Mathematics (AM.I.H) is the General-bank subject area candidates most often lose easy points on. Nothing in it is advanced: fractions and decimals, percentages, ratio and proportion, one-unknown algebra, powers and roots, and the area and volume formulas you use for tanks, cylinders, and sheet stock. What makes an answer wrong is almost always a unit or a direction rather than the arithmetic. Drill the setups until they are automatic and this becomes one of the most reliable scoring areas on the General test.
The mathematics chapter of FAA-H-8083-30 defines the scope, and the questions stay inside it. Arithmetic comes first: adding and reducing fractions, converting between fractions, decimals, and percentages, working with signed numbers, and rounding to a stated place. Stems such as convert 5/8 to a decimal, or round 7.846 to the nearest tenth, are exactly what they look like - the points get lost by rushing, not by difficulty. Ratio and proportion carry more weight than their share of the questions suggests, because they turn up disguised. Gear and pulley problems, compression ratio, mixture and dilution ratios, and scale readings all reduce to the same setup. Expect to simplify a ratio such as 16 to 4, and to apply one, as in a 3-to-1 reduction driven at 1,500 rpm. Algebra is limited to a single unknown: solve 3x + 6 = 18, or rearrange a formula so the quantity you want stands alone. Powers, roots, and scientific notation appear on their own and inside the area formulas. Geometry and mensuration finish the area: area of a rectangle, triangle, and circle; volume of a rectangular solid and a cylinder; surface area for material and finish estimates. Tank problems are the classic case. Find the volume in cubic inches first, then convert at 231 cubic inches per gallon. Keep 144 square inches per square foot and 1,728 cubic inches per cubic foot ready too, because the distractors are built out of the wrong conversion.
ACS AM.I.H is tested on the FAA General written test, one of 1,558 ACS-tagged questions in the General bank. Every question tagged to this area carries a worked rationale and its FAA handbook reference, so you can drill the code itself rather than the whole test.
A rectangular fuel tank measures 30 inches long, 20 inches wide, and 12 inches deep. What is its volume in cubic inches?
A gear ratio is given as 3 to 1. If the driving gear turns 1,500 rpm, how fast does the driven gear turn when the ratio reduces speed?
Convert the fraction 5/8 to a decimal.
A part originally costing $80 is marked up 25 percent. What is the new price?
What is the square root of 144?
Express the ratio 16 to 4 in its simplest form.
Solve for x in the equation 3x + 6 = 18.
ACS code: AM.I.H
Correct answer: 7,200 cubic inches
Rationale: The volume of a rectangular solid equals length times width times height. Here 30 x 20 x 12 = 7,200 cubic inches. The 3,600 value comes from omitting one dimension, and 600 is only length times width, which gives surface area of one face, not volume.
ACS code: AM.I.H
Correct answer: 500 rpm
Rationale: A 3-to-1 reduction means the output turns one-third as fast as the input. Dividing 1,500 by 3 gives 500 rpm. Multiplying by 3 (4,500) would be a speed increase, and 1,500 would mean no ratio change at all.
ACS code: AM.I.H
Correct answer: 0.625
Rationale: A fraction is converted to a decimal by dividing the numerator by the denominator: 5 divided by 8 equals 0.625. The 0.580 value simply re-reads the digits as a decimal, and 1.600 is the result of dividing 8 by 5, which inverts the fraction.
ACS code: AM.I.H
Correct answer: $100
Rationale: A 25 percent markup is found by multiplying 80 by 0.25, giving 20, then adding it to the original: 80 + 20 = 100. The $105 value adds the wrong amount, and $85 adds only $5, which would be a much smaller percentage.
ACS code: AM.I.H
Correct answer: 12
Rationale: The square root of a number is the value that, multiplied by itself, equals that number. Since 12 x 12 = 144, the square root is 12. The value 72 is simply half of 144, and 14 does not square to 144 (14 x 14 = 196).
ACS code: AM.I.H
Correct answer: 4 to 1
Rationale: A ratio is reduced by dividing both terms by their greatest common factor, which is 4: 16/4 = 4 and 4/4 = 1, giving 4 to 1. The 8 to 2 form is correct in value but not fully reduced, and 1 to 4 reverses the order of the terms.
ACS code: AM.I.H
Correct answer: x = 4
Rationale: First subtract 6 from both sides to isolate the term with x: 3x = 12. Then divide both sides by 3 to find x = 4. The value 8 results from adding instead of subtracting the 6, and 6 results from dividing 18 by 3 without first removing the 6.
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