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Math and Science Academy - High School Courses
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High School Courses


New York State Regents


We prepare students for all math and science Regents courses and Exams! 

Math:

Math A, Math B, Integrated Algebra, Geometry, Algebra 2 / Trigonometry.

Science:

Biology, Chemistry, Living Environment, Physics, Earth Science.

For course descriptions, see the NY Regents page.


Advanced Placement (AP) Courses


We prepare students for all math and science AP courses and exams. For course descriptions, visit the Collegeboard website at: http://www.collegeboard.com/student/testing/ap/subjects.html


SAT I, SAT II, ACT, and GED Preparation


Individual and group lessons are available for SAT I and SAT II(subject test), ACT, and GED preparation. We will customize a learning program that will fit your needs. Studying with us guarantees a higher score on your College Admissions Tests.


Math Curricula


Arithmetic

Fundamentals of arithmetic. Fractions, decimals, percents, signed numbers, ratios, proportions and rates, word problems.

Pre-Algebra

Review of fundamentals of elementary Algebra. Focus on mathematical translation of expressions and verbal statements.**

Algebra I

Operations with polynomials, rational and square root expressions, exponents, solving and understanding linear and quadratic equations, basic applications and graphing.

Algebra II

Absolute value equations, inequalities, and their graphs, radical expressions, rational exponents, quadratic equations and inequalities, logarithms, introduction to functions, and topics in analytic geometry.

Trigonometry

Angles, trigonometric functions of a general angle, trigonometric functions of an acute angle, right triangles, applications, reduction to functions of positive acute angles, reduction of functions of positive acute angles, basic relationships and identities, variation and graphs of the trigonometric functions, trigonometric functions of two angles, sum, difference, and product formulas. Oblique triangles, area of a triangle, inverses of trigonometric functions, trigonometric equations, Complex numbers, De Moivre's Theorem.

Geometry I

Introduction to Geometry. Lines, angles, triangles, congruent triangles, parallel lines, distances and angle sums. Parallelograms, trapezoids, medians, and midpoints. Methods of proof.

Geometry II

The geometry of the circle, similarity, areas, regular polygons, locus, inequalities and indirect reasoning, transformations, constructions, improvement of reasoning, proof of important theorems.

Geometry III (Stereometry – 3-Dimensional Geometry)

The geometry of the three-dimensional plane, vectors, solids, functions and their graphs, proofs.

Advanced Elementary Geometry

This course covers everything in Geometry I, II, III, from an advanced standpoint. More attention is given to proofs. This course is taken by our Math Club students to prepare for the Mathematics Competitions and Olympiads.

Preparation for the Math Competitions/Olympiads

This course, which is held at the Math Club prepares students for the Math Competitions or Olympiads. Various topics from advanced elementary mathematics are covered. Special attention is given to problem solving, proofs, and non standard approaches to solving problems.

Pre-Calculus

Functions and their graphs: polynomial, rational, exponential, logarithmic and trigonometric functions; conic sections; topics in trigonometry; graphical and analytical solutions of systems of equations and inequalities, trigonometric forms of a Complex number and De Moivre's Theorem; sequences and series.

Calculus AB

Limits, continuity, and differentiation of algebraic functions. Applications of differentiation; exponential, logarithmic, and trigonometric functions and their derivatives; optimization problems, the definite integral and the fundamental theorem of calculus. Application of the integral. The Riemann sum, Intermediate Value Theorem, Mean Value Theorem, L'Hospital's rule and more.

Calculus BC

Theoretical treatments and Applications of Definite Integrals. Techniques of Integration. Infinite sequences and series and convergence and divergence of series. Taylor Series and polynomial Approximations. Line integrals. Parametric equations and polar coordinates. Elementary differential equations. Basic proof methods.


Physics Curricula


Units and Dimensions

Units that are used for Various Physical Quantities, Conversions from one unit to other, SI units, Dimensions and Dimensional Analysis.

Kinematics in One Dimension

Distance, Speed and Acceleration. Uniform Speed motion. Constant Acceleration motion. The Three Formulae.

