Courses | KHS MATH DEPARTMENT

The Math Department offers a wide range of courses from Core Algebra to Advanced Placement Computer Science, Advanced Placement Statistics, and Advanced Placement Calculus. In addition, students are invited to join the Mathematics Team and compete at the local, state, and national levels. Math placement is dependent on a combination of factors: placement tests, transcripts, and teacher recommendations.

A graphing calculator is REQUIRED for use in math, science, as well as the SAT/PSAT tests and in college. We highly recommend students purchase a TI-84 Series or TI-Nspire graphing calculator (cost range is about $110-135). A limited supply of graphing calculators will be available for purchase at the Kamehameha bookstore. Please contact your respective math teacher for more specific information.

Honors & Advanced Placement courses are 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; and
Willingness to spend extra time and effort in studying mathematics and solving challenging problems.

Acceleration in Kamehameha’s Mathematics program is possible through Kamehameha summer school courses. Such acceleration is based on the recommendation of a student’s current mathematics teacher to ensure that the student’s best interest is met.

The following flow chart illustrates the recommended course progression in the high school math program:

Course Descriptions

Core Algebra [KH01283]

Semester 1, Prerequisite: Placement subject to Kamehameha Math Placement test scores, grades, standardized test scores, and teacher recommendation, if available.

This course is the first of three semesters of Algebra 1 in the Kamehameha math program and is designed for students who have completed either Pre-Algebra or KMS Math 8 coursework. The course focuses on the development and practice of the essential concepts of mathematics leading to the study of Algebra. Course topics include a review of real numbers and operations, estimation techniques, and absolute value, properties of real numbers, and multiple representations of linear models. Other topics include solving one-variable equations, inequalities, word problems and real life applications.

Algebra 1A [KH01284]

Semester, Prerequisite: Completion of Core Algebra or teacher recommendation.

This is the second course in the Algebra 1 sequence and seeks to develop and strengthen student understanding of linear relationships. Topics include solving and graphing linear equations and inequalities, graphing linear functions and relations, and writing linear functions, and interpreting statistics and data.

Algebra 1B [KH01285]

Semester, Prerequisite: Completion of Algebra 1A with teacher recommendation.

This is the final course in the Algebra 1 sequence. This course continues to develop and strengthen student understanding of linear relationships. However, the main focus of this course is to develop student understanding of non-linear relationships. Topics include solving systems of linear equations and inequalities, exponents and quadratic equations, and polynomial operations, and interpreting statistics and data.

Geometry A [KH01286]

Semester, Prerequisite: Completion of Algebra 1B with teacher recommendation.

Proficiency in Algebra 1 is required because many of the geometry problems are done by setting up and solving equations.
This course will begin with students working on compass and straightedge constructions and gradually building up to formal proof. They will extend what they learned about probability in past years to consider probabilities of combined events, including geometric probability. Finally, students build on the study of transformations of figures, connecting ideas from algebra and geometry through coordinate geometry, and use transformation-based definitions of congruence and similarity to rigorously prove theorems about quadrilaterals, isosceles triangles, and other figures.

Geometry B [KH01287]

Semester, Prerequisite: Completion of Geometry A with teacher recommendation.

Proficiency in Algebra 1 is required because many of the geometry problems are done by setting up and solving equations.

This course extends students’ understanding of similarity by studying right triangle trigonometry. Students will derive volume formulas and study the effect of dilation on both area and volume. Finally, they use transformations and the Pythagorean Theorem to build equations of circles from definitions and analyze relationships between segments and angles in circles.

Honors Geometry [KH01228]

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.

Algebra 2A [KH01288]

Semester, Prerequisite: Completion of Algebra 1B, completion of Geometry A/B, and teacher recommendation.

This semester course develops students’ understanding of operations with the following topics: functions, transformation of functions, absolute value functions, linear functions, quadratic functions, and the real and complex number system.

Algebra 2B [KH01289]

Semester, Prerequisite: Completion of Algebra 2A with teacher recommendation.

