ALGEBRA IICOURSE DESCRIPTION: This second-year algebra course commences by reviewing the objectives introduced in the first-year algebra course. These topics are further enhanced and expanded to include more complicated topics. The real number system is expanded to include complex numbers and other important algebraic topics such as conic sections and logarithms are introduced. The course concludes with basic trigonometry to assist the student in the transition into next year’s trigonometry or Algebra III courses. The Ti-83 Plus graphing calculator will be used throughout the course. Project work will also be incorporated - usually one project each semester will be assigned.
COURSE OBJECTIVES: To review and extend the concepts of algebra from a first-year algebra course. The topics that are covered will be extremely helpful in understanding further mathematics and scientific concepts. The student is taught more methods for solving problems and is given a broad understanding of the usefulness of mathematics in many different areas of life by solving a variety of application problems. The course also prepares a student for trigonometry and third-year algebra courses and subsequent college mathematics courses.
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Chapter |
Competencies |
Assessment |
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Chapter 1 Equations and Inequalities |
At the end of the chapter, the student will be able to use a number line to graph and order real numbers, identify properties of and use operations with real numbers, evaluate algebraic expressions, simplify algebraic expressions by combining like terms, solve linear equations, use linear equations to solve real-life problems, rewrite equations with more than one variable, rewrite common formulas, use a general problem solving plan to solve real-life problems, use other problem solving strategies to solve real-life problems, solve simple inequalities, solve compound inequalities, solve absolute value equations and inequalities, and use absolute value equations and inequalities to solve real-life problems. |
Homework Class discussion Quizzes Tests |
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Chapter 2 Linear Equations and Functions |
At the end of this chapter, the student will be able to represent relations and functions, graph and evaluate linear functions find slopes of lines and classify parallel and perpendicular lines, use slope to solve real-life problems, use the slope-intercept form of a linear equation to graph linear equations, use the standard form of a linear equation to graph linear equations, write linear equations, write direct variation equations, use a scatter plot to identify the correlation shown by a set of data, approximate the best-fitting line for set of data, graph linear inequalities in two variables, use linear inequalities to solve real-life problems, represent piecewise functions, use piecewise functions to model real-life quantities, represent absolute value functions, use absolute value functions to model real-life situations. involving the absolute value function (both graphically and algebraically). The techniques used to solve inequalities are displayed both symbolically and in a word problem context. |
Homework Class discussion Quizzes Tests |
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Chapter 3 Systems of Linear Equations and Inequalities
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At the end of this chapter, the student will be able to graph and solve systems of linear equations in two variables, use linear systems to solve real-life problems, use algebraic methods to solve linear systems, use linear systems to model real-life situations, graph a system of linear inequalities to find the solutions of the system, use systems of linear inequalities to solve real-life problems, solve linear programming problems, use linear programming to solve real-life problems, graph linear equations in three variables and evaluate linear functions of two variables, use functions of two variables to model real-life situations, solve systems of linear equations in three variables, and use linear systems in three variables to model real-life situations. |
Homework Class discussion Quizzes Tests
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Chapter 4 Matrices and Determinants
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At the end of this chapter, the student will be able to add and subtract matrices, multiply a matrix by a scalar, and solve matrix equations, use matrices in real-life situations, multiply two matrices, use matrix multiplication in real-life situations, evaluate determinants of 2 × 2 and 3 × 3 matrices, use Cramer's rule to solve systems of linear equations, find and use inverse matrices, use inverse matrices in real-life situations, solve systems of linear equations using inverse matrices, and use systems of linear equations to solve real-life problems. |
Homework Class discussion Quizzes Tests
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Chapter 5 Quadratic Functions
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At the end of this chapter, the student will be able to graph quadratic functions, use quadratic functions to solve real-life problems, factor quadratic expressions and solve quadratic equations by factoring, find zeros of quadratic functions, solve quadratic equations by finding square roots, use quadratic equations to solve real-life problems, solve quadratic equations with complex solutions and perform operations with complex numbers, apply complex numbers to fractal geometry, solve quadratic equations by completing the square, use completing the square to write quadratic functions in vertex form, solve quadratic equations using the quadratic formula, use the quadratic formula in real-life situations, graph quadratic inequalities in two variables, solve quadratic inequalities in one variable, write quadratic functions given characteristics of their graphs, and use technology to find quadratic models for data. |
Homework Class discussion Quizzes Tests
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Chapter 6 Polynomials and Polynomial Functions
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At the end of this chapter, the student will be able to use properties of exponents to evaluate and simplify express-ions involving powers, use exponents and scientific notation to solve real-life problems, evaluate a polynomial function, graph a polynomial function, add, subtract, and multiply polynomials, use polynomial operations in real-life problems, factor polynomial expressions, use factoring to solve polynomial equations, divide polynomials and relate the result to the remainder theorem and the factor theorem, use polynomial division in real-life problems, find the rational zeros of polynomial function, use polynomial equations to solve real-life problems, use the fundamental theorem of algebra to determine the number of zeros of a polynomial function, use technology to approximate the real zeros of a polynomial function, analyzing Graphs of Polynomial Functions, analyze the graph of a polynomial function, use the graph of a polynomial function to answer questions about real-life situations, use finite differences to determine the degree of a polynomial function that will fit a set of data, and use technology to find polynomial models for real-life data. |
