This component points; it does not teach. The facts are in a public-domain handbook written by the regulator and used by every examiner, and rewriting them would add a second version of the truth with no benefit (the curriculum architecture).
Source: FAA-H-8083-30B, Aviation Maintenance Technician Handbook — General, mathematics chapter. Public domain. Read the handbook; use the table below to know which parts answer which element, and what the handbook leaves out.
Chapter and section verified against FAA-H-8083-30B, 2023 edition, on 28 August 2026. Page numbers are deliberately not cited: they move between printings, and a citation that rots silently is worse than a coarser one that stays true. Checked by our handbook citation check against our index of the handbook's chapters and sections.
What to read for each element
| Element | The ACS asks for | In the handbook | Where in FAA-H-8083-30B | What it does not give you |
|---|---|---|---|---|
K1 |
Areas of geometrical shapes | Area formulae — rectangle, triangle, trapezoid, circle | Ch. 3 — Computing Area of Two-Dimensional Solids; Units of Area; Rectangle; Triangle; Trapezoid; Circle | Which shape an aircraft part actually is. See GEN-H Concepts §2 |
K2 |
Volumes of geometrical shapes | Volume formulae — prism, cylinder, sphere | Ch. 3 — Solids; Units of Volume; Rectangular Solid; Cube; Cylinder; Sphere; Cone | The cubic-inch to gallon step, which is where tank problems are lost |
K3 |
Geometrical terms — the ACS names polygon, pi, diameter, radius and hypotenuse | Definitions — radius, diameter, chord, circumference; pi as 3.1416, the number the diameter is multiplied by to give the circumference; the hypotenuse as the side of a right triangle across from the right angle, and always its longest side | Ch. 3 — Circle; Functions of Numbers Chart; Right Triangle, Sides, and Angles; Pythagorean Theorem | Polygon. The handbook uses polygons throughout and never defines the word. Our definition, not the FAA's: a polygon is a closed flat figure bounded by straight sides. Triangles, rectangles, trapezoids and parallelograms are polygons; a circle and an ellipse are not, because their boundary is curved |
K4 |
Ratio problems, and where they are used in aircraft maintenance | Ratio arithmetic | Ch. 3 — Ratio; Aviation Applications | The aviation applications. The ACS requires them; the handbook does not supply them. GEN-H Concepts §3 |
K5 |
Proportion and percentage, with aircraft applications | Proportion and percentage arithmetic | Ch. 3 — Proportion; Solving Proportions; Extremes and Means; Percentage | As above |
K6 |
Algebraic operations, with aircraft applications | Transposition, solving for an unknown | Ch. 3 — Algebra; Algebraic Rules; Equations; Solving for a Variable; Order of Operation for Algebraic Equations | As above |
K7 |
When metric conversion may be necessary | Conversion factors and worked conversions | Ch. 3 — Measurement Systems & Conversions; Metric System; Conventional (U.S. or English) System | Which fasteners, instruments and manuals are metric in practice |
K8 |
Scientific, decimal, fractional and binary notation | All four, with conversion between them | Ch. 3 — Scientific Notation; The Decimal Number System; Fractions; The Binary Number System | Why binary appears at all — GEN-H Concepts §6 |
K9 |
Rounding numbers | Rounding rules and significant figures | Ch. 3 — Rounding Off Decimal Numbers; Place Values | When to round, which is the risk, not the rule. GEN-H Concepts §5 |
K10 |
Powers and special powers | Exponents, squares, roots | Ch. 3 — Powers; Special Powers; Powers of Ten; Roots; Square Roots; Cube Roots; Law of Exponents | — |
K11 |
Measurement systems | Imperial, US customary and SI | Ch. 3 — Measurement Systems; Metric System; Conventional (U.S. or English) System | The places the two collide on one aircraft |
K12 |
Positive and negative integers | Signed arithmetic | Ch. 3 — Addition of Positive & Negative Numbers; Subtraction of Positive & Negative Numbers; Multiplication of Positive & Negative Numbers | Why sign is an airworthiness matter. GEN-H Concepts §4 |
K13 |
The four basic functions | — | Ch. 3 — Addition of Whole Numbers; Subtraction of Whole Numbers; Division of Whole Numbers | — |
R1 |
Precedence of operations | Order of operations | Ch. 3 — Order of Operation; Use of Parentheses | Why the ACS classifies this as a risk and not knowledge. GEN-H Concepts §5 |
R2 |
Signed integers in operations | — | Ch. 3 — Addition of Positive & Negative Numbers; Multiplication of Positive & Negative Numbers | As K12 |
R3 |
Rounding off calculations | — | Ch. 3 — Rounding Off Decimal Numbers | As K9 |
Two constants worth committing to memory
Both are exact, both appear in the procedures in GEN-H Procedures, and both are the step candidates most often miss.
- 231 cubic inches = 1 US gallon. Exact by definition. Every tank and compartment problem ends here.
- 12 inch-pounds = 1 foot-pound. Exact. Every torque conversion is this and nothing else.
Other sources
- The aircraft's own documents for anything specific: the TCDS for weights and limits, the maintenance manual for torque values, the engine data plate for displacement.
- The handbook is not the authority on any aircraft. It teaches method; the aircraft's approved data governs the numbers (GEN-I).
License
CC BY-SA 4.0 (Licensing). The handbook material referenced here is US Government work in the public domain.