Benchmark
A.1.1. Students use properties of operations on real numbers to simplify and evaluate numerical and algebraic expressions.
Indicators
1. Know, understand, and apply the properties of real numbers including commutative, associative, identity, inverse, distributive, closure, reflexive, symmetric, and transitive properties.
2. Compare and contrast multiple one-variable data sets, using statistical techniques including measures of central tendency, range, and box-and-whisker plots. (A.17)
3. Represent verbal quantitative expressions as algebraic expressions. (A.2)
4. Evaluate algebraic expressions for a given replacement set. (A.2)
5. Justify the steps in simplifying and evaluating algebraic expressions by using concrete objects, pictorial representations, and the properties of operations on real numbers. (A.3)
6. Evaluate and simplify absolute value expressions.
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Benchmark
A.2.1. Students solve multistep linear equations and inequalities in one variable and use linear equations and inequalities to solve practical problems.
Indicators
1. Solve multistep linear equations in one variable. (A.1)
2. Solve practical problems by using a linear equation in one variable. (A.1)
3. Justify the steps in solving equations by using concrete objects, pictorial representations, and the properties of operations on real numbers. (A.3)
4. Solve absolute value equations in one variable algebraically.
5. Solve multistep linear inequalities in one variable. (A.1)
6. Justify the steps in solving inequalities by using concrete objects, pictorial representations, and the properties of operations on real numbers. (A.3)
7. Determine whether a given solution satisfies an equation or an inequality by using substitution and a graphing calculator. (A.1)
8. Solve literal equations, including formulas, for a specified variable. (A.1)
9. Graph the solution to a linear inequality. (A.1)
10. Write solution sets for inequalities in set notation and interval notation.
11. Solve compound inequalities involving conjunction and disjunction.
12. Solve practical problems, including scientific relationships, by using literal equations. (A.1)
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Benchmark
A.3.1. Students solve systems of linear equations and inequalities in two and three variables and use systems of equations to solve practical problems.
Indicators
1. Solve a system of linear equations algebraically using substitution or elimination techniques. (A.9)
2. Solve a system of linear equations graphically, including the use of a graphing calculator. (A.9)
3. Determine whether a given solution satisfies a system of equations using substitution and a graphing calculator.
4. Determine if a system of linear equations has one solution, no solutions, or infinitely many solutions.
5. Interpret and determine the reasonableness of the solution of a system in practical problems.
6. Solve practical problems by using systems of linear equations. (A.9)
7. Use matrices to organize and manipulate data, including matrix addition, subtraction, and scalar multiplication. (A.4)
8. Multiply matrices manually and with a graphing calculator.
9. Solve practical problems including business, industrial, and consumer situations by applying matrix techniques. (A.4)
10. Solve systems of equations using matrices on a graphing calculator.
11. Solve a system of three or more linear equations with the use of a graphing calculator.
12. Solve systems of inequalities graphically.
13. Apply linear programming techniques to graphically solve practical problems.
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Benchmark
A.4.1. Students select, justify, and apply appropriate techniques to graph and determine the equations of linear functions, absolute functions, and linear inequalities in two variables.
Indicators
1. Describe slope as a constant rate of change. (A.7)
2. Recognize and describe a line with a slope that is positive, negative, zero, or undefined. (A.7)
3. Determine the slope of a line when given the coordinates of two points on the line, the equation of the line, or the graph of the line. (A.7)
4. Investigate the effects of changes in the slope of the graph of a line using a graphing calculator. (A.7)
5. Describe the relationship between slopes of parallel lines.
6. Describe the relationship between slopes of perpendicular lines.
7. Recognize and describe the effects that changes in the equation have on the graph of a linear function by using the line 
as a reference. (A.6, A.7)
8. Recognize and describe the effects that changes in the equation have on the graph of an absolute value function by using 
as a reference.
