The six moves

SkillFormulaDrill
TranspositionS' = S + C; C' = -C; axis rotates 90practice
Prentice's ruleP = c x F in the meridian of decentrationpractice
Vertex compensationF' = F / (1 - d x F)practice
Meridian powerF = S + C x sin^2(theta - axis)practice
Minimum blank sizeED + 2 x decentration + allowancepractice
Vertical imbalancePer-eye Prentice at the reading drop; differencepractice

Supporting knowledge

Two table-reading skills ride along: the ANSI Z80.1 tolerance brackets, drilled with the tolerance checker and summarized in the reference table, and the base-direction conventions for induced prism. The spectacle magnification power factor appears occasionally and reuses the vertex denominator.

A practice plan that works

  1. One skill per sitting until its drill streak reaches ten with the worked steps feeling redundant.
  2. Switch to the mixed drill so formula selection itself gets practiced.
  3. Finish with timed exam runs. Time pressure is a separate skill; rehearse it before exam day, not on it.
  4. Keep the formula sheet printed beside you until you notice you have stopped looking at it.

Units, the recurring villain

Prentice wants centimeters, vertex wants meters, blank size stays in millimeters, and the axis lives on a 1 to 180 scale where 180 is written instead of 0. Most wrong answers on calculation questions are unit slips, which is exactly what repetition drills out.

Frequently asked questions

What math does the ABO exam actually test?

Almost all of it reduces to six moves: transposition, Prentice's rule, vertex compensation, meridian power, minimum blank size, and vertical imbalance, plus reading tolerance tables. Each has a drill on this site.

How should I practice for the calculation questions?

Short daily sets beat cramming. Drill each skill until the worked steps feel redundant, then switch to the mixed drill and timed exam mode so switching between formulas becomes automatic too.