Part-66 Module 1 Exam Flashcards

Q: How many questions are on the EASA Part-66 Module 1 exam?

Category B1 and B2 candidates sit 32 multiple-choice questions in 40 minutes. Category A candidates sit a shorter version with 16 questions in 20 minutes. Both categories must reach the same 75% pass mark. The official exam uses 3-option multiple choice, while this flashcard set and the matching practice bank use 4 options for tougher revision.

Q: What topics does Module 1 Mathematics cover?

The syllabus has three official sections: 1.1 Arithmetic (fractions, decimals, ratio, percentages, averages, areas, volumes, roots), 1.2 Algebra (expressions, linear and simultaneous equations, indices, binary/octal/hex number systems, quadratics, logarithms), and 1.3 Geometry (constructions, graphs of functions, and simple trigonometry with rectangular and polar coordinates).

Q: What happens if I fail a Part-66 module exam?

You may re-sit a failed module up to three consecutive attempts with no mandatory waiting period between them. After a third failed attempt, a 90-day waiting period applies before you can try again. There is no published limit on total lifetime attempts beyond this 90-day reset rule.

Q: Do I need to memorise formulas, or is a formula sheet provided?

Policies vary by National Aviation Authority and Part-147 training organisation, so check with your test centre. Because rules differ, it is safest to memorise core formulas and standard trig values (sin 30 = 0.5, sin 45 = cos 45 ≈ 0.707, sin 60 = cos 30 ≈ 0.866, tan 45 = 1.0) rather than assume a reference sheet will be supplied.

Q: Which regulation sets the current Module 1 syllabus, and does it affect these flashcards?

The current syllabus is Commission Implementing Regulation (EU) 2023/989, applicable from 12 June 2024. Training started under the previous standard must be completed by 12 June 2026. These flashcards follow the 2023/989 syllabus structure, so they remain valid for both transitioning and new candidates.

Question 1

How do you add two fractions with different denominators, such as 1/3 + 1/4?

Accepted Answer

Convert both fractions to a common denominator first, then add the numerators. 1/3 = 4/12 and 1/4 = 3/12, so 1/3 + 1/4 = 7/12. You cannot add numerators and denominators separately.

Question 2

Convert the fraction 5/8 to a decimal and a percentage.

Accepted Answer

5/8 = 0.625 = 62.5%. Divide the numerator by the denominator to get the decimal, then multiply by 100 for the percentage.

Question 3

What is the rule for dividing one fraction by another, e.g. 2/3 divided by 4/5?

Accepted Answer

Multiply by the reciprocal of the second fraction: 2/3 divided by 4/5 = 2/3 times 5/4 = 10/12 = 5/6. 'Keep, change, flip' - keep the first fraction, change the divide sign to multiply, flip the second fraction.

Question 4

Divide 120 in the ratio 2:3:5. What is each share?

Accepted Answer

The ratio parts total 2+3+5 = 10, so one part = 120 divided by 10 = 12. The shares are 2x12=24, 3x12=36, and 5x12=60, which sum back to 120.

Question 5

A value increases from 80 to 100. What is the percentage increase?

Accepted Answer

Percentage increase = (increase divided by original) times 100 = (20 divided by 80) times 100 = 25%. Always divide by the ORIGINAL value, not the new one.

Question 6

What is the mean (average) of the measurements 4, 7, 9, 12, and 13?

Accepted Answer

Mean = sum of values divided by number of values = (4+7+9+12+13) divided by 5 = 45 divided by 5 = 9.

Question 7

What is the area of a circle with radius 7 cm (use pi = 22/7)?

Accepted Answer

Area = pi r squared = (22/7) x 7 squared = (22/7) x 49 = 154 cm squared. The radius must be squared before multiplying by pi.

Question 8

A cylindrical fuel tank has radius 2 m and height 5 m. What is its volume?

Accepted Answer

Volume = pi r squared h = pi x 2 squared x 5 = pi x 4 x 5 = 20 pi, approximately 62.8 cubic metres. Volume formulas for solids extend the matching area formula by the extra dimension.

Question 9

What is the area of a right triangle with base 10 cm and height 6 cm?

