Mathematics

Welcome to the State College High School Mathematics Program!

The State College Area School District has a comprehensive mathematics program for students with varying interests, backgrounds, and aptitudes in mathematics. There are College Preparatory and Advanced course sequences.  All course sequences are designed to prepare students for continuing education after high school.

Each course sequence includes experiences with Common-Core Mathematics strands of Number and Quantity, Algebra, Functions, Modeling, Geometry, Statistics and Probability.  The College-Prep courses cover all state-required competencies, but also include more in depth experiences.  Advanced courses are more mathematically rigorous, including rich experiences with reasoning, proof, and mathematical modeling.

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.

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 conceptions and skills of 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

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 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, discrete math, and trigonometry. The analysis of quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions connects symbolic, graphical, and contextualized representations of functions. Discrete math topics to be explored are sequences and series. 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 an emphasis on business 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.

IB Math: Applications and Interpretation SL (Year 2)

Mathematics: Applications and Interpretations SL, a two-year course, is appropriate for students who are interested in developing their mathematics for describing our world and solving practical problems. They will also be interested in harnessing the power of technology alongside exploring mathematical models. Students who take Mathematics: Applications and Interpretations will be those who enjoy mathematics best when seen in a practical context. This subject is aimed at students who will go on to study subjects such as social sciences, natural sciences, statistics, business, some economics, psychology, and design, for example. Content will include the study of topics in number, algebra, functions, geometry, trigonometry, statistics, probability, and calculus. Students will complete investigation, inquiry and problem-solving activities including completing an assessment which enables students to undertake a piece of research which interests them and models the type of mathematical activity undertaken in the modern world. Year one of IB Math: Applications and Interpretation SL is a prerequisite for this course. Note: this course will not be offered after the 2025-2026 school year.

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

CP Algebra 1 A/B

Linear equations, functions, and inequalities 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 conceptions and skills of linear equations and inequalities. Equivalent expressions involving exponents, polynomials, rationals, and radicals are another primary focus of this 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. This two-credit Algebra 1 course meets everyday for the full year.

Geometry

The general goal of this course is to develop a working knowledge of geometric principles and logical thinking skills necessary to use these principles. This course is designed for students to be actively engaged through the use of hands on activities. Students will work in cooperative groups frequently to develop an understanding of geometric principles and to develop the ability to create a plan to find solutions to problems. The topics to be covered include properties of angles, lines, polygons and congruence, similarity, coordinate geometry, justification and proof, right triangles, circles, two-dimensional and three-dimensional shapes and figures. Students will also review and apply algebraic concepts throughout their study of geometric concepts. CP Algebra 1 A/B is a prerequisite for this course.

Algebra 2

The primary focus of this course is to further develop algebraic skills and apply them to real-world problems. This course extends Algebra 1 concepts through the use of experiments and explorations. The course includes a study of the following topics: linear functions in context, quadratic functions, polynomial functions, radical functions and rational exponents, exponential functions, and probability. 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. Significant algebra skills including factoring polynomials, solving quadratic equations by factoring, solving one-variable equations, simplifying expressions, and writing and solving systems of linear equations will be used to work problems in most units. 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, matrices and systems of equations, polynomial, rational, quadratic, exponential, logarithmic, and radical functions, radicals and rational exponents, conic sections and probability. 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, discrete math, and trigonometry. The analysis of quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions connects symbolic, graphical, and contextualized representations of functions. Discrete math topics to be explored are counting, probability, sequences, and series. An abstract and contextual understanding of right and oblique triangle trigonometry, radian measure, the unit circle, and polar coordinates 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 graphics 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 graphics 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, and 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

AP Computer Science 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, hierarchies, and interfaces will be fundamental. Searching and sorting algorithms and their efficiencies will be discussed. At the end of the course, students will explore components that make programs more viable. Topics include streams and files, graphics, GUI components, mouse, keyboard, sound, and images. Advanced Algebra 2 with completion of a CTC Computer Programming course OR Advanced Precalculus is a prerequisite for this course. 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.

Advanced Topics in Mathematics

Advanced Topics in Mathematics focuses on multivariable and vector calculus. 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. 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. The course continues with the study of Linear Algebra. Throughout the course, students will be expected to explore additional topics not typically found in a high school mathematics course. AP Calculus BC is a prerequisite for this course.

IB Math: Analysis and Approaches HL (Year 2)

Mathematics: Analysis and Approaches HL, a two-year course, is appropriate for students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. They will also be fascinated by exploring real and abstract applications of these ideas, with and without the use of technology. Students who take Mathematics: Analysis and Approaches will be those who enjoy the thrill of mathematical problem solving and generalization. This subject is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or economics for example. Mathematics: Analysis and Approaches HL includes all of the content of the SL course and substantial additional and more complex content in number, algebra, functions, geometry, trigonometry, statistics, probability, and calculus. Students will complete investigation, inquiry and problem-solving activities including completing an assessment which enables students to undertake a piece of research which interests them and models the type of mathematical activity undertaken in the modern world. Completion of year one of  IB Math: Analysis and Approaches HL is a prerequisite for this course. Note: this course will not be offered after the 2025-2026 school year.

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, 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 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.