Part-66 Prep
Free practice

Use your browser's print dialog and choose "Save as PDF" to download.

Module 1 Mathematics: 50 practice questions

Real EASA paper: Category A 16 Q / 20 min · B1.1 32 Q / 40 min · B1.2 32 Q / 40 min · B1.3 32 Q / 40 min · B2 32 Q / 40 min · B2L 32 Q / 40 min · B3 32 Q / 40 min. Three options, 75% to pass. Answer key on the last page. From part66exam.com · independent study aid, not an official exam or a past paper.

  1. 1. Expand 3(2x − 4).

    1. A. 6x − 4
    2. B. 5x − 7
    3. C. 6x − 12

  2. 2. The gradient of a curve at a particular point is found from:

    1. A. the chord from the origin
    2. B. the area under the curve
    3. C. the tangent drawn at that point

  3. 3. Five cylinder compression readings are 73, 79, 78, 72 and 75 psi. What is the mean reading?

    1. A. 94.2 psi
    2. B. 75.4 psi
    3. C. 60.4 psi

  4. 4. What is 16^¼?

    1. A. 4
    2. B. 2
    3. C. 64

  5. 5. What is the y-intercept of the line 2y = 6x + 8?

    1. A. 8
    2. B. 3
    3. C. 4

  6. 6. What is the lowest common multiple (LCM) of 6 and 8?

    1. A. 48
    2. B. 24
    3. C. 2

  7. 7. Evaluate 20 − 6 + 4.

    1. A. 10
    2. B. 30
    3. C. 18

  8. 8. A graph of output against input for a device shows a straight line that levels off at high input. The levelled region indicates:

    1. A. complete failure of the device
    2. B. an inverse relationship
    3. C. saturation (no further output gain)

  9. 9. A hole is to be reamed to 0.763 in and drilled 1/64 in undersize first. Which drill should be used?

    1. A. 3/4 in
    2. B. 49/64 in
    3. C. 25/32 in

  10. 10. Solve the simultaneous equations 2x + 3y = 34 and x + y = 13. What is y?

    1. A. 5
    2. B. 21
    3. C. 8

  11. 11. A right angle can be laid out without a square by marking a triangle with sides in the ratio:

    1. A. 1 : 2 : 3
    2. B. 3 : 4 : 5
    3. C. 2 : 3 : 4

  12. 12. A triangular gusset has a base of 19 cm and a perpendicular height of 21 cm. What is its area?

    1. A. 399 cm²
    2. B. 199.5 cm²
    3. C. 20 cm²

  13. 13. If m = 3, n = −2, what is the value of m² n?

    1. A. −18
    2. B. 36
    3. C. 12

  14. 14. On a combination square, which head is used to find the centre of a round bar?

    1. A. Stock head
    2. B. Protractor head
    3. C. Centre head

  15. 15. A bolt grip length is 4 in. What is this in millimetres? (1 in = 25.4 mm)

    1. A. 101.6 mm
    2. B. 0.16 mm
    3. C. 10.16 mm

  16. 16. Using CT = 1/(1/C1 + 1/C2 + 1/C3), find CT for C1 = 0.1 µF, C2 = 0.015 µF, C3 = 0.05 µF.

    1. A. 0.165 µF
    2. B. 96.7 µF
    3. C. 0.0103 µF

  17. 17. The perpendicular bisector of a line segment is the line that:

    1. A. joins its ends by an arc
    2. B. divides it in the ratio 1:2
    3. C. passes through its midpoint at 90°

  18. 18. What is 4.1 × 10^4 written in ordinary (standard) notation?

    1. A. 410000
    2. B. 41000
    3. C. 4100

  19. 19. Solve 3N = 21.

    1. A. N = 63
    2. B. N = 7
    3. C. N = 18

  20. 20. Two straight lines on the same axes are parallel when they have:

    1. A. the same y-intercept
    2. B. the same gradient
    3. C. gradients that multiply to −1

  21. 21. How many square inches are there in one square foot?

    1. A. 12
    2. B. 1 728
    3. C. 144

  22. 22. What is log₁₀ 1?

    1. A. 1
    2. B. 10
    3. C. 0

  23. 23. Which point lies on the line y = 2x − 1?

    1. A. (3, 5)
    2. B. (5, 3)
    3. C. (2, 5)

  24. 24. A floor panel measures 26 in by 46 in. What is its area in square feet?

    1. A. 8.31 ft²
    2. B. 99.67 ft²
    3. C. 172224 ft²

  25. 25. The natural logarithm (ln) uses which base?

    1. A. 10
    2. B. e ≈ 2.718
    3. C. 2

  26. 26. What is tan 45°?

    1. A. 1
    2. B. 0.707
    3. C. 0

  27. 27. Using the estimation method, between which two whole numbers does √31 lie?

    1. A. 4 and 5
    2. B. 15 and 16
    3. C. 5 and 6

  28. 28. Simplify (a²b³)².

