Algebra I is an introductory course designed for incoming Third Formers. After a review of arithmetic operations, the first semester focuses on the basic concepts of algebra: using variables to represent numbers, evaluating formulas, solving algebraic equations, and the graphing of linear equations and basic transformations. The second semester looks at systems of linear equations, functional notation, quadratic equations and rational expressions. Use of the graphing calculator will be developed as an aid to solving systems of equations and quadratic equations.

This standard course provides a comprehensive introduction to Euclidean geometry. Topics covered include foundations of geometry, deductive reasoning and proof, transformations, coordinate geometry, congruence and similarity, polygons, circles, area, and volume. The advanced geometry course includes a rigorous treatment of mathematical proof, and students will be expected to justify the major theorems of the course. The students will also be expected to connect concepts and the most successful students will solve problems creatively.

The standard level course is a comprehensive curriculum with particular emphasis on the practical/computational components of the subject and on the use of functions as mathematical models for solving real-world problems. The advanced course covers all of the topics in the standard class, but in a much more rigorous fashion. This course delves much deeper into the theory underpinning the basics and considers a wider range of topics. The curriculum reaches well beyond the Common Core requirements and prepares the students to tackle PreCalculus at the advanced level the following year.

Standard-level Precalculus provides a comprehensive preparation for the study of Calculus at Haverford or an Introductory Calculus course in college. Polynomial, exponential, and logarithmic functions are emphasized in the first semester and trigonometry, sequences and series, and probability are the focus of the second semester. Real-world models are developed throughout. The advanced course covers all of the topics in standard course, as well as conic sections, parametric equations, polar coordinates, vectors, and the complex plane. Connections with the sciences, economics and other real world applications are developed throughout. This course will also develop the student’s skills in the use of the graphing calculator, in all of its modes.

The standard course begins with a brief review of logarithmic, exponential and trigonometric functions. After exploring the ideas of limits and continuity, the course will focus on the two major concepts of Differential and Integral Calculus. Students will learn methods for taking derivatives and antiderivatives and use these methods in various applications. Although not as theoretical as the advanced class, a strong working knowledge of previous courses, the ability to work independently, and a desire to learn high-level mathematics are required. The advanced level course is a thorough and challenging analysis of limits, derivatives, and Riemann integration. In addition to numerous applications, this course includes a theoretical component and advanced methods of differentiation and integration that will not be covered in Standard Calculus. This course will prepare students to take Calculus II* at THS or move into a more theoretical Calculus course in college, such as required for Mathematics, Engineering or applied science majors.

This extremely rigorous and challenging course is an extension and development of the topics studied in Calculus I*. Advanced topics covered will include techniques of integration, special methods for finding limits, the application of calculus to polar, vector and parametric functions, infinite series (including Maclaurin and Taylor series, and tests for convergence), and applications and solutions of differential equations in physics, engineering, and biology.

The standard level of statistics is intended to provide students a framework to think about the world “statistically.” Real-world problems will be solved using 21st century methodologies, i.e. by incorporating useful technologies and working collaboratively; the process will be project-based, highly interactive, and engaging. The advanced class is a comprehensive survey of the foundations of probability theory and statistical methods for collecting, organizing, displaying, analyzing and drawing conclusions from data. Emphasis is placed on clear and accurate reporting of the results obtained from these activities. Students, having successfully completed Statistics*, may successfully sit for the AP Examination in the spring. Technology will be used extensively for solving problems contemplated in the course. Students may take this course concurrently with Calculus, Calculus I* or Calculus II*.

This course explores the theories and applications of both simple and compound interest. We will learn the basics of general annuities and perpetuities; amortization tables and sinking funds will be developed; bonds and equity instruments will be compared and contrasted; and capital budgeting will be discussed. A major goal of the course will be to teach students effective problem-solving techniques using real-world monetary transactions. Technological solutions to all of the problems contemplated will be emphasized.

This conceptually challenging VI Form elective covers the main ideas of macroeconomics, the study of the large-scale structure of the national and world economy. The mathematical level is comparable to that of an introductory college class in macroeconomics. Topics include national income accounting (GDP), economic growth, unemployment and inflation, the financial sector, money and banking, aggregate supply and demand, and fiscal and monetary policy. Prerequisite: Students must be enrolled in or have completed a Calculus course.