MATH/SCIENCE

 

CALCULUS                                                                                                          

 

Stephen J. Martin

 

Calculus is offered to students who have successfully completed Pre-calculus.

 

First, functions, including exponential and logarithmic functions, will be reviewed.  Then, the concept of limit will be investigated.  The concept of rate of change of a function will be introduced, leading to the definition of the derivative of a function.  Rules of differentiation will be proven: the power rule and the addition rule will be derived.  Derivatives of products and quotients will be found.  The second derivative will be defined and applied.

 

The chain rule will be used to calculate derivatives of composite functions.  Implicit differentiation will be used in dealing with relations.  The relationship between rates of change of related functions will be investigated.

           

The first derivative test will be used to determine maxima and minima of functions.  Concavity will be related to the second derivative: the second derivative test will be used to determine maxima and minima.  Optimization problems will be studied.  Differentials will be explored.

 

Credit will be earned through the satisfactory completion of in-class and homework assignments, quizzes and examinations, as well as good attendance.  Students must own a graphing calculator.

 

 

PRE-CALCULUS                                                                                                 

 

Stephen J. Martin

 

This upper level math course is offered to students who have successfully completed the standard math sequence, including Advanced Algebra.

           

In the fall trimester, in our desire to know all the angles, we will study trigonometry.  There will be a review of geometry in the plane: the relationships of angles, lengths, and areas will be investigated.  The sine, cosine, and tangent functions will be defined.  The important theorems and laws will be explored, such as the Pythagorean Theorem, the Law of Sines and the Law of Cosines.  The trigonometric functions and the relevant laws of trigonometry will be used to solve problems involving triangles (both ideal and idealized) that are found in various mathematical and scientific disciplines.  3-dimensional objects will be studied if time permits.

           

There will be a review of exponents, factoring, rational expressions, and inequalities.  General functions will be studied: graphs and inverse functions will be analyzed.  Polynomial functions and rational functions will be investigated: complex numbers and zeros of polynomial functions will be explored.  Exponential and logarithmic functions will be studied.

 

Credit will be earned through the satisfactory completion of all in-class and homework assignments, quizzes and examinations as well as good attendance.  Students must own a graphing calculator.

 

 

ADVANCED ALGEBRA                                                                                    

 

Stephen J. Martin

 

Do you hate word problems?  Do equations and graphs look like hieroglyphs?  Embrace your fears and explore the world of algebra!

 

This trimester in Advanced Algebra the algebra of linear systems will be explored.  Linear systems will be modeled on graphs and in equations.  Word problems involving linear equations will be investigated.  Systems of equations (some with fractions or decimals as coefficients) will be solved by graphing, addition, and substitution.  Word problems will be solved by using systems of equations.  Students will also be exposed to three-variable systems.

 

Credit will be earned by successful completion of in-class and homework assignments, quizzes and examinations, as well as good attendance.

 

Prerequisites:  Students should have completed both Geometry and Intermediate Algebra or have consent of department chair.  Students must own a scientific calculator.

 

 

INTERMEDIATE ALGEBRA: Equations                                                    

 

Christina McKenrick

 

Do you tremble at the thought of word problems?  Do you bury your head in your hands when confronted with fractions?  Never fear!  We will work together to solidify and increase your understanding of algebra.   

 

In the fall trimester, there will be a review of the laws of algebra.  The students will be reacquainted with the properties of addition, subtraction, multiplication and division (including the distributive law).  Expressions will be simplified using the order of operations.

 

As preparation for solving equations, addition and subtraction of like terms will be reviewed.  The solution of linear equations in one variable will be studied, including the special cases resulting in no solution or an infinity of solutions.  The equations will be solved for whole-number coefficients, decimal coefficients and fractional coefficients.

 

Word problems will be posed in which one must solve a linear equation in one variable: the unknowns will be given in terms of one variable.

 

Credit will be earned by successful completion of assignments, quizzes and tests as well as by good attendance.

 

 

GEOMETRY                                                                                                  

 

Christina McKenrick

 

Explorers needed to know where they had been and needed to determine accurately where they were going.  Geometry, or the measurement of the earth, grew out of their interests and also those of landowners who wished to determine the boundaries of their properties.   Artists, architects, builders, inventors, engineers, surveyors and planners all use geometry in their work.  Geometry is the result of mankind’s attempts to understand space, shape and dimensions.  We will spend the year studying geometry’s practical and theoretical facets.