Accepted Answer

Area = half x base x height = half x 10 x 6 = 30 cm squared. This halves the rectangle formed by the base and height.

Question 10

What is the square root of 144, and the cube root of 27?

Accepted Answer

The square root of 144 is 12, because 12 squared = 144. The cube root of 27 is 3, because 3 cubed = 27. Roots reverse the corresponding power.

Question 11

Convert 2.5 metres into millimetres.

Accepted Answer

1 metre = 1000 mm, so 2.5 m = 2.5 x 1000 = 2500 mm. Multiply by 1000 when converting from metres down to millimetres.

Question 12

A drawing uses a scale of 1:50. A component measures 3 cm on the drawing. What is its real length?

Accepted Answer

Real length = drawing length x scale factor = 3 cm x 50 = 150 cm (1.5 m). A scale of 1:50 means every unit on the drawing represents 50 units in real life.

Question 13

Simplify the expression 3x + 5y - x + 2y.

Accepted Answer

Collect like terms separately: (3x - x) + (5y + 2y) = 2x + 7y. Only terms with the same variable can be combined.

Question 14

Expand the bracket 4(2x - 3).

Accepted Answer

Multiply each term inside the bracket by 4: 4 x 2x - 4 x 3 = 8x - 12.

Question 15

If x = 3, what is the value of 2x squared + 5?

Accepted Answer

Substitute x = 3: 2(3 squared) + 5 = 2(9) + 5 = 18 + 5 = 23. Apply the power to x before multiplying by the coefficient.

Question 16

Simplify the algebraic fraction 6x squared over 2x.

Accepted Answer

Cancel the common factor of 2x: 6x squared over 2x = 3x. Divide the numeric coefficients and subtract the powers of x (x squared divided by x equals x).

Question 17

Solve for x: 3x + 7 = 22.

Accepted Answer

Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Whatever operation you apply, apply it to BOTH sides of the equation.

Question 18

Solve the simultaneous equations x + y = 10 and x - y = 4.

Accepted Answer

Add the two equations to eliminate y: 2x = 14, so x = 7. Substitute back into the first equation: 7 + y = 10, so y = 3.

Question 19

Why do you need two equations to solve for two unknowns like x and y?

Accepted Answer

One equation with two unknowns has infinitely many solutions; a second, independent equation narrows the possibilities down to exactly one solution. This is why simultaneous equations must be solved together, not separately.

Question 20

Solve using substitution: y = 2x and 3x + y = 20.

Accepted Answer

Substitute y = 2x into the second equation: 3x + 2x = 20, so 5x = 20, giving x = 4. Then y = 2(4) = 8.

Question 21

After solving 5x - 3 = 17 to get x = 4, how do you check the answer?

Accepted Answer

Substitute x = 4 back into the original equation: 5(4) - 3 = 20 - 3 = 17, which matches the right-hand side, confirming the solution is correct.

Question 22

Solve for x: (x/2) + 3 = 9.

Accepted Answer

Subtract 3 from both sides: x/2 = 6. Multiply both sides by 2 to clear the fraction: x = 12.

Question 23

Simplify x to the power 4, times x to the power 3, using the laws of indices.

Accepted Answer

When multiplying powers of the same base, add the indices: x^4 x x^3 = x^(4+3) = x^7.

Question 24

Simplify x to the power 6 divided by x to the power 2, and explain what x to the power 0 equals.

Accepted Answer

Subtract the indices when dividing: x^6 / x^2 = x^(6-2) = x^4. Any non-zero base raised to the power 0 always equals 1 (x^0 = 1).

Question 25

What does a negative index mean, e.g. x to the power negative 3?

Accepted Answer

A negative index means take the reciprocal: x^-3 = 1 / x^3. The negative sign inverts the value into a fraction; it does not make the result negative.

Question 26

Evaluate 8 to the power one-third, and explain what a fractional index means.

Accepted Answer

A fractional index represents a root: the denominator of the fraction is the root to take. 8^(1/3) is the cube root of 8, which equals 2, since 2 cubed = 8.

Question 27

Convert the binary number 1011 to decimal.

Accepted Answer

Using place values 8, 4, 2, 1: (1x8) + (0x4) + (1x2) + (1x1) = 8+0+2+1 = 11. Binary place values double moving left, starting at 1.

