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Math Courses

Course: Adv. Algebra I A,B/Algebra I A,B
Category: P G W
Credits: 10
Grade Level: 9-12
Prerequisite: Mastery of Pre-Algebra B or equivalent
Overview: This is a two semester course for the first year of algebra. The first semester emphasizes the language of algebra, operating with rational numbers, inequalities, monomials, and polynomials. The second semester emphasizes functions and graphs, lines and slopes, systems of open sentences, radicals, quadratics, and factoring.
Course Essentials:

• Arithmetic Properties (CA Standard 1.0, 2.0)
o Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
o Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
• B.Functions (CA Standard 16.0, 17.0, 18.0)
o 16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.
o 17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.
o 18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.
• Polynomials (CA Standard 10.0, 12.0)
o 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.
o 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.
• D.Factoring (CA Standard 11.0)
o 11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
• E.Rational Expressions (CA Standard 13.0)
o 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.

• F.Equations (CA Standard 3.0, 4.0, 8.0, 9.0)/Inequalities (CA Standard 3.0, 4.0)
o Students solve equations and inequalities involving absolute values.
o Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
o 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
o 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
• G.Quadratics Equations (CA Standard 140, 19.0, 20.0, 21.0, 22.0, 23.0)
o 14.0 Students solve a quadratic equation by factoring or completing the square.
o 19.0 Students know the quadratic formula and are familiar with its proof by completing the square.
o 20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
o 21.0 Students graph quadratic functions and know that their roots are the x- intercepts.
o 22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
o 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
• H.Graphs (CA Standard 6.0, 7.0)
o Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
o Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
• I.Axioms (CA Standard 24.0, 25.0)
o 24.0 Students use and know simple aspects of a logical argument:
25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:
• K. Word Problems (CA Standard 5.0, 15.0)
o 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
o 15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

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: Algebra II A,B (P)
Category: P
Credits: 5
Grade Level: 10-12
Prerequisite: Mastery of Adv. Algebra I or Adv. Geometry
Overview: This two semester course studies operations of powers, exponents, radicals, quadratics, and polynomials. The second semester studies exponents, exponential and logarithmic functions, probability, statistics, and trigonometric functions and identities.
Course Essentials: 1. Equations and Inequalities: Students solve linear equations, linear inequalities and absolute value equations and inequalities.
2. Linear Equations and Functions: Students graph linear and absolute value functions. They graph linear inequalities and write equations of lines.
3. Systems of Linear Equations and Inequalities: Students solve systems of equations in two and three variables by using methods of graphing, substitution, and elimination. They graph and solve systems of linear inequalities.
4. Quadratic Functions: Students graph quadratic functions and solve quadratic equations by factoring, completing the square, and using the quadratic formula. Students add, subtract, multiply and divide complex numbers. They can graph complex numbers.
5. Polynomials and Polynomial Functions: Students add, subtract, multiply, and divide polynomials. Students graph and solve polynomial functions.
6. Powers, Roots, and Radicals: Students operate with rational exponents and exponential functions. They solve radical equations. Students add, subtract, multiply and divide functions. They find inverses and compositions of two functions.

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.

Course: Business Math
Category: G W
Credits: 5-10
Grade Level: 9-12
Prerequisite: Director Approval
Overview: This course develops basic mathematical skills in personal and business related tasks. Areas of study include gross and net income; cash purchases; checking, savings, and charge accounts; loans; auto, housing and insurance costs; record keeping; and business math central to personnel costs, production, purchasing, sales, marketing, warehousing, and accounting.
Course Essentials: 1. Calculate gross and net income through application of the mathematical skills of changing fractions to decimals, multiplying decimals, adding decimals, rounding decimals, finding percentages, subtracting decimals, dividing decimals, and reading tables.
2. Calculate cash purchase expenses of sales tax, total purchase price, unit price, markdown, and sale price using basic decimal skills.
3. Perform basic mathematical operations central to an understanding of checking accounts, saving accounts, charge accounts, and credit cards.
4. Calculate loan costs, APR, and finance charges associated with loan transactions.
5. Calculate the costs associated with purchasing new and used automobiles, automobile insurance, automobile leasing, maintenance, and operation.
6. Calculate housing costs, including: mortgage loans, closing costs, monthly payment, real estate taxes, and homeowner's insurance.
7. Calculate insurance and investment costs and benefits.
8. Calculate average monthly expenditures; prepare and use a budget.
9. Perform business mathematics tasks associated with personnel and production costs, benefits, and analyses.
10. Calculate purchasing discounts.
11. Calculate sales markup, net profit, selling price, and markdowns.
12. Compute marketing projections, including: opinion surveys, sales potential and market share; graph sales projections; calculate advertising costs and selling price that will result in the highest possible net profit.
13. Perform business mathematics tasks associated with warehousing and distribution, including: storage space; taking, valuing, and carrying an inventory; and total shipping costs.
14. Calculate service expenses related to building rental, maintenance, equipment rental, utility costs, and the costs of professional services.
15. Perform accounting operations pertaining to payroll, business expenses and apportionment, Pre-Algebra, Merrill, 1996and depreciation.

