MATHEMATICS DEPARTMENT

Students will build on their knowledge of equations by relating a graph to the story it tells and to the equation whose solution it pictures. The skills of graphing will be extended to include slope, parallel and perpendicular lines, and absolute value equations.

Students will extend their ability to solve problems by using equations and inequalities that include exponents and polynomials.

Students will extend their skills in graphing and solving equations and in equalities to include using the quadratic formula, completing the square, factoring, radical expressions and rational expressions.

This course reviews algebra, geometry, and the math state standards. This class readies the students for the Prairie State Achievement Exam and the ACT.

This is a traditional course in Algebra I and includes the following topics:
1.  Using the basic operations with real numbers, algebraic equations, and polynomials.
2.  Factoring polynomials.
3.  Using the basic operations to simplify algebraic fractions.
4.  Using algebraic fractions to solve ratios, proportions, and mixture and work problems.
5.  Solving and graphing inequalities in one and two variables.
6.  Solving linear systems by graphing, addition-subtraction, and substitution.
  

This course is designed to prepare students for careers which need a more thorough understanding of mathematics and to serve as a prerequisite for future endeavors in mathematics and science. This course includes the following topics: 1. Basic concepts of Algebra. 2. Inequalities. 3. Linear Equations and functions. 4. Products and Factors of Polynomials. 5. Rational Expressions. 6. Irrational and Complex Numbers. 7. Quadratic Equations and Functions. 8. Variation and Polynomial Equations. 9. Analytic Geometry. 10. Exponential and Logarithmic functions. 11. Sequences and Series. 12. Triangular Trigonometry. 13. Statistics and Probability. 14. Matrices and Determinants.

Precalculus is designed with a two-fold purpose: to prepare juniors for senior year calculus and to serve as an exit level advanced math course for those students who need a solid math basis for college courses in engineering, science, pre-medical, nursing, and business.
Topics covered include: Coordinate geometry and advanced graphing; Polynomials, inequalities and functions; Review and extension of trigonometry; Exponents and logarithms; Conic sections; Polar coordinates and complex numbers; Vectors and determinants; Finite and infinite sequences and series; Probability and statistics.

Calculus is the capstone course that rests upon classes that began with arithmetic in elementary school, continued with algebra in the middle school and geometry, trigonometry, and advanced algebra (pre-calculus) in high school. This course provides the mathematical background for those students pursuing careers in science, engineering, business, and medicine. Its content covers roughly the equivalent of one and one-half semesters of college calculus.

Topics include:
1. Functions, limits and continuity.
2. Derivatives using power rule, product rule, quotient rule, chain rule, and implicit differentiation.
3. Derivatives of algebraic, trigonometric, inverse trigonometric, logarithmic, exponential, hyperbolic, and inverse hyperbolic functions
4. Relative maxima and minima, points of inflection, intervals of increase and decrease, intervals of concavity, and points of nondifferentiability
5. Definite and indefinite integrals using u-substitution, partial fractions, parts, and trigonometric substitutions.
6. Calculator or computer assisted differentiation and integration
7. Improper integrals and L'Hopital's Rule.
8. Areas, volumes, surface areas, and line lengths using definite integrals.
9. Miscellaneous applications of derivatives and integrals in science, business, and engineering.