IXL - South Carolina algebra standards

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Skills available for South Carolina algebra standards

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Standards document:

2010 Common Core State Standards 2010 Common Core State Standards
2007 South Carolina Curriculum Standards 2007 South Carolina Curriculum Standards

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EA-1 The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.
EA-1.2 Connect algebra with other branches of mathematics.
EA-1.3 Apply algebraic methods to solve problems in real-world contexts.
EA-1.4 Judge the reasonableness of mathematical solutions.
EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).
EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.
EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

EA-2 The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA-2.1 Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).
EA-2.2 Apply the laws of exponents and roots to solve problems.
EA-2.3 Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.
EA-2.4 Use dimensional analysis to convert units of measure within a system.
EA-2.5 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.
EA-2.6 Carry out a procedure to evaluate an expression by substituting a value for the variable.
EA-2.7 Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.
EA-2.8 Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).
EA-2.9 Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).
EA-2.10 Represent applied problems by using matrices.
- Systems of linear equations: Solve a system of equations using augmented matrices: word problems (Algebra - U.13)

EA-3 The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA-3.1 Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.
- Relations and functions: Identify functions (Algebra - Q.4)
- Relations and functions: Identify functions: vertical line test (Algebra - Q.5)
EA-3.2 Use function notation to represent functional relationships.
- Relations and functions: Write a function rule: word problems (Algebra - Q.10)
- Relations and functions: Write a rule for a function table (Algebra - Q.12)
EA-3.3 Carry out a procedure to evaluate a function for a given element in the domain.
EA-3.4 Analyze the graph of a continuous function to determine the domain and range of the function.
EA-3.5 Carry out a procedure to graph parent functions (including y = x, y = x², y = the square root of x, y = the absolute value of x, and y = 1/x).
EA-3.6 Classify a variation as either direct or inverse.
EA-3.7 Carry out a procedure to solve literal equations for a specified variable.
EA-3.8 Apply proportional reasoning to solve problems.

EA-4 The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA-4.1 Carry out a procedure to write an equation of a line with a given slope and a y-intercept.
- Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
- Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
EA-4.2 Carry out a procedure to write an equation of a line with a given slope passing through a given point.
- Linear functions: Point-slope form: write an equation from a graph (Algebra - S.15)
- Linear functions: Point-slope form: write an equation (Algebra - S.16)
EA-4.3 Carry out a procedure to write an equation of a line passing through two given points.
- Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
- Linear functions: Point-slope form: write an equation (Algebra - S.16)
EA-4.4 Use a procedure to write an equation of a trend line from a given scatterplot.
- Charts and graphs: Scatter plots: line of best fit (Algebra - N.7)
EA-4.5 Analyze a scatterplot to make predictions.
- Charts and graphs: Interpret a scatter plot (Algebra - N.6)
EA-4.6 Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).
EA-4.7 Carry out procedures to solve linear equations for one variable algebraically.
EA-4.8 Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.
EA-4.9 Carry out a procedure to solve systems of two linear equations graphically.
EA-4.10 Carry out a procedure to solve systems of two linear equations algebraically.

EA-5 The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA-5.1 Carry out a procedure to graph a line when given the equation of the line.
EA-5.2 Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.
- Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
EA-5.3 Carry out a procedure to graph the line with a given slope and a y-intercept.
- Linear functions: Slope-intercept form: graph an equation (Algebra - S.5)
EA-5.4 Carry out a procedure to graph the line with a given slope passing through a given point.
- Linear functions: Point-slope form: graph an equation (Algebra - S.14)
EA-5.5 Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally.
- Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
- Linear functions: Standard form: find x- and y-intercepts (Algebra - S.10)
EA-5.6 Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.
EA-5.7 Apply the concept of slope as a rate of change to solve problems.
EA-5.8 Analyze the equations of two lines to determine whether the lines are perpendicular or parallel.
- Linear functions: Slopes of parallel and perpendicular lines (Algebra - S.17)
- Linear functions: Write an equation for a parallel or perpendicular line (Algebra - S.18)
EA-5.9 Analyze given information to write a linear function that models a given problem situation.
- Linear functions: Linear function word problems (Algebra - S.8)
EA-5.10 Analyze given information to determine the domain and range of a linear function in a problem situation.
EA-5.11 Analyze given information to write a system of linear equations that models a given problem situation.
EA-5.12 Analyze given information to write a linear inequality in one variable that models a given problem situation.
- Single-variable inequalities: Write inequalities from graphs (Algebra - K.2)
- Single-variable inequalities: Write compound inequalities from graphs (Algebra - K.13)

EA-6 The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA-6.1 Analyze the effects of changing the leading coefficient a on the graph of y = ax².
EA-6.2 Analyze the effects of changing the constant c on the graph of y = x² + c.
EA-6.3 Analyze the graph of a quadratic function to determine its equation.
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
EA-6.4 Carry out a procedure to solve quadratic equations by factoring.
EA-6.5 Carry out a graphic procedure to approximate the solutions of quadratic equations.
EA-6.6 Analyze given information to determine the domain of a quadratic function in a problem situation.