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Algebra Objectives I. Basics of Algebra The student will be able to: 1. Add, subtract, multiply, and divide positive and negative numbers, including rational numbers. (This might be evaluating a numeric expression or evaluating an algebraic expression with exponents.) 2. Write algebraic expressions. 3. Use the distributive property, add like terms, and simplify expressions with parentheses. 4. Solve equations. (Specific types of equations are listed in the Step by Step Review.) II. Fundamentals of Applied Algebra The student will be able to: 5. Solve percent problems. 6. Use the Solve an Equation problem-solving strategy to solve problems. 7. Given real world information involving rates, solve problems. That is, answer questions involving rates. Specific techniques for solving rate problems include: (a) Finding rates (by dividing), (b) Setting up a proportion, (c) Multiplying rates and amounts, (d) Multiplying rates to get a rate, (e) Dividing rates or using the reciprocal of a rate, (f) Using a combination of the above. 8. Generate examples of rates from real-world contexts and generate example word problems from real-world contexts. III. Algebraic Modeling The student will be able to: 9. Given real world information and a formula, evaluate. 10. Determine inputs and outputs of a function from an equation (“formula”), table, graph, or words. 11. Given real world information, in words, create a model. That is, create a model which includes 3 parts: (a) definition of the input variable, (b) definition of the output variable, (c) equation (function) relating the two variables. 12. Find maximum and minimum values of a function (using trace and table). 13. Find rate of change from a formula or table. 14. Find initial and limiting values of a function. 15. Given two points, find the slope of the line through the points. 16. Use a model to answer questions. Including: a. Interpret the slope. b. Interpret the y-intercept. c. Find and interpret the x-intercept(s). d. Given an output (y) value, find the input (x) value. 17. Given real world information, create a linear model [with 3 parts as above]. 18. Use regression to create a linear model [with 3 parts as above] from data. 19. Given real world information, create an exponential model [with 3 parts as above]. 20. Use regression to create an exponential model from data. Terms Evaluate (an algebraic expression) Exponential growth Evaluate (a function) Exponential model Solve Rate of change Integers Slope Rational numbers y-intercept Irrational numbers Initial value (of a function) Linear growth Limiting value (of a function) Linear model