Honors Math Program
This program is intended for students who have demonstrated a high proficiency in mathematics, both in attitude and performance. It is designed to prepare students for future work in mathematics and math-related fields at the college level. A student must maintain a B grade or higher math average to continue in this program.
Students are required to sign a commitment stating that they will continue to demonstrate:
- High ability in learning mathematics
- Sincere interest in the study of mathematics
- Willingness to spend extra time and effort in studying mathematics and solving challenging problems
Course Descriptions
Honors Geometry [KHO1228]
Year, Prerequisite: B+ grade or higher in KMS Algebra 1 or 8th grade Accelerated Algebra and teacher recommendation. B+ grade or higher in Algebra 1 at KHS and teacher recommendation.
This course is for students with a high proficiency in mathematics. It requires the acquisition and application of logical reasoning skills through the study of Euclidean Geometry. Deductive and inductive reasoning skills are developed through informal justifications and formal two-column and paragraph proofs. The course emphasizes vocabulary, properties of geometric figures, principles of logical reasoning, algebraic concepts, coordinate geometry, transformations, and real-world applications.
Honors Algebra 2 [KHO1229-M] [KHO1230-U]
Year, Prerequisite: B grade or higher in Honors Algebra 1 and Honors Geometry and teacher recommendation.
Honors Algebra 2 is a continuation of the algebra of real numbers studied in Honors Algebra 1. There is an emphasis on application of algebra skills, problem solving, and demonstrating the process used to solve problems. Topics that may be covered include: real numbers, solving equations and inequalities, including those involving absolute values; transformations of functions, linear equations and functions; operations with polynomials; rational expressions and equations; irrational and complex numbers; operations with radicals and solving radical equations; quadratic equations and functions; analytic geometry; exponential and logarithmic functions; sequences and series; permutations, combinations, and probability; and matrices and determinants.
Prior to the end of the school year preceding this course, every student registering for Honors Algebra 2 will be provided with review materials for Algebra 1. The purpose of this review is to help the student recall the basic concepts learned in Algebra 1; to provide a number of practice problems covering the major topics in Algebra 1; and to give the student an awareness of and sense of confidence for starting Honors Algebra 2. An Algebra 1 exam will be given the second day of school to diagnose the student’s mastery of the concepts necessary for success in Honors Algebra 2.
AP Pre-Calculus [KHO1231]
Year, Prerequisite: B grade or higher in Honors Algebra 2 or teacher recommendation.
This is an AP course intended for those students who (1) intend to go further in the study of mathematics, (2) need more advanced mathematics because they are interested in science, and (3) like mathematics and the satisfaction that comes from the ability to reason and solve difficult problems. This course undertakes a study of a myriad of topics including: mathematical systems, sequences, series, functions, relations, matrices, conic sections, the Binomial Theorem, analytic geometry, and other modern mathematical developments, as well as a brief introduction to the graphing calculator. In the general topic of functions, students study the properties of circular and trigonometric functions and their applications, as well as logarithms and exponential equations.
Throughout this course, students are asked to justify their work by applying mathematical algorithms and explaining the concept orally.
NOTE: Each student in AP Pre-Calculus is required to complete a summer packet to help students make the transition to this course as smooth as possible and to keep their math skills from deteriorating from lack of use. Completion of the packet is required before the start of the course.
Advanced Placement Calculus [KHO1240]
Year, Prerequisite: B grade or higher in Honors Pre-Calculus or Pre-Calculus with teacher recommendation.
This course is intended for students who have a thorough knowledge of algebra, geometry, trigonometry, and analytic geometry. The course is valuable to the future engineering or science student who may take courses that require knowledge of basic calculus. Topics covered in this course include limits, continuity, derivatives, slope fields, integrals, infinite sequences and series, and applications involving derivatives and integrals. Though this course is titled Advanced Placement Calculus, it covers nearly two semesters of college and not just one as the title may apply. Students are expected to take either the AB or BC version of the Advanced Placement Calculus exam at the end of the year. Successful completion of either of these exams may give the student preferential placement at some colleges and possible college credit.