Course: Calculus A, B
Category: P
Credits: 10
Grade Level: 11-12
Prerequisite: Mastery of Pre-Calculus B (grade of "B" or better)
Overview: This two semester, college preparatory course examines derivatives, the chain rule, derivatives of trigonometric functions, applications of derivatives (concavity, points of inflection, maxima and minima) definite and indefinite integrals, application of definite integrals, transcendental functions, and methods of integration. The second semester examines conic sections and other plane curves, parametric equations for conics, hyperbolic functions, inverse hyperbolic functions, polar equations of conic sections and other curves, integrals in polar coordinates, infinite sequences and infinite series, power series and taylor polynomials, vectors, vector functions and motion, and differential equations--first order, second order and higher order equations.
Course Essentials: 1. Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity:
2. Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.
3. Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.
4. Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:
5. Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.
6. Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.
7. Students compute derivatives of higher orders.
8. Students know and can apply Rolle's theorem, the mean value theorem, and L'Hôpital's rule.
9. Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
10. Students know Newton's method for approximating the zeros of a function.
11. Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.
12. Students use differentiation to solve related rate problems in a variety of pure and applied contexts.
13. Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals.
14. Students apply the definition of the integral to model problems in physics, economics, and so forth, obtaining results in terms of integrals.
15. Students demonstrate knowledge and proof of the fundamental theorem of calculus and use it to interpret integrals as antiderivatives.
16. Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
17. Students compute, by hand, the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution. They can also combine these techniques when appropriate.
18. Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as indefinite integrals.
19. Students compute, by hand, the integrals of rational functions by combining the techniques in standard 17.0 with the algebraic techniques of partial fractions and completing the square.
20. Students compute the integrals of trigonometric functions by using the techniques noted above.
21. Students understand the algorithms involved in Simpson's rule and Newton's method. They use calculators or computers or both to approximate integrals numerically.
22. Students understand improper integrals as limits of definite integrals.
23. Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges.
24. Students understand and can compute the radius (interval) of the convergence of power series.
25. Students differentiate and integrate the terms of a power series in order to form new series from known ones.
26. Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.
27. Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems.

Course: Integrated Math I A,B
Category: P
Credits: 10
Grade Level: 9-12
Prerequisite: Mastery of Pre-Algebra B or equivalent
Overview: This college preparatory course examines integrated mathematics, which includes concepts from algebra, geometry, logic, probability, and statistics.

Course: Integrated Math II A,B
Category: P
Credits: 10
Grade Level: 9-12
Prerequisite: Integrated Math I
Overview: This college preparatory course examines integrated mathematics, which includes concepts from algebra, geometry, logic, probability, and statistics.

Course: Integrated Math III A,B
Category: P
Credits: 10
Grade Level: 9-12
Prerequisite: Integrated Math II
Overview: This college preparatory course examines integrated mathematics, which includes concepts from algebra, geometry, logic, probability, and statistics.

