Math

OA Graduation and UC requirement: 3 years

Our program is designed to meet students where they are and help them progress at their own pace. In addition, we are fully equipped to prepare students for a future in mathematics and/or the sciences. We take extra care to prepare our students for standardized exams and the AP Calculus Exam.

Elementary Algebra

Elementary Algebra is a slower-paced algebra course covering the same material as Algebra I over two years' time.
The first year, students learn about equations and functions: graphing and using real numbers including the order of operations and the commutative, associative and distributive properties; solving equations for a variable; graphing on a dimensional coordinate plane; writing the equation of a line; and solving and graphing linear inequalities.
The second year, students continue the study of algebra with learning how to solve systems of equations; using exponents in functions including learning about scientific notation and geometric sequences; using arithmetic operations on polynomial functions and factoring to find a solution; graphing and solving quadratic equations; connecting algebra concepts to geometry with radical equations, Pythagorean theorem and distance and midpoint formulas; using rational equations to find inverses, divide polynomials, and solve problems; and an introduction to probability and statistics.

Algebra 1

During first semester, students learn about equations and functions: graphing and using real numbers including the order of operations and the commutative, associative and distributive properties; solving equations for a variable; graphing on a dimensional coordinate plane; writing the equation of a line; and solving and graphing linear inequalities. The second semester, students continue the study of algebra with learning how to solve systems of equations; using exponents in functions including learning about scientific notation and geometric sequences; using arithmetic operations on polynomial functions and factoring to find a solution; graphing and solving quadratic equations; connecting algebra concepts to geometry with radical equations, Pythagorean theorem and distance and midpoint formulas; using rational equations to find inverses, divide polynomials, and solve problems; and an introduction to probability and statistics.

Geometry

Geometry is a course in logic, proof, and measurement. Students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. Some of the topics covered include definitions, postulates, and theorems regarding angles, segments, and lines, arcs, congruent triangles, similar triangles, special quadrilaterals, parallel lines, circles, coordinate geometry, area and volume formulas, transformations, constructions, and right triangle trigonometry.

Algebra II

Algebra II reviews solving and graphing equations and inequalities; solving systems of linear equations and inequalities; using matrix operations and solving matrix equations to find solutions to systems of linear equations both by hand and with the use of technology; solving and graphing quadratic equations; introduction to and use of complex numbers; graphing and solving polynomial functions; graphing and solving radical and fractional exponent equations; graphing and using exponential and logarithmic functions, including the rules of simplifying logarithmic equations; graphing and solving rational functions; an introduction to conic sections and how to solve nonlinear systems of equations; an introduction to sequences and series, focusing on patterns in sequences and series of numbers; some basic probability introducing factorials, permutations, combinations and the binomial expansions.

Algebra II with Trigonometry

Algebra II with Trigonometry reviews solving and graphing equations and inequalities; solving systems of linear equations and inequalities; using matrix operations and solving matrix equations to find solutions to systems of linear equations both by hand and with the use of technology; solving and graphing quadratic equations; introduction to and use of complex numbers; graphing and solving polynomial functions; graphing and solving radical and fractional exponent equations; graphing and using exponential and logarithmic functions, including the rules of simplifying logarithmic equations; graphing and solving rational functions; an introduction to conic sections and how to solve nonlinear systems of equations; an introduction to sequences and series, focusing on patterns in sequences and series of numbers; some basic probability introducing factorials, permutations, combinations and the binomial expansions; and some trigonometry, introducing trigonometric ratios, radians, solving a right triangle, graphing trig functions and using basic trig identities to simplify expressions, solve equations and prove trigonometric statements.

Pre-calculus

Precalculus begins with a review of functions and graphing; moves on to polynomial and rational functions with an emphasis on dividing polynomials, finding solutions with factoring, and graphing rational functions; using logarithms and exponents to solve equations, and applying logs and exponents to real world problems including financial applications; an in-depth look at trigonometry with a review of trigonometric ratios, graphing translated trigonometric functions, and using trigonometric identities to solve a triangle, solve equations and prove identities; an introduction to vectors, including finding a sum and product of vectors, the angle between vectors, and vector projection; revisiting matrices and using matrix algebra to solve a system of equations; examining conic sections and degenerate conics; introducing polar and parametric equations; using complex numbers in algebraic expressions and as solutions to equations; some discrete math, including arithmetic and geometric sequences and solutions, more probability and an introduction to induction proofs; an introduction to calculus with a look at function limits and discrete area calculations; an introduction to statistics with mean, median, and mode, data display options, and ways to model data; and an introduction to logic and set theory with a discussion of "and" and "or," and the use of "If-then" statements.

Calculus

Calculus is divided into two main sections. The first semester begins with a review of functions, limits, and continuity, and then derivatives are introduced. Students learn the definition of a derivative, and how to find the derivative of a variety of function forms using product, quotient, and chain rules, implicit differentiation, and logarithmic differentiation. Derivatives are applied to solve problems like related rates problems, finding the limit of functions in indeterminate forms, optimization, and finding the error of approximation. The first and second derivatives are used to estimate the shape of a function and graph the original function. In the second semester, students first learn about integration by finding the area under a curve using Riemann Sum approximations. They learn how to integrate different functions next by finding the antiderivative and using techniques like substitution, trigonometric substitution, integration by parts, and finding partial fractions. The Fundamental Theorem of Calculus is introduced with definite integrals, and integration is used to solve problems like finding the area between curves, calculating the volume of an object, finding the length of a curve, and applying integration to physics and statistics problems. Infinite sequences and series are considered at the end of the year, and students learn to determine if a sequence has limit or a series one solution.

Calculus 2 / Advanced Math Topics

Calculus 2 will cover multi-variable calculus including partial derivatives, and more in-depth work with differential equations. This course will strike a balance between the theory and applications of advanced mathematics. Our goal is to offer students an even clearer understanding of calculus and deeper insight into mathematics. We will includes a wealth of rich problem sets which makes advanced calculus relevant for students. Additionally, this course is designed to prepare students for the optional AP Calculus BC exam.

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