Topics on the ELM Test

Numbers and Data (approximately 35 percent)

  • 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 visually presenting data 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 (approximately 35 percent)

  • 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 (approximately 30 percent)

  • 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