Math Course: Algebra II Grade 10
Math Course: Algebra II Grade 10
Math Course: Algebra II Grade 10
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MATH 401 <strong>Algebra</strong> <strong>II</strong>1/2 credit5 times per week (1 st Semester)Taught in English<strong>Math</strong><strong>Course</strong>: <strong>Algebra</strong> <strong>II</strong><strong>Grade</strong> <strong>10</strong>This is a required class for all <strong>10</strong> th grade students in the Mexican and/or U.S. Diploma program. Major content areas in theclass include properties of real numbers, solving equations in one variable, solving inequalities and absolute valueproblems, graphs of linear equations, slope, solving systems of equations and linear inequalities, properties of polynomialsand operations involving polynomials, and factoring polynomials, word and application problems are emphasizedthroughout the course.Textbook: Bellman, Allan E., <strong>Algebra</strong> 2. Prentice/Hall: Upper Saddle River, NJ(2007 Edition)Prerequisite: MATH 300MAT 402 <strong>Algebra</strong> <strong>II</strong>1/2 credit5 times per week (2 nd Semester)Taught in EnglishThis is a required class for all <strong>10</strong> th grade students in the Mexican and/or U.S. diploma program. Major content areas in theclass include using laws of exponents, operations using rational expressions, solving fractional equations, properties ofradicals, simplifying radicals, real and complex numbers, solving quadratic equations, graphing quadratic equations, directand inverse variation, operations involving polynomial equations, and solving polynomial equations.Textbook: Bellman, Allan E., <strong>Algebra</strong> 2. Prentice/Hall: Upper Saddle River, NJ(2004 Edition).Prerequisite: MATH 401Benchmark Code – Subject: <strong>Algebra</strong> <strong>II</strong> = A<strong>II</strong>Strand 1: MatricesStrand 2: Quadratic Equations and FunctionsStrand 3: Polynomials and Polynomial FunctionsStrand 4: Radical Functions and Rational ExponentsStrand 5: Exponential and Logarithmic FunctionsStrand 6: Rational FunctionsStrand 7: Sequences and SeriesSubject.<strong>Grade</strong>.Strand#.Standard#. Benchmark#Example: A<strong>II</strong>.<strong>10</strong>.1.1.3 – <strong>Algebra</strong> 2, <strong>Grade</strong> <strong>10</strong>, Strand 1, Standard 1, Benchmark 3Strand 1: MatricesStandard 1: The student creates matrices to represent data, solves problems by using matrix logic,performs operations with matrices, uses matrices to achieve transformations of geometric figures,and uses matrices to solve systems of equations.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.1.1.1 The student will use a graphing calculator to perform operations withmatrices and find variables.A<strong>II</strong>.<strong>10</strong>.1.1.2 The student will perform scalar multiplication on a matrix and solvematrices for determinants and inverses.Revised May 2012
A<strong>II</strong>.<strong>10</strong>.1.1.3 The student will solve problems using matrix logic.A<strong>II</strong>.<strong>10</strong>.1.1.4 The student will add, subtract, and multiply matrices.A<strong>II</strong>.<strong>10</strong>.1.1.5 The student will evaluate the determinant of a 3 x 3 matrix.A<strong>II</strong>.<strong>10</strong>.1.1.6 The student will find the inverse of a 2 x 2 matrix.A<strong>II</strong>.<strong>10</strong>.1.1.7 The student will solve systems of linear equations by using inversematrices.A<strong>II</strong>.<strong>10</strong>.1.1.8 The student will solve systems of linear equations by using augmentedmatrices.A<strong>II</strong>.<strong>10</strong>.1.1.9 The student will use a graphing calculator to solve systems of linearequations.Strand 2: Quadratic Equations and FunctionsStandard 1: The student graphs quadratic functions, solves quadratic equations, solves problemsusing the guess-and-check strategy, and analyzes graphs of quadratic functions and inequalities.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.2.1.1 The student will use a graphing calculator to graph and solve quadraticequations.A<strong>II</strong>.<strong>10</strong>.2.1.2 The student will write functions in quadratic form, graph, and solve bygraphing.A<strong>II</strong>.<strong>10</strong>.2.1.3 The student will solve problems by using the guess-and-check strategy.A<strong>II</strong>.<strong>10</strong>.2.1.4A<strong>II</strong>.<strong>10</strong>.2.1.5A<strong>II</strong>.<strong>10</strong>.2.1.6A<strong>II</strong>.<strong>10</strong>.2.1.7A<strong>II</strong>.<strong>10</strong>.2.1.8A<strong>II</strong>.<strong>10</strong>.2.1.9A<strong>II</strong>.<strong>10</strong>.2.1.<strong>10</strong>A<strong>II</strong>.