The Prep Mathematics department is committed to educating the student as a whole person by emphasizing Ignatian values both in and outside the classroom. Following the tradition of Prep teachers such as Fr. Aloysius Galvin, S.J., the math department seeks to instill in students the discipline necessary to excel in mathematics and other areas of study.
The department’s goal is for students to develop the necessary perseverance to work through challenging problems using critical thinking while at the same time taking personal responsibility for their individual learning. In addition to competency in math fundamentals, we want students to gain an appreciation for the study of math as well as its applications in the world.
The Math Program
Prep offers a four year rigorous mathematics program which serves the needs of students of all abilities. The program is flexible enough to allow students from any freshman math class the opportunity to accelerate eventually into Advanced Placement Calculus classes. To view the map of course sequences, click here.
The curriculum is designed to give students a solid foundation in mathematics so that they can succeed in Calculus and college level math. In each class, students are challenged to use their critical thinking skills to solve problems by hand and to interpret these functions in practical terms. Calculators are only used in advanced classes. In addition, through the direction of a teacher, students are encouraged to make connections between mathematical concepts and to understand how functions can be models for change.
In the 2007 Advanced Placement Report to the Nation, Georgetown Prep was recognized for having an Exemplary AP Calculus AB Program. This honor was based on Prep students leading the nation in achieving a score of 3 or higher on the AP exam for medium sized private schools (300 -799 students). In 2011, all 39 students earned a 5 on the AP Calculus AB exam, and on the Calculus BC exam, twenty students scored a 5 and one student scored a 4. In AP Statistics, there were eleven students who took the exam, and their mean score was 4.6.
The Math Office
The math office is a unique place on campus where students can receive extra help in math throughout the entire school day. Each math teacher has a desk in the office so that he or she is readily available to work with students in need of additional instruction. The math office is a supportive environment where students understand that they are cooperative partners with their teachers in the pursuit of learning math.
Course Offerings
Multivariable Calculus
Topics include vectors and vector valued functions in 2-space and 3-space, cylindrical and spherical coordinates, partial derivatives, limits, continuity, differentiability, directional derivatives, the gradient, maxima and minima, optimization using Language multipliers, parametric surfaces, double and triple integrals, change of variable and Jacobian, line integrals, vector fields, surface integrals and the classical theorems of Green, Gauss and Stokes.
Prerequisite: placement by the Math Department (completion of Calculus BC)
AP AB Calculus
The course follows the Advanced Placement AB Calculus syllabus. The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include limits and continuity, differentiation and integration with applications, the Fundamental Theorem of Calculus, numerical approximations and elementary differential equations. The use of technology is an important part of this course. A TI-83+ or TI-84 graphics calculator is required. Students are required to sit for the AP Exam.
Prerequisites: placement by the Math Department (completion of Algebra 3/Trig or Introduction to Calculus)
AP BC Calculus
This course covers all the topics in the Advanced Placement BC Calculus syllabus and goes beyond. The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include vectors and vector-valued functions, parametric equations, polar functions and polar area, differentiation, integration and the Fundamental Theorem of Calculus, improper integrals, sequences and series, Taylor expansions with Lagrange Error Bound, logistic differential equations.
Topics covered beyond the BC syllabus include integral applications to physics and engineering, biology and economics – work, electricity, energy, hydrostatic force, moments, centers of mass, Poiseuille’s Law, cardiac output, consumer surplus, present and future value – surface area, probability, advanced techniques of integration, epsilon-delta definition of limit, curvature, modeling using differential equations, predator-prey systems and Fourier series. A TI-83+ or TI-84 graphics calculator is required. Students are required to sit for the AP Exam.
Prerequisite: placement by the Math Department (completion of Intro or AB)
Introduction to Calculus
This course is divided into 2 parts. Part I is a study of the elementary functions – polynomial, rational, linear, logarithmic, trigonometric and inverse trigonometric – and rates of change – with an eye towards calculus ahead. Topics are examined according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Part II is a beginning study of the calculus of a single variable. Topics include limits, continuity, derivatives, and anti-derivatives. The use of technology is an important part of this course. A TI-83+ or TI-84 graphics calculator is required.
