Section B.1 MTH 60
This information is accurate as of July 2024. For the complete, most recent CCOG, visit www.pcc.edu/ccog.
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- Algebraic Expressions and Equations
- Simplify algebraic expressions using the distributive, commutative, and associative properties.
- Evaluate algebraic expressions.
- Translate phrases and sentences into algebraic expressions and equations, and vice versa.
- Distinguish between factors and terms.
- Distinguish between evaluating expressions, simplifying expressions, and solving equations.
- Linear Equations and Inequalities in One Variable
- Identify linear equations and inequalities in one variable.
- Use the definition of a solution to an equation or inequality to check if a given value is a solution.
- Solve linear equations, including proportions, and non-compound linear inequalities symbolically.
- Express inequality solution sets graphically and with interval notation.
- Create and solve linear equations and inequalities in one variable that model real life situations.
- Properly define variables; include units in variable definitions.
- State contextual conclusions using complete sentences.
- Use estimation to determine reasonableness of solutions.
- Solve an equation for a specified variable in terms of other variables.
- Solve applications in which two values are unknown but their total is known; for example, a 10-foot board cut into two pieces where one piece is 2.5 feet longer than the other piece.
- Introduction to Tables and Graphs
- Plot points on the Cartesian coordinate system, including pairs of values from a table.
- Determine coordinates of points by reading a Cartesian graph.
- 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.
- Classify points by quadrant or as points on an axis; identify the origin.
- Label and scale axes on all graphs.
- 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).
- Interpret graphs, intercepts and other points in the context of an application. Express intercepts as ordered pairs.
- Create tables and graphs with labels that communicate the context of an application problem and its dependent and independent quantities.
- Slope
- Write and interpret a slope as a rate of change in context (include the unit of the slope).
- Find the slope of a line from a graph, from two points, and from a table of values.
- Find the slope from all forms of a linear equation.
- 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.
- Linear Equations in Two Variables
- Identify a linear equation in two variables.
- Manipulate a linear equation into slope-intercept form; identify the slope and the vertical intercept given a linear equation.
- Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined.
- Write the equation of a line in slope-intercept form.
- Write the equation of a line in point-slope form.
- Graphing Linear Equations in Two Variables
- Graph a line with a known point and slope.
- Emphasize that the graph of a line is a visual representation of the solution set to a linear equation.
- Given a linear equation, find at least three ordered pairs that satisfy the equation and graph the line using those ordered pairs.
- Given an equation in slope-intercept form, plot its graph using the slope and vertical intercept.
- Given an equation in point-slope form, plot its graph using the slope and the suggested point.
- Given an equation in standard form, plot its graph by calculating horizontal and vertical intercepts, and check with a third point.
- Given an equation for a vertical or horizontal line, plot its graph.
- Create and graph a linear model based on data and make predictions based upon the model.
- Systems of Linear Equations in Two Variables
- Solve and check systems of equations using the following methods: graphically, using the substitution method, and using the addition/elimination method.
- Create and solve real-world models involving systems of linear equations in two variables.
- Properly define variables; include units in variable definitions.
- State contextual conclusions using complete sentences.
- Given the equations of two lines, classify them as parallel, perpendicular, or neither.