MATHEMATICS CURRICULUM ALGEBRA II 1 Williamsville C.U.S.D. #15 Mathematics Curriculum Program Title: Algebra II Program Description: Algebra II is a full-year course and is open to students who have completed Algebra I and Geometry. This course covers additional material in each topic of Algebra. New material consists of quadratic, polynomial functions, complex numbers, sequences, and series. Students will be instructed on the use of a calculator and allowed to use them when appropriate. Prerequisite: Algebra I and Geometry. Program Content: Algebra II reviews Algebra I and covers new material involving quadratic, polynomial functions, complex numbers, sequence, and series. Program Guide August Basic properties Set notations, intersections, unions, introduction to 6.A.4 8.A.3b 8.A.4 September Properties of operations Solving Axioms of real numbers, properties of addition Properties of products, differences, quotients Sum and difference of polynomials, solve 6.A.4 6.B 7.A.3b 8.A.3b 8.B.4 Solving Word problems with linear solve Solving absolute value Compound sentences, absolute value equalities and
MATHEMATICS CURRICULUM ALGEBRA II 2 October Linear functions and relations Relations, functions, mapping, and graphing Graphs of linear and Slope of a line formulas, find eq of line (form) 6.D.4 8.B.4 8.B.5 8.D.3b November Systems of linear or Direct variation and word problems Solve a system of by graph, linear combo, substitution Solve system by determinants and Cramer s rule 8.B.4 8.C 9.A.4a 9.A.4b Solve word problems by system graph linear system Graphs in space; determinants Graph in space (pts), graph planes in space December Graphs in space; ddeterminants System of equality in 3 variables, third order determinants 8.B.4a Solve system in 3 variables, 4th order determinants
MATHEMATICS CURRICULUM ALGEBRA II 3 January Working with Laws of exponents, polynomials multiple polynomials Factoring polynomials, solve by factoring Solve by factoring 6.A.3 6.B.3b 6.B.5 February Rational algebraic expressions Simplify rational exponents, divide polynomials Multiply, divide, add, subtract rational expressions Use polynomials with rational coefficients 6.B.3b 6.D.4 7.C.5b Radicals Solving fractional Power functions., variation, proportions, nth roots
MATHEMATICS CURRICULUM ALGEBRA II 4 March Radicals and radical Finding roots of polynomial, irrational # s STD notation, estimating, convert fractions to real numbers Properties of radicals, operations with radicals 6.A.3 6.A.4 6.A.5 8.A.4a April Complex numbers Solving with radicals, simplifying imaginary numbers Add, subtract, multiply, divide complex numbers 6.A.5 8.B.4a Solving Quadratic Equations Solve by complete the square or quadratic formula Find the value of discriminant and nature of the roots, use sum and product formulas to write Graph quadratic functions, minimum and max
MATHEMATICS CURRICULUM ALGEBRA II 5 May Polynomial functions Graph quadratic Mathematics Learning Standards Use synthetic substitution and division Solve polynomial eq using synthetic division State Goal 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios, and proportions. 1. Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots. 2. Perform addition, subtraction, and multiplication of complex numbers and graph the results in the complex plane. 3. Determine whether exact values or approximations are appropriate (e.g., bid a job, determine gas mileage for a trip). 4. Determine the level of accuracy needed for computations involving measurement and irrational numbers. State Goal 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy. 1. Apply units and scales to describe and compare numerical data and physical objects. 2. Apply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density, and monetary values. State Goal 8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results. 1. Represent mathematical patterns and describe their properties using variables and mathematical symbols. 2. Represent algebraic concepts with physical materials, words, diagrams, tables, graphs,, and and use appropriate technology. 3. Use the basic functions of absolute value, square root, linear, quadratic, and step to describe numerical relationships. 4. Analyze and report of the effects of changing coefficients, exponents, and other
MATHEMATICS CURRICULUM ALGEBRA II 6 parameters on functions and their graphs. 5. Apply algebraic properties and procedures with matrices, vectors, functions, and sequences using data found in business, industry, and consumer situations. 6. Formulate and solve linear and quadratic and linear algebraically and investigate nonlinear using graphs, tables, calculators, and computers. State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes, and space. 1. Construct a model of a three-dimensional figure from a two-dimensional pattern. 2. Make perspective drawings, tessellations, and scale drawings, with and without the use of technology. 3. Recognize and apply relationships within and among geometric figures. State Goal 10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. Selected References and Other Materials Textbook: Algebra II and Trigonometry (Houghton Mifflin, 1992) Teaching Resources: Readings: Films and Videotapes: Audiotapes and CDS: Computer Software: Internet Sites: Equipment: Field Trips: Assessment: Algebra II and Trigonometry Teaching Resources (Houghton Mifflin, 1992) Calculators Daily Work Section Quizzes Chapter Tests Semester Exams