Math Program & Faculty
The Mathematics Department strives for its students to attain mastery in high school mathematics so that they may be fully prepared for any post-secondary curriculum that they may choose. Various approaches are utilized in an effort to provide greater depth of comprehension. Handheld technology is consistently integrated into the curriculum, as it quickly and easily enhances learning from a numeric and graphical standpoint. Traditional algebraic methods support the observations made during investigations and explorations, and students learn to use both deductive and inductive reasoning processes to confirm their findings. Students should also be able to discuss mathematics in their own words and be able to apply their knowledge to real-world situations. Placement in a Walnut Hill math course is determined by the level of math completed prior to acceptance to the School and/or a math placement test.
Requirements in Math
All students are required to complete three credits of high school mathematics. The minimum sequence is Algebra 1, Geometry, and Introductory Algebra 2. In addition, students are encouraged to take Advanced Algebra 2. Electives in Statistics and Math Applications are available for students once they have completed Introductory Algebra 2. It is recommended that students take a math course each year, for a total of at least four math credits.
Courses in Math
INTRODUCTORY ALGEBRA 1
This course covers the foundations for algebra, which include a study of the real number system and its properties as well as the operations on real numbers. Also included in this course are topics on solving equations and inequalities, working with functions, and an introduction to linear functions. This course is offered only when enrollment is sufficient and is for those students with no experience in algebra.
ADVANCED ALGEBRA 1
This course continues the Algebra 1 curriculum with topics that include solving systems of linear equations and inequalities, properties of exponents and exponential functions, polynomials and factoring, and quadratic equations and functions. When time permits, the student will be introduced to radical and rational functions. Students registering for this course have previous algebra experience but may require an additional term on these topics to enable them to move forward in their math studies.
This course covers the basic geometric concepts of reasoning and proof, along with the traditional topics, which include a study of parallel and perpendicular lines, congruent triangles, and other relationships involving triangles. Students will also observe various properties of quadrilaterals, polygons, and circles.
Prerequisite: Algebra 1
INTRODUCTORY ALGEBRA 2
This course covers the first half of a traditional Algebra 2 course, including a review of topics from Algebra 1 with greater depth and more challenge. Additional topics include functions, equations, and their graphs, with emphasis on families of functions, transformations of functions, and operations on functions. Emphasis is on linear, quadratic, and polynomial functions.
Prerequisite: Algebra 1
ADVANCED ALGEBRA 2
This course covers advanced topics in algebra that are necessary to fully complete an Algebra 2 course. Topics include the study of rational and radical functions, exponential and logarithmic functions, conic sections, and sequences and series. When time permits, students will have an introduction to probability and statistics.
Prerequisite: Completion of Introductory Algebra 2 with a grade of B or higher
This course provides foundational skills necessary for success in Calculus. It includes the study of basic functions, both algebraic and transcendental. The behavior of these functions is discussed in greater depth than encountered in prior courses. Students also complete a comprehensive study of trigonometry as part of the curriculum. Applications of the mathematics studied are seen throughout the course.
Prerequisite: Completion of Advanced Algebra 2 with a grade of B or higher
This course includes an in-depth study of the limit as it pertains to functions, as well as the continuity theorems, and leads to the study of differentiation. The derivative is presented from a four-point perspective and students see how the various differentiation formulae are derived. These are then applied to polynomial, rational, trigonometric, inverse trigonometric, implicit, exponential, and logarithmic functions in an effort to more deeply address their behavior. Application topics include using extrema to form accurate graphs, and functions from physics.
Prerequisite: Completion of Precalculus with a grade of B or higher
Calculus 2 focuses on antidifferentiation, beginning with the area under a curve and the Fundamental Theorem of Calculus. Students learn to compute the customary antiderivatives of functions and to apply antidifferentiation to their study of volumes of solids of revolution, finding the average value of a function, and they will see many applications to real-world phenomena. L’Hopital’s Rule and the evaluation of improper integrals will conclude the topics studied. This course is only offered when enrollment is sufficient. Interested students should contact the faculty of the Math Department or the Director of Studies to inquire.
Prerequisite: Completion of Calculus 1 with a grade of B or higher
This is an introductory course. Topics include data collection and experimental design, measures of central tendency and variation, elementary probability theory, normal distributions and their applications, and confidence intervals. Handheld technology enhances the study of these topics. This course is designed to show students the use of statistics in the world around them.
Prerequisite: Introductory Algebra 2
This course is designed for juniors and seniors who have completed the math requirements through Introductory Algebra 2 and would like an additional course in math to solidify those topics that they have studied in their previous classes. The goal is to help students gain mathematical literacy by showing them how mathematics can be applied to their lives in interesting, enjoyable, and meaningful ways. Topics include inductive and deductive reasoning and problem solving, set theory, number theory, topics in algebra and geometry, personal finance applications, and topics in probability and statistics.
Prerequisite: Introductory Algebra 2