<strong>10</strong>.2.1.11Revised May 2012The student will solve quadratic equations by factoring, completing thesquare, and by using the quadratic formula.The student will use discriminants to determine the nature of the roots ofquadratic equations.The student will find the sum and product of the roots of quadraticequations.The student will find a quadratic equation to fit a given condition.The student will use a graphing calculator to graph and exploresimilarities between parabolas.The student will determine the equation of a parabola by using points onits graph.The student will use a graphing calculator to graph and solve quadraticinequalities.The student will graph quadratic inequalities and solve inequalities in onevariable.A<strong>II</strong>.<strong>10</strong>.2.1.12 The student will solve non-quadratic equations by using quadratictechniques.Strand 3: Polynomials and Polynomial FunctionsStandard 1: The student simplifies expressions containing polynomials, factors polynomials; andsolves problems by identifying and achieving sub-goals, evaluates polynomial functions, andidentifies general shapes of the graphs of polynomial functions.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.3.1.1 The student will multiply and divide monomials.A<strong>II</strong>.<strong>10</strong>.3.1.2The student will represent numbers in scientific notation and multiply and
A<strong>II</strong>.<strong>10</strong>.3.1.3A<strong>II</strong>.<strong>10</strong>.3.1.4A<strong>II</strong>.<strong>10</strong>.3.1.5A<strong>II</strong>.<strong>10</strong>.3.1.6A<strong>II</strong>.<strong>10</strong>.3.1.7A<strong>II</strong>.<strong>10</strong>.3.1.8A<strong>II</strong>.<strong>10</strong>.3.1.9A<strong>II</strong>.<strong>10</strong>.3.1.<strong>10</strong>A<strong>II</strong>.<strong>10</strong>.3.1.11A<strong>II</strong>.<strong>10</strong>.3.1.12A<strong>II</strong>.<strong>10</strong>.3.1.13A<strong>II</strong>.<strong>10</strong>.3.1.14Revised May 2012divide expressions written in scientific notation.The student will add, subtract, and multiply polynomials; divide usinglong division.The student will divide polynomials by binomials using syntheticdivision.The student will factor polynomials and simplify polynomial quotients byfactoring.The student will solve problems by identifying and achieving sub-goals.The student will evaluate polynomial functions and identify generalshapes of the graphs of polynomial functions.The student will find factors of polynomials by using the factor theoremand synthetic division.The student will use a graphing calculator to graph polynomial functionsand approximate the real zeros of the functions.The student will find the number and type of zeros of a polynomialfunction.The student will identify all possible rational zeros of a polynomialfunction by using the rational zero theorem.The student will find zeros of polynomial functions.The student will solve non-quadratic equations.The student will find the composition of functions.A<strong>II</strong>.<strong>10</strong>.3.1.15 The student will graph the iterations of a function.Strand 4: Radical Functions and Rational ExponentsStandard 1: The student simplifies expressions containing radicals, complex numbers, or rationalexponents, and solves equations containing radicals.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.4.1.1 The student will simplify radicals having various indices.A<strong>II</strong>.<strong>10</strong>.4.1.2A<strong>II</strong>.<strong>10</strong>.4.1.3A<strong>II</strong>.<strong>10</strong>.4.1.4A<strong>II</strong>.<strong>10</strong>.4.1.5A<strong>II</strong>.<strong>10</strong>.4.1.6A<strong>II</strong>.<strong>10</strong>.4.1.7A<strong>II</strong>.<strong>10</strong>.4.1.8A<strong>II</strong>.<strong>10</strong>.4.1.9A<strong>II</strong>.<strong>10</strong>.4.1.<strong>10</strong>A<strong>II</strong>.<strong>10</strong>.4.1.11The student will use a calculator to estimate roots of numbers.The student will simplify radical expressions and add, subtract, multiply,and divide radical expressionsThe student will rationalize the denominator of a fraction containing aradical expression.The student will write expressions with radical exponents in simplestradical form and vice versa.The student will evaluate expressions in either exponential or radicalform.The student will solve equations containing radicals.The student will simplify square roots containing negative radicands.The student will solve quadratic equations that have pure imaginarysolutionsThe student will add, subtract, and multiply complex numbers.The student will simplify rational expressions containing complexnumbers in the denominator.
