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Cardinal Team I Math - Algebra
Text: Algebra: Tools for a Changing World, Prentice Hall, c. 1998
The curriculum is in line with the standards established by the National Council of Teachers of Mathematics as found in Principles and Standards for School Mathematics, 2000. It also meets the criteria of the Essential Academic Learning Requirements (EALRs) of the state of Washington. This syllabus is not in the order of the 10 NCTM standards or the 5 EALRs, but in the order in which the topics are presented during the year.
- Tools of Algebra
displaying data relationships with line plots, multiple line, bar graphs
modeling relationships with variables
evaluating expressions with order of operations, 4 operations, integers
identifying, defining rational, real numbers, reciprocals
finding experimental probabilities, conducting a simulation with random numbers
organizing data in matrices, adding, subtracting matrices
using properties of numbers to simplify variable expressions
- Functions and Their Graphs
using scatter plots to analyze positive, negative, no correlation in data
linking graphs, tables, equations of functions and relations
defining functions, writing function rules correct function notation
identifying from graphs families of functions: linear,quadratic,absolute value
looking at the outcome of an event as impossible, certain, complement
- Algebraic Concepts and Simple Equation
modeling, solving 1- and 2-step equations with +, --, x, / properties of equality
combining like terms, using the distributive property to solve equations with rationals
writing and solving percent equations
writing equations for dependent events and solving
- Equations and Inequalities
using proportions in scale drawings, similar geometric figures and cross-multiplying
solving equations with variables in both members
solving absolute value equations transforming formula, solving for a different variable
solving multi-step inequalities and graphing the solutions
solving compound inequalities with "and", "or" and graphing solutions
- Graphing and Writing Linear Equations
finding slope of a line, of a set of data as rate of change
identifying and writing an equation for direct variation
finding the equation of a line in slope-intercept form from a graph, graphing from same
writing the equation of a line from slope and intercept, slope and a point, two points
writing an equation for a line of best fit from a scatter plot
identifying parallel, perpendicular lines from their equations
graphing from x-intercept and slope or x- and y-intercepts
- Systems of Equations and Inequalities
solving systems of 2 equations in 2 unknowns using graphing, substitution, elimination
identifying inconsistent equations, consistent (independent or dependent) equations
writing and solving systems of equations for real life situations
graphing linear inequalities and solving systems of linear inequalities graphically
investigating simple linear programming for optimization
solving systems of non-linear equations and verifying algebraically
- Quadratic Equations and Functions
defining, exploring, and graphing with tables of values quadratic functions
solving quadratic equations by formula
using the discriminant to determine the number of real solutions for a quadratic equation.
- Exponents and Exponential Functions
exploring uses of exponential functions
modeling exponential functions with exponential growth, decay, compound interest
applying negative and zero exponents, especially in Scientific Notation computations
applying the laws of exponents: multiplying, dividing powers, raising powers to a power
- Right Triangles and Radical Expressions
deriving and using the distance formula for 2 points in the plane (Pythagorean Theorem)
defining and using the trigonometric ratios tangent, sine, cosine in simple applications
simplifying, adding/subtracting like radicals
solving radical equations, checking for extraneous roots
graphing square root functions
analyzing data using standard deviation by hand and using a scientific calculator
- Polynomials
defining, categorizing, adding and subtracting polynomials
multiplying polynomials by monomials and monomial factoring
multiplying binomials and polynomials
factoring trinomials with tiles, FOIL, guess and test, special cases (difference of squares)
solving quadratic equations by graphing, square roots, completing the square, factoring, or formula
- Rational Expressions and Functions
identifying and graphing inverse variation functions
graphing rational functions with tables of values, finding asymptotes
determining the domain and range for rational functions
performing operation with rational expressions: +, --, x, / using factoring
solving rational equations
counting outcomes (counting principle), permutation, combinations
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