Rome GA High School | Darlington School

Darlington School
Academics
    

Mathematics

Chad Woods
Mathematics Department Chairman

Mathematics plays a vital role in our ability to solve the complex problems that arise in our increasingly technical world. Because of this, problem solving forms the core of the mathematics program at Darlington School. Students develop skills in the fundamental operations, thus strengthening their ability to use reasoning and logic. In addition, they are encouraged to develop an appreciation for the structural beauty and power of mathematics. Because of its prevalence in modern life and its power in problem solving, appropriate use of technology such as computers and graphing calculators is also emphasized. 

Pursuing the Honors program will enable a student to take AP Calculus as a senior. To remain in the Honors program, a student should maintain an average of at least 87. To move into the Honors program, a highly motivated student should have the teacher’s recommendation and an average of 95 or higher.

Because of its prevalence in modern life and its power in problem solving, appropriate use of technology such as computers and graphing calculators is also emphasized. A graphing calculator is required for every Upper School math class.  (TI-84 plus or TI-84 plus c is recommended).
 
All students enrolled in AP courses are required to take the AP Exam.

 

Algebra 1

Emphasizing basic algebraic concepts, mathematical language, and problem solving, this course includes a study of variables, real numbers, polynomials, ratio and proportion, functions, variations, linear and quadratic equations, and inequalities. Factoring and solving equations and inequalities are essential skills taught at this level of Algebra.

Skills Developed

  • Factoring
  • Solving equations
  • Inequalities are essential skills practiced at this level of Algebra.

Knowledge Developed

Emphasizing basic algebraic concepts

  • Mathematical language
  • Problem solving
  • Study of variables
  • Real numbers, polynomials, ratio and proportion, functions, variations, linear and quadratic equations, and inequalities

Required Prerequisites

Pre-Algebra

 

Algebra 2

Algebra 2 is a continuation and extension of the two courses that precede it. While developing the algebraic techniques that will be required of those students who continue their study of mathematics, this course is also intended to continue developing alternative solution strategies and algorithms. Graphing calculator skills will be taught and used extensively in this course.

Skills Developed

Students in this course will develop critical thinking, problem solving, and logical reasoning.

Knowledge Developed

This course is a further development of:

  • Equations
  • Factoring
  • Rational expressions
  • Radicals
  • Quadratics
  • Exponents

 New topics will include:

  • Logarithms
  • Trigonometry
  • Inequalities
  • Elementary statistics
  • Complex numbers
  • Matrices
  • Conics
  • Sequences and series

Required Prerequisites

Algebra 1

 

Algebra 2 Honors

Honors level Algebra 2 includes a detailed treatment of Algebra 2 topics and designed for the highly motivated mathematics student.

Skills Developed

Students in the Honors course will be able to view mathematics:

  • Graphically
  • Numerically
  • Analytically
  • Through writing

Knowledge Developed

This course is designed to build upon skills developed in Algebra and Geometry. We will introduce /expand the following topics in order to ready you for further math courses here at Darlington and beyond.

  • Imaginary numbers
  • Exponential functions
  • Logarithms
  • Conics
  • Trigonometry
  • Unit circle

Required Prerequisites

Teacher recommendation and

  • 90 in Algebra 1
  • 85 in Algebra 1 Honors

 

Algebra 3

Not ready for Pre-calculus? Need a solid review on the most important Algebraic concepts? Want to learn how to think outside the box? This is the course for you!  Critical thinking, problem solving and logical reasoning skills will be enhanced through a review of all things Algebra, as well as an introduction to more trigonometric and statistical branches of mathematics.

Skills Developed

Critical thinking, problem solving, logical reasoning

Knowledge Developed

  • Equations and inequalities
  • Basic functions and their graphs
  • Trigonometry
  • Sequences, series, probability

Required Prerequisites

70 in Algebra 2

 

Geometry

This systematic approach to the nature of proofs and relationships between figures involves an examination of the properties of triangles, circles, and other plane figures. Real world applications reinforce the geometric concepts. Area, volume, properties of solid figures, and coordinate geometry and trigonometry are also studied.  

