# Mathematics

The Mathematics Department is committed to providing its students with the opportunity to gain the mathematical knowledge, understanding, and skills necessary for success at the college entrance level appropriate to the student’s ability; all students are required to take four years of mathematics for high school credit. The stable and structured environment existing in the Academy allows the student to focus on the academic challenges and opportunities at hand. Many of the students work together and assist each other in a community effort to learn and succeed together.

**Pre- Algebra **is designed for students to investigate real, rational, and irrational numbers. They will begin to work with graphing, linear equations, and functions while using variables to solve real-world problems. Students will develop their problem-solving skills by interpreting data, graphs, and tables and apply this to using probability.

**Algebra I** covers basic algebraic operations, properties of real numbers, solving equations, simplifying polynomials, factoring, ratios and percentages, systems of linear equations, linear and quadratic functions, graphing on a coordinate plane, inequalities, rational numbers, powers and exponents, problem-solving, and an introduction to the use of a graphing calculator. **Geometry **covers the development of reasoning and problem-solving skills using triangles, circles, polygons, perpendicularity, parallelism, congruence, similarity, and the application of mathematics as used in the Pythagorean Theorem. The students will be introduced to the use of solving skills in reference to area, volume, and coordinate geometry. **Prerequisite: **Algebra I

**Pre Advanced Placement Geometry **is similar in content to Geometry, but it is taught at a more challenging level and demands a greater mastery of Algebra I. More emphasis is given to proofs and applications involving Algebra II and Trigonometry. **Prerequisites: **Algebra I; Approval of the Department and Academic Dean

**Algebra II **expands on the basic concepts of algebra, including problem-solving, polynomials, rational, exponential and logarithmic functions, powers, roots, radicals, irrational and complex numbers, and sequences and series. **Prerequisites: **Geometry

**Pre Advanced Placement Algebra II **is similar to Algebra II but is taught at a more challenging level and includes trigonometry and probability. **Prerequisites: **Geometry; Approval of Mathematics Department and Academic Dean

**Pre Advanced Placement Pre-Calculus **emphasizes functions (linear, quadratic, polynomial, trigonometric, logarithmic, and exponential), their graphs and applications, problem-solving, analytic geometry, polar and parametric equations, vectors, permutations, combinations, and probability. **Prerequisites: **PAP Algebra II; Approval of Department and Academic Dean

**Algebra III **considers functions (linear, quadratic, polynomial, and exponential), inequalities, logarithms, trigonometry, sequences and series, matrices, permutations, combinations, and statistics. Special emphasis is given to prepare students for college entrance exams. **Prerequisites: **Algebra II; Approval of Department and Academic Dean

**Advanced Placement Statistics **will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Concepts include probability, simple combinatorics, and major probability distributions including normal, t, binomial, geometric, and chi-squared distributions. This course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. **Prerequisites:** Algebra II; Approval of the Department and Academic Dean

**Advanced Placement Calculus AB** introduces limits, differentiation, and integration of functions. Students find and evaluate finite and infinite limits graphically, numerically, and analytically. They find derivatives using a variety of methods including The Chain Rule and Implicit Differentiation. They use the First Derivative Test and The Second Derivative Test to analyze and sketch functions. Subsequently, students will find antiderivatives using a variety of methods including substitution. They will evaluate integrals using a variety of methods including numerical integration. They will understand and apply Riemann sums, definite integrals, and The Fundamental Theorem of Calculus. In particular, they will differentiate and integrate logarithmic, exponential, and inverse trigonometric functions. They will solve simple differential equations that can be solved by separation of variables and use them to solve applied problems. They will use integration to determine the area between two curves and the volume of solids. **Prerequisites: **Pre-Calculus; Approval of the Department and Academic Dean

**Advanced Placement Calculus BC **course will include all topics of Calculus AB plus additional topics in differential and integral calculus (including parametric, polar, and vector functions) and series. **Prerequisites: **Pre-Calculus; Approval of the Department and Academic Dean

**Personal Finance** is a course designed to help students understand the impact of individual decisions on college and occupational goals as well as future earnings potential. This course will provide a foundational understanding for making informed personal financial decisions with regard to budgeting, the use of credit, strategies for saving money as well as the use of various financial instruments with a focus on a view of the global economy.