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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

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

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