Free CAAS SAR-66 Mathematics (M01) — Category B1 Practice Questions

Sample Practice Questions

Try these 10 sample questions from the CAAS SAR-66 Mathematics (M01) — Category B1 practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Two fractional lengths, 2/3 m and 1/4 m, are placed end to end. What is their total length?

   1. A.3/7 m
   2. B.11/12 mCorrect answer: B
   3. C.3/4 m
   4. D.5/12 m

   Explanation: The FAA handbook states: "In order to add fractions, the denominators must be the same number." Use denominator 12: 2/3 + 1/4 = 8/12 + 3/12 = 11/12 m. Adding numerators and denominators gives the incorrect 3/7; 3/4 and 5/12 result from incorrect equivalent fractions.

   Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Addition of Fractions, p. 3-2

2. 2Evaluate 2x² + 3x − 4 when x = −3.

   1. A.−31
   2. B.23
   3. C.5Correct answer: C
   4. D.−19

   Explanation: FAA Aviation Maintenance Technician Handbook—General states: "First, substitute the given values into the formula:" Substitute −3: 2(−3)² + 3(−3) − 4 = 18 − 9 − 4 = 5. −31 fails to square the negative correctly; 23 loses the sign in 3x; −19 ignores the square: 2(−3) + 3(−3) − 4 = −19.

   Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Solving for a Variable, p. 3-16

3. 3A line parallel to AB is to be constructed at a prescribed perpendicular distance d. Equal-radius arcs of radius d are drawn from two different points on AB. Which line completes this offset construction?

   1. A.The line through both arc centres
   2. B.A common tangent to both arcs on the chosen sideCorrect answer: B
   3. C.A line through either centre and one arc end
   4. D.The perpendicular bisector of the two centres

   Explanation: The Navy drafting text states: "A line A'B' drawn tangent to (barely touching) the arcs is parallel to AB, and located CD distance from AB." The common tangent on the selected side is at the arc radius from both centres, giving the required offset parallel. The centre line is AB itself, a radius line passes through AB, and the perpendicular bisector has the wrong direction.

   Reference: U.S. Navy Engineering Aid Basic—Drafting: Geometric Construction — Chapter 5, 1.0.0, Figure 5-2, p. 5-4

4. 4What is the result of (5/6) ÷ (5/12), expressed as a whole number?

   1. A.1
   2. B.4
   3. C.3
   4. D.2Correct answer: D

   Explanation: The FAA handbook states: "To divide fractions, first change the division symbol to multiplication. Next, invert the second fraction." (5/6) × (12/5) = 60/30 = 2. The result 1 ignores the different denominators; 4 incorrectly doubles the quotient; 3 uses the wrong reciprocal.

   Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Division of Fractions, p. 3-3

5. 5What is the value of 3[8 − (2 + 1)]?

   1. A.15Correct answer: A
   2. B.21
   3. C.5
   4. D.19

   Explanation: The FAA handbook states: "The operations inside the parentheses are always performed first in algebraic equations." Evaluate 2 + 1 = 3, then 8 − 3 = 5, then 3 × 5 = 15. The value 21 follows from dropping the inner grouping and using 3(8 − 2 + 1); 5 omits the outer multiplier; 19 follows from moving the inner +1 outside both groups, 3(8 − 2) + 1.

   Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Use of Parentheses, p. 3-17

6. 6To drop a perpendicular from external point P to line AB, an arc centred at P cuts AB at C and D. Equal arcs centred at C and D meet at E, distinct from P. Which line is the required perpendicular?

   1. A.CD
   2. B.CE
   3. C.DE
   4. D.PECorrect answer: D

   Explanation: The Navy drafting text states: "A line from P through E is perpendicular to AB." C and D are equally distant from P; the common arc intersection E is also equidistant from them. PE is their symmetry line. CD lies along AB, and CE and DE are construction radii rather than the required line through P.

   Reference: U.S. Navy Engineering Aid Basic—Drafting: Geometric Construction — Chapter 5, 1.0.0, Figure 5-3, p. 5-5

7. 7Which fraction is 42/56 expressed in lowest terms?

   1. A.3/4Correct answer: A
   2. B.6/8
   3. C.7/8
   4. D.4/3

   Explanation: The FAA handbook states: "To reduce a fraction, determine what the common factor(s) are and divide these out of the numerator and denominator." Divide numerator and denominator by their greatest common factor, 14: 42/56 = 3/4. Although 6/8 is equivalent, it is not in lowest terms. 7/8 changes the value; 4/3 reverses it.

   Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Reducing Fractions, p. 3-3

8. 8In the expression 48 ÷ 4 × 3, division and multiplication have equal priority. What value follows the standard order of operations?

   1. A.4
   2. B.16
   3. C.12
   4. D.36Correct answer: D

   Explanation: FAA Aviation Maintenance Technician Handbook—General states: "multiply/divide or add/subtract in one sweep from left to right, not separately." Evaluate left to right: (48 ÷ 4) × 3 = 12 × 3 = 36. 4 groups 4 × 3 as a denominator; 16 divides by 3; 12 stops after the first operation.

   Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Order of Operation, pp. 3-17–3-18

9. 9A 10 cm line segment is to be bisected using arcs of the same radius drawn from its endpoints. Which radius allows the two circles to intersect at two distinct points?

   1. A.6 cmCorrect answer: A
   2. B.5 cm
   3. C.4 cm
   4. D.3 cm

   Explanation: The Navy drafting text states: "set a compass to a radius greater than one-half the length of AB" Half the segment is 5 cm. A radius of 6 cm exceeds it and gives two intersections. At 5 cm the circles only touch; at 4 cm or 3 cm they do not meet. The question asks for a usable radius, not whether every larger value is disallowed.

   Reference: U.S. Navy Engineering Aid Basic—Drafting: Geometric Construction — Chapter 5, 1.1.0 Bisection of a Line, p. 5-5

10. 10A length of 8.4 m has pieces of 0.75 m and 0.125 m removed. How much remains?

    1. A.7.650 m
    2. B.7.400 m
    3. C.7.525 mCorrect answer: C
    4. D.8.275 m

    Explanation: The FAA handbook states: "To subtract decimal numbers, they must first be arranged so that the decimal points are aligned vertically and according to place value." 8.400 − 0.750 − 0.125 = 7.525 m. 7.650 omits the second removal; 7.400 misaligns its place value; 8.275 omits the first removal.

    Reference: FAA Aviation Maintenance Technician Handbook—General — Chapter 3, Subtraction of Decimal Numbers, pp. 3-4–3-5