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Mathematics

Our mathematics curriculum will help move American children, who ranked fifteenth in international math and science competitions in 2001, into top percentiles on standardized tests and into the most exciting jobs in the Silicon Valley. Our small classes, computer technology and expert teachers propel children into Algebra I by seventh grade and Algebra II or Geometry by eighth grade; this prepares them to take AP Calculus, Statistics, Chemistry and Physics in high school.

Pre-Algebra

Pre-algebra classes offered at The School of Choice introduce students to Algebra incorporating word problem solving, logic and mathematical applications to science. While students develop mastery of essential mathematics skills such as fractions, proportions, percents, prime factorizations, geometry, and word problems (without the use of calculators), this course presents basic algebra concepts in a rigorous but exciting manner. By integrating these concepts with problems in science, this course allows students to develop a wider perspective, while emphasizing a well-grounded mathematical background.

Topics covered include: fractions, decimals, mixed numbers, signed numbers, numbers in base two, arithmetic operations involving all these forms of numbers, order of operations, percents, proportions, ratios, divisibility, rounding, place value, unit conversions, scientific notation, word problems involving these pre-algebra concepts, evaluation and simplification of algebraic expressions, solution of linear equations in one unknown and geometric concepts such as perimeter, area, surface area, volume, classification of geometric figures and solids, geometric constructions, and symmetry.

Algebra I

A continuation of The School of Choice’s pre-algebra class, this is the first half of a two year rigorous training in Algebra emphasizing advanced methods and concepts in problem solving and data analysis. A wide variety of problems in science and other related fields reinforce the concepts through applications.

Topics covered include: the properties of real numbers, absolute values and equations and inequalities involving absolute value, solutions of equations in one unknown and solutions of simultaneous equations, the algebra of polynomials and rational expressions, word problems requiring algebra for their solution, graphical solution of equations, the Pythagorean theorem, solution of quadratic equations via factoring and completing the square, functions and functional notations. In addition, students learn to compute the perimeter and areas of two-dimensional regions, computation of the surface area and volume of a wide variety of geometric solids, and statistics and probability.

Algebra II

As the second half of The School of Choice’s Algebra course, this class emphasizes conceptual thinking and rigorous proofs. It also offers an introduction to imaginary numbers and trigonometry. A wide variety of problems in science and other related fields reinforce concepts through applications. Advanced applications in science may include gas laws, force vector calculations, chemical reactions and population genetics.

Topics covered include: symbolic mathematics, logic, analytic proof, detour proof, indirect proof, roots of quadratic equations including complex roots, basic trigonometric functions, direct and inverse variation, and exponential growth, algebra of polynomials, vectors, polar and rectangular coordinate system, sequences and series. The course also introduces formal Euclidian geometry with proofs.

Geometry and Trigonometry

This course assumes a very strong background in Algebra and completes a rigorous training in mathematical proofs and abstract concepts. In addition to formal geometric theory and trigonometry, the curriculum offers introductory topics in functional analysis. Students who complete this course will obtain the required background to take pre-Calculus or even Calculus by the tenth grade.

Topics covered include: planar geometry theory and practice, solid geometry theory and practice, mathematical modeling, advanced symbolic mathematics, logarithms, antilogarithms, and exponential functions, trigonometric identities, inverse trigonometric functions, graphs of sinusoids, rectangular and polar representations of complex numbers and introduction to functional analysis and the use of graphing calculators.

Pre-Calculus

The Pre-calculus course at The School of Choice is a thorough preparation for Advanced Placement Calculus AB and BC. Through a rigorous treatment of functional analysis, linear algebra and probability, students will develop the intuition and skills necessary to tackle most advanced mathematical problems. They will be systematically trained in the appropriate and optimal use of computational tools such as graphical calculators and computers and learn to make the proper interpretation of the data and results they obtain. This course emphasizes advanced applications to important issues in physics, chemistry, biology, computer science, engineering, economics, and psychology.

Topics covered include: zeros and roots of general polynomials, graphs of polynomials, rectangular and polar representations of complex numbers, asymptotes, parametric equations, and many important theorems in functional analysis such as the De Moivre theorem, the Rational Roots theorem, the remainder theorem, and the upper and lower bound theorem. To better prepare students for Calculus, we present an introduction to continuity, limits, derivatives, and integration in a simple and intuitive manner, together with the traditional definitions and theorems. We complete the course with selected topics in Applied Mathematics such as Linear Algebra (matrices and determinants), Statistics and Data Analysis.

Eleventh and Twelfth Grades

Students may continue from this point into the two AP Calculus courses (AB & BC) or take AP Statistics.