How are the properties of real numbers and the order of operations used to simplify an expression and/or solve an algebraic equation or inequality?

Transcription

1 Topic: Algebra I Review Key Learning: Review Algebraic concepts of single-variable expressions and equations using the order of operations, sets of real numbers and the properties of real numbers. How are the properties of real numbers and the order of operations used to simplify an expression and/or solve an algebraic equation or inequality? Order of Operations Properties of Real Numbers Solve and Graph 1- Variable Equations and Inequalities What is the purpose of the order of How do you differentiate between the operations? subsets of real numbers? How do you use the order of operations? How do you use t he properties of real numbers to simplify algebraic expressions and solve algebraic equations? How do you solve and graph onevariable equations and inequalities? Solve and Graph Compound Inequalities (inc. Abs. Val.) How do you solve and graph onevariable, compound inequalities? How do you solve and graph onevariable, absolute value equations and inequalities? compound inequality, extraneous solution

2 Topic: Linear Functions, Inequalities and Graphs Key Learning: Linear equations are used to show patterns and make predictions. Graphs are used to represent solutions to equations and inequalities. How can a pattern or graph be used to identify solutions to an equation or inequality? Relations and Functions Graphing Linear Equations Graphing Linear Inequalities How do you distinguish between a What is the process for graphing lines function and a relation? from slope-intercept form? How can functions be identified from a set of ordered pairs and/or a graph? How are intercepts used to graph lines? How are vertical lines and horizontal lines graphed? How do solutions to linear equations in two variables differ from solutions to linear inequalities in two variables? How are linear inequalities in two variables graphed? How can linear inequalities be used to solve real-life problems? relation, function, domain, range, slope-intercept form, standard form, x- linear inequality in two variables, vertical line test intercept, y-intercept boundary line, solution, half-plane Lines of Best fit How do you write the equation of the line of best fit? What does the line of best fit represent and how can its equation be used? line of best fit, prediction equation

3 Topic: Linear Systems of Equations/Inequalities Key Learning: Solve systems of equations and inequalities using various methods. Systems of equations can be used in real-world applications. How is a solution to a system of equations found? What does the solution to a system of equations represent? Solve Systems of Linear Equations in 2 Variables Solving Systems of Inequalities in 2 Variables Linear Programming How do you find the solution to a How do you solve a system of linear How are the vertices of the feasible system of equations graphically? inequalities? region found? How are systems solved algebraically (substitution / elimination)? What are the three possible situations for solutions to a system of equations and what does each indicate about the lines? How does the solution to a system of linear inequalities differ from the solution to a system of linear equations? How are vertices used to optimize the objective function? systems of linear equations, substitution, elimination, consistent, inconsistent system of linear inequalities linear programming, feasible region, vertices, constraints, objective function Solving Systems of Equations in 3 Variables What does an equation in three variables represent? How is elimination used to solve a system with three variables? ordered triple, system in three variables

4 Topic: Quadratic Functions, Inequalities and Graphs Key Learning: Quadratic functions represent a family of curves with real or complex solutions. Quadratic equations can be solved using a variety of techniques. How do you solve a quadratic equation? What do the solutions of a quadratic equation represent? How do you find the maximum or minimum a quadratic equation? Simplifying Quadratic and Radical Expressions Graphing Quadratic Functions Solving Quadratic Equations What are the steps used to factor a How is the Zero-Product Property used quadratic expression? to solve quadratic equations? How do we simplify a radical? What is the shape and basic properties of the graph of a quadratic function? What steps must be taken to graph a quadratic function given in vertex form? How do we graph a quadratic function in standard form? How do you solve a quadratic equation by completing the square? How do you solve a quadratic equation using the quadratic formula? How is the discriminant used to determine the number and types of solutions of a quadratic equation? How do you decide which method to use to solve a quadratic equation? (ET) parabola, vertex of a parabola, axis of symmetry, standard form, vertex form Zero-Product Property, Completing the Square, Quadratic Formula, discriminant Solving Quadratic Applications (Max/Min) How do we find the vertex of a quadratic function? How is the concept of minimum or maximum values used in real world problems? (ET) minimum, maximum

5 Topic: Radical Functions and Rational Exponents Key Learning: Properties of rational exponents can be used to simplify and solve radical equations. How can the properties of rational exponents be used to simplify and solve radical equations? Rational Exponents Operations with Radical Expressions Solving Radical Equations What is teh relationship between How do we multiply and divide radical How are inverse operations used to radical form and exponent form? expressions? solve radical equations? How do you use the properties of exponents to simplify expressions with rational exponents? How do you rationalize a denominator? How do you add and subtract radical expressions? How do we multiply binomial expressions containing radicals? How are rational exponents used to solve radical equations? rational exponent rationalize the denominator, like radical equation radicals

6 Topic: Rational Expessions and Equations Key Learning: Properties of ratios and proportions can be used to simplify and solve rational expressions and equations, including inverse variation. How are rational expressions and equations simplified and solved? Operations on Rational Expressions Solving Rational Equations Inverse Variation How do you add, subtract, multiply, divide, and simplify rational expressions? What process is used solve rational equations? What does it mean to 'vary inversly'? How do you simplify a complex fraction? How do you graph inverse variations? rational expression, complex fraction, extraneous solution inverse variation restrictions on domain

7 Topic: Polynomials Key Learning: The Fundamental Theorem of Algebra leads to the conclusisons that polynomial equations of degree n have exactly n complex solutions. Given an nth degree polynomial equation, how can the number, types, and values of solutions be determined? Classifying Polynomials Operations on Polynomials Graphing Higher Degree Polynomials How are polynomials classified by How can synthetic division be used to degree? factor higher order polynomials? How does the degree relate to the number of solutions? How can basic algebra rules be used to simplfy polynomials? How are the solutions to a polynomial equation utilized in graphing the polynomial? How are maximum and minimum values of a polynomial equation utilized in graphing the polynomial? degree/order, Fundamental Theorem synthetic division minimum/maximum, zero of the of Algebra function

8 Topic: Probability Key Learning: Simple probability, compound propbability, and odds can be used to determine the likelihood an event will occur. How can simple probability, compound propbability, and odds be used to determine the likelihood an event will occur? Calculating and Comparing Probability and Odds Calculating Compound Probability Permutations and Combinations How do we use probability to predict How do you decide when to use a outcomes? permutation or a combination? What is the difference between the probability and odds of an outcome? How is the Counting Principle used in determining the number of outcomes? How can we calculate probabilities for independent, dependent or compound events? How can you represent probabilites in multiple forms? How do you calculate permutations and combinations? counting principle independent, dependent, compound combination, permutation events

9 Topic: Exponential and Logarithmic Functions Key Learning: Logarithmic and exponential functions can be used to model real-life applications. How can L\logarithmic and exponential functions be used to model real-life applications. Simplifying Exponentials and Logarithms Graphing Exponentials and Logarithms Solving Exponential and Logarithmic Equations How are the properties of exponents What are the characteristics of the used to evaluate expressions? graphs of exponential functions? How are the properties of logarithms used to evaluate expressions? How are the graphs of exponential and logarithmic functions related? What are some methods for solving exponential and logarithmic equations? How does the change of base formula help to solve exponential equations? exponential function, logarithmic asymptote change of base function, common log, natural log Applications of Exponentials and Logarithms How do exponential growth and decay functions differ from each other? What real life applications can be modeled by exponential functions? (ET)