Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions.
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- Algebra I
Algebra I is a course of study primarily designed to prepare students for Algebra II. The 2007 Saxon Textbook Series is used and emphasizes constant review of topics that have been covered in the past. These topics include solving equations, graphing, various word problems, factoring, area and volume problems, fractions, solving systems, radicals, exponents and scientific notation. The course is structured to introduce a new topic each day. Assignments generally include 4-5 new problems and 25 review problems from past lessons. (Students who fail to maintain a “C” or higher average in Algebra I will have great difficulty passing Algebra II.)
- Algebra II Honors
This is a study of traditional algebra concepts integrated with the study of geometry. First and second degree equations, conic sections, trigonometry, logarithms, and problem solving are some of the concepts taught. The correct use of the calculator is emphasized. Prerequisite: This course is offered to ninth grade students who have had Algebra I in middle school, and are recommended by the middle school faculty.
- Algebra II
This is a study of traditional algebra concepts integrated with the study of geometry. First and second degree equations are studied in depth and there is a heavy emphasis on problem solving. Trigonometry is introduced and the correct use of the calculator is taught. Of the thirty problems assigned nightly, only three or four are of the newly introduced lesson. The remaining problems are review problems. Half of the instructional period is spent in teacher assisted work on these problems. Tests are given following each fourth lesson.
- Geometry (Honors) IV
This course is an advanced study of Euclidean Geometry. In addition to the topics covered in the regular geometry course, this course will emphasize proof and deductive reasoning. The class will move at a more rapid pace and will provide an in-depth study of each concept. Prerequisite: This course is offered to tenth grade students who desire to study four years of math in high school and who have been recommended for Honors Mathematics classes.
In this course the student will obtain knowledge of the vocabulary, symbols, diagrams, theorems, postulates and proofs used in geometry. Specifically the course covers points, lines, planes, angles, parallel lines and planes, congruent triangles, similar polygons, right triangles, circles, areas of plane figures, areas and volumes of solids, coordinate geometry, constructions, loci and transformations.
- Pre-Calculus (Honors)
The students in Pre-Calculus Honors should be juniors who are on tract to take AP Calculus during their senior year. The content of the curriculum will be much the same as the other Pre-Calculus courses offered at DLHS. The main difference in the honor's course is that all students will be assumed to take AP Calculus. Effectively, this class will be the first year of a two year sequence. More emphasis will be given to interpreting problems verbally, numerically, graphically, as well as analytically. The students will be expected to transfer knowledge to various situations in an effort to prepare them for AP Calculus and the AP Calculus exam.
This course is designed primarily for seniors, or for juniors who plan to take Statistics in their senior year. Early in the year, much emphasis will be given to analytical geometry and the study of functions. The TI83+ or TI89 will be used extensively by the students and teacher via computer projection equipment to study the relationships between functions and graphs. The "reform" movement in mathematics gives much more emphasis in studying functions analytically as well as through tables and graphs. Technology improvements have dramatically changed the way Pre-Calculus is taught. Nearly a third of the year will then be given to the study of trigonometry. Circle trigonometry goes beyond the geometric concept of an angle. Circular representations of angles allow us to study many real world phenomena that are periodic in nature. Triangle trigonometry uses the geometric concepts to find distances and areas given any polygonal region. Logarithms will be studied to be able to solve problems with exponential variables as is often the case in Chemistry as well as Economics. Conics and their interesting reflective properties will be studied. As time allows, some topics of discrete mathematics including sequences will be studied. Elementary probability will give students a concept of the likelihood of an event. These ideas would be very important as a beginning point for those taking Statistics.
- AP Calculus AB
Advanced Placement Calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is required that students who take AP Calculus will seek college credit by taking the AP Exam. Most of the year will be devoted to topics in differential and integral calculus. The course emphasizes a multi-representational approach of calculus, with concepts, results, and problems being expressed graphically, numerically, analytically and verbally. Also note that a detailed course description including philosophy, goals, prerequisites, and topical outline are given at: http://apcentral.collegeboard.com/courses/descriptions/1,,151-162-0-8879,00.html Prerequisite – teacher approval and summer review on teacher wiki located at http://dlhscalculus.wikispaces.com
- Pre-College Algebra
This class is designed for students with grades below B- (85) in Algebra II who need to develop better math skills to prepare for college math and for students who will not require a high level of mathematics in their chosen careers. Students with grades of B-(85) or above in Algebra II should take Pre-Calculus or Statistics. Teacher recommendation will be necessary to take this class.
Statistics is the science of gaining information from numerical data. Although statistics can be extremely complicated in theory, this course will be concerned with the practice of statistics. There are three basic parts to the practice of statistics, which will be incorporated in this course. Data analysis concerns methods and ideas for organizing and describing data using graphs, numerical summaries, and more elaborate mathematical descriptions. Data production includes some basic concepts about how to select samples and design experiments. Finally, statistical inference moves beyond data in order to draw conclusions about a wide universe. In other words, we will attempt to put data in context.
- Dual Credit College Algebra
This University level course will involve a quick review of equations and inequalities; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; systems of equations and inequalities; sequences, series, and probability. Prerequisite: two years of high school Algebra and at least a 21 ACT or 590 SAT math score.
- Dual Credit College Trigonometry and Analytic Geometry
This University level course will involve trigonometric and circular functions; trigonometric analysis; analytical geometry of the plane and three space including the conic sections, rotation of axes, polar coordinates, polar equations of conics, plane curves and parametric equations. Prerequisite: two years of high school Algebra and at least a 26 ACT or 590 SAT math score or College Algebra.