Cracking the Compass

All you could ever want to know (and that you are allowed to know) about the Compass can be found the reference manual below. A shorter overview is also available.

Full Compass Reference Manual
http://www.act.org/compass/pdf/CompassReferenceManual.pdf

Short overview
http://www.act.org/compass/pdf/MathPlacementGuide.pdf

When a student takes the Compass Math Test, they actually go through a series of tests that are seamlessly linked together into a stream of 25-35 questions. Before answering any questions, the student starts with a minimum score of 17 on the Pre-Algebra Test, and as they answer questions correctly, their score gradually increases. If their score surpasses 29, they are eventually taken off the Pre-Algebra test and re-routed to the beginning of the Algebra test. If their score increases beyond 43 on the Algebra test, they are eventually re-routed to a third test--College Algebra--and then, potentially, a fourth test--Trigonometry. Most students do not reach a high enough score on the Algebra test to move on to the third and fourth tests. The progression through the first two tests is illustrated in the "Compass Crawl" below.

The tables below are excerpted from the Compass Reference Manual, which outlines the content of each test.

PRE-ALGEBRA

ALGEBRA TEST:

By re-arranging the Algebra test content items in the table above, it is clear that 70% of the test questions are comprised by less than half of the topic list (shown below).

Compass Algebra test topics arranged by frequency

		Topic
70%	11%	Linear equations in one variable (using integers, fractions, and decimals as coefficients)
	10%	Substituting values into algebraic expressions
	8%	Basic operations with polynomials
	8%	Linear equations/inequalities in two variables
	7%	Setting up equations for given situations
	6%	Factoring polynomials
	6%	Rational expressions
	5%	Solving polynomial equations by factoring
	5%	Exponents and radicals
	4%	Linear inequalities in one variable
30%	4%	Systems of linear equations in two variables
	4%	Graphing conics (circle, parabola, etc)
	4%	Graphing relations in the plane
	3%	Formula manipulation and field axioms
	3%	Exponents, radical expressions, and equations
	3%	Distance and midpoint formulas in the plane
	2%	Quadratic formula and completing the square
	2%	Graphing parallel and perpendicular lines
	2%	Graphing systems of equations/inequalities
	1%	Number theory and/or properties
	1%	Absolute value equations and inequalities
	1%	Fitting parameters to equations and models