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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