DEMONSTRATION ONLY: This demonstration presents an abbreviated version of the complete ELM course. Click 'Next' at the bottom of the screen or make a selection from the links on the left to begin. Not all links are available for the demo. Mathematics Competencies Tested on the ELM
The ELM is divided into three sections: Numbers and Data, Algebra, and Geometry. An outline showing the three sections is shown below.
Numbers and Data
 Carry out basic arithmetic calculations
 Understand and use percent in context
 Compare and order rational numbers expressed as fractions and/or decimals
 Solve problems involving fractions and/or decimals in context
 Interpret and use ratio and proportion in context
 Use estimation appropriately
 Evaluate and estimate square roots
 Represent and understand data presented in tables, pie charts, bar and line graphs, histograms, or other formats for presenting data visually used in print and electronic media
 Interpret and calculate the arithmetic mean
 Interpret and calculate the median
 Make estimates and predictions based on data
Algebra
 Evaluate and interpret algebraic expressions
 Simplify algebraic expressions
 Express relationships among quantities using variables
 Use properties of exponents
 Perform polynomial arithmetic (add, subtract, multiply, divide, and factor)
 Perform arithmetic operations involving rational expressions
 Solve linear equations (with both numerical and literal coefficients)
 Solve systems of linear equations in two unknowns
 Solve linear inequalities
 Solve problems in context that are modeled by linear equations
 Solve quadratic and rational equations (with both numerical and literal coefficients; real solutions only)
 Solve problems in context that are modeled by quadratic equations
 Solve equations involving absolute value (in one variable)
 Solve inequalities involving absolute value (in one variable)
 Find and use slopes and intercepts of lines
 Use constant and average rates to solve problems in context (using appropriate units)
Geometry
 Find the perimeter, area, or volume of geometric figures (including triangles, quadrilaterals, rectangular parallelepipeds, circles, cylinders, and combinations of these figures)
 Calculate the ratio of corresponding geometric measurements of similar figures (e.g., if the perimeters are in a 3:2 ratio, the areas are in a 9:4 ratio)
 Use the Pythagorean Theorem
 Use properties of congruent or similar geometric objects
 Solve geometric problems using the properties of basic geometric figures (including triangles, quadrilaterals, polygons, and circles)
 Determine angles in the plane (using properties of intersecting lines, parallel lines, and perpendicular lines)
 Identify and plot points on the number line
 Identify and plot points in the coordinate plane
 Plot points on the graph of a function determined by an algebraic expression
 Graph linear functions in one variable
 Graph quadratic functions in one variable
 Relate basic information about a function to features of its graph (e.g., linearity, positivity or negativity, increasing or decreasing)
 Find the length or midpoint of a line segment in the coordinate plane
