Mathematics

At King’s Academy, there is an appreciation for the intrinsic value of the study of mathematics: its power lies not within the mere manipulation of numbers, but in developing a mental discipline for approaching the solution of problems methodically and rationally. Leveraging a solid basis of mathematical knowledge and expertise in fundamental skills, the focus of the curriculum is the development of critical thinking by incorporating an ever increasing number of word problems of greater complexity as students transition from introductory to advanced courses in mathematics.

King’s Academy has adopted a well-tested and proven course program that moves from Algebra I and Geometry to Algebra II to establish basic mathematical thought processes and skills in both computation and visualization. Having completed those, students have a variety of higher level math courses from which to choose, including Pre-calculus, Calculus, AP Statistics, AP Calculus AB and AP Calculus BC. Mathematics is one of the tools at the school’s disposal to prepare students to meet challenging problems in their future lives.

Courses in this department for 2017-2018:

Algebra I

This is a course in first-year algebra with a focus on numerical, algebraic, graphing and verbal methods of problem-solving. The algebra topics of study include equations, proportions, and inequalities in one variable, writing, solving and graphing linear equations and inequalities, solving and graphing systems of linear equations, operations involving polynomials and factoring, solving quadratic equations, fractions, exponents and data analysis. Following Algebra I, students take either Integrated Mathematics or Geometry.
Course length: One year
Prerequisites: Department consent

Geometry

The Geometry course is designed to provide a solid foundation of basic and fundamental algebraic and geometric concepts. Upon completion of the course, students should have a firm and confident grasp of Euclidean geometry and be well prepared for further study in mathematics, namely Algebra II and beyond. Constructions, investigations, proofs and projects are used to explore the various facets of geometry. The topics include both inductive and deductive reasoning, and plane, spatial, coordinate, and transformational geometry.
Course length: One year
Prerequisites: Department consent

Integrated Mathematics

Covering all major topics of algebra and geometry, Integrated Mathematics is the foundation for all higher-level math courses. It enables students from a range of math backgrounds to tackle challenging problems with a variety of approaches and to improve their critical thinking skills. The algebra topics of study include writing, solving and graphing linear equations and inequalities, solving and graphing systems of linear equations, operations involving polynomials and factoring, solving quadratic equations, and exponents and radicals, while the geometry topics of study include the properties of lines in a plane, triangles, polygons, similar polygons and right triangles including trigonometric ratios, circles, area and volume.
Course length: One year
Prerequisites: Department consent

Algebra II

Fundamental to the study of advanced Algebra is the thorough development of the concept of functions. Course material includes an emphasis on slope as an average rate of change, introduction of inverse functions, exponential and logarithmic functions, polynomial functions, rational expressions and functions, radical expressions and functions, the introduction of imaginary numbers, right triangle trigonometry and matrices, and an overview of statistics and probability. A graphing calculator is required.
Course length: One year
Prerequisites: Completion of Algebra I and Geometry or Integrated Mathematics

Algebra II Honors

Algebra II Honors includes conic sections, series and sequences and partial fractions along with all Algebra II topics (linear functions and systems, matrices, quadratic and polynomial functions, exponential and logarithmic functions, radical and rational functions, right triangle trigonometry and probability and statistics) with particular emphasis on challenging word problems and applications of the concepts. This course is an excellent choice for students who want to enhance and develop furthermore their critical thinking and problem-solving skills and prepare well for the Pre-Calculus Honors course the year after. A graphing calculator is required.
Course length: One year
Prerequisites: Completion of Algebra I and Geometry or Integrated Mathematics and department consent

Functions, Statistics, and Trigonometry (FST)

Designed to supplement the material presented in Algebra II, FST completes the study of the elementary functions; linear, quadratic, exponential, logarithmic and trigonometric. Additionally, the course develops some material from finite mathematics including an introduction to probability and statistics, additional applications of trigonometry, and sequences and series. The topics cover a wide range of mathematics and are designed to significantly enhance students' ability to undertake the study of advanced statistical applications. Throughout the entire course, modeling of real phenomena is emphasized. A graphing calculator is required.
Course length: One year
Prerequisites: Algebra II and department consent

