. 

Students without previous coding experience are strongly encouraged to gain some experience with programming before taking this course. This could be accomplished by completing AP Computer Science Principles or a CTC computer programming course before taking AP Computer Science A.

Advanced Topics in Mathematics

Advanced Topics in Mathematics focuses on multivariable and vector calculus with an introduction to linear algebra. Additionally, students will be expected to explore other mathematical concepts not typically found in a high school curriculum. The course begins with vectors in space and the appropriate operations, lines, planes, cylinders, and quadric surfaces. It continues with Vector-Valued Functions, the unit tangent vector, the unit normal vector, curvature, torsion, and the TNB frame. There is a brief unit that introduces select topics in linear algebra. We will examine multivariable functions, limits and continuity, partial derivatives, gradient vectors, Lagrange Multipliers, and Taylor’s Formula. Students will investigate double and triple integrals in various coordinate systems. The vector calculus portion of the course finishes with the study of vector fields, line integrals, surface integrals, Green’s theorem, Stoke’s Theorem, and the Divergence (Gauss) Theorem.

AP Calculus BC is a prerequisite for this course.

Frequently Asked Questions

Do I have to register for the course that my teacher recommended?

Recommendations are exactly that, recommendations. If you were recommended for a college-prep-level course for instance and you want to work extra hard and challenge yourself, you can register the advanced level of that course. Please keep in mind that teachers have a great deal of experience in making these decisions and do a very good job of recommending courses for students based on guidelines that are reviewed annually by the mathematics department. However, we also know that this is not an exact science and that personal motivation, determination, and available time are big factors in success.

Can I take two math courses at the same time?

Other than electives like Statistics, AP Statistics, and AP Computer Science A, the only courses that are not sequential prerequisites are Algebra 2 and Geometry of any level and so those are the only courses that can be taken simultaneously.

My path doesn’t look like I’ll get to calculus. What can I do to get to calculus in high school?

First, know that calculus in high school is not the key to success and happiness in life and it also is not necessary for future careers in math and science related fields. Ask any Penn State math professor and they will tell you that they would prefer students have a stronger math preparation leading to calculus to be taken at the university than to rush to calculus in high school at the cost of a very strong precalculus background. The one place in the curriculum that enables advancing a year for this purpose is simultaneous enrollment in Geometry and Algebra 2.

Can I take a course if I have not taken a noted prerequisite course?

No. The prerequisites to any course are listed because students will need strong understanding of the content of the prerequisite course for success in the subsequent course. Much of mathematics is sequential in nature and builds upon itself. Prerequisites represent the required learning needed for each course.

AP Computer Science A looks like fun! Should I have computer programming experience before taking this course?

Our official prerequisites are that students must have completed both Advanced Algebra 2 and a CTC Computer Programming course OR have completed Advanced Precalculus. Even if you have the Advanced Precalculus option completed, some students may find the course challenging without previous coding experience since programming is very much similar to learning a language (and lots of fun logic!). Students without previous coding experience are strongly encouraged to gain some experience with programming before taking this course. This could be accomplished by completing AP Computer Science Principles or a CTC computer programming course before enrolling in AP Computer Science A.