 

During trimester one, we will become familiar with the vocabulary of geometry, formulating our own definitions and discovering generalizations through investigation.  Many of the geometric investigations will be carried out in small cooperative groups in which students jointly plan and find solutions with other students.  Students will derive formulas for regular quadrilaterals and triangles, convert linear and square measurements and learn the vocabulary of polygons, points, lines and planes.  We will discern patterns and use inferential thinking.   Students will become proficient with a compass and straight edge and will be able to create classical constructions including bisecting angles, drawing congruent angles, creating perpendicular and parallel lines as well as creating works of art.  We will go over SAT and PSAT review questions for seniors and juniors as well as other interested students. 

 

Assessment will be based on timely completion of homework, frequent short quizzes, occasional tests, participation in class and attendance.  A project, such as the creation of a polygon book, may be assigned.  All areas will be considered when assigning credit.

 

 

BEGINNING ALGEBRA: Equations                                                                          

 

Laurie Spry

 

This class is for those of you starting at the beginning of algebra.  We will cover the order of operations, solve one and two step equations, use simple equations to solve regular and word problems and use simple formulas to solve practical problems. We’ll look at number lines, basic mathematical properties and some simple formulas.  Along the way we’ll be reviewing fractions, percents, decimals and negative numbers as they occur in our work.

 

To be successful in this class, you’ll need to be doing homework regularly.  I’ll expect you to take responsibility and come for help with homework after school if it still seems confusing when class is over. The math teachers are committed to supporting students who are willing to work with us to solidify their understanding. If you focus in class and take good notes, ask questions and bravely volunteer answers, you should be well prepared to earn credit in math classes.

 

Course credit will be earned for satisfactory completion of in-class and homework assignments, attendance, quizzes and tests. 

 

 

ECONOMICS ILLUSTRATED                                                                                   

 

Chris McKenrick

 

Are you interested in finding out why the housing market crashed? What is a recession or a double dip recession? More generally, how is math applied to the broad spectrum of life in the twenty-first century? We will start off the trimester by reading and discussing excerpts from Freakonomics: A Rogue Economist Explores the Hidden Side of Everything by Steven Levitt and Stephen Dubner. Students will learn economic terms such as elasticity, externalities, opportunity costs and free riding. This class will also prepare students to take the math competency exam. Students who have passed the math comp will be able to delve more fully into mathematical concepts such as the history of math, theories of the universe, stock market analysis and the debate over whether mathematics was discovered or invented.

 

Credit will be based upon attendance, timely completion of weekly comp practice, special projects, tests and quizzes on the reading assignments and math covered in class. Students who have not yet passed the math comp will be required to attend each taking of the comp.

 

 

PHYSICS                                                                                                               

 

Stephen J. Martin

 

Prerequisites:  Completion of 2 years of high school science and Advanced Algebra (or Adv. Alg. concurrently).  Ownership of scientific calculator.                                           

 

The laws of physics constitute a “User’s Guide” to the universe.  Physics helps us to understand all the phenomena we encounter whether on earth or in space.  It explains the motion of planets in the solar system, the motion of electrons in atoms, and the motion of cars on a roller coaster.  We will learn from Galileo, Newton, Einstein, von Braun and many others.

 

In the fall trimester, mechanics, the science of mass, force and motion, will be explored.  Motion will be studied in one dimension: velocity and acceleration will be analyzed.  Two-dimensional motion will be studied: vectors will be introduced.  Newton’s Laws are the foundation of mechanics and all classical physics.  The statics of rigid bodies will be studied: the force and torque vectors must each sum to zero.  The linear motion of rigid bodies will be studied from the point of view of “dynamics,” using the concepts of velocity, acceleration and force.  Motion will also be studied from the point of view of “energy,” using the concepts of work, kinetic energy and potential energy. 

           

Collisions will be analyzed using the conservation of linear momentum.  In uniform circular motion, the body is subjected to centripetal force.  The angular motion of rigid bodies will be investigated using the concepts of angular velocity, angular acceleration, torque and angular momentum.  Finally, fluid mechanics will be studied for liquids and gases.

           

This course has a laboratory component.  The experiments will utilize instruments which will measure time and other quantities with precision.  Lab reports will adhere to standards of clarity, accuracy and precision.  Course credit is earned through the satisfactory completion of in-class and homework assignments, lab reports, quizzes and examinations, as well as good attendance.