Vectors

Definition of a Vector, Difference between Scalar and Vector, Examples. Components of Vectors, Addition and Subtraction of Vectors, Resultant for set of Vectors, Use of Trigonometry in solving Vector Problems.

Kinematics in Two Dimensions

Relation between the motions in two dimensions, acceleration due to gravity, The Three Formulae in two dimensions.

Forces

Definition of Force, Newton's Laws, Force and Acceleration, Free Body Diagrams, Newtonian Gravity, Momentum, Collisions, Elastic and Inelastic Collisions, Law of Conservation of Momentum, Impulse, Friction, Equilibrium of Forces.

Angular/Rotational Motion

Radian Measure, Conversion between Radians and Degrees, Angular Velocity, Angular Acceleration, The Three Formulae for Angular motion, Centripetal Acceleration.

Rotational Dynamics

Moment of Inertia, Torque, Gravitation, Satellites, Bodies in Equilibrium.

Energy and Power

Types of Mechanical Energy (Kinetic and Potential Energy), Work done, Work Energy Theorem, Conservative and Non-Conservative Forces.

Electrostatics and Magnetism

Charges, Electric Field, Electric Potential, Parallel Plates, Coulomb's Force (Inverse-Square law), Magnetic Field, Magnetic Force.

Electricity

Current, Resistance, Resistors, Parallel and Series Equivalents of Resistors, Ohm's law, Kirchhoff's laws, Electric Power.

Electromagnetic Theory

Motion of Charges Particle in Magnetic Field, Fleming's Right Hand Rule, Lenz's Law, Lorenz Force, Gauss's Law, Ampere's Law, Maxwell's Equations, Electromagnetic Induction.

Vibrations and Waves

Oscillatory Motion, Pendulum, Period, Frequency and Amplitude of a Wave, Types of Waves.

Light and Sound

EM Waves, Reflection, Refraction, Interference, Resonance, Diffraction, Standing Waves, Dispersion, Beats, Doppler Effect, Practical Applications ( RADAR, LASER, LIDAR, Communications etc).

Fluids

Pressure, Density, Buoyancy, Buoyant Force, Archimedes Principle, Bernoulli's Equation.

Heat and Thermodynamics

Units of Measure (Celsius, Fahrenheit and Kelvin Scale),Absolute Zero, Conduction, Convection and Radiation, Heat Flow, Thermal Expansion of Solids, Liquids and Gases, Gas Laws, Kinetic Theory of Gases, Specific Heats and Heat Capacity, Latent Heat, Internal Energy, Phase Changes, Laws of Thermodynamics.

Quantum and Nuclear Theory

Atom, Atomic Models, Sub-Atomic Particles, Energy Quantization and Electron Configuration, Heisenberg Uncertainty Principle, Pauli's Exclusion Principle, Valency, Quantum, Wave-Particle Duality, The Nucleus, Nuclear Forces, Radioactivity.

Modern Physics

Relativity, Time Dilation, Length Elongation, Twin Paradox, Special and General Theories of Relativity, Simultaneity, Black Holes, Space-Time Continuum, etc.


Chemistry Curricula


Units of Measurements

Units, Dimensions, Dimensional Analysis.

Chemical Compounds and Formulae

Atomic and Molecular weights, Equivalent Weights, Chemical Composition-Weight and Volume Percentage.

Atomic Theory

Atomic Theory, Valence and Electron Dot Diagrams, Ionic and Covalent Bonding, Electro-negativity, Polarity of Bonds.

Periodic Table

Elements, Properties of a Group, Pauli Exclusion Principle, Hund's Rule and Electronic Configuration, Molecular Orbital Theory.

Stoichiometry

Techniques of Balancing, Ion-Electron Method, Oxidation-Reduction Method, Calculations using Chemical Arithmetic, Weight-Weight Problems, Reactions involving limiting reagents, Volume-Volume problems, Weight-Volume Problems.

Chemical Kinetics

Rates of Reaction etc.

