This course covers the Algebra II with Trigonometry topics in greater depth and covers a few additional topics: Linear programming, sequences and series and a few additional skills such as polynomial long division and synthetic division. 

This course contains the usual introductory algebra content—i.e., operations on integers; absolute value, solving linear equations, inequalities, and systems; probability and statistics; exponents; polynomials and simple quadratic and rational equations. All of these concepts are covered in the context of problem solving which occasionally uses simple geometric relationships. Several different functions are introduced as a way to describe numerical patterns and a few of them are studied in depth during the course of the year. 

This course reviews and extends the fundamental principles and skills of algebra and geometry with an emphasis on applications. Students will solve equations and graph functions of the following types: linear, absolute value, quadratic, radical, exponential, logarithmic, inverse and rational functions. Students will solve and graph systems of linear equations, quadratic equations and inequalities. Students will apply the arithmetic operations to polynomials, rational expressions, functions, matrices and complex numbers. Students will explore combination and combinations including the Binomial Expansion Theorem. Students will learn and apply right triangle and unit circle definitions, and the inverse of the trigonometric functions. Although analytical methods are emphasized, the TI-8X calculator is used to verify results and facilitate real data analysis. 

Advanced Placement Calculus, a yearlong college-level course, begins with the formal study of limits, which is the foundation of all upper-division mathematics. The students will learn both differential and integral calculus and their traditional and non-traditional applications. The Fundamental Theorem of Calculus is used to connect the two branches and to motivate the Natural Logarithm and Exponential Functions. The syllabus is aligned with the College Board’s syllabus and thus prepares the students to take the Advanced Placement Examination in the spring. Students will be required to complete an assignment over the summer prior to the beginning of the school year. 

This course covers the statistics and probability curriculum with greater depth and mathematical rigor. Topics include summarizing and displaying data; distribution of one-variable data; regression with two-variable data; gathering data with simulations, surveys, studies and experiments; computing probabilities; sampling distributions, hypothesis tests and confidence intervals; Student’s t-distribution; chi-square and t-tests. The course prepares students to take the Advanced Placement examination in the spring. Students will be required to complete an assignment over the summer prior to the beginning of the school year. 

This course contains the usual geometry content-transformations, congruence, similarity, right triangle trigonometry, perimeter, circumference and area for plane geometry (including a coordinate approach); perspective drawing, surface area and volume for solid geometry; and the process of logical reasoning (both deductive and inductive) and proof (both formal and informal). Integrated within these topics are applications and connections to the planet on which we live. Writing and solving algebraic equations is used often to keep skills sharp and to demonstrate the close relationship of geometry to algebra. 

This course adds to the geometry curriculum a more complete study of the formal aspects of the subject, which includes indirect and coordinate proofs, application of geometry to a sphere, compass and straight-edge constructions and a more thorough introduction to trigonometry. 

In this course, students use the Cartesian Coordinate System to study in depth graphing techniques and applications of conics, polynomial, rational, piece-wise, and trigonometric functions. Students also learn the Fundamental Theorem of Algebra and apply it to solve polynomials equations of degree three or higher and solve systems of non-linear equations. 

This course covers the Precalculus topics in greater depth and covers a few additional topics: Exponential and logarithmic functions, trigonometric identities and polar and parametric equations. This course is a formal preparation for calculus, whether taken here at Immaculate Heart or as a first course in college. 

This course is an introduction to fundamental ideas in statistics and probability and is divided into four general categories: gathering data, summarizing data, probability, and statistical inference. Students learn about the process of data collection, how to summarize data, important probability ideas, and how to draw conclusions based upon data. Students learn statistical concepts through classroom instruction, current research, classroom activities as well as a data gathering project.