Question 28

What base do binary, octal, and hexadecimal number systems use, and which digits are valid in each?

Accepted Answer

Binary is base 2 (digits 0-1), octal is base 8 (digits 0-7), and hexadecimal is base 16 (digits 0-9 then A-F, where A=10 through F=15).

Question 29

Convert the decimal number 26 into binary.

Accepted Answer

Break 26 into binary place values: 16+8+2 = 26 (the place values 4 and 1 are not needed). This gives binary 11010, checked as 16+8+0+2+0 = 26.

Question 30

What does log base 10 of 1000 equal, and why?

Accepted Answer

log10(1000) = 3, because a logarithm asks 'what power must the base be raised to, to get this number,' and 10 cubed = 1000.

Question 31

What is the rule for log(a times b) in terms of log(a) and log(b)?

Accepted Answer

log(a x b) = log(a) + log(b). Logarithms convert multiplication into addition, which is why they were historically used to simplify long calculations.

Question 32

Solve the quadratic equation x squared = 25 for x.

Accepted Answer

Taking the square root of both sides gives two solutions: x = +5 or x = -5, since both 5 squared and (-5) squared equal 25. An equation in this form always has two roots (or one repeated root).

Question 33

What is the defining property of a right angle, and how is it usually marked in a diagram?

Accepted Answer

A right angle measures exactly 90 degrees, formed where two lines are perpendicular to each other; it is typically marked with a small square symbol at the vertex.

Question 34

What does it mean to bisect a line or an angle?

Accepted Answer

Bisecting means dividing something into two exactly equal parts. Bisecting a line finds its exact midpoint; bisecting an angle splits it into two equal angles.

Question 35

How do you tell whether two lines are parallel versus perpendicular?

Accepted Answer

Parallel lines run in the same direction and never meet, no matter how far extended. Perpendicular lines cross at exactly 90 degrees. A pair of lines cannot be both at once.

Question 36

In the straight-line equation y = mx + c, what do m and c represent?

Accepted Answer

m is the gradient (slope) of the line - how steep it is - and c is the y-intercept, the value of y where the line crosses the y-axis (at x = 0).

Question 37

How do you calculate the gradient of a straight line between two points?

Accepted Answer

Gradient = rise divided by run = (change in y) divided by (change in x) between two points on the line. A steeper line has a larger gradient magnitude.

Question 38

Find the gradient and y-intercept of the line y = 3x - 4.

Accepted Answer

Comparing to y = mx + c, the gradient m = 3 and the y-intercept c = -4, meaning the line crosses the y-axis at (0, -4) and rises 3 units for every 1 unit across.

Question 39

What does the x-intercept of a graph represent, and how do you find it?

Accepted Answer

The x-intercept is where the line crosses the x-axis, meaning y = 0 at that point. Set y = 0 in the equation and solve for x to find it.

Question 40

On a distance-time graph, what does the gradient represent?

Accepted Answer

The gradient of a distance-time graph equals speed, since speed is distance divided by time. A steeper gradient means a faster speed; a flat, zero gradient means stationary.

Question 41

On a speed-time graph, what does the gradient represent?

Accepted Answer

The gradient of a speed-time graph equals acceleration, since acceleration is the rate of change of speed with time. A negative gradient indicates deceleration.

Question 42

What does the mnemonic SOH-CAH-TOA stand for?

Accepted Answer

SOH: Sine = Opposite/Hypotenuse. CAH: Cosine = Adjacent/Hypotenuse. TOA: Tangent = Opposite/Adjacent. It defines the three basic trigonometric ratios for a right-angled triangle.

Question 43

What are the values of sin 30 degrees and cos 60 degrees, and why are they equal?

Accepted Answer

Both sin 30 degrees and cos 60 degrees equal 0.5. They are equal because sine and cosine of complementary angles (angles that sum to 90 degrees) are always equal.

Question 44

What is the value of tan 45 degrees, and why does it equal that value?

Accepted Answer

tan 45 degrees = 1.0 exactly, because at 45 degrees the opposite and adjacent sides of a right triangle are equal in length, