Math Course: Algebra II Grade 10


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1 MATH 401 Algebra II 1/2 credit 5 times per week (1 st Semester) Taught in English Math Course: Algebra II Grade 10 This is a required class for all 10 th grade students in the Mexican and/or U.S. Diploma program. Major content areas in the class include properties of real numbers, solving equations in one variable, solving inequalities and absolute value problems, graphs of linear equations, slope, solving systems of equations and linear inequalities, properties of polynomials and operations involving polynomials, and factoring polynomials, word and application problems are emphasized throughout the course. Textbook: Bellman, Allan E., Algebra 2. Prentice/Hall: Upper Saddle River, NJ (2007 Edition) Prerequisite: MATH 300 MAT 402 Algebra II 1/2 credit 5 times per week (2 nd Semester) Taught in English This is a required class for all 10 th grade students in the Mexican and/or U.S. diploma program. Major content areas in the class include using laws of exponents, operations using rational expressions, solving fractional equations, properties of radicals, simplifying radicals, real and complex numbers, solving quadratic equations, graphing quadratic equations, direct and inverse variation, operations involving polynomial equations, and solving polynomial Textbook: Bellman, Allan E., Algebra 2. Prentice/Hall: Upper Saddle River, NJ (2004 Edition). Prerequisite: MATH 401 Subject: Algebra II = AII Strand 1: Matrices Strand 2: Quadratic Equations and Functions Strand 3: Polynomials and Polynomial Functions Strand 4: Radical Functions and Rational Exponents Strand 5: Exponential and Logarithmic Functions Strand 6: Rational Functions Strand 7: Sequences and Series Subject.Grade.Strand#.Standard#. # Example: AII Algebra 2, Grade 10, Strand 1, Standard 1, 3 Strand 1: Matrices Standard 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 AII The student will use a graphing calculator to perform operations with matrices and find variables. AII The student will perform scalar multiplication on a matrix and solve matrices for determinants and inverses.
2 AII The student will solve problems using matrix logic. AII The student will add, subtract, and multiply matrices. AII The student will evaluate the determinant of a 3 x 3 matrix. AII The student will find the inverse of a 2 x 2 matrix. AII The student will solve systems of linear equations by using inverse matrices. AII The student will solve systems of linear equations by using augmented matrices. AII The student will use a graphing calculator to solve systems of linear Strand 2: Quadratic Equations and Functions Standard 1: The student graphs quadratic functions, solves quadratic equations, solves problems using the guessandcheck strategy, and analyzes graphs of quadratic functions and inequalities. AII The student will use a graphing calculator to graph and solve quadratic AII The student will write functions in quadratic form, graph, and solve by graphing. AII The student will solve problems by using the guessandcheck strategy. AII AII AII AII AII AII AII AII The student will solve quadratic equations by factoring, completing the square, and by using the quadratic formula. The student will use discriminants to determine the nature of the roots of quadratic The student will find the sum and product of the roots of quadratic The student will find a quadratic equation to fit a given condition. The student will use a graphing calculator to graph and explore similarities between parabolas. The student will determine the equation of a parabola by using points on its graph. The student will use a graphing calculator to graph and solve quadratic inequalities. The student will graph quadratic inequalities and solve inequalities in one variable. AII The student will solve nonquadratic equations by using quadratic techniques. Strand 3: Polynomials and Polynomial Functions Standard 1: The student simplifies expressions containing polynomials, factors polynomials; and solves problems by identifying and achieving subgoals, evaluates polynomial functions, and identifies general shapes of the graphs of polynomial AII The student will multiply and divide monomials. AII The student will represent numbers in scientific notation and multiply and
3 AII AII AII AII AII AII AII AII AII AII AII AII divide expressions written in scientific notation. The student will add, subtract, and multiply polynomials; divide using long division. The student will divide polynomials by binomials using synthetic division. The student will factor polynomials and simplify polynomial quotients by factoring. The student will solve problems by identifying and achieving subgoals. The student will evaluate polynomial functions and identify general shapes of the graphs of polynomial The student will find factors of polynomials by using the factor theorem and synthetic division. The student will use a graphing calculator to graph polynomial functions and approximate the real zeros of the The student will find the number and type of zeros of a polynomial function. The student will identify all possible rational zeros of a polynomial function by using the rational zero theorem. The student will find zeros of polynomial The student will solve nonquadratic The student will find the composition of AII The student will graph the iterations of a function. Strand 4: Radical Functions and Rational Exponents Standard 1: The student simplifies expressions containing radicals, complex numbers, or rational exponents, and solves equations containing radicals. AII The student will simplify radicals having various indices. AII AII AII AII AII AII AII AII AII AII The student will use a calculator to estimate roots of numbers. The student will simplify radical expressions and add, subtract, multiply, and divide radical expressions The student will rationalize the denominator of a fraction containing a radical expression. The student will write expressions with radical exponents in simplest radical form and vice versa. The student will evaluate expressions in either exponential or radical form. 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 imaginary solutions The student will add, subtract, and multiply complex numbers. The student will simplify rational expressions containing complex numbers in the denominator.
4 AII The student will determine the inverse of a function or relation. AII The student will graph functions and their inverses. AII The student will work backward to solve problems. AII The student will graph and analyze square root functions and graph square root inequalities. Strand 5: Exponential and Logarithmic Functions Standard 1: The student simplifies expressions and solves equations involving real exponents, writes exponential equations in logarithmic form and vice versa, evaluates expressions and solves equations involving logarithms, finds common and natural logarithms and antilogarithms, and solves equations with variable exponents by using logarithms. AII The student will use a graphing calculator to draw graphs of exponential AII The student will simplify expressions and solve equations and inequalities involving real exponents. AII The student will use a graphing calculator to fit a curve to a scatter plot of realworld data. AII AII AII AII AII AII AII AII AII The student will write exponential equations in logarithmic form and vice versa. The student will evaluate logarithmic expressions. The student will solve equations and inequalities involving logarithmic The student will simplify and evaluate expressions using properties of logarithms. The student will solve equations involving logarithms. The student will identify the characteristic and the mantissa of a logarithm. 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 using logarithms. AII The student will use logarithms to solve problems involving growth and decay. Strand 6: Rational Functions Standard 1: The student graphs rational functions, solve problems involving direct, inverse, and joint variation, simplify rational expressions, solve rational equations and solve problems by organizing data. AII The student will use a graphing calculator to explore graphs of rational AII AII The student will graph rational The student will solve problems involving direct, inverse, and joint variation.
5 AII AII The student will simplify rational expressions. The student will simplify complex fractions. The student will find the least common denominator of two or more algebraic expressions. AII The student will add and subtract rational expressions. AII The student will solve rational equations inequalities. Strand 7: Sequences and Series Standard 1: The student is introduced to arithmetic and geometric sequences, and arithmetic and geometric series. AII The student will identify and generate arithmetic sequences and geometric sequences. AII AII The student will evaluate arithmetic series and geometric series. The student will use rectangles to approximate the area under a curve.
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