# OUR CURRICULUM: MATHEMATICS

For those students entering in middle school, we offer a **Pre-Algebra** course which teaches them all the topics they will need in order to excel at algebra. These topics include:

- fractions and their arithmetic operations
- decimals and their arithmetic operations
- mixed numbers and their arithmetic operations
- signed numbers and their arithmetic operations
- translating from words to algebraic expressions
- order of operations
- percents
- proportions
- ratios
- divisibility
- rounding
- place value
- unit conversions
- scientific notation
- data representation
- evaluation of algebraic expressions
- the simplification of algebraic expressions
- the solution of linear equations in one unknown
- word problems involving pre-algebraic concepts
- perimeter
- area
- surface area
- volume
- classification of geometric figures and solids
- geometric constructions
- symmetry

**Algebra 1**continues these topics and introduces:

- arithmetic and evaluation of expressions involving signed numbers, exponents, and roots
- properties of real numbers
- absolute value
- equations and inequalities involving absolute value
- scientific notation
- unit conversions
- solution of equations in one unknown
- solution of simultaneous equations
- the algebra of polynomials and rational expressions
- word problems requiring algebra for the solution (such as uniform motion and coin problems)
- graphical solution of simultaneous equations
- graphs of a variety of functions: linear, quadratic, cubic, square root, absolute value, etc.
- translations and reflections of graphs
- factoring
- Pythagorean theorem
- algebraic proofs
- functional notation and functions
- solution of quadratic equations by factoring, completing the square, and quadratic formula
- direct and inverse variation
- exponential growth
- computation of the perimeter and area of two-dimensional regions
- computation of the surface area and volume of a wide variety of geometric solids
- statistics
- probability

For **Geometry**, our students learn from the second most widely published book of all time, surpassed only by the Holy Bible, Euclid's *Elements*. Since it was written, *the Elements* has been used by almost all great thinkers of western civilization to develop their ability to reason and use logic.

**Algebra 2**, in addition to reviewing the topics learned in **Algebra 1**, introduces these concepts:

- graphical solution of simultaneous equations
- scientific notation
- radicals
- roots of quadratic equations including complex roots
- properties of real numbers
- factoring
- inequalities and systems of inequalities
- logarithms and antilogarithms
- conic sections
- exponential equations
- basic trigonometric functions
- algebra of polynomials
- vectors in polar and rectangular form
- algebraic word problem

**Advanced Mathematics**continues the student's study of algebra and begins to introduce them to concepts which will aid them in the study of Calculus. The following material is introduced:

- permutations and combinations
- inverse trigonometric functions
- conic sections
- graphs of sinusoids
- rectangular and polar representation of complex numbers
- trigonometric identities
- De Moivre's theorem
- matrices and determinants
- the binomial theorem
- the rational roots theorem

**Calculus**for those students who demonstrate an above-average ability in mathematics. It is an AP Course, and students may earn college credit by taking the AP Calculus Test.