This semester course develops students’ understanding of operations with the following topics: polynomials; rational expressions and equations; irrational and complex numbers; operations with radicals and solving radical equations; quadratic equations and functions; exponential functions and intro to logarithmic functions; inverse functions. Algebra 2B is strongly recommended for all students planning to apply to a four-year academic institution, as colleges require this course for those who expect to pursue physical or social sciences, engineering, or mathematics.

DC Algebra 2B [KH01358] – MATH 1105, Hawaiʻi Pacific University

Honors Algebra 2 [KH01229]

Year, Prerequisite: B grade or higher in Honors Geometry and teacher recommendation or teacher recommendation from current Geometry teacher.

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; matrices and determinants; and number systems.

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.

ADVANCED MATH COURSES

Advanced Algebra with Financial Applications [KH01321]

Year, Prerequisite: Completion of Algebra 2B.

Do you want you and your family to be financially successful? Do you know how to save yourself ONE MILLION DOLLARS before you retire? Learn and master the big ideas of personal financial independence for your future, possibly the most important mathematics you can learn. Financial Algebra is a course that is algebra-based, applications-oriented, and technology-dependent. This course addresses college mathematical topics from Algebra 2, Statistics, Probability, Pre-Calculus, and Calculus under seven financial umbrellas: Banking, Investing, Credit, Employment and Income Taxes, Automobile Ownership, Independent Living, and Retirement Planning and Household Budgeting. Financial Algebra allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. It provides students a motivating, young-adult centered, financial context for understanding and applying the mathematics they are guaranteed to use in the future.

Advanced Placement Computer Science Principles [KH01222]

Year, Prerequisite: B grade or higher in Algebra 2B or Honors Algebra 2, or consent of the teacher. Open to grades 11 and 12.

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: $98.00 – payable at the beginning of the second semester.

College Algebra [KH01207]

Semester 1, Prerequisite: Completion of Algebra 2B.Open to grades 11 and 12.

The rigor of this course is at a college level. College Algebra allows students to master Algebra 2 topics while increasing rigor in order to be more successful in college. Topics include: polynomial functions, rational functions, inverse, exponential, and logarithmic functions; analytical geometry, and sequences and series. All topics will include solving real-world application problems. Students that have taken Precalculus, DC Precalculus Honors, AP Precalculus, Calculus, DC Calculus, or AP Calculus cannot take this class.

DC College Linear Algebra [KH01362 (Alt 11, 12)] – MATH 3305, Hawaiʻi Pacific University

Semester 2, Prerequisite: Completion of AP Calculus BC (must score 4 or higher on the AP Calculus BC exam, or Calculus DC (MATH 2214 & 2215) teacher recommendation, and completion of first semester Multivariable Calculus DC.

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 or change coordinates 9. Find eigenvalues, eigenvectors, diagonalize a matrix if possible.

Competitive Math [KH01262 (Alt 10, 11, 12)]

Year, Prerequisite: Consent of instructor. Students enrolling in this course for the first time should have participated on the Kamehameha Math Team in the previous school year. May be repeated. This course does not satisfy the math graduation requirement.

Be part of a nationally recognized team of mathematical excellence!! This course is intended for students who would like to represent Kamehameha at local and national math competitions. It expands upon topics covered in the required math curriculum at Kamehameha and deepens conceptual understanding of these topics. This course will also introduce students to other topics in mathematics, such as set theory, formal logic, and number theory. Students will also learn test-taking strategies and problem-solving skills. There will also be an emphasis placed on the development of leadership skills and the building of strong character. Students will be required to attend math team events outside of regular school hours.

Number Theory Online [KH01367]

Semester, Prerequisite: Must have completed Precalculus and a desire to do rigorous mathematics and proofs. Open to grades 11 or 12. Fulfills 0.5 credit of math graduation requirement. This online course is offered via Global Online Academy (GOA). While coursework is completed asynchronously, students will attend occasional synchronous Zoom sessions for group challenges and whole group discussions.

