# Math Courses

 Course: Adv. Algebra/Trigonometry A,B Category: P Credits: 10 Grade Level: 10-12 Prerequisite: Mastery of Adv. Geometry (grade of "B" or better) Overview: This two semester, college preparatory course examines linear, circular, trigonometric, and logarithmic functions; matrices, vectors, and linear systems; and trigonometric formulas, graphs, inverses, and their applications. The second semester examines polar coordinates; sequences and series with introduction of limits; graphs of lines and conics; probability and descriptive statistics.
 Course: Adv. Geometry A,B/Geometry A,B (Basic) Category: P G W Credits: 10 Grade Level: 9-12 Prerequisite: Mastery of Algebra I Overview: This two semester course develops methods of logical thinking areas used to develop a collection of useful statements about plane figures and relationships between them. All basic geometric content and many applications are presented--points, lines, distances, angles, and other figures. The second half develops methods of logical thinking used to examine statements about plane figures and relationships between them. All basic geometric content and many applications are presented--points, lines, distances, angles, and other figures. Course Essentials: 1. Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 2. Students write geometric proofs, including proofs by contradiction. 3. Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 4. Students prove basic theorems involving congruence and similarity. 5. Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. 6. Students know and are able to use the triangle inequality theorem. 7. Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 8. Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 9. Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. 10. Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. 11. Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. 12. Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. 13. Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 14. Students prove the Pythagorean theorem. 15. Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. 16. Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 17. Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 18. Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2 + (cos( x )) 2 = 1. 19. Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. 20. Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles. 21. Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 22. Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
 Course: Algebra I W (P)/Algebra I W Category: P G W Credits: 5 Grade Level: 9-12 Prerequisite: Mastery of Pre-Algebra B or equivalent Overview: This is the first semester of a two-year course in Algebra. The first semester emphasizes the language of algebra, operating with rational numbers and inequalities. Course Essentials: 1. Evaluate exponents.2. Evaluate expressions using the order of operations.3. Use basic algebraic properties.4. Solve word problems using formulas.5. Write equations for verbal problems.6. Graph integers on a number line.7. Add rational numbers.8. Subtract rational numbers.9. Multiply rational numbers.10. Divide rational numbers.11. Solve word problems involving rational numbers.12. Solve equations using one or more operations.13. Solve ratio and proportion problems.14. Graph inequalities on the number line.15. Solve inequalities using basic operations.16. Compare rational numbers.17. Solve compound sentences and graph their solutions.18. Solve open sentences containing absolute value and graph their solutions.19. Use inequalities to solve word problems.
 Course: Algebra I X (P)/Algebra I X Category: P G W Credits: 5 Grade Level: 9-12 Prerequisite: Mastery of Algebra I W Overview: This is the second semester of a two-year course in Algebra. This semester emphasizes monomials, polynomials, and factoring. Course Essentials: 1. Multiply monomials.2. Divide monomials.3. Find products and quotients of numbers in scientific notation.4. Recognize problems which contain insufficient or unnecessary information.5. Use a chart to solve mixture problems.6. Solve problems involving percent increase and decrease.7. Classify polynomials and find their degree.8. Add and subtract polynomials.9. Multiply monomials and polynomials.10. Multiply binomials.11. Divide polynomials using long division.12. Solve word problems using formulas.13. Factor monomials and binomials.14. Factor differences and squares.15. Solve equations by factoring.16. Factor trinomials.17. Solve equations by factoring.18. Solve consecutive integer problems by factoring.19. Solve problems involving velocity and area.
 Course: Algebra I Y (P)/Algebra I Y Category: P G W Credits: 5 Grade Level: 9-12 Prerequisite: Mastery of Algebra I X Overview: This is the third semester of a two-year course in Algebra. This semester emphasizes functions and graphs, lines and slopes, systems of open sentences, and radicals. Course Essentials: 1. Graph ordered pairs.2. Apply domain and range when solving equations.3. Graph linear equations.4. Determine whether a given relation is a function.5. Graph inequalities in the coordinate plane.6. Determine the slope of a line.7. Graph equations using standard and slope intercept form.8. Determine the equation of a line.9. Recognize equations of parallel and perpendicular lines.10. Determine distance and midpoint of a line.11. Solve systems of equations by graphing, elimination, and substitution.12. Graph systems of inequalities.13. Solve uniform motion problems.14. Solve digit motion problems.15. Simplify radicals.16. Approximate square roots.17. Evaluate radical expressions.18. Simplify irrational square roots.19. Solve equations with radicals.20. Use the Pythagorean theorem.
 Course: Algebra I Z (P)/Algebra I Z Category: P G W Credits: 5 Grade Level: 9-12 Prerequisite: Mastery of Algebra I Y Overview: This is the fourth semester of a two-year course in Algebra. This semester emphasizes quadratics and rational expressions. Course Essentials: 1. Estimate the graph of a quadratic function.2. Locate roots of a quadratic equation.3. Solve quadratic equations using the quadratic formula.4. Determine the nature of roots using the discriminant.5. Solve word problems involving quadratic equations.6. Simplify algebraic fractions.7. Multiply algebraic fractions.8. Divide algebraic fractions.9. Add and subtract algebraic fractions.10. Simplify mixed expressions and complex fractions.11. Solve equations containing rational expressions.12. Use formulas to solve word problems.13. Solve direct variation problems.14. Solve inverse variation problems.15. Solve problems involving rational expressions.16. Determine the complement and supplement of an angle.17. Use proportions to find the missing measures for similar triangles.
 Course: Basic Mathematics Category: W Credits: 5-10 Grade Level: 9-12 Prerequisite: Director Approval Overview: This course enables the student to practice and improve fundamental skills in everyday arithmetic. Student learns basic math concepts of numeration, computation, and problem solving. Course Essentials: 1. Develop skills necessary for success in math.2. Add two or more numbers, regrouping as necessary, using 4- to 6-digit numbers.3. Subtract a 4- or 5-digit number from a 5- or 6-digit number, with regrouping.4. Multiply a 3- or 4-digit number by a 3-digit number, using numbers with one or more zeros.5. Divide a 2- to 4-digit number by a 1- or 2-digit number and write the answer as a decimal.6.Change fractions and mixed numbers to lowest terms.7. Rename a whole number or mixed number as an equivalent mixed number.8. Add and subtract mixed numbers with unlike denominators.9. Multiply a mixed number or whole number by a mixed number.10. Divide a whole number or a fraction or a mixed number by a mixed number.11. Write decimals as fractions and mixed numbers.12. Add, subtract, multiply and divide decimals.13. Calculate unit rates; write and solve proportions.14. Solve each of three forms of percent problems.15. Identify the question and insufficient information in word problems.16. Identify distractors (extra facts) in problems.17. Develop a strategy by determining the pattern or organization of word problems.18. Use the strategy of estimation to test a problem.19. Use the strategy of working backward to solve a problem.20. Use bar, line and circle graphs and tables to gain information to problem solve.21. Organize data into a table, diagram, or graph.22. Apply the seven steps of problem-solving.23. Identify standard units of measurement.24. Select appropriate metric unit to measure weight and distance; convert, add, subtract, multiply and divide metric and non-metric units.24. Find perimeters, areas and volumes of geometric forms.25. Analyze, simplify and solve algebraic expressions; use formulas to solve problems.26. Be able to read and interpret schedules, charts, and maps.27. Be able to add and subtract negative numbers on a number line.28. Be able to compare negative numbers using a number line.29. Solve word problems using a calculator.