Catholic Central High School

Transcription

1 Catholic Central High School Course: Basic Algebra 2 Department: Mathematics Length: One year Credit: 1 Prerequisite: Completion of Basic Algebra 1 or Algebra 1, Basic Plane Geometry or Plane Geometry, and Departmental Permission Textbook: McKeague, Charles; Intermediate Algebra; Thomson Brooks/Cole Course Goals and Objectives: Basic Algebra 2 covers the same topics and concepts as those taught in Algebra 2. The concepts are the same as those required by the State of Michigan for an Algebra 2 course. Basic Algebra 2 classes are smaller to allow the students more individual attention. Students successfully completing Basic Algebra 2 have the opportunity to select College Algebra, Precalculus, and/or Probability and Statistics the following year. Course Description: First Semester: Basic Properties and Definitions: Fundamental Definitions and Notation: Comparison Symbols: Less than/less than or equal to Not less than/not less than or equal to Greater than/greater than or equal to Not greater than/not greater than or equal to Equivalent to Order of Operations: Simplify numbers with exponents within each expression, working from left to right if more than one expression. Perform any multiplication and/or division working from left to right

2 Perform any addition and/or subtraction, working from left to right Operations with Sets: Union of two sets Intersection of two sets Real Numbers: Graph simple and compound inequalities Translate sentences and phrases written in English into inequalities List the elements in subsets of real numbers Factor positive integers into the product of primes Reduce fractions to lowest terms Properties of Real Numbers: Finding the opposite of a real number Multiply fractions Simplify absolute value expressions Recognize and apply the properties of real numbers Add and subtract fractions Simplify algebraic expressions Arithmetic Operations with Real Numbers: Add and subtract real numbers Multiply and divide real numbers Apply the rules for order of operations Simplify algebraic expressions Divide fractions Find the value of an expression Arithmetic, Geometric and Fibonacci Sequences: Recognize a pattern in a sequence of numbers Extend an arithmetic sequence Extend a geometric sequence Recognize and extend a Fibonacci sequence Equations and Inequalities with One Variable: Linear Equations with One Variable: Solve a linear equation with one variable

3 Formulas: Solve a formula with numerical replacements for all but one of the variables Solve formulas for the indicated variable Solve percent problems by translating them into equations Applications (Percent, Area, Investment Story Problems): Apply problem solving strategies to a variety of application problems Use a formula to construct a table of paired data Linear Inequalities with One Variable: Solve a linear inequality in one variable and graph the solution set Solve a compound inequality and graph the solution set Write solutions to inequalities using interval notation Solve application problems using inequalities Absolute Value Equations: Solve equations with absolute value symbols Absolute Value Inequalities: Solve inequalities with absolute value and graph the solution set Equations and Inequalities with Two Variables: Paired Data and the Rectangular Coordinate System: Graph ordered pairs on a rectangular coordinate system Graph linear equations by finding intercepts or making a table Graph horizontal and vertical lines Slope of a Line: Find the slope of a line given its graph Find the slope of a line given two points on the line Equation of a Line (Slope-Intercept Form, Standard Form, Point-Slope Form): Find the equation of a line given the slope and y intercept Find the slope and y intercept given the equation of the line

4 Find the equation of a line given the slope and a point on the line Find the equation of a line given two points on the line Linear Inequalities with Two Variables: Graph linear inequalities in two variables Introduction to Functions: Construct a table or graph from a function rule Identify the domain and range of a function or relation Determine whether a relation is also a function Function Notation: Use function notation to find the value of a function for a given value of the variable Algebra and Composition with Functions: Find the sum, difference, product and quotient of two functions Find the composition of two functions Variation (Direct, Inverse and Joint): Set up and solve problems with direct, inverse and joint variation Systems of Linear Equations and Inequalities: Systems of Equations with Two Variables: Solve systems of linear equations in two variables by graphing Solve systems of linear equations in two variables by the addition method Solve systems of linear equations in two variables by the substitution method Systems of Equations with Three Variables: Solve systems of equations in three variables Introduction to Matrices: Adding and subtracting matrices Multiplying matrices Introduction to Determinants: Find the value of a 2 x 2 determinant

5 Find the value of a 3 x 3 determinant Cramer s Rule: Solve a system of linear equations in two variables using Cramer s rule Solve a system of linear equations in three variables using Cramer s rule Applications (Story Problems with Two or More Variables): Solve application problems whose solutions are found through systems of linear equations Graphing Systems of Linear Inequalities: Graph the solution to a system of linear inequalities in two variables Exponents and Polynomials: Properties of Exponents: Simplify expressions using the properties of exponents Convert back and forth between scientific notation and expanded form Multiply and divide expressions written in scientific notation Polynomials Sums and Differences: Give the degree of the polynomial Add and subtract polynomials Evaluate a polynomial for a given value of its variable Multiplication of Polynomials: Multiply polynomials Finding Greatest Common Factor and Factoring by Grouping: Factor by factoring out the greatest common factor Factor by grouping Factoring Trinomials: Factor trinomials in which the lead coefficient is 1 Factor trinomials in which the lead coefficient is not 1