 

 

GENERAL CHEMISTRY                                                                                              

 

Jodi Lyons

 

What do you think of when you hear the word Chemistry? Bubbling flasks, explosive experiments, a mad scientist?  Don’t worry, you won’t become a geeky mad scientist, but you will explore chemistry in the real world…your world. Together we will look at what things are made of and how they react with each other and transform into new things.  Most importantly, what does all this mean in our world?!  This course will begin with atoms and molecules and build, build, build into all the things we know around us. Additionally, this course will study chemistry with an environmental and economic perspective: two very important current issues in our society.

 

This course will use class discussion, hands-on activities, group projects and various assignments as tools to learn about chemistry. Everyday elements, places and events are fundamental to seeing chemistry in our daily lives. Wait until you discover how chemistry is all around you!

 

This course takes place over three trimesters. Lab reports, group projects, class participation and assignments will be used to assess credit. As it meets only twice a week, you will need to be very responsible about doing homework thoroughly between classes and seeking help promptly if needed.

 

Chemistry is open to students with two years of high school science credit or the approval of the department coordinator.

 

 

INTRODUCTION TO PSYCHOLOGY                                                     

 

Siobhan Ritchie Cute

 

“Love and work are the cornerstones of our humanness.” Sigmund Freud

 

What makes us human?  What defines healthy...stable...normal?  Why do we do what we do?  For more than 100 years, psychologists have been attempting answers to these questions through controlled experiments and analysis of data.  Since the beginning of time, however, we humans have been attempting the same through basic observation and thought.  Why did he do that?  Why didn’t she do that?  Why do I feel this way?  How can I change?  The answers are elusive.  Experts even disagree about how to approach answering the questions. 

 

In this introductory course, we will examine the foundations of the very broad and diverse discipline of psychology. We will examine the groundwork for a field devoted to the study of the mind laid by philosophers and biologists.  Students will gain familiarity with important pioneers in the field, including Freud, Skinner, Piaget and others.  We will determine the relevance that their works have today.  We will talk about the role psychology plays in our everyday lives.

 

Students will earn credit by completing reading assignments outside of class, participating in discussions and demonstrating knowledge and commitment through quizzes and project work.

 

 

BIOLOGY A: Small Worlds                                                                              

 

Laurie Spry

 

Living things are made of tiny units called cells. How do one-celled creatures respond to their environment to protect themselves, to get food, to find mates? How do they cooperate to form larger organisms? What are the current scientific theories about the origin of life? Why are there so many kinds of living things? Which of them are in danger of extinction, and which could endanger our future? How do you feel about genetically engineered forms of life? Should those genes, or your genes, be patented? (They already are!)  These are some of the questions I’d like to explore with you this year.

 

This first trimester we’ll examine the ‘small worlds’ of bacteria and then of planaria (a type of flatworm). You’ll be using microscopes, designing some experiments, maintaining a notebook and of course keeping up with homework (our text is online, so you don’t have to lug the book home).  We’ll also be listening to some lectures from the Howard Hughes Medical Institute high school series.

 

Students earning credit will maintain neat, well organized notebooks, come to class on time prepared to learn, study for and pass quizzes and do homework regularly. To enroll in Biology, you should have credit for one year of science or be recommended for it by Laurie (Department Coordinator).

 

 

SCIENCE FOUNDATIONS: Forensics Lab I                                                             

 

Laurie Spry

 

Everyone loves mysteries!  If you watch CSI, you’re already familiar with how science can be used to recreate scenes, track down suspects and piece together evidence to catch criminals. Many of the same techniques are relevant in solving crimes against wildlife. Poachers kill animals intentionally for many reasons including for trophies, food and medicine. Animals are also unintentionally killed to support the illegal pet trade or when civil war sweeps over their habitat. Many of our most critically endangered species need our protection from these crimes.

 

This class consists of ten labs over two trimesters to prepare you to solve the final wildlife crime. We’ll study wildlife issues as well as use microscopes, electrophoresis, chemical indicators and other lab techniques to catch a glimpse of the skills and information used in forensic laboratories.

 

You’ll need to keep a complete binder of notes and handouts, maintain a lab journal (supplied), complete homework regularly, pass a lab safety test and find your way down there on time to earn credit in this class.  Students work in teams, but each is responsible for his/her own binder and lab journal.

 

Forensics Lab I is especially suited to freshmen but could also fulfill a lab credit for students not headed off to MIT.   Check with Laurie if you’re not sure you should take it.