Prerequisites: placement by the Math department (completion of Algebra 3/Trig)
Precalculus
The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. An exploration at a greater level of abstraction of the elementary functions (linear, quadratic, polynomial and rational) and their transformations, the transcendental functions: exponential, trigonometric functions and their inverses and logarithmic functions, composition, asymptotic behavior, polar coordinates, complex numbers, solving and graphing systems of equations and inequalities, elementary probability and statistics and modeling with word problems. A TI-83+ or TI-84 graphics calculator is required.
Prerequisites: successful completion of Algebra II/Trig – Placement by Math Department.
Algebra II/Trigonometry
A continuation of the study of algebra. Topics include factoring, exponents, radicals, solving polynomial equations, polynomial division, elementary probability and statistics inverse functions, logarithms and conic sections, complex numbers, logarithmic functions, and exponential functions, modeling with word problems. Topics in trigonometry include trigonometric ratios, graphing trigonometric functions, solving trigonometric equations, using trigonometric identities, transformations, inverse trigonometric functions, and modeling with word problems. The use of technology is an important part of this course. A TI-83+ or TI-84 graphics calculator is required.
Prerequisites: successful completion of Geometry – Placement by Math Department
Algebra 3/Trigonometry
An advanced exploration of linear, quadratic, polynomial and rational functions and the transcendental functions – exponential, logarithmic, trigonometric, inverse trigonometric. Topics include transformations, composition, asymptotic behavior, polar coordinates, complex numbers, DeMoivre’s Theorem, solving systems of equations and inequalities, conic sections, matrices and determinants, sequences and series, elementary probability and statistics and modeling with word problems. A TI-*3+ or TI-84 graphics calculator is required.
Prerequisites: successful completion of Geometry – Placement by Math Department
Geometry
A first course in geometry using Euclid’s Elements as the text Topics include definitions axioms, postulates, angle and line relationships, properties of parallel lines, congruence theory, triangles, Euclid’s proof of the Pythagorean Theorem, circles, perimeter and area of plane figures, surface area and volume of solids, the Platonic solids, similarity, ratio, proportion, geometric constructions and algebraic applications. This course spends a great deal of time on geometrical proofs, both direct and indirect. A straightedge and compass are required.
Prerequisites: successful completion of Algebra I or Intermediate Algebra – Placement by Math Department
Freshman Geometry
The first three quarters of this course will focus on Geometry. The Geometry course uses Euclid’s Elements as the primary text. Topics include definitions, axioms, postulates, angle and line relationships, properties of parallel lines, congruence theory, triangles, and Euclid’s proof of the Pythagorean Theorem, circles, perimeter and area of plane figures, surface area and volume of solids, the Platonic solids, similarity, ratio, proportion, geometric constructions and algebraic applications. The fourth quarter focuses on advanced Algebra and Trigonometry. Topics include rational expressions and equations, functional notation, literal equations, right triangle trigonometry, and trigonometric functions.
Intermediate Algebra
Intermediate Algebra continues the study of algebra. Topics include order of operations, evaluation of expressions, using rules of exponents, solving and graphing linear and quadratic equations, modeling with word problems, simplification of radicals, factoring, solving and graphing quadratic equations, analysis of graphs, distance formula, elementary probability and statistics, right angle trigonometry, polynomial, exponential and rational functions and logarithms. A TI-83+ or TI-84 graphics calculator is required.
Prerequisites: superior score on the Math Placement Test given to incoming students – Placement by Math Department.
Algebra I
The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include order of operations, evaluation of expressions, using rules of exponents, radical expressions and equations, solving and graphing linear equations and inequalities, modeling with word problems, quadratic functions, the quadratic formula, polynomial, rational and exponential functions, ratio, proportion, elementary statistics and probability. The use of technology is an important part of this course. A TI-83+ or TI-84 graphics calculator is required. Placement by Math Department.
AP Statistics
A standard course in college-level statistics, this course follows the AP syllabus. Topics include regression analysis, correlation and causation, randomization and experiment design, probability models, confidence intervals and a study of the lives and theories of those thinkers who have contributed significantly to the science of statistics: Galileo, Fermat, Pascal, Bernoulli, Keynes and Stephen J. Gould. Using technology is an important part of this course. A TI-83+ or TI-84 graphics calculator is required. Students are required to sit for the AP exam.
Prerequisite: placement of the Math Department (completion of Algebra II/Trig). This course is an elective and will not replace the mathematics or social studies requirement for graduation.