ESSENTIALS OF ALGEBRA II

ESSENTIALS OF ALGEBRA II Grades 11-12 Draft: January 2003 Killingly Public Schools

Essentials of Algebra II Grades 11-12 Mathematical Models and Matrices CONTENT STANDARD 11-12 EAII 1: The student will gain experience in organize data into mathematical models, using the models to analyze the data, and in extending the range of the data to make predications. The student is able to find patterns in real-world data and 11-12EAII 1.1 learn to model the data mathematically. 1.1.1 -graphs a relationship between two sets of data, identifies any trend, and describes any association. 1.1.2 -expresses the relationship between two variables in an equation. 1.1.3 -recognizes and uses function notation and the general properties of functions (domain and range). 11-12EAII 1.2 The student is able to calculate probabilities from theory, experiments, and simulations. 1.2.1 -recognizes and finds two distinct methods of measuring the probability of an event (theoretical and experimental). 1.2.2 -uses and conducts simulations as a method for estimating probability. The student is able to transfer real-world data into 11-12EAII 1.3 matrix models and understand and apply the properties of additive and multiplicative operations. 1.3.1 -translates data into matrices. 1.3.2 -demonstrates matrix addition and scalar multiplication. 1.3.3 -extends the use of matrices to include their products.

Linear Functions, Equations, and Inequalities CONTENT STANDARD 11-12 EAII 2: The student will extend their knowledge and expertise in working with linear functions, equations, and inequalities. The student understands how to interpret linear models and 11-12EAII 2.1 graphs to make predictions. 2.1.1 -uses rate of change to recognize linear functions and understands direct variation and slope. 2.1.2 -integrates an understanding of slope and y-intercept with linear graphs and form of linear equations. The student is able to extend their methods of locating 11-12EAII 2.2 a trend line from visual observation to finding lines of best fit. 2.2.1 -writes and uses the equation of a trend line to make predictions. 2.2.2 -finds a line of best fit mathematically (median-median line). 2.2.3 -finds a line of best fit graphically (using linear regression calculators). The student is able to use their knowledge of 11-12EAII 2.3 properties of equalities and their graphs to support their exploration of inequalities and absolute value functions. 2.3.1 -interprets, solves, and graphs one-variable inequalities. 2.3.2 -interprets, solves, and graphs absolute value equations and inequalities. 2.3.3 -graphs and solves linear and absolute value inequalities in two variables.

Systems of Linear Equations and Inequalities CONTENT STANDARD 11-12 EAII 3: The student will gain experience solving systems of equations by various methods and transfer that knowledge to solving systems of linear inequalities. The student is able to solve systems of equations in 11-12EAII 3.1 various ways. 3.1.1 -solves linear systems by graphing. 3.1.2 -solves linear systems algebraically using substitution and linear combinations. 3.1.3 -solves linear systems by using inverse matrices. 3.1.4 -solves 3 x 3 systems using calculator. The student understands the connection between solving 11-12EAII 3.2 linear equations and systems and solving linear inequalities and systems. 3.2.1 -solves systems of linear inequalities. 3.2.2 -sees how real-world constraints of a linear programming problem can be modeled by systems of inequalities. 3.2.3 -solves linear programming problems.

Algebraic Structures CONTENT STANDARD 11-12EAII 4: The student will explore the complex number system. The student understands the field structure of the real and 11-12EAII 4.1 complex number systems and is able to operate on complex numbers. 4.1.1 -investigates the mathematical structure of fields (field properties). 4.1.2 -simplifies square root expressions and classifies their values (rational/irrational). 4.1.3 -defines and uses imaginary and complex numbers. 4.1.4 -performs basic operations on imaginary numbers.

Quadratic Functions and Equations CONTENT STANDARD 11-12 EAII 5: The student will explore quadratic functions and quadratic equations. The student understands the characteristics of a quadratic 9-11-12EAII 5.1 function. 5.1.1 -investigates the parabola and its characteristics. 5.1.2 -determines the affect a has on the graph: f(x)=ax 2. 5.1.3 -uses translations to identify features and sketches graphs of quadratic functions. 11-12EAII 5.2 The student is able to solve quadratic equations. 5.2.1 -solves quadratic equations by graphing, and finds the number of real roots. 5.2.2 -solves quadratic equations by factoring. 5.2.3 -solves quadratic equations by using the quadratic formula. 5.2.4 -classifies the number of solutions by use of the discriminant. The student understands how quadratics are related to the 11-12EAII 5.3 real world. 5.3.1 -explores real-world problems which are modeled by quadratic equations.

Roots and Powers CONTENT STANDARD 11-12 EAII 6: The student will explore properties of exponents and powers. The student is able to recognize and apply the 11-12EAII 6.1 properties of exponents. 6.1.1 -simplifies expressions with exponents using the following properties: product of powers power of powers power of products quotient of powers power of quotients zero and integer powers 6.1.2 -writes standard numbers in scientific notation form (and vise versa). The student is able to evaluate and simplify 11-12EAII 6.2 expressions with radicals and rational exponents. 6.2.1 -uses rational-number powers and explores the relationship between radicals and exponents. 6.2.2 -evaluates expressions containing real-number exponents. 6.2.3 -solves simple radical equations. 6.2.4 -solves equations containing two or more radical expressions.

Combining Functions CONTENT STANDARD 11-12 EAII 7: The student will explore properties of functions. 11-12EAII 7.1 The student is able to combine functions. 7.1.1 -adds, subtracts, and multiplies functions. 7.1.2 -composes functions. 7.1.3 -uses composite functions in real-world situations. 11-12EAII 7.2 The student understands inverse relations and functions. 7.2.1 -identifies inverse functions and relations. 7.2.2 -finds the inverse of functions.

Polynomials and Polynomial Functions CONTENT STANDARD 11-12 EAII 8: The student will work with polynomial functions and their graphs, polynomial equations, and rational expressions. The student understands the graphs of polynomials of 11-12EAII 8.1 varying degrees. 8.1.1 -explores the graphs of polynomial functions using the T1-82. 8.1.2 -finds the zeros and maximum/minimum of graphs. The student is able to use factoring and graphing to 11-12EAII 8.2 solve polynomial equations. 8.2.1 -uses the graph of a polynomial equation to solve and understand the nature of its solution. 8.2.2 -solves polynomial equations by dividing and factoring polynomials. 11-12EAII 8.3 The student is able to simplify rational expressions. 8.3.1 -writes, evaluates, multiplies, divides, and simplifies rational expressions. 8.3.2 -simplifies sums/differences of rational expressions. 8.3.3 -solves equations involving rational expressions.

Exponential and Logarithmic Functions CONTENT STANDARD 11-12 EAII 9: The student will explore basic exponential and logarithmic functions. The student is able to identify the characteristics of 11-12EAII 9.1 and work with exponential functions. 9.1.1 -identifies exponential functions. 9.1.2 -graphs exponential functions. 9.1.3 -uses exponential functions to model exponential growth and decay. The student is able to identify the characteristics of and 11-12EAII 9.2 work with logarithmic functions. 9.2.1 -understands the inverse relationship between exponential and logarithmic functions. 9.2.2 -uses logarithms to solve exponential equations. 9.2.3 -uses properties of logarithms.