AP EXAM FEE: $95 per exam – payable at the beginning of the second semester.
Dual Credit for Multivariable Calculus III [KHOXXXX1361 (Alt 11, 12)]
Semester, Prerequisite: AP Calculus
Students must complete Hawaiʻi Pacific University and KHS paperwork in order to be enrolled in this dual credit semester course. A score of 4 or higher on AP Calculus BC exam, or HPU math department approval, is also required. Students who do NOT complete the paperwork will be registered into the non-DC course.
Multivariable Calculus covers a third semester of a standard 3-semester calculus sequence. The course gives a thorough introduction to multivariable calculus and mathematical methods needed to understand real work problems involving quantities changing over time in multiple dimensions. Topics include vectors, lines, planes, curves, and surfaces in 3D-space; limits, continuity, and differentiation of multivariable functions; gradient, chain rule, linear approximation, optimization of multivariable functions; double and triple integrals in different coordinate systems; vector fields and vector calculus in 2D-and 3D-space, line integrals, flux integrals, and integration theorems generalizing the Fundamental Theorems of Calculus (Green’s theorem, Stokes’ theorem and Gauss’s theorem, also known as the divergence theorem). Furthermore, the course provides important mathematical foundations for advanced studies in life sciences, physical sciences, social sciences, computer science and engineering, building vocabulary and tools to describe and understand phenomena in the natural world, and improving analytic and problem-solving skills valuable in many disciplines.
Dual Credit for College Linear Algebra [KHOXXXX1362 (Alt 11, 12)]
Semester, Prerequisite: AP Calculus and completion of Multivariable Calculus III
Students must complete Hawaiʻi Pacific University and KHS paperwork in order to be enrolled in this dual credit semester course. Students who do NOT complete the paperwork will be registered into the non-DC course.
Elementary linear algebra with applications in the sciences, to computers and economics. Topics include: systems of linear equations; matrix theory, determinants and eigenvalues, geometry of Euclidean n-space; abstract vector spaces, bases, linear independence, and spanning sets, linear transformations, null space and range, diagonalization of matrices; eigenvalues and eigenvectors. Upon successful completion of the course, students will: 1. Know and apply the definition of span, arguing algebraically and geometrically 2. Know and apply the definitions of linear dependence and independence 3. Take matrices to RREF, identify matrices in RREF 4. Solve systems of equations or show there is no solution, including the use of parametric form 5. Compute with matrices and vectors (scalar multiply, add multiply, find inverses, determinants) 6. Know and apply the definition of linear transformation, identify linear or nonlinear transformations, find the matrix of a linear transformation 7. Determine whether a set is a basis, find a basis of sample 8. Find of or change coordinates 9. Find eigenvalues, eigenvectors, diagonalize a matrix if possible.
Advanced Placement Computer Science Principles [KHO1222]
Year, Prerequisite: B grade or higher in Algebra 2 or Honors Algebra 2, or consent of the teacher. Open to Grades 11 and 12. This course does not satisfy the math graduation requirement.
Whether it’s 3D animation, engineering, music, app development, medicine, visual design, robotics, or political analysis, computer science is the engine that powers the technology, productivity, and innovation that drive the world. Computer science experience has become imperative for today’s students and the workforce of tomorrow. The goal of AP Computer Science Principles is to develop leaders in computer science fields as well as to attract and engage those who are traditionally underrepresented with essential computing tools and multidisciplinary opportunities.
AP EXAM FEE: $95 per exam – Payable at the beginning of second semester.
Advanced Placement Statistics [KHO1276]
Year, Prerequisite: B grade or higher in Algebra 2 or Honors Algebra 2, or consent of the teacher. Open to Grades 11 and 12. This course does not satisfy the math graduation requirement.
The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. This course is for students interested in career fields in business, science, research or other areas that use data analysis.
AP EXAM FEE: $95 per exam – Payable at the beginning of second semester.