# 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