Download Secondary Algebra II Objectives

Secondary Algebra II Objectives
Chapter 1- Equations and Inequalities
Students will learn to evaluate and simplify numerical and algebraic expressions
in order to solve linear and absolute value equations and inequalities. Students
will use this understanding of 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.
• Simplify problems using mathematical operations.
• Add, subtract, and multiply monomial 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 functions
• Use function notation.
• Write equations of lines in standard and slope-intercept form.
• Specify locations and describe spatial relationships using coordinate geometry
• Graph linear equations
• Specify locations and describe spatial relationships using coordinate geometry.
• Transforming the graphs of absolute value functions by stretching, shifting, and reflecting.
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.
• Evaluate, solve, and analyze mathematical situations using algebraic properties and
symbols.
• Solve systems of linear equations in two variables algebraically and graphically.
• Solve and graph systems of linear inequalities.
• Evaluate, solve, and analyze mathematical situations using algebraic properties and
symbols.
• Solving systems of equations with three variables.
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.
• Simplify problems using mathematical operations.
• Add, subtract, multiply, and divide complex numbers.
• Raise the imaginary unit to a power.
• Simplify radical expressions of any index.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve quadratic equations by factoring and the quadratic formula.
• Solve radical equations, including those with extraneous solutions.
• Write a quadratic equation when given the rational roots or zeros of the function.
• Represent quantitative relationships using mathematical modals and symbols.
• Solve real world problems using the methods for solving quadratic equations.
• Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of
a quadratic function.
• Apply the steps of factoring.
• Factor a quadratic trinomial with a leading coefficient.
• Factor using multiple steps.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph quadratic functions.
Chapter 6 - Polynomial Functions
Students will learn to perform operations on polynomials. Students will learn to
evaluate, graph, and find the zeros of polynomial functions.
• Simplify problems using mathematical operations.
• Simplify numerical expressions with exponents of any degree.
• Add, subtract, and multiply polynomial expressions with any number of terms.
• Divide polynomial expressions using synthetic division.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• 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 quadratic trinomial with a leading coeffiecient.
• Factor by grouping.
• Factor using multiple steps.
• Factor polynomials of 3rd, 4th, or 5th degree.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph polynomial functions.
• Simplify problems using mathematical operations.
• Finding the zeros of a polynomial function.
Chapter 7 – Powers, Roots & Radicals
Students will learn how to evaluate nth roots of real numbers using both radicals
and exponential notation.
• Simplify problems using mathematical operations.
• Simplify using rational exponents.
• Simplify radical expressions of any index.
• Use patterns, relations, and functions to represent mathematical situations.
• Identify the domain and range of radical functions.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve radical equations, including those with extraneous roots.
• Recognize that rational exponents and radicals can be used to represent each
other.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph square root functions.
• Use patterns, relations, and functions to represent mathematical situations.
• Finding the inverse of a function by interchanging the values of domain and range,
reflecting across the line y = x, or by using algebraic methods.
• Finding the compositions and combinations of two simple 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.
• Understand the relationship between exponents and logarithms.
• Apply Euler’s number and its relationship to logarithms.
• Use the laws of logarithms to simplify logarithmic expressions and solve logarithmic
equations.
• Convert logarithmic equations into exponential equations and vice-versa.
• Use the laws of exponents to solve exponential equations.
• Use patterns, relations, and functions to represent mathematical situations.
• Finding the inverse of a function by interchanging the values of domain and range,
reflecting across the line y = x, or by using algebraic methods.
• Understand the relationship between exponents and logarithms.
• Graphing exponential and logarithmic functions.
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.
• Simplify problems using mathematical operations.
• Simplify rational exponents.
• Use patterns, relations, and functions to represent mathematical situations
• Represent quantitative relationships using direct and inverse variation.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Graph simple rational equations.
• Solve rational equations.
• Specify locations and describe spatial relationships using coordinate geometry.
• 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.
• Represent quantitative relationships using mathematical models and symbols.
• Write the equations of conic sections in standard form.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph conic sections.
• Write the equations of functions when given the graph or information about the
graph.
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.
• Use patterns, relations, and functions to represent mathematical situations.
• Express angle measure in degrees or radians when given the trigonometric value.
• Represent quantitative relationships using mathematical models and symbols.
• 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 the angle of a right triangle.
• Evaluate the trig functions for the angle of a 45-45-90 or a 30-60-90 triangle.
• Evaluate the trig functions for an angle in standard position.
• Solve triangles.
• Solve right triangles.
• Apply the ratios of 45-45-90and 30-60-90 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, in degrees, of the unit circle.
• Calculate the inverse trigonometric functions with a calculator.
• Solve trigonometric equations.
• Apply the Law of Sines and the Law of Cosines to solve oblique triangles.