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Common Math courses and concepts

Students are taught the four basic operations of numbers (+ - x \div ) in whole number, fractional, and decimal form.  In early grades, students will learn place value, rounding/estimating, time, money, shapes, perimeter, comparisons, and + / story problems.  Upper elementary focuses on fractional and decimal numbers, elapsed time, x / \div  story problems, conversions, measurements, area, volume, average, and graphing points.

Pre-Algebra (middle school)

Students are taught the four basic operations (+ - x \div) as it relates to positive and negative numbers.  This course will also cover order of operations, one and two step equations with a variable, linear functions and graphing, inequalities, absolute value, Pythagorean Theorem, combining like terms, and factoring polynomials.

Algebra 1 (middle school or high school)

Students continue to build on the fundamentals they learned in pre-algebra to solve more complex equations.  Algebra 1 focuses on types of functions (linear, exponential, quadratics) and how to solve and graph them.  Students will learn how to solve systems of equations and inequalities, + / - / x / \div  polynomials, simplify and solve rational expressions, and solve rate/time/distance/mixture story problems.

Geometry (high school)

Geometry allows students to practice applying algebraic concepts to shapes and graphs.  Geometry focuses on measurements, conversions, and theorems of visual representations of shapes and their various parts.  Students will learn how to develop reasonable proofs from theorems to support conclusions.  Deductive and inductive reasoning skills will be essential in properly constructing geometric proofs.   Students will also be introduced to basic trigonometric functions.

Algebra 2 (high school)

Algebra 2 reviews the solving, graphing, and differentiating between linear, exponential, quadratic, cubic, and absolute value functions. It also covers the solving of 3 variable functions using matrices and determinants; advanced factoring of quadratic functions; simplifying rational expressions and radicals; solving rational equations. Advanced concepts may also include composition of functions, complex numbers, exponential/logarithmic/trigonometric functions, and arithmetic/geometric sequences and series.

Statistics (high school)

This course is often offered as an elective math course for students as an alternative to pre-calculus or calculus.  Statistics deals with the collection, organization, and interpretation of data. The main concepts covered include: probability properties; population samples; common, discrete, continuous, and bivariate distributions; random variables and variance; bias; and predictions.  Students can opt to take AP Statistics for higher GPA.  Students who pass the AP Statistics exam at the end of the year can receive college credit for the class.

Pre-Calculus (high school)

This course is usually divided into two parts: trigonometry and math analysis.  The trigonometry section involves the study of triangles and covers trigonometric functions, graphs, identities, and equations.  It will also introduce graphing on polar and complex coordinate systems.  Having a strong mastery of geometric theorems and construction of proofs is essential in navigating this portion of pre-calculus.  Math analysis is more algebra based and covers complex algebraic functions (polynomial, exponential, logarithmic, rational, power), domain and range, and end behavior.  Students will be required to not only solve functions but represent them in various formats using different modalities.  Pre-calculus solidifies concepts presented in earlier mathematics while introducing more complex equations and systems that will be further explored in Calculus.

Calculus (high school)

This course is usually considered the highest level of mathematics for a high school student.  Pre-requisites include: Algebra 1, Geometry, Algebra 2, and Pre-Calculus.  Students who plan on taking Calculus need a strong understanding of the following functions: linear, quadratic, polynomial, rational, power, inverse, exponential, logarithmic, and trigonometric functions.  Calculus will explore limits, continuity, and derivatives of functions as well as cover the rules for differentiation and integration of functions.  Calculus requires not only the mastery of formulas but the application of them in various story problems that are usually physics or engineering based.

Most students who desire to take this course their senior year of high school should complete Algebra 1 in middle school and take Geometry their freshman year of high school.  Some students who take Algebra 1 their freshman year can take Geometry during summer school to allow them to take Algebra 2 as a sophomore.  Students can opt to take AP Calculus for higher GPA.  Students who pass the AP Calculus exam at the end of the year can receive college credit for the class.