Skills Developed

  • Critical thinking
  • Logical thinking
  • Problem solving

Knowledge Developed

Topics include:

  • Points
  • Lines
  • Planes
  • Angles
  • Triangles
  • Parallel and perpendicular lines
  • Quadrilaterals
  • Polygons
  • Circles
  • Area and volume

Required Prerequisites

Algebra 2

 

Geometry Honors 

Honors Geometry is designed for the ninth-grade or tenth-grade students who have confidently completed Algebra I. Emphasis is placed on deductive logical reasoning through the use of two-column proofs. Basic constructions and accurate language of Euclidean Geometry is mastered. The foundation of the course begins by studying the undefined terms of geometry and builds into an extensive study of angles, triangles, polygons, circles and how they relate to our world.

Skills Developed

Students in the Honors Geometry course will be able to view geometry from:

  • The graphical perspective
  • The numerical perspective
  • The analytical perspective
  • The writing perspective

Knowledge Developed:

The student will acquire:

  • The accurate language of geometry including a glimpse at how the roots of geometric terms can be seen across the curriculum.
  • An appreciation for the history of geometry and influential mathematicians.
  • A logical thought process through the study of two-column proofs. 
  • Mastery of the concepts of points, lines, planes, angles, triangles, right triangles, circles, quadrilaterals, and polygons with a general understanding of basic constructions.
  • Basic knowledge of The Unit Circle, the sine, cosine, and tangent functions of trigonometry.
  • Confidence in measurement using the English System as well as the Metric System for finding areas, volumes, and perimeters.
  • Methods to find missing values of geometric figures using the previously mastered skills of solving linear equations, factoring quadratic equations, solving systems of equations, and using the Quadratic Formula.

Required Prerequisites

Teacher recommendation and

  • 90 in Algebra 2
  • 85 in Algebra 2 Honors

or

Course equivalent including solving equations, systems of equations, graphing, factoring, Quadratic Formula, basics of graphing

and

90 in the above course

 

Pre-Calculus

Are you interested in taking Calculus? Then you need Pre-Calculus! This class will bridge the gap between Algebra and Calculus and make your Algebra skills better; as well as introduce you to Calculus concepts.

Skills Developed

  • Critical thinking
  • Problem solving
  • Logical reasoning skills

Knowledge Developed

  • Functions
  • Exponential, power, and rational functions
  • Trigonometric functions
  • Analytic trigonometry
  • Systems and matrices
  • Discrete mathematics

Required Prerequisites

Teacher recommendation and

  • 85 in Algebra 2
  • 70 in Algebra 2 Honors

 

Pre-Calculus Honors

Are you interested in taking Calculus? Then you need Pre-Calculus! This class will bridge the gap between Algebra and Calculus and make your Algebra skills better; as well as introduce you to Calculus concepts. 

Skills Developed

  • Critical thinking
  • Problem solving
  • Logical reasoning skills

Knowledge Developed

  • Functions
  • Exponential, power, and rational functions
  • Trigonometric functions
  • Analytic trigonometry
  • Systems and matrices
  • Discrete mathematics

Required Prerequisites

Teacher recommendation and

  • 90 in Algebra 2
  • 85 in Algebra 2 Honors

 

Calculus

Primarily for seniors who have completed the regular four years of math but do not qualify for Advanced Placement, this course is devoted to learning the basic rules of both differential and integral calculus, with examples illustrating calculus at work in the physical world and in business.

Skills Developed

Critical thinking, problem solving, logical reasoning

Knowledge

  • Limits and continuity
  • Derivatives and applications of derivatives
  • Integrals and applications of integrals
  • Differential equations and slope fields

Required Prerequisites

Teacher recommendation and

80 in Pre Calculus

or

70 in Pre Calculus Honors

 

Calculus/Statistics

Primarily for seniors who have completed the regular four years of math but do not qualify for Advanced Placement, the first semester of this course is devoted to learning the basic rules of both differential and integral calculus, with examples illustrating calculus at work in the physical world and in business. The second semester is divided into four major stats themes: exploratory analysis, planning a study, probability, and statistical inference.

This course uses a hands-on approach to learning the techniques and concepts presented, and relies heavily on technology (computer and graphing calculator) to enhance student learning. The graphing calculator and Minitab, a statistical software package, are incorporated throughout the course.