Homework Class discussion Quizzes Tests
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Chapter 7 Powers, Roots, and Radicals
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At the end of this chapter, the student will be able to evaluate nth roots of real numbers using both radical notation and rational exponent notation, use nth roots to solve real-life problems, use properties of rational exponents to evaluate and simplify expressions, use properties of rational exponents to solve real-life problems, perform operations with functions including power functions, use power functions and function operations to solve real-life problems, find inverses of linear functions, find inverses of nonlinear functions, graph square root and cube root functions, use square root and cube root functions to find real-life quantities, solve equations that contain radicals or rational exponents, use radical equations to solve real-life problems, use measures of central tendency and measures of dispersion to describe data sets, and use box-and-whisker plots and histograms to represent data graphically. |
Homework Class discussion Quizzes Tests
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Chapter 8 Exponential and Logarithmic Functions |
At the end of this chapter, the student will be able to graph exponential growth functions, use exponential growth functions to model real-life situations, graph exponential decay functions, use exponential decay functions to model real-life situations, use the number e as the base of exponential functions, use the natural base e in real-life situations, evaluate logarithmic functions, graph logarithmic functions, use properties of logarithms, use properties of logarithms to solve real-life problems, solve exponential equations, solve logarithmic equations, model data with exponential functions, model data with power functions, evaluate and graph logistic growth functions, and use logistic growth functions to model real-life situations. |
Homework Class discussion Quizzes Tests |
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Chapter 9 Rational Equations and Functions |
At the end of this chapter, the student will be able to write and use inverse variation models, Write and use joint variation models, graph simple rational functions, use the graph of a rational function to solve real-life problems, graph general rational functions, use the graph of a rational function to solve real-life problems, multiply and divide rational expressions, use rational expressions to model real-life quantities, add and subtract rational expressions, simplify complex fractions, solve rational equations, and use rational equations to solve real-life problems. |
Homework Class discussion Quizzes Tests |
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Chapter 10 Quadratic Relations and Conic Sections |
At the end of this chapter, the student will be able to find the distance between two points and find the midpoint of the line segment joining two points, use the distance and midpoint formulas in real-life situations, graph and write equations of parabolas, use parabolas to solve real-life problems, graph and write equations of circles, use circles to solve real-life problems, graph and write equations of ellipses, use ellipses in real-life situations, graph and write equations of hyperbolas, use hyperbolas to solve real-life problems, write and graph an equation of a parabola with its vertex at (h, k) and an equation of a circle, ellipse, or hyperbola with its center at (h, k), classify a conic using its equation, solve systems of quadratic equations, and use quadratic systems to solve real-life problems. |
Homework Class discussion Quizzes Tests |
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Chapter 11 Sequences and Series |
At the end of this chapter, the student will be able to use and write sequences, use summation notation to write series and find sums of series, write rules for arithmetic sequences and find sums of arithmetic series, use arithmetic sequences and series in real-life problems, write rules for geometric sequences and find sums of geometric series, use geometric sequences and series to model real-life quantities, find sums of infinite geometric series, use infinite geometric series as models of real-life situations, evaluate and write recursive rules for sequences, and use recursive rules to solve real-life problems, |
Homework Class discussion Quizzes Tests |
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Chapter 12 Probability and Statistics |
At the end of this chapter, the student will be able to use the fundamental counting principle to count the number of ways an event can happen, use permutations to count the number of ways an event can happen, use combinations to count the number of ways an event can happen, use the binomial theorem to expand a binomial that is raised to a power, find theoretical and experimental probabilities, find geometric probabilities, find probabilities of unions and intersections of two events, use complements to find the probability of an event, find the probability of independent events, find the probability of dependent events, calculate probabilities using normal distributions, and use normal distributions to approximate binomial distributions. |
Homework Class discussion Quizzes Tests |
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Chapter 13 Trigonometric Ratios and Functions |
At the end of this chapter, the student will be able to use trigonometric relationships to evaluate trigonometric functions of acute angles, use trigonometric functions to solve real-life problems, measure angles in standard position using degree measure and radian measure, calculate arc lengths and areas of sectors, evaluate trigonometric functions of any angle, use trigonometric functions to solve real-life problems, evaluate inverse trigonometric functions, use inverse trigonometric functions to solve real-life problems, use the Law of Sines to find the sides and angles of a triangle, find the area of any triangle, use parametric equations to represent motion in a plane, and use parametric equations to represent projectile motion. |
Homework Class discussion Quizzes Tests |
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Chapter 14 Trigonometric Graphs, Identities, and Equations |
At the end of this chapter, the student will be able to graph sine and cosine functions, graph tangent functions, graph translations and reflections of sine and cosine graphs, graph translations and reflections of tangent graphs, use trigonometric identities to simplify trigonometric expressions and to verify other identities, use trigonometric identities to solve real-life problems, solve a trigonometric equation, solve real-life trigonometric equations, model data with a sine or cosine function, use technology to write a trigonometric model, evaluate trigonometric functions of the sum or difference of two angles, use sum and difference formulas to solve real-life problems, evaluate expressions using double- and half-angle formulas, and use double- and half-angle formulas to solve real-life problem. |
Homework Class discussion Quizzes Tests |
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Mr. Nakamoto's Homepage Mathematics Department Homepage