    1. A. a⁴b⁵
    2. B. a⁴b⁶
    3. C. 2a²b³

  29. 29. As an angle increases from 0° to 90°, its cosine:

    1. A. increases from 0 to 1
    2. B. decreases from 1 to 0
    3. C. stays constant

  30. 30. Express 5/8 as a percentage.

    1. A. 58%
    2. B. 6.25%
    3. C. 62.5%

  31. 31. What is the hexadecimal number 2F in decimal?

    1. A. 32
    2. B. 215
    3. C. 47

  32. 32. A tangent to a circle is always:

    1. A. perpendicular to the radius at the point of contact
    2. B. parallel to the radius at the point of contact
    3. C. a line passing through the centre

  33. 33. A pinion of 8 teeth meshes with a spur gear of 28 teeth. What is the gear ratio in lowest terms?

    1. A. 2:7
    2. B. 7:2
    3. C. 8:28

  34. 34. To keep an equation balanced when solving for an unknown, you must:

    1. A. apply the same operation to both sides
    2. B. apply the inverse operation to one side only
    3. C. change the sign of every term on one side

  35. 35. A straight line has gradient 4 and passes through (1, 7). What is its equation?

    1. A. y = 4x + 3
    2. B. y = 4x + 7
    3. C. y = 7x + 4

  36. 36. What is the highest common factor (HCF) of 36 and 60?

    1. A. 6
    2. B. 12
    3. C. 180

  37. 37. In the expression 7x³, the number 7 is called the:

    1. A. index
    2. B. coefficient
    3. C. constant term

  38. 38. What is the sum of the interior angles of a hexagon?

    1. A. 540°
    2. B. 1 080°
    3. C. 720°

  39. 39. A tapered wing has a span of 50 ft and a mean chord of 6 ft 8 in. What is its area?

    1. A. 333.3 ft²
    2. B. 340 ft²
    3. C. 300 ft²

  40. 40. Simplify 10⁴ ÷ 10².

    1. A. 10²
    2. B. 10⁸
    3. C. 1²

  41. 41. A force of 450 N acts at 70° above the horizontal. What is its vertical component?

    1. A. 153.9 N
    2. B. 422.9 N
    3. C. 1236.4 N

  42. 42. In binary arithmetic, what is 1 + 1?

    1. A. 10
    2. B. 2
    3. C. 11

  43. 43. The point where the x-axis and y-axis cross is called the:

    1. A. origin
    2. B. intercept
    3. C. vertex

  44. 44. For resistors in series R = R1 + R2 + R3. If R = 39.93 Ω, R1 = 2.34 Ω and R3 = 0.09 Ω, what is R2?

    1. A. 42.36 Ω
    2. B. 37.5 Ω
    3. C. 37.59 Ω

  45. 45. The graph of y = mx + c is a straight line in which m represents the:

    1. A. gradient (slope)
    2. B. y-intercept
    3. C. x-intercept

  46. 46. What is log₁₀ 0.01?

    1. A. 0.2
    2. B. −0.01
    3. C. −2

  47. 47. In a pie chart, what sector angle represents 25% of the total?

    1. A. 25°
    2. B. 90°
    3. C. 45°

  48. 48. What is the base (radix) of the binary number system?

    1. A. 2
    2. B. 8
    3. C. 10

  49. 49. On a stress-strain graph for a metal, the straight initial portion shows that stress is:

    1. A. proportional to strain
    2. B. independent of strain
    3. C. inversely proportional to strain

  50. 50. Simplify (12a³b²)/(4ab).