Equilibrium

Equilibrium Constant, Equilibrium Calculations, The Shifting of Equilibrium and Le-Chatelier's Principles.

Solids

Crystals, Crystalline Structures, Phase Diagrams.

Properties of Liquids

Density, Freezing Point Depression and Boiling Point Elevation, Raoult's Law and Vapor Pressure, Osmotic Pressure.

Solutions

Density and Formality, Molality, Molarity, Normality, Neutralization.

Acids, Bases and Salts

Autoionization of Water, Autoprotolysis, pH Value, Ionization Constant, Dissociation Constant, Hydrolysis Constant, Neutralization.

Gases

Pressure, Gas Laws, Boyle's Law, Charles' Law, Law of Gay-Lussac, Combined Gas Laws, Avogadro's Law, The Concept of Mole, Ideal Gas law, Mole Fraction, Daltons Law of Partial Pressures.

Thermo Chemistry

Bond Energies, Heat Capacity, Enthalpy, Enthalpy Calculations using First law of Thermodynamics, Heats of Fusion and Vaporization, Entropy, Free Energy, Equilibrium Calculations

Electro Chemistry

Redox Reactions, Electrode Potential, Electrochemical Cell Reactions.

Organic Chemistry

Alkanes, Alkenes and Alkynes, Alcohols, Aldehydes, Ketones, Sugars, Organic acids, Other Functional Groups, Stereochemistry, Nomenclature.

Nuclear Chemistry

Radioactivity, Radioactive reactions.

Food Chemistry

Nutrients, Sugar Chemistry.

Chemistry in Industry

Soaps and Detergents, Pesticides and Insecticides, Fertilizers.


Earth Sciences Curricula


Introduction to Earth Science

Basic Definitions, Goals.

Planet Earth

Shape, Size, Dimensions and Internal Heat

Minerals

Chemical Composition, Structure, Identification, Rock Forming Minerals.

Rocks

Types of Rocks, Igneous, Sedimentary and Metamorphic.

Resources

Renewable, Non-Renewable, Energy resources, Alternate Sources of Energy, Problems related to Energy.

Soil

Weathering, Mass movements, Erosion, Deposition, Landscapes, Soil Conservation.

Water

Fresh water and Salt Water, Water in the Ground, Water Level, Ground Water Characteristics, Caverns and Mineral Deposits, Stream Erosion and Transportation, The River valley, Waterfalls and River Deposits, The Flood Plains and Floods.

Glaciers

Types of Glaciers, Glacier movement, Glacier Deposits, Ice Age.

Effects of Wind, Waves and Current

Wind as an Agent of Change, Waves in the Sea, Shoreline features.

Plate Tectonics

Definition, Evidence, Plate Boundaries, Continental Drift, Wegner's Theory.

Volcanoes

Types of Volcanoes, Examples of Volcanic Eruptions, Plutonic Activity.

Earth Quakes

Occurrence, Locating, Measuring and Examples.

Mountains

Formations, Features of Collision of Mountains, Evidence of Mountain Building.

Oceans

Salinity of Seawater, Temperature of the Sea, Life in the Sea, Ocean Floor, Continental Margin, Ocean Basin, Ocean Currents.

Universe

Telescope, Visible and Beyond Visible light Astronomy, Stars and Characteristics, Galaxies, The Sun, Solar Systems, Planets, Satellites, Comets, Asteroids and Meteoroids, Moon and Earth's Motion.

Atmospheric Science

Weather and Atmosphere, Evaporation, Condensation and Precipitation, Air Pressure and Winds, Air masses and Fronts, Storms and Weather Forecast, Climate and Climate Changes.

Earth's History

Fossils, Reading fossils, Paleozoic Era, Mesozoic Era, Cenozoic Era.

Weather Systems

Weather Tracking, Weather Forecast, Weather Monitoring.

Environmental Awareness

Protection of Environment, Green House Effect, Melting of Ice Caps, Ocean Drilling, Plastic Wastes, Recycling, Radioactive Wastes, Green Peace and Other Organizations.


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