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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


  • 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)


  • 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