Course: Intermediate Algebra A,B
Category: G W
Credits: 5
Grade Level: 10-12
Prerequisite: Mastery of Algebra I or Geometry
Overview: (Not recommended for college bound Math/Science majors.) (Can not be used as a prerequisite toward fourth year of math.) This two semester course studies operations of powers, exponents, radicals, quadratics, and polynomials. The second half studies exponents, exponential and logarithmic functions, probability, statistics, and trigonometric functions and identities.
Course Essentials: 1. Extent knowledge of exponents and:
  Simplify expressions with negative integers.
  Express large and small numbers in scientific notation.
  Perform computations involving scientific notation.
  Write expressions written in either radical or exponent form.
 2. Recognize and apply the basic properties of logarithms.
  Recognize the exponential and logarithmic functions are inverses.
  Evaluate logarithmic expressions.
  Solve verbal problems using logarithms.
Solve equations using the product, quotient, and power properties of logarithms.
Express logarithms as the sum or difference of simpler logarithmic expressions.
  Use logarithms to compute powers and roots.
 3. Achieve and understanding of sequence and series, including:
  Arithmetic  Factorial notation  Geometric
  Special sequences  Binomial expansion  General Term of sequence
 4. Use probability mathematics.
  Calculate combinations  Calculate permutations
  Find the probability and odds of success and failure
 5. Use basic statistical methods.
  Use table and graphs to present data.
  Calculate - mean, mode, median, standard deviation
  Use prediction equations.
6. Strengthen past learned skills acquired in the first course of algebra, and:
  Follow order of operations.
  Evaluate expressions.
Apply the addition, subtraction, multiplication and division properties of equality to solve equations.
  Translate and solve verbal expressions.
Evaluate expressions with absolute value and solve equations with absolute value.
  Compare numbers and expressions using inequality symbols.
  Solve inequalities using inequality properties.
 7. Calculate and graph using the coordinate plane.
  Find the value of a function for a given element of the domain.
  Graph linear equations.
  Find the slope of the line passing through a given pair of points.
  Find the slope, y-intercept, and x-intercept from a given linear equation.
 8. Solve systems of linear equations using:
  Graphs  Substitution  Elimination  Three Variables
  Calculate for graphs of equations which parallel, perpendicular or neither.
 9. Operate with polynomials, including:
  Simplification  Factorization  Long Division of Polynomials
  Addition  Subtraction  Multiplication  Division
 10. Operate with radical expressions and:
  Find a given root of numbers and algebraic expressions.
  Simplify and multiply radicals.
  Add and subtract radicals; multiply radicals using FOIL
Divide radicals; name conjugates; rationalize the denominator; simplify; approximate value to three decimals.
 11.  Solve quadratic equations by:
  Factoring.
Representing word problems with pictures, then writing and solving quadratic equations.
  Completing the square.
  Using the quadratic formula.
 12. Operate with rational polynomial expressions to:
  Simplify and multiply expressions.
  Find monomial, binomial, and trinomial LCD's.
  Add and subtract expressions.
  Solve rational equations.
  Use rational expressions to solve problems.

Course: Math Analysis A, B
Category: P
Credits: 10
Grade Level: 11-12
Prerequisite: Mastery of Algebra II B (grade of "B" or better)
Overview: This two semester, college preparatory course examines linear and quadratic functions, polynomial functions, inequalities in one and two variables, exponents and logarithms, trigonometric functions, equations and applications including sine curves, cosine curves, and trigonometric identities. The second semester examines triangle trigonometry: solving right triangles, law of sines, law of cosines, trigonometric additions formulas, matrices, combinatorics, probability including the binomial probability theorem, probability of combinations, and descriptive statistics.
Course Essentials: 1. Find an equation of a line given the geometric properties of the slope.      
2. Model real-world situations by means of linear functions.  
3. Solve and graph quadratic equations when solutions are both real and complex.
4. Use synthetic division to apply the remainder and factor theorems.                    
5. Find maximum and minimums of polynomial functions.
6. Solve polynomial equations.
7. Solve applied problems using linear programming.                         
8. Use exponential and logarithmic functions: use the natural logarithm.            
8. Solve exponential equations.
9. Find the arc length and area of a sector of a circle and solve problems of apparent size.
10. Evaluate the six trigonometric functions and solve trigonometric equations.
11. Evaluate the inverse trigonometric functions.
12. Find the equations of different sine and cosine curves in applications.
13. Use trigonometric functions to model periodic behavior.
14. Prove trigonometric identities. 
15. Use a graphical calculator to study linear, polynomial and trigonometric functions.
16. Use trigonometry to find unknown sides or angles of a right triangle.
17. Find the area of a triangle given the length of two sides and the measure of the included angle.
18. Use the law of sines and cosines.                                      
19. Use the trigonometric addition formulas.
20. Use identities to solve trigonometric equations.
21. Find the sum, difference, scalar multiples, and products of matrices.
22. Find the inverse of a 2x2 matrix and solve linear systems using matrices.
23. Solve communications network problems using matrices.                       
24. Solve problems involving permutations and combinations.
25. Solve counting problems that involve permutations with repetition and circular permutations.
26. Use the binomial theorem and Pascal’s triangle.
27. Find a sample space of an experiment and the probability of an event or either two events two events.
28. Find the probability of events occurring together and to determine whether two events are independent
29. Use the binomial probability theorem.
30. Use combinations to solve probability problems.
31. Calculate the mean, median, mode, variance and standard deviation of a set of data.
32. Use tables, graphs, box-and -whisker plots for data analysis.
33. Analyze the normal distribution.

