Algebraic Expressions and Equations

1. Simplify algebraic expressions using the distributive, commutative, and associative properties
2. Evaluate algebraic expressions
3. Translate phrases and sentences into algebraic expressions and equations, and vice versa
4. Distinguish between factors and terms
5. Distinguish between evaluating expressions, simplifying expressions, and solving equations

1. identify linear equations and inequalities in one variable.
2. Use the definition of a solution to an equation or inequality to check if a given value is a solution.
3. Solve linear equations and non-compound linear inequalities symbolically.
4. Express inequality solution sets graphically and with interval notation.
5. Create and solve linear equations and inequalities in one variable that model real life situations
   
   1. Properly define variables; include units in variable definitions
   2. State contextual conclusions using complete sentences
   3. Use estimation to determine reasonableness of solutions
6. Solve an equation for a specified variable in terms of other variables
7. Solve applications in which two values are unknown but their total is known; for example, a 10-foot board cut into two pieces of where one piece is 2.5 feet longer than the other piece

1. Plot points on the Cartesian coordinate system, including pairs of values from a table.
2. Determine coordinates of points by reading a Cartesian graph.
3. Create a table of values from an equation or application. Make a plot from the table. When appropriate, correctly identify the independent variable with the horizontal axis and the dependent variable with the vertical axis.
4. Classify points by quadrant or as points on an axis; identify the origin
5. Label and scale axes on all graphs
6. Create graphs where the axes are required to have different scales (e.g. -10 to 10 on the horizontal axis and -1000 to 1000 on the vertical axis).
7. Interpret graphs, intercepts and other points in the context of an application. Express intercepts as ordered pairs.
8. Create tables and graphs with labels that communicate the context of an application problem and its dependent and independent quantities

1. Write and interpret a slope as a rate of change in context (include the unit of the slope)
2. Find the slope of a line from a graph, from two points, and from a table of values.
3. Find the slope from all forms of a linear equation.
4. Given the graph of a line, identify the slope as positive, negative, zero, or undefined. Given two non-vertical lines, identify the line with greater slope.

1. Identify a linear equation in two variables
2. Manipulate a linear equation into slope-intercept form; identify the slope and the vertical intercept given a linear equation
3. Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
4. Write the equation of a line in slope-intercept form
5. Write the equation of a line in point-slope form

1. Graph a line with a known point and slope.
2. Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
3. Given a linear equation, find at least three ordered pairs that satisfy the equation and graph the line using those ordered pairs.
4. Given an equation in slope-intercept, plot its graph using the slope and vertical intercept
5. Given an equation in point-slope, plot its graph using the slope and the suggested point
6. Given an equation in standard form, plot its graph by calculating horizontal and vertical intercepts, and check with a third point
7. Given an equation for a vertical or horizontal line, plot its graph.
8. Create and graph a linear model based on data and make predictions based upon the model

1. Solve and check systems of equations using the following methods: graphically, using the substitution method, and using the addition/elimination method
2. Create and solve real-world models involving systems of linear equations in two variables
3. Properly define variables; include units in variable definitions.
4. State contextual conclusions using complete sentences
5. Given the equations of two lines, classify them as parallel, perpendicular, or neither

1. Develop exponent rules including for negative exponents and apply them when helpful in algebraic manipulations
2. Add, subtract, multiply and square polynomials
3. Divide polynomials by a monomial
4. Convert between scientific notation and standard form to demonstrate an understanding of magnitude
5. Perform multiplication and division operations in scientific notation in context

1. Evaluate \(n\)th roots numerically with and without technology
2. Recognize that an even root of a negative number is not real
3. Convert radical expressions to expressions with rational exponents and vice versa
4. Simplify, add, subtract, multiply and divide radical expressions
5. Use rational exponents to simplify radical expressions (e.g. \(\sqrt[3]{x^8}\), \(\sqrt{x}\cdot\sqrt[3]{x}\))
6. Rationalize denominators with square roots in them (e.g. \(\frac{5}{\sqrt{2}}\), \(\frac{5}{1+\sqrt{2}}\))
7. Use a calculator to approximate radicals using rational exponents
8. [This item may end up in MTH 95] Add, subtract, and multiply complex numbers and write the result in \(a+bi\) form

1. Solve quadratic equations using the square root property
2. Solve quadratic equations using the quadratic formula including complex solutions
3. [This item may end up in MTH 95] Solve quadratic equations by completing the square
4. Solve radical equations that have a single radical term
5. Verify solutions algebraically and graphically, noting when extraneous solutions may result
6. Solve a formula for a specific variable
7. Solve linear, quadratic, and radical equations when mixed up in a problem set
8. Solve real-world models involving quadratic and radical equations

1. Algebraically find the vertex (using the formula \(x=-\frac{b}{2a}\)), the axis of symmetry, and the vertical and horizontal intercepts
   
   1. The vertex and intercept(s) should be written as ordered pairs
   2. The axis of symmetry should be written as an equation
2. Graph by hand a quadratic equation by finding the vertex, plotting at least two additional points on one side and using symmetry to complete the graph
3. Create, use, and interpret quadratic models of real-world situations algebraically and graphically
   
   1. Interpret the vertex as a maximum or minimum in context with units
   2. Interpret the intercept(s) in context with units
4. In a mixed problem set, distinguish between linear and quadratic equations and graph them

1. Know and apply appropriate units for various situations; e.g. perimeter units, area units, volume units, rate units, etc.
2. Memorize and apply the perimeter and area formulas for rectangles, circles, and triangles
3. Memorize and apply the volume formula for a rectangular solid and a right circular cylinder
4. Use the appropriate geometric formula(s) for a given shape to find a desired quantity
5. Use estimation to determine reasonableness of solution.
6. Use unit fractions to convert time, length, area, volume, mass, density, and speed to other units, including metric-nonmetric conversions

1. Given an equation, solve using a graphing utility by finding points of intersection
2. Given an inequality, solve using a graphing utility and express the solution in interval notation