A<strong>II</strong>.<strong>10</strong>.4.1.12Revised May 2012The student will determine the inverse of a function or relation.A<strong>II</strong>.<strong>10</strong>.4.1.13 The student will graph functions and their inverses.A<strong>II</strong>.<strong>10</strong>.4.1.14 The student will work backward to solve problems.A<strong>II</strong>.<strong>10</strong>.4.1.15 The student will graph and analyze square root functions and graphsquare root inequalities.Strand 5: Exponential and Logarithmic FunctionsStandard 1: The student simplifies expressions and solves equations involving real exponents, writesexponential equations in logarithmic form and vice versa, evaluates expressions and solves equationsinvolving logarithms, finds common and natural logarithms and antilogarithms, and solves equationswith variable exponents by using logarithms.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.5.1.1 The student will use a graphing calculator to draw graphs of exponentialfunctions.A<strong>II</strong>.<strong>10</strong>.5.1.2 The student will simplify expressions and solve equations and inequalitiesinvolving real exponents.A<strong>II</strong>.<strong>10</strong>.5.1.3 The student will use a graphing calculator to fit a curve to a scatter plot ofreal-world data.A<strong>II</strong>.<strong>10</strong>.5.1.4A<strong>II</strong>.<strong>10</strong>.5.1.5A<strong>II</strong>.<strong>10</strong>.5.1.6A<strong>II</strong>.<strong>10</strong>.5.1.7A<strong>II</strong>.<strong>10</strong>.5.1.8A<strong>II</strong>.<strong>10</strong>.5.1.9A<strong>II</strong>.<strong>10</strong>.5.1.<strong>10</strong>A<strong>II</strong>.<strong>10</strong>.5.1.11A<strong>II</strong>.<strong>10</strong>.5.1.12The student will write exponential equations in logarithmic form and viceversa.The student will evaluate logarithmic expressions.The student will solve equations and inequalities involving logarithmicfunctions.The student will simplify and evaluate expressions using properties oflogarithms.The student will solve equations involving logarithms.The student will identify the characteristic and the mantissa of alogarithm.The student will find common logarithms and antilogarithms.The student will find natural logarithms of numbers.The student will solve equations with variable exponents by usinglogarithms.A<strong>II</strong>.<strong>10</strong>.5.1.13 The student will use logarithms to solve problems involving growth anddecay.Strand 6: Rational FunctionsStandard 1: The student graphs rational functions, solve problems involving direct, inverse, andjoint variation, simplify rational expressions, solve rational equations and solve problems byorganizing data.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.6.1.1 The student will use a graphing calculator to explore graphs of rationalfunctions.A<strong>II</strong>.<strong>10</strong>.6.1.2A<strong>II</strong>.<strong>10</strong>.6.1.3The student will graph rational functions.The student will solve problems involving direct, inverse, and jointvariation.
A<strong>II</strong>.<strong>10</strong>.6.1.4A<strong>II</strong>.<strong>10</strong>.6.1.5The student will simplify rational expressions. The student will simplifycomplex fractions.The student will find the least common denominator of two or morealgebraic expressions.A<strong>II</strong>.<strong>10</strong>.6.1.6 The student will add and subtract rational expressions.A<strong>II</strong>.<strong>10</strong>.6.1.7 The student will solve rational equations inequalities.Strand 7: Sequences and SeriesStandard 1: The student is introduced to arithmetic and geometric sequences, and arithmetic andgeometric series.Benchmark CodeBenchmarkA<strong>II</strong>.<strong>10</strong>.7.1.1 The student will identify and generate arithmetic sequences andgeometric sequences.A<strong>II</strong>.<strong>10</strong>.7.1.2A<strong>II</strong>.<strong>10</strong>.7.1.3The student will evaluate arithmetic series and geometric series.The student will use rectangles to approximate the area under a curve.Revised May 2012
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