Pre-Calculus

Pre-Calculus is not a specific, discrete study in mathematics, but rather a course that focuses upon establishing the student's knowledge and skills in preparation for undertaking more advanced math studies. While many of the topics introduced in Algebra II are revisited, they are covered in greater depth and breadth. Included are more challenging studies in functions, analysis of their domains and ranges, recognition of families of curves and their transformations, the study of conic sections, advanced trigonometry, arithmetic and geometric series, and statistics and probability. A graphing calculator is required and integral to the course as methods of solution include algebraic, numeric and graphical approaches.
Course length: One year
Prerequisites: Algebra II, Algebra II Honors or FST, and department consent

Pre-Calculus Honors

Pre-Calculus Honors consolidates algebra and geometry skills, and emphasizes application and synthesis of those topics as a preparation for AP Calculus. The topics include solving algebraic equations and inequalities, function operations, polynomial and rational function analysis, exponential and logarithmic functions, trigonometric functions and applications, sequences and series, and conic sections. Problems are solved numerically, graphically and algebraically, and a graphing calculator is used extensively for modeling and analyzing functions.
Course length: One year
Prerequisites: Algebra II or Algebra II Honors and department consent

Introductory Statistics

From opinion polls and customer satisfaction surveys to drug trials, people seem to be surrounded by data everywhere. The importance of statistical literacy has been steadily increasing over the years, and data analyses often drive decision-making. Thus, students taking this course will rarely question the relevance of course content to real life. Introductory Statistics is primarily a project-based course in which students often collect and analyze their own data. They study proper collection and inference techniques to determine the significance of the data they collected. Students also learn how to build probability models by observing data and design experiments to reduce variability. A graphing calculator is required.
Course length: One year
Prerequisites: Pre-Calculus or Functions, Statistics and Trigonometry and department consent

Calculus

This course covers all of the first semester as well as some of the second semester topics of a college-level calculus survey course. Included are studies in limits and continuity, derivatives and integrals and selected applications of them and an introduction to differential equations. Pre-calculus topics are reviewed when appropriate to ensure contextual presentation of new material. A graphing calculator is required.
Course length: One year
Prerequisites: Pre-Calculus or Pre-Calculus Honors and department consent

AP Statistics

This course follows the College Board Advanced Placement syllabus and is designed to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad-conceptual themes: exploring data (describing patterns and departures from patterns), sampling and experimentation (planning and conducting a study), anticipating patterns (exploring random phenomena using probability and simulation) and statistical inference (estimating population parameters and testing hypotheses). A graphing calculator is required. After the completion of this course, students are expected to take the AP Exam.
Course length: One year
Prerequisites: Pre-Calculus, Pre-Calculus Honors, or Functions, Statistics and Trigonometry and department consent

AP Calculus AB

A rigorous and challenging course comparable to courses in colleges and universities, AP Calculus AB is designed for students with excellent mathematical skills who seek college credit, college placement or both from institutions of higher learning. Based on the College Board Advanced Placement AB syllabus, the course approaches the calculus concepts (limits and continuity, derivatives and integrals and their applications) from multiple perspectives – graphically, analytically, numerically and verbally. A graphing calculator is required. After the completion of this course, students are expected to take the AP Exam.
Course length: One year
Prerequisites: Pre-Calculus or Pre-Calculus Honors and department consent

AP Calculus BC

Designed as an extension of Calculus AB rather than an enhancement, AP Calculus BC includes, along with all Calculus AB topics, additional topics such as: integration by parts and by tables, improper integrals, Euler’s Method and L’Hôpital’s Rule, infinite series, parametric equations, and polar coordinates and polar graphs. A graphing calculator is required. After the completion of this course, students are expected to take the AP Exam.
Course length: One year
Prerequisites: AP Calculus AB and department consent

Multivariable Calculus

Unlike AP Calculus AB and BC in which students study calculus of a single variable, Multivariable Calculus is a rigorous college course focused on functions of two or more independent variables. The concepts studied in this course are applied in many different fields – thermodynamics, electricity and magnetism, economics, modeling fluid or heat flow, etc. The topics included are vectors and the geometry of space, vector-valued functions, functions of several variables, multiple integration, vector analysis, and second order differential equations. A graphing calculator is required.
Course length: One year
Prerequisites: AP Calculus BC

Last updated
April 24, 2017