9. Select, justify, and apply an appropriate technique to graph linear functions and linear inequalities in two variables. Techniques will include using the slope and intercept; x- and y-intercepts; graphing by transformations; and the graphing calculator. (A.6)
10. Compare the slopes and y-intercepts of graphs of linear functions using a graphing calculator.
11. Write the equation of a line when given the coordinates of two points on the line; the slope and the y-intercept of the line; the slope and any point on the line; one point on a vertical line; one point on a horizontal line; or the graph of the line. (A.8)
12. Write the equation of a line in slope-intercept form, point-slope form, and standard form with integral coefficients.
13. Determine the equation of a linear function from a table of values using the method of finite differences.
14. Interpret the meaning of slope in practical problems and use the slope to make predictions.
15. Write an equation for a line of best-fit for data that is linear by using regression techniques on a graphing calculator. (A.16)
16. Make predictions about unknown outcomes by using the equation of the line of best-fit. (A.16)
17. Determine whether a direct variation exists in a relation and, if possible, represent it algebraically and graphically. (A.18)
18. Identify the domain and range of a linear relation when given a set of ordered pairs, a table, a mapping, or a graph. (A.5)
19. Write a linear function using function notation, such as f(x).
20. Determine if a linear relation is a function by examining a set of ordered pairs, a table, a mapping, or a graph. (A.5)
21. Analyze tables, graphs, or other representations of a set of data to determine if a pattern exists. (A.5)
22. Find f(x) for each value of x, when given a rule or a graph of a function. (A.15)
23. Identify the zeros of a function using algebra and a graph. (A.15)
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Benchmark
A.5.1. Students perform operations with polynomials using concrete objects, pictorial representations, and algebraic manipulations.
Indicators
1. Identify the base, exponent, and coefficient of a monomial.
2. Recognize polynomials and classify them according to the number of terms they have or by the degree of the polynomial.
3. Discover the laws of exponents by examining patterns and apply the laws of exponents while performing operations on expressions with integral exponents, using scientific notation when appropriate. (A.10)
4. Simplify expressions with fractional exponents by applying the laws of exponents.
5. Estimate the square root of a number to the nearest tenth. (A.13)
6. Write the square root of an expression in simplest radical form by applying the product property. (A.13)
7. Simplify a radical by rationalizing the denominator or by using conjugates.
8. Add, subtract, and multiply polynomials using concrete objects, pictorials, area representations, and algebraic manipulation. (A.11)
9. Divide polynomials by monomial and binomial divisors, including the use of long division. (A.11)
10. Add, subtract, multiply, and divide numbers written in scientific notation. (A.10)
11. Factor completely first- and second-degree binomials and trinomials in one or two variables. (A.12)
12. Identify quadratic expressions that cannot be factored over the set of real numbers by determining the discriminant.
13. Factor polynomials that are the difference of cubes or the sum of cubes.
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Benchmark
A.6.1. Students solve non-linear equations and functions in one variable both algebraically and graphically and solve practical problems using non-linear functions.
Indicators
1. Determine the equation of a quadratic or cubic function from the table of values using the method of finite differences.
2. Factor and solve quadratic equations by completing the square.
3. Derive the quadratic formula using the completing-the-square method.
4. Determine the number of solutions to a quadratic equation using the discriminant or a graph of the function.
5. Solve quadratic equations by graphing the equation and finding the x-intercepts of the graph. (A.14)
6. Solve quadratic equations algebraically by factoring (zero product property) or by using the quadratic formula. (A.14)
7. Determine whether a given solution satisfies a quadratic equation by using substitution or graphing.
8. Solve practical problems by using quadratic equations.
9. Graph quadratic equations that arise from a variety of practical problems.
10. Recognize and describe the effects that changes to the equation have on the graph of a quadratic function by using 
as a reference.
11. Determine the domain and range of a quadratic function. (A.15)
12. Derive the distance formula from the Pythagorean Theorem.
13. Recognize and describe the effects of transformations on the graphs and equations of higher degree polynomials including cubic, quartic, and exponential functions, by using a graphing calculator.
14. Write an equation for a line of best-fit for data that is quadratic, cubic, quartic, or exponential using regression techniques on the graphing calculator.
15. Graph an inverse variation function from a table of values.
16. Determine whether a direct variation exists in a non-linear function and represent it algebraically and graphically, if possible.
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