Standard Approach Courses

Algebra 1B

Algebra 1

  • Introductory topics:

    • fundamentals with directed numbers
    • the solution of linear equations and inequalities
    • the solution of related word problems such as consecutive integer, angles, coin, mixture, and motion
    • an introduction to functions in verbal, tabular, and equation format
    • graphing lines, and finding the equations of lines in various forms given a variety of information.
    • Topics such as percents, probability, rates of change, and direct and inverse variation
    • systems of equations in 2 variables

  • Advanced topics:

    • operations with monomials and polynomials
    • factoring polynomials
    • solving quadratic equations by factoring
    • simplification of square root radicals
    • real numbers
    • algebraic word problems
    • quadratic equations by completing the square and the quadratic formula
    • radicals
    • graphs of quadratic and exponential functions and related word problems.
    • Introduction to Statistics
    • Transformations of Linear, Quadratic, Absolute Value, Exponential, and Quadratic Graphs
Geometry 1B

Geometry

  • Course Fundamentals:

    • points
    • lines
    • planes
    • angles
    • polygons
    • solid figures
    • parallel & perpendicular lines
    • circles
    • symmetry
    • properties of right triangles

  • The advanced part of this course includes:

    • undefined terms
    • postulates 
    • theorems
    • congruence & similarity of triangles & polygons
    • applications of corresponding parts of congruent & similar triangles
    • right triangle trigonometry
    • circles
    • coordinate geometry
    • areas of planar figures
    • introductory solid geometry
    • introductory transformational geometry
    • loci, logic, truth tables and basic Constructions
Algebra 2B

Algebra 2

  • Introduction: solution of equations and inequalities, including those with:

    • absolute values
    • linear equations and inequalities
    • systems of linear equations and inequalities
    • systems of equations in 3 variables
    • matrices
    • polynomials
    • factoring
    • radicals
    • complex numbers
    • quadratic equations
    • the conic sections
    • systems of simultaneous quadratics
    • polynomial functions
    • function composition and inverses
    • variation problems
    • the arithmetic of rational expressions
    • solving both radical and rational equations
    • an introduction to Sequences and Series

  • Students in advanced-level mathematics also see:

    • complex fractions
    • a wider variety of word problems
    • the theory of higher degree equations
    • conic section theory
    • exponential and logarithmic functions
    • Permutations
    • Combinations
    • Probability
Trigonometry & Precalc

Precalculus & Trigonometry

  • Introduction: review & build onto Algebra II skills:

    • Functions: Linear, Quadratic & Polynomial
    • Inequalities in 1 or 2 variables
    • Properties and graphs of functions in relation to Algebra & Geometry
    • Inverses

  • Advanced topics:

    • Polar Coordinates
    • Vectors
    • Parametric equations
    • Equations of lines and planes in space
    • Graphs of algebraic and rational functions
    • Exponential and logarithmic functions
    • Conic sections
    • Translations
    • Rotations
    • Advanced sequences & series
    • Matrices
    • Introduction to Differential Calculus
Riemann sum equation and graph

Calculus

  • Introductory topics:

    • review Precalc/Intro to Calculus to refresh the topic
    • revisit  Precalc/Intro to Calculus topics as new related topics are introduced throughout the course
    • Functions
    • Limits
    • Derivatives of Algebraic & Trigonomic functions
    • Antiderivatives
    • Definite & Indefinite Integration
    • Integrals
    • Fundamental Theorem of Calculus

  • Optional Topics for AP Calculus Exam:

    • advanced topics in analytic geometry
    • hyperbolic functions
    • advanced topics in polar coordinates
    • infinite sequences and series
    • Taylor expansions of functions
    • introduction to differential equations using slope fields
    • function work: graphs, numbers, analysis

Integrated Approach Courses

math 1

Math I

  • Introductory topics:

    • interpretation of problems
    • reasoning & constructing arguments
    • modeling, structure & regularity
    • mathematical tools: graphing calculators and computer software.
    • reason quantitatively
    • interpret mathematical expressions

  • Advanced topics:

    • create equations to describe relationships
    • use the concept and notation of functions
    • examine linear and exponential functions using algebraic and graphical approaches, and use these function types for modeling and problem solving. olve linear equations and inequalities
    • systems of equations
    • descriptive statistics to summarize, represent, and interpret one-variable and two-variable data involving categorical or quantitative variables.
    • transformations of the plane
    • transformations to establish triangle congruence criteria
    • coordinate geometry
math 2

Math II

  • Introductory topics:

    • Quadratic functions & modeling
    • Rewriting expressions
    • Exponent properties
    • Solving equations
    • Geometric concepts of congruence & similarity in terms of transformations

  • Advanced topics:

    • Geometry theorems: triangles, parallel lines & circles
    • Writing deductive & coordinate proofs
    • Probabilities: compound events & conditional
    • Reasoning & constructing arguments
    • Modeling
    • How to use structure & regularity
Pie chart, circle and equations for circumference and area, and y > = - x with graph

Math III

  • Introductory Topics:

    • expanding on the understanding of functions: polynomial, exponential, logarithmic, & trigonometric  
    • trigonometric functions for general triangle solving, sinusoidal modeling, & algebra
    • use of number systems to include the complex numbers & make use of sequences & series 
    • draw inferences & conclusions from data using probability & statistics

     

  • Advanced Topics:

    • learn to make sense of problems
    • reasoning & constructing arguments
    • use structure & regularity
    • use functions & geometry to: create & evaluate mathematical models & solve contextual problems

Entrance Exams Courses

SAT & ACT main image & artwork

SAT & ACT Preparation

  • SAT Section:

    • Number and Operations
    • Algebra & Functions
    • Geometry & Measurement
    • Data Analysis, Statistics, and Elementary & Geometric Probability

  • ACT Section:

    • Pre-Algebra
    • Elementary Algebra
    • Intermediate Algebra
    • Coordinate Geometry
    • Plane Geometry
    • Trigonometry
gre

GMAT Preparation

  • Quantitative reasoning:

    • Arithmetic
    • Algebra
    • Geometry
    • Exponents
    • Percents
    • Ratios
    • Rates
    • Probability
    • Combinatorics
    • Statistics
    • Number Properties

  • Integrated reasoning:

    • Graphical interpretation
    • Organization & sorting of information in tables
    • Combination of quantitative & verbal questions
GRE

GRE Preparation

  • Why this test is important:

    • prepares student for graduate school and business school admissions
    • allows student to stand out among peer applicants
    • demonstrates the student's level of preparedness for higher-level academics

  • The math section is weighed heavily by all admissions departments.  
    Here is what is included:

    • over half of the exam is Calculus
    • differential & integral Calculus with one or more variables
    • calculus-based applications & fundamentals attributed to coordinate geometry, Trigonometry, differential equations, and other situations
    • around 1/4 of the exam is Algebra
    • Basic algebraic techniques
    • Linear Algebra
    • Abstract Algebra & number theory
    • Introductory real analysis
    • Discrete mathematics
    • General topology
    • Geometry
    • Complex variables
    • Probability & statistics
    • Numerical analysis