6 Special Factoring (Difference of Squares, Perfect Square Trinomials, Cubic Polynomials): Factor perfect square trinomials Factor the difference of squares Factor the sum or difference of two cubes Solving Equations by Factoring: Solving equations by factoring Apply problem solving strategies to solve application problems whose solutions involve quadratic equations Solve problems that contain formulas that are quadratic Rational Expressions and Rational Functions: Basic Properties and Reducing to Lowest Terms: Reduce rational expressions to lowest terms Find function values for rational functions Work with ratios Division of Polynomials and Difference Quotients: Divide a polynomial by a monomial Divide a polynomial by a polynomial Multiplication and Division of Rational Expressions: Multiply and divide rational expressions Addition and Subtraction of Rational Expressions: Add and subtract rational expressions with a common denominator Add and subtract rational expressions with unlike Denominators Complex Fractions: Simplify complex fractions Solving Rational Equations: Solve equations containing rational expressions Solve formulas containing rational expressions Applications Involving Rational Expressions/Equations: Solve application problems using equations containing

7 rational expressions Solve conversion problems using unit analysis Second Semester: Rational Exponents and Roots: Rational Exponents: Simplify radical expressions using definition for roots Simplify expressions with rational exponents Expressions Involving Rational Exponents: Multiply expressions with rational exponents Divide expressions with rational exponents Factor expressions with rational exponents Add and subtract expressions with rational exponents Simplifying Radicals: Write radical expressions in simplified form Rationalize a denominator that contains only one term Addition and Subtraction of Radical Expressions: Add and subtract radicals Multiplication and Division of Radical Expressions (Including Rationalizing the Denominator): Multiply expressions containing radicals Rationalize a denominator containing two terms Radical Equations: Solve equations containing radicals Graph simple square root and cube root equations in two variables Complex Numbers (Simplify, Add, Subtract, Multiply, Divide): Simplify square roots of negative numbers Simplify powers of i Solve for unknown variables by equating the real parts and equating the imaginary parts of two complex numbers Add and subtract complex numbers

8 Multiply complex numbers Divide complex numbers Quadratic Functions: Completing the Square: Solving quadratic equations by taking the square root of both sides Solve quadratic equations by completing the square Use quadratic equations to solve for missing parts of right triangles Quadratic Formula: Solve quadratic equations by using the Quadratic Formula Solve application problems using quadratic equations Additional Items Involving Solutions to Equations (Using the Discriminant, Writing Quadratic Equations Given the Roots): Find the number and kind of solutions to a quadratic equation by using the discriminant Find an unknown constant in a quadratic equation so there is exactly one solution Find an equation from its solutions Equations in Quadratic Form: Solve equations that are reducible to a quadratic equation Solve application problems using equations in quadratic form Graphing Parabolas: Graph a parabola Solve application problems using information on a graph Find an equation from its graph Quadratic Inequalities: Solve quadratic inequalities and graph the solution set Exponential and Logarithmic Functions: Exponential Functions: Find function values for exponential functions Graph exponential functions

9 Work problems involving exponential growth and decay The Inverse of a Function: Find the equation of the inverse of a function Sketch the graph of a function and its inverse Logarithms: Convert between logarithmic form and exponential form Use the definition of logarithms to solve logarithmic equations Sketch the graph of a logarithmic function Simplify expressions using logarithms Properties of Logarithms: Use the properties of logarithms to convert between expanded form and single logarithms Use the properties of logarithms to solve logarithmic equations Common Logarithms and Natural Logarithms: Use a calculator to find common logarithms Use a calculator to find a number given its common logarithm Simplify expressions containing natural logarithms Exponential Equations and Change of Base Formula: Solve exponential equations Use change-of-base property Solve application problems whose solutions are found by solving logarithmic or exponential equations Conic Sections: Circles: Use the distance formula Write the equation of a circle given its center and radius Find the center and radius of a circle from its equation, then sketch its graph Ellipses and Hyperbolas: Graph an ellipse Graph a hyperbola Second Degree Inequalities and Nonlinear Systems:

10 Graph second degree inequalities Solve systems of nonlinear equations Graph the solution sets to systems of inequalities Sequences and Series: Sequences: Use a formula to find the terms of a sequence Use a recursive formula Find the general term of a sequence Series: Expand and simplify an expression written with summation notation Write a series using summation notation Arithmetic Sequences: Find the common difference for an arithmetic sequence Find the general term of an arithmetic sequence Find the sum of the first n terms of an arithmetic sequence Geometric Sequences: Find the common ratio for a geometric sequence Find the nth term of a geometric sequence Find the general term for a geometric sequence Find the sum of the first n terms of a geometric sequence Find the sum of all terms of an infinite geometric sequence Binomial Expansion and Pascal s Triangle: Calculate binomial coefficients Use the binomial formula to expand binomial powers Find a particular term of a binomial expansion Combinations: Factorial Use the formula for combinations to solve application problems Permutations: Use the formula for permutations to solve application problems

11 Trigonometry: Probability: Sample space Experimental and theoretical probability Solving application problems involving probability Statistics: Measures of Central Tendency Standard deviation Trigonometric Ratios: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent Trigonometric Graphs, Equations: Graphing trigonometric functions Graphing inverse trigonometric functions Trigonometric Identities Solving trigonometric equations and functions Finding zeros of a trigonometric function Extraneous solutions Using identities to solve a trigonometric equation Course Assignments: Homework is assigned nightly and checked the next day. Tests and quizzes are given periodically throughout the quarter. A comprehensive semester examination is given at the end of each semester.