Course: Mathematics 7
Category: Jr. H.S.
Credits: 10
Grade Level: 7
Prerequisite: Required
Overview: This course enables the student to improve fundamental skills in everyday arithmetic, including basic operations of decimals and percents and solving problems with geometric shapes.
Course Essentials: Number Sense
1. Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
2. Students use exponents, powers, and roots and use exponents in working with fractions:
Algebra and Functions
1. Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
2. Students interpret and evaluate expressions involving integer powers and simple roots:
3. Students graph and interpret linear and some nonlinear functions:
4. Students solve simple linear equations and inequalities over the rational numbers:
Measurement and Geometry
1. Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
2. Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
3. Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
Statistics, Data Analysis, and Probability
1. Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
Mathematical Reasoning
1. Students make decisions about how to approach problems:
2. Students use strategies, skills, and concepts in finding solutions:
3. Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.

Course: Mathematics 8
Category: Jr. H.S.
Credits: 10
Grade Level: 8
Prerequisite: Required
Overview: This course enables the student to practice and improve fundamental skills in everyday arithmetic, including addition, subtraction, multiplication and division of fractions and decimals.
Course Essentials: 1. Add two or more numbers, regrouping as necessary, using 4-to 6- digit numbers.
2. Subtract a 4- or 5- digit number from a 5- or 6- digit number, with regrouping.
3. Multiply a 3- or 4- digit number by a 3-digit number, using numbers with one or more zeros.
4. Divide a 2- to 4- digit number by a 1- or 2- digit number and write the answer as a decimal.
5. Change fractions and mixed numbers to lowest terms.
6. Rename a whole number or mixed number as an equivalent mixed number.
7. Add mixed numbers with unlike denominators.
8. 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. Apply whole numbers, fractions, decimals, proportions and percents to solve consumer, technical, and business problems.

Course: Pre-Algebra A, B
Category: G W
Credits: 10
Grade Level: 7-12
Prerequisite: Director Approval
Overview: This two semester course enables the student to practice and improve fundamental skills prerequisite to those encountered in formal algebra. Course content includes percents, measurements, conversions, formulas, and pre-algebra tasks and applications.
Course Essentials: 1. Determine if proportions are true; write and solve proportions with the unknown in each of four positions.
2. Convert fractions, decimals, and percents.
3. Find a percentage of a given number.
4. Find what percent one number is of another.
5. Find a number if a percentage of the number is known.
6. Graph, add, subtract, multiply and divide integers.
7. Rewrite numbers with positive and negative exponents; simplify expressions with and without parentheses; evaluate and write numbers using scientific notation.
8. Evaluate and simplify variable expressions.
9. Translate verbal expressions into mathematical expressions using given variables or by assigning variable names.
10. Solve equations of the forms; x + a = b; ax = b; ax + b = c.
11. Solve equations with unknowns on both sides.
12. Solve equations containing parentheses.
13. Solve a formula for one variable, given the values of the other variables.
14. Translate verbal sentences into mathematical sentences and solve.
15. Use equations to solve consumer, technical and business problems.

Course: Pre-Calculus A,B
Category: P
Credits: 10
Grade Level: 11-12
Prerequisite: Mastery of Adv. Alg II/Trig B
Overview: This two semester, college preparatory course examines polynomial functions, exponents and logs, trigonometric functions (equations and applications) triangle trigonometry (law of sine and cosine) trigonometric addition formulas, and solving trigonometric equations. The second semester examines analytic geometry, polar coordinates, geometric representation of complex numbers, powers of complex numbers, roots of complex numbers, vectors and determinants, sequences, series, limits and iterated functions, and introduction to calculus, including finding derivatives of curves, using derivatives in curve sketching, extreme value problems, and velocity and acceleration.
Course Essentials: 1. Use synthetic division to apply the remainder and factor theorems.                 
2. Find maximums and minimums of polynomial functions by graphing.
3. Solve polynomial equations.                                                
4. Use exponential and logarithmic functions; use the natural logarithm.
5. Solve exponential equations.
6. Find the arc length and the area of a sector of a circle and solve problems of apparent size.
7. Evaluate the six trigonometric functions and solve trigonometric equations.
8. Evaluate the inverse trigonometric functions.
9. Find the equations of different sine and cosine curves in applications.
10. Use the trigonometric functions to model periodic behavior.
11. Prove trigonometric functions.                                  
12. Use trigonometry to find unknown sides or angles of a right triangle.
13. Find the area of a triangle given the length of two sides and the measure of the included angle.  
14. Use the law of sines and cosines.                                               
15. Use the trigonometric additions formulas.                           
16. Use identities to solve trigonometric equations.
17. Use a graphical calculator to study linear, polynomial and trigonometric functions.
18. Find equations of circles and find the coordinates of any points where circles and lines meet.
19. Find equations of ellipses, hyperboles and paraboles.
20. Solve systems of second-degree equations.                                
21. Graph polar equations.
22. Write complex numbers in polar form and find products in polar form.
23. Use De Moivre’s theorem to find powers of complex numbers.
24. Find roots of complex numbers.
25. Use vector and parametric equations to describe motion in the plane.
26. Apply dot and cross product.
27. Extend vectors to three dimensions and apply them.
28. Find the formula for the nth term of an arithmetic and geometric sequence.
29. Use sequences recursively to solve problems.                         
30. Find the sum of a finite arithmetic and geometric series.                                      
31. Find the limit of an infinite sequence: determine when limit does not exist.
32. Find the sum of an infinite geometric series.
33. Use identities to solve trigonometric equations.
34. Use mathematical induction to prove that a statement is true.
35. Determine whether a function is continuous.
36. Use limits to graph rational functions.
37. Use the power series of a given function to find an infinite series for a functional value or a related function.
38. Find derivatives of functions.
39. Sketch the graphs of functions using derivatives.
40. Solve extreme value problems using derivatives.
41. Find instantaneous velocities and accelerations.
42. Use a graphic calculator to study functions.