Once thought of as the purest but least applicable part of mathematics, number theory is now by far the most commonly applied: every one of the millions of secure internet transmissions occurring each second is encrypted using ideas from number theory. This course will cover the fundamentals of this classical, elegant, yet supremely relevant subject. It will provide a foundation for further study of number theory, but even more, it will develop the skills of mathematical reasoning and proof in a concrete and intuitive way, good preparation for any future course in upper-level college mathematics or theoretical computer science, all of which are based on rigor and proof.

We will progressively develop the tools needed to understand the RSA algorithm, the most common encryption scheme used worldwide. Along the way we will invent some encryption schemes of our own and discover how to play games using number theory. We will also get a taste of the history of the subject, which involves the most famous mathematicians from antiquity to the present day, and we will see parts of the story of Fermat’s Last Theorem, a 350-year-old statement that was fully proved only twenty years ago. While most calculations will be simple enough to do by hand, we will sometimes use the computer to see how the fundamental ideas can be applied to the huge numbers needed for modern applications.

Precalculus [KH01243]

Year, Prerequisite: Completion of Algebra 2B w/ teacher recommendation or completion of College Algebra/Trigonometry with teacher recommendation.

Pre-Calculus emphasizes the essential concepts needed to pursue the study of calculus and other advanced math courses. The course is intended for students who are on a Calculus track and are interested in a STEM related field of study after high school. Students should enter the course having acquired a strong command of algebraic properties, an understanding of common algebraic functions and their graphs and exhibit inductive and deductive reasoning techniques. Topics covered include a review of quadratic, polynomial, rational, exponential and logarithmic functions, inverse functions, sequences and series, trigonometric functions, conic sections, polar coordinates, complex numbers, and limits. We also seek to develop the studentʻs analytical thinking and problem solving skills in preparation for their transition to Calculus.

DC Precalculus MATH 1130 [Sem 1, KH01331] & 1140 [Sem 2, KH01333], Hawaiʻi Pacific University

Year, Prerequisite: Completion of Algebra 2B (DC) with a C- or higher and HPU placement test.

MATH 1130 Fulfills AA Distribution Requirement: Quantitative Analysis and Symbolic Reasoning
MATH 1140 Fulfills AA Distribution Elective

Advanced Placement Precalculus [KH01366]

Year, Prerequisite: B grade or higher in Honors Algebra 2 or teacher recommendation.

This is a Pre-Calculus course intended for those students with a strong mathematical background 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 studies a myriad of topics including: mathematical systems, sequences, series, functions, relations, matrices, conic sections, binomial theorem, analytic geometry, vectors, 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. This course is rigorous and moves quickly. The topics covered require a more conceptual understanding and the problems are more difficult than courses that precursor this math course.

AP EXAM FEE: $98.00 per exam- payable at the beginning of the second semester.

Calculus [KH01254]

Year, Prerequisite: Completion of Precalculus with teacher recommendation.

Calculus, the mathematical study of change, is a branch that goes beyond what Algebra and geometry offer. Calculus is required for degrees in science, economics, business, engineering, computer science, medical and dental school, and even an MBA. This course is intended for students who have successfully completed math courses through Precalculus. Topics covered include: review of Precalculus, limits, continuity, derivatives, integrals, applications of derivatives and integrals, finding area between two curves, and volumes of revolution. This course covers material found in a typical first semester college calculus course.

DC Calculus MATH 2214 [Sem 1, KH01332] & 2215 [Sem 2, KH01334], Hawaiʻi Pacific University

Year, Prerequisite: Completion of Precalculus (DC) with a C- or higher OR HPU Math Placement Test.

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. The dual credit curriculum will follow college standards, therefore the pace and rigor will be different from the high school curriculum. Courses offered for Calculus dual credit include both MATH 2214 & MATH 2215 taught at any college/university. Curriculum aligns with AP Calculus BC taught in high school. Grading methods may be different than those of the traditional Kamehameha math class.
MATH 2214 Fulfills AA Distribution Requirement: Quantitative Analysis and Symbolic Reasoning
MATH 2215 Fulfills AA Distribution Elective

Advanced Placement Calculus AB [KH0xxxx] formerly known as AP Calculus

Year, Prerequisite: B grade or higher in Honors Pre-Calculus or recommendation from Precalculus/Precalculus DC teacher.

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, and applications involving derivatives and integrals. Though this course is titled Advanced Placement Calculus AB, it covers nearly two semesters of college and not just one as the title may imply.

*Students enrolled in this course may choose to take the AP Calculus BC exam instead of the AB exam if they complete extra assignments.

AP EXAM FEE: $98.00 – payable at the beginning of the second semester.

Advanced Placement Calculus BC [KH01365]

Year, Prerequisite: Completion of Honors Pre-Calculus or AP Calculus AB, or recommendation from Pre-Calculus/Precalculus DC teacher.

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, integration and differentiation of polar/parametric equations, and applications involving derivatives and integrals. Students are expected to take the BC version of the Advanced Placement Calculus exam at the end of the year.

AP EXAM FEE: $98 per exam – payable at the beginning of the second semester.

DC Multivariable Calculus [KH01361 (Alt 11, 12)] – MATH 2216, Hawaiʻi Pacific University

Semester 1, Prerequisite: Completion of AP Calculus BC (must score a 4 or higher on the AP Calculus BC exam) or with Calculus DC (MATH 2214 & 2215) teacher recommendation.

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.

Probability and Statistics [KH01281]

Semester 1 or , Prerequisite: Algebra 2A/2B and teacher recommendation or Senior standing with completion of Algebra 1A/1B, Geometry A/B and DH approval.

Statistics enables a student to critically think about data in the world around them, recognizing patterns, trends, and connections to their lives. . It is critical in fields as wide as operations analysis, urban planning, computer programming, Psychology, Environmental Science, and Meteorology.

Statistics is the grammar of science. To be fluent in life, knowing how to interpret and communicate mathematically is a valuable life skill. This is an introductory course to topics in probability and statistics. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. Topics include measures of central tendency, conditional probability, binomial probability,, variability, sampling, and analyzing data.

DC Probability and Statistics [KH01360] – MATH 1123, Hawaiʻi Pacific University

MATH 1123 Fulfills AA Distribution Requirement: Quantitative Analysis and Symbolic Reasoning

Advanced Placement Statistics [KH01276]

Year, Prerequisite: B grade or higher in Algebra 2 or Honors Algebra 2, or consent of the teacher. Open to Grades 11 and 12.

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: $98.00 – payable at the beginning of the second semester.

Topics in Discrete Math [KH01280]

Semester 1, Prerequisite: Students who have successfully completed Algebra 1A/1B, Geometry A/B, and Algebra 2A/2B and teacher recommendation or Senior standing with completion of Geometry A/B and DH approval.

This math course will teach you to think about how things in the world operate and to develop a student’s ability to understand and create mathematical arguments. Topics in Discrete Math provide the mathematical foundation for advanced mathematics and computer science courses. An introductory course covers a wide variety of mathematical topics such as theory, matrix, operations and applications, and recursion. Emphasis is placed on problem-solving and reasoning skills. The content of the course is supplemented with preparation for the SAT. It is critical in the working fields of operations analysis, urban planning, computer programming, psychology, environmental science, and meteorology to name a few.

Trigonometry [KH01239]

Semester 2, Prerequisite: Completion of Algebra 2B.

Trigonometry is critical for success in higher level maths, and is used daily in careers like architecture, radiology/medical fields, construction surveying, and digital game design. The rigor of this course is at a college level. Trigonometry is offered as the second semester course after College Algebra. Topics include: functions, circular functions and their graphs, trigonometric identities and equations, and applications of trigonometry. Students that have taken Precalculus, Honors Precalculus, AP Precalculus, Calculus or AP Calculus cannot take this class