Skills Developed

  • Critical thinking, problem solving, logical reasoning
  • Graphical, numerical and analytical approaches to viewing mathematics

Knowledge Developed

  • Limits and continuity
  • Derivatives and applications of derivatives
  • Integrals and applications of integrals
  • Differential equations and slope fields
  • Data analysis
  • Experimental design
  • Planning a study
  • Statistical inference

Required Prerequisites

Teacher recommendation and

80 in Pre Calculus

or

70 in Pre Calculus Honors

 

AP Calculus AB and BC

The student who has successfully pursued an Honors mathematics program finds a challenge in the senior year with this top-level mathematics course. It is a full year of work in calculus and related topics comparable to courses in college, preparing students for the AP Exam. Use of the graphing calculator is incorporated into many areas of study. A graphing calculator is required on the AP Exam. Most students prepare for the AB-level exam, but the BC-level is offered.

Skills Developed

  • Critical thinking, problem solving, logical reasoning
  • Graphical, numerical and analytical approaches to viewing mathematics

Knowledge Developed

  • Limits and continuity
  • Derivatives and applications of derivatives
  • Integrals and applications of integrals
  • Differential equations and slope fields

Required Prerequisites

AB: 85 in Pre-Calculus Honors; 90 in Regular Pre-Calculus and teacher recommendation

BC: 96 in Pre Calculus Honors and teacher recommendation

AP Application required for both levels

 

Probability and Statistics

Probability and Statistics is an option for juniors and seniors who have successfully completed at least Algebra 2, or can be taken concurrently with Algebra 3 or higher, regardless of the student’s intended college major. The topics for Probability and Statistics are divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference. This course uses a hands-on approach to learning the techniques and concepts presented, and relies heavily on technology (computer and graphing calculator) to enhance student learning. The graphing calculator and Minitab, a statistical software package, are incorporated throughout the course.

Skills Developed

  • Critical thinking
  • Problem solving
  • Logical reasoning

Knowledge Developed

  • Data analysis
  • Experimental design
  • Planning a study
  • Statistical inference

Required Prerequisites

This class is designed for juniors and seniors only

 

AP Statistics

Have you ever wondered how the Evening news knows who is in the lead in the Presidential race? If so, AP Statistics is the place for you. This course is for the highly motivated student interested in receiving college credit.

Skills Developed  Students in AP Statistics will be able to view statistics:

  • Graphically
  • Numerically
  • Analytically
  • Through writing

Knowledge Developed

  • Exploratory analysis
  • Experimental design
  • Probability
  • Planning a study
  • Statistical inference

Required Prerequisites

Teacher recommendation and

  • 90 in Pre Calculus
  • 85 in Pre Calculus Honors

AP Application completion required

 

Multivariable Calculus

This course is for students who have completed AP Calculus BC. The course will examine the calculus of real functions of two or more variables. The course begins with a review of some AP Calculus BC topics including polar coordinate systems and vector calculus. Differential calculus topics including functions of several variables and their derivatives, continuity, and derivatives will be covered. The course extends into integral calculus and incorporates the following concepts: double and triple integrals, and surface area.

Skills Developed

  • Critical thinking
  • Problem solving
  • Logical reasoning

Knowledge Developed

  • Analyze Functions of several variables
  • Work with Vector-Valued Functions
  • Partial and Ordinary Differential Equations
  • Double and Triple Integration
  • Work with Matrices
  • Analyze Modern Algebra problems

 

AP Computer Science A

Software is everywhere: in your phone, television, car, and thermostat, as well as in the applications and Web pages on your computer. This course seeks to build an appreciation for our reliance on software by building an understanding of intermediate programming methodology, problem-solving and algorithm development. The course will teach the fundamentals of computer programming using Java syntax along with exploring ethics and current events. This course is open to interested students with or without prior programming experience. A strong background in mathematics, particularly algebra, is necessary.

Skills Developed
Technical, problem solving, coding, logical

Knowledge Developed
Programming fundamentals, Java syntax, algorithmic problem solving

Required Prerequisites
Approval of teacher and 90 in Algebra 2 or 85 in Algebra 2 Honors

AP Application completion required

 


    

    

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