Secondary Honors Algebra II Objectives


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1 Secondary Honors Algebra II Objectives Chapter 1 Equations and Inequalities Students will learn to evaluate and simplify numerical and algebraic expressions, to solve linear and absolute value equations and inequalities, to use algebra to model and solve real life problems. Solve Linear equations and inequalities. Solve absolute value equations. Solve compound inequalities; including absolute value inequalities. Graph the solution sets of compound inequalities. Multiply polynomial expressions. Chapter 2 Linear Equations and Functions Students will learn to graph and write equations for linear equations and inequalities in 2 variables, and absolute value functions. Use patterns, relations, and functions to represent mathematical situations. Compare and contrast relations and functions. Identify the domain and range of the absolute value, quadratic, and radical functions. Use function notation. Find the vertex and axis of symmetry of an absolute value function algebraically and graphically. Specify locations and describe spatial relationships using coordinate geometry Graph quadratic, polynomial, square and cube root, and absolute value functions. Transform the graphs of linear, absolute value, quadratic, and radical functions by stretching, shifting, and reflecting. Graphing piecewise and step functions. Chapter 3 Systems of Linear Equations and Inequalities Students will learn how to solve linear systems of 2 or 3 variables by graphing and algebraic methods and how to write and use linear systems to solve real life problems. and symbols. Solve systems of equations with three variables. Solve real world problems using the methods for systems of 2 and 3 linear equations. Solve problems using visualization, spatial reasoning, and geometric modeling. Use linear programming to solve real life problems. Chapter 4 Matrices and Determinants Students will add, subtract, and multiply matrices. Students will evaluate 2 nd and 3 rd order determinants. Students will solve linear systems using Cramer s Rule and inverse matrices. Evaluate 2nd and 3rd order determinants.
2 Use patterns, relations, and functions to represent mathematical situations. Perform arithmetic operations on matrices. Solve systems of equations using Cramer s Rule. Solve systems of equations using matrix equations. Chapter 5 Quadratic Functions Students will learn to factor quadratic polynomials. Students will learn the complex number system and the rules for working in it. Students will learn 4 methods for solving quadratic equations and how to graph quadratic functions and inequalities. Represent complex numbers in a variety of ways. Extend the number system to include complex numbers in a + bi form. Identify the use for the square root of a negative number and define the imaginary unit. Simplify square roots, including those containing negative radicands. Add, subtract, multiply, divide, and raise complex numbers to a power. Solve quadratic equations by factoring, the Quadratic Formula, and completing the square. Solve radical equations, including those with extraneous solutions. Solve singlevariable quadratic inequalities. Solve quadratic inequalities in 2 variables. Write a quadratic equation when given the rational roots or zeros of the function. Solve real world problems with the methods for solving quadratic equations. Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of a quadratic function algebraically and graphically. Apply the steps of factoring. Factor a quadratic trinomial with a leading coefficient. Factor using multiple steps. Graph quadratic functions. Graph quadratic inequalities in 2 variables. Write the equations of functions given the graph or information about the graph. Chapter 6 Polynomial Function Students will learn to perform operations on polynomials. Students will learn to evaluate, graph, and find the zeros of polynomial functions. Simplify numerical expressions with exponents of any degree. Multiply polynomial expressions with any number of terms. Divide polynomial expressions using synthetic and long division.
3 Find the zeros of a polynomial function. Solve polynomial equations by factoring. Recognize that negative exponents mean reciprocals. Use synthetic substitution to evaluate polynomial functions. Apply the steps of factoring. Factor a sum or difference of cubes. Factor by grouping. Factor using multiple steps. Factor polynomials of 3rd, 4th, or 5th degree. Graph polynomial functions. Chapter 7 Powers, Roots, and Radicals Students will learn how to use rational exponents and nth roots of numbers, how to perform operations with and find inverses of functions, and how to graph radical functions and solve radical equations. Represent complex numbers in a variety of ways. Simplify radical expressions of any index. Simplify using rational exponents. Use patterns, relations, and functions to represent mathematical situations. Find the inverse of a function by interchanging the values of domain and range, reflecting across the line y = x, or by using algebraic methods. Find the compositions or combinations of two simple functions. Solve radical equations including those with extraneous roots. Recognize that rational exponents are used to represent radicals. Graph square root and cube root functions. Chapter 8 Exponential and Logarithmic Functions Students will learn how to graph and use exponential, logarithmic, and logistic growth functions. Students will learn about the number e and the properties of logarithms. Students will learn to solve exponential and logarithmic equations. Solve real world problems using the methods for solving exponential and logarithmic equations. Understand the relationship between exponents and logarithms. Graph exponential and logarithmic functions. Apply Euler s number and its relationship to logarithms. Use the laws of logarithms to simplify logarithmic expressions and solve logarithmic equations.
4 Convert logarithmic equations into exponential equations and vice versa. Use the laws of exponents to solve exponential equations. Chapter 9 Rational Functions Students will learn how to simplify and perform operations with rational expressions, how to graph rational functions, and how to solve rational equations. Evaluate solve, and analyze mathematical situations using algebraic properties and symbols. Solve rational equations. Graph rational functions. Chapter 10 Conic Sections Students will use the distance and midpoint formulas; classify, graph, and write equations of conics; and solve systems of quadratic equations. Solve systems containing quadratic equations. Write the equations of conic sections in standard form. Graph conic sections. Write the equations of functions when given the graph or information about the graph. Chapter 12 Probability and Statistics Students will learn to compute the number of ways an event can happen, how to calculate and use probabilities, and how to expand binomials. Calculate the number of possible outcomes. Use the fundamental counting principle to compute the number of ways an event may occur. Use permutations to compute the number of ways an event may occur. Use combinations to compute the number of ways an event may occur. Expand a binomial using the Binomial Theorem. Find the probability of an event. Find geometric probabilities. Find probabilities of unions and intersections of 2 events. Use complements to find the probability of events. Find the probability of independent and dependent events. Evaluating series Use sigma notation to express sums. Chapter 13 Trigonometry Students will learn to evaluate trigonometric functions and inverse trigonometric functions and to find side lengths, angle measures, and areas of triangles.
5 Use patterns, relations, and functions to represent mathematical situations. Express angle measure in degrees or radians when given the trigonometric value. Solve real world problems using the methods for right triangle and general trigonometric equations. Calculate the exact values of the sine, cosine, and tangent functions. Evaluate the trig functions for an angle of a right triangle. Evaluate the trig functions for an angle of a or a triangle. Evaluate the trig functions for an angle in standard position. Solve triangles. Solve right triangles. Apply the ratios of and triangles. Work with the units and processes of the measurement of rotational angles. Convert angle measurements between radians and degrees. Calculate the exact values of the sine, cosine, and tangent angles for the special angles of the unit circle. Calculate the exact values of inverse trigonometric functions. Solve simple trigonometric equations. Apply the Law of Sines and the Law of Cosines to solve oblique triangles.
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