    1. A. 3a³b
    2. B. 3a²b
    3. C. 8a²b

Answer key

  1. 1. C — Every term inside the bracket is multiplied by 3: 3 × 2x = 6x and 3 × (−4) = −12.
  2. 2. C — The slope of the tangent at a point gives the instantaneous rate of change there.
  3. 3. B — Mean = sum of readings ÷ number of readings = (73 + 79 + 78 + 72 + 75) ÷ 5 = 75.4 psi.
  4. 4. B — The index ¼ means the fourth root: 2 × 2 × 2 × 2 = 16, so 16^¼ = 2.
  5. 5. C — Divide by 2 to get y = 3x + 4, so c = 4.
  6. 6. B — Multiples of 6: 6, 12, 18, 24…; of 8: 8, 16, 24… The smallest in both lists is 24. The LCM is used as the least common denominator.
  7. 7. C — Addition and subtraction are carried out left to right in one sweep: 20 − 6 = 14, 14 + 4 = 18.
  8. 8. C — When the curve flattens, the gradient approaches zero: increasing the input no longer increases the output (e.g. magnetic saturation).
  9. 9. A — 0.763 × 64 = 48.8 ≈ 49, so the finished size is 49/64 in. Subtracting 1/64 gives 48/64 = 3/4 in.
  10. 10. C — Multiply the second equation by 2: 2x + 2y = 2 × 13. Subtract from the first: y = 34 − 2 × 13 = 8.
  11. 11. B — 3² + 4² = 5², so a triangle with sides 3, 4 and 5 units must contain a right angle (converse of Pythagoras).
  12. 12. B — Area of a triangle = ½ × base × height = 0.5 × 19 × 21 = 199.5 cm².
  13. 13. A — m² n = 9 × (−2) = −18. Only m is squared.
  14. 14. C — The centre head uses one side of the blade as the bisector of a 90° V; two lines scribed about 90° apart cross at the centre of the shaft.
  15. 15. A — 4 in × 25.4 mm/in = 101.6 mm.
  16. 16. C — 1/0.1 + 1/0.015 + 1/0.05 = 10 + 66.67 + 20 = 96.67; CT = 1/96.67 ≈ 0.0103 µF.
  17. 17. C — A perpendicular bisector cuts the segment into two equal halves and meets it at a right angle. Every point on it is equidistant from both ends.
  18. 18. B — Move the decimal point 4 places to the right: 4.1 × 10^4 = 41000.
  19. 19. B — Divide both sides by 3: N = 21 ÷ 3 = 7.
  20. 20. B — Parallel lines never meet, which requires equal gradients (different intercepts).
  21. 21. C — 1 ft = 12 in, so 1 ft² = 12 × 12 = 144 in². To convert square feet to square inches multiply by 144.
  22. 22. C — 10⁰ = 1, so the logarithm of 1 in any base is 0.
  23. 23. A — Substitute x = 3: y = 2(3) − 1 = 5, so (3, 5) satisfies the equation.
  24. 24. A — Area = 26 × 46 in²; 1 ft² = 12 × 12 = 144 in², so area = 8.31 ft².
  25. 25. B — Natural logarithms use the base e ≈ 2.718; common logarithms (log) use base 10.
  26. 26. A — At 45° the opposite and adjacent sides are equal, so tan 45° = 1.
  27. 27. C — 31 lies between the perfect squares 25 (5²) and 36 (6²), so √31 lies between 5 and 6 (√31 ≈ 5.568).
  28. 28. B — Each index inside the bracket is multiplied by the outer index 2: a⁴b⁶.
  29. 29. B — cos 0° = 1 and cos 90° = 0; the sine does the opposite, rising from 0 to 1.
  30. 30. C — 5 ÷ 8 = 0.625; multiply by 100 to express as a percentage: 62.5%.
  31. 31. C — Hex F = 15. 2F = 2 × 16 + 15 = 47.
  32. 32. A — A tangent touches the circle at one point and is at 90° to the radius drawn to that point - the basis of constructing a tangent.
  33. 33. A — Gear ratio = 8:28; dividing both terms by 4 gives 2:7. The speed ratio is the inverse, 7:2.
  34. 34. A — Whatever is added, subtracted, multiplied or divided on one side must be done to the other side so the equality holds.
  35. 35. A — c = y − mx = 7 − 4(1) = 3, so y = 4x + 3.
  36. 36. B — Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 60 include 12 but not 18 or 36. The largest shared factor is 12.
  37. 37. B — The coefficient is the numerical multiplier of the variable; the 3 is the index (power) and a constant term contains no variable.
  38. 38. C — Sum of interior angles = (n − 2) × 180° = 4 × 180° = 720°.
  39. 39. A — Wing area = span × mean chord. 8 in = 8/12 ft = 0.667 ft, so the mean chord is 6.667 ft and the area = 50 × 6.667 ≈ 333.3 ft².
  40. 40. A — When dividing powers of the same base, subtract the indices: 10⁴⁻² = 10² = 100.
  41. 41. B — The vertical component is y = r sin θ = 450 × sin 70° = 422.9 N.
  42. 42. A — In base 2 there is no digit 2: 1 + 1 = 0 carry 1, written 10 (decimal two).
  43. 43. A — The origin is the point (0, 0). An intercept is where a graph crosses an axis; a vertex is the turning point of a parabola.
  44. 44. B — Transpose: R2 = R − R1 − R3 = 39.93 − 2.34 − 0.09 = 37.5 Ω.
  45. 45. A — In y = mx + c, m is the gradient (change in y per unit change in x) and c is where the line crosses the y-axis.
  46. 46. C — 0.01 = 10⁻², so log₁₀ 0.01 = −2. Logarithms of numbers between 0 and 1 are negative.
  47. 47. B — The whole circle is 360°, so 25% corresponds to 0.25 × 360° = 90°.
  48. 48. A — Binary uses only the digits 0 and 1, and each place value is a power of 2.
  49. 49. A — Within the elastic limit stress/strain is constant (Hooke's law); its gradient is Young's modulus.
  50. 50. B — Divide coefficients (12 ÷ 4 = 3) and subtract indices of like letters: a³⁻¹ = a², b²⁻¹ = b.

Want timed papers with scoring by sub-module? part66exam.com/practice/a/module-1