Carpenter, Just and Shell wrote down five rules in 1990 and every APM item they analysed used one or more of them. This course teaches them under its own plain names, and drills four of them separately; the fifth is too rare to fill a drill and is taught inside the lesson it belongs to.
| Constant in a row | an attribute stays the same along the row and changes between rows |
| Steps up or down | quantitative pairwise progression: a count, size, angle or position changes by a fixed step between neighbours |
| Adding and taking away | figure addition or subtraction: components are combined, superimposed or removed to make another cell |
| Once per row | distribution of three values: three values each appear once through a row or column |
| One value missing | distribution of two values plus null: two values appear and the third place is empty; the hardest rule |
Why the count is the difficulty
Their account of difficulty has two parts. The number of rules an item carries, and the type: constant is easiest, then steps, then the permutations, then the logical rules, in the order later measured by Vodegel Matzen and colleagues. Behind both sits what they called correspondence finding: deciding which figural elements belong to which rule. A cell with a circle, a bar and a dot may run three rules at once, one per element, and the solver who keeps them apart is the solver who scores.
How the course maps them
- Set I, the orientation set: one of each, as the real form gives it.
- Steps up or down: the progression rule, on any attribute.
- Once per row: distribution of three, unchanged tokens. One value missing lives inside this lesson.
- Transformed once per row: the distributed values are also changed, or a cell names a transformation applied elsewhere.
- Adding and taking away: the four set operations, union, intersection, what is in exactly one, and difference, separated or superimposed.
- Two rules at once: items carrying three or more rules, which is most of Set II.
Sources: Carpenter, Just and Shell 1990 (primary); Vodegel Matzen et al. 1994 on the order of difficulty, via the site’s taxonomy reference; the bank’s own APM taxonomy for the family crosswalk. Read 2026-09-21. This is independent practice material. It is not a Pearson product and uses none of Raven's items. Figures come from Pearson's own pages and the primary literature; where only third parties state a figure, the text says so.