Course: Probability and Statistics A,B
Category: P
Credits: 10
Grade Level: 11-12
Prerequisite: Mastery of Algebra II
Overview: This two semester, college preparatory course provides a solid background in descriptive statistics, probability, random variables, and discrete and continuous distributions.
Course Essentials: 1. Define "independent events" and demonstrate the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces
2. Define "conditional probability" and solve for probabilities in finite ample space.
3. Solve for probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin toss using "Discrete Random Variables"
4. Use standards (normal, binomial, and exponential) to solve events in problems in which the distribution belongs to those families.
5. Determine the mean and the standard deviation of a normally distributed random variable
6. Define mean, median, and mode of a distribution of data and compute each in particular situations. 
7. Compute the variance and standard deviation of a distribution of data
8. Using frequency tables, histograms, standard line and bar-graphs, stem and leaf displays, scatterplots and box-and-whisker plots, organize and describe distributions of data.

Course: Statistics
Category: P
Credits: 5
Grade Level: 11-12
Prerequisite: Mastery of Algebra II
Overview: This one semester, college preparatory course examines all standard topics in statistics through two-way analysis of variance. Concentration is on the basic concepts with secondary emphasis on their application.
Course Essentials: 1. Gain knowledge of methods used for describing data including the mean, median, mode, standard deviation, and variance.
2. Understand probability including the additive rule, multiplicative rule and random sampling.
3. Comprehend probability distributions.
4. Acquire skills in handling discrete random variables.
5. Understand the normal distribution and the binomial distribution approximating the normal distribution.
6. Gain knowledge of random samples of populations and sampling techniques.
7. Understand and explored inferences based on one sample and two samples.
8. Show a fundamental understanding of analysis of variance, nonparametric statistics, the Chi Square Test and Simple linear regression.

Course: Trigonometry
Category: P
Credits: 5
Grade Level: 11-12
Prerequisite: Mastery of Algebra II
Overview: This one semester, college preparatory course examines trigonometric functions, inverse trigonometric functions, analytic trigonometry, graphing of functions, and additional topics such as Law of Sines and Cosines.
Course Essentials: 1. Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.
2. Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
3. Students know the identity cos 2 (x) + sin 2 (x) = 1:
4. Students graph functions of the form f(t) = A sin ( Bt + C ) or f(t) = A cos ( Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.
5. Students know the definitions of the tangent and cotangent functions and can graph them.
6. Students know the definitions of the secant and cosecant functions and can graph them.
7. Students know that the tangent of the angle that a line makes with the x- axis is equal to the slope of the line.
8. Students know the definitions of the inverse trigonometric functions and can graph the functions.
9. Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.
10. Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/ or simplify other trigonometric identities.
11. Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/ or simplify other trigonometric identities.
12. Students use trigonometry to determine unknown sides or angles in right triangles.
13. Students know the law of sines and the law of cosines and apply those laws to solve problems.
14. Students determine the area of a triangle, given one angle and the two adjacent sides.
15. Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.
16. Students represent equations given in rectangular coordinates in terms of polar coordinates.
17. Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.
18. Students know DeMoivre's theorem and can give n th roots of a complex number given in polar form.
19. Students are adept at using trigonometry in a variety of applications and word problems.