Math

High School Graduation Requirements: 4 credits of math during Grades 9-12, including one course for which Algebra II is a prerequisite. Credits earned in middle school may be included on high school transcripts, but students will still be required to earn four credits during high school.

IMPORTANT NOTES:

Students and parents should remember that the public Arizona universities require one year of math beyond Algebra II. Students who take Pre-Algebra in the ninth grade and who plan to go to a public university in Arizona must take math courses in summer school in order to complete Algebra I, Geometry, Algebra II, and Algebra III before graduating from NPA.

Sequence of Mathematics Courses

The mathematics program at Northland Preparatory Academy (NPA) follows an orderly progression through a series of courses that each build upon all of the previous courses from the sequence. Incoming sixth graders are assessed and placed in either Math 6 or Pre-Algebra, depending on their math capabilities at that time. New students who enter NPA after sixth grade are assessed and placed at the appropriate level in the math course sequence. Students then progress through the sequence, as diagrammed below. After completing Algebra II, students are placed into either Algebra III or PreCalculus, depending on their math performance to that point.

Upper-Level Courses

While the diagram above illustrates many of the possible movements through the course sequence past Algebra II, it should be noted that the movements depicted are not exhaustive. There is the potential for some flexibility in moving between these courses, and each student’s progression is handled on an individual basis. Advanced Placement (AP) Calculus AB will continue to be a required prerequisite for AP Calculus BC. For AP Statistics, students have the potential to transition into this course from a number of different courses the previous year (Statistics and Applied Math is not a prerequisite for AP Statistics). More detailed descriptions of all mathematics courses follow.

Advancement in Math Courses at NPA

The nature of the study of mathematics is such that an appropriate level of mastery of each stage is necessary before a student can move on to the next course. Students must demonstrate this level of mastery on a consistent basis throughout each school year. All students in Math 6 will move to PreAlgebra the following year, and will be provided additional support when necessary. For the next four courses in the sequence, advancement standards vary somewhat by grade level. Because students who are at the youngest grade level for these courses (6th graders in Pre-Algebra, 7th graders in Algebra I, 8th graders in Geometry, 9th graders in Algebra II) are considered to be in an advanced course, the standards for advancement are higher for these students. These standards are outlined in the table below. To read the table, find the current math course and overall grade average for a given student (note: this grade average needs to be maintained for the entire school year for advancement consideration), then read the entry that applies to the grade level of that student. The bolded categories are described below. It should also be noted that these advancement procedures may be modified for those students with individualized educational plans (IEPs).

Next Course: The student will automatically be placed in the next course in the sequence.

Possibly Eligible: The student may or may not be placed in the next course in the sequence. The teachers in the math department will analyze such cases individually, and make a decision about possible course changes based on all relevant factors (for example, in some cases, it is recommended that a student complete some sort of summer work in order to advance in the course sequence).

Same Course: The student will spend an additional school year at that same level in order to improve his or her level of mastery.

Advancement through the math course sequence beyond Algebra II is handled on a more individualized basis. However, the general procedure is that a student is required to have an ‘A’ average (90% or better) in Algebra II to be eligible for Pre-Calculus.

It is the position of the NPA math department that no student can ever fail any of these courses, but instead that different students simply take differing amounts of time to develop appropriate levels of mastery of mathematical content. The overall goal of this advancement procedure is to ensure that all students at NPA experience success and competence throughout their study of mathematics.

Courses

MA006 – Math 6

Students will prepare for pre-algebra and beyond by developing problem solving skills, increasing vocabulary database including use of language and symbols, and improving conceptual understanding. Students are introduced to graphing concepts, basic probability and statistics, and two- and three- dimensional geometric concepts. The focus, however, is on each student solidifying his or her understanding of basic concepts and problem solving.

MA010 – Advanced Math Concepts

Students will further their understanding of the concepts covered in Math 6. Students will develop a deeper understanding of how to analyze and solve problems. They will also be introduced to problems that are written in a more complex form. This course is designed for students who need additional time and practice to master basic concepts before moving into Pre-Algebra.

MA011 – Pre-Algebra

This course provides final preparation for formally studying algebra. Students are exposed to a broad range of topics including number concepts, computations, estimation, algebraic functions, solving equations and inequalities, data analysis, probability, geometric concepts, analyzing proportional relationships, and graphing concepts useful in everyday life. Throughout the course, each student solidifies his or her understanding of basic concepts and problem solving. Emphasis will be placed on developing an understanding of the relationship between these areas and how they interact and apply to real-world situations.

MA321 – Algebra I

This is a standard high school level algebra course that covers the following topics: operational symbols and their properties; integers and rational numbers and their properties; equation solving; inequalities and their solutions; factoring; linear equations and graphing; quadratic equations – solving and graphing. Algebra I is the foundation for all higher level math courses.

MA401 – Geometry

The geometry course provides a general overview of geometric principles with a review of algebraic concepts and factoring. Topics for geometry include, but are not limited to: constructions, transformations, triangle relationships, parallel line relationships, circle relationships, areas, and volumes.

MA501 – Algebra II

This second course in algebra reviews and expands on the concepts introduced in Algebra I. New topics include polynomials, matrices, trigonometry, exponents, and logarithms. A graphing calculator is necessary, and it is recommended that students use a TI-83 or TI-84, the calculator that the instructor will be using to explain the material. The same calculator is required for all subsequent math courses.

MA601 – Algebra III

This course is a further expansion of the topics from Algebra II (but not at the level of complexity as is covered in Pre-Calculus). Topics covered include functions, sequences, parametric equations, and trigonometric relationships. This course provided materials for students to learn to display, describe, transform, and interpret numerical information in the form of data, graphs, or equations.

MA611 – Statistics and Applied Mathematics

In this course, students will use mathematics to model and analyze problems from the natural and social sciences. In order to perform effectively as professionals and citizens, students must become competent in quantitative data and in applying basic quantitative skills to the solution of real-life problems. This course will enhance the student’s ability to understand and apply the language of mathematics. Topics to be covered include descriptive statistics; inferential statistics; probability; linear, exponential or logistic growth and decay models; finance; discrete models in scheduling, and organization of ordering of tasks. Appropriate use of units and dimensions, estimates, mathematical notation and available technology will be emphasized throughout the course.

MA701 – Pre-Calculus

This course expands on many previously-learned algebra, geometry, and analysis topics, and introduces more abstract mathematical concepts such as limits. Topics covered include functions (polynomial, power, rational, exponential, logistic, logarithmic, trigonometric), analytic trigonometry, vectors, parametric and polar equations, matrices, analytic geometry, and an overview of discrete mathematics. This course prepares students to study all levels of calculus.

MA901 – AP Calculus AB

This course prepares students for the Advanced Placement Calculus AB exam which is administered in May. Topics include: displacement; velocity and acceleration as derivatives; derivatives of trigonometric, exponential and logarithmic functions; implicit differentiation; finding critical points; anti-differentiation; Fundamental Theorem of Calculus; antiderivatives and slope fields; integrations by parts and by substitution; exponential growth and decay; areas in the plane; volumes; applications to science and statistics.
AP Exam Fee (from 2018; may be higher in 2019): $94

MA911 – AP Calculus BC

This course prepares students for the Advanced Placement Calculus BC exam which is administered in May. The course covers all of the same topics as AP Calculus AB, but at a more advanced level, and in addition, the following additional topics: L’Hopital’s rule; Euler’s method; derivatives of parametric, polar, and vector functions; improper integrals; integration by parts; logistic differential equations; polynomial approximations; series of constants; Taylor and Maclaurin series.
AP Exam Fee (from 2018; may be higher in 2019): $94

MA921 – AP Statistics

This course prepares students for the Advanced Placement Statistics exam which is administered in May. The course provides introduction to the basic ideas and methods of collecting, representing and analyzing data to report findings using elementary techniques from statistics and probability. Topics include: frequency distributions; histograms and frequency polygons; measures of central tendency and variability; conditional probability; percentiles; Z-scores; normal and binomial distributions; confidence intervals; hypothesis testing; regression and correlation.
AP Exam Fee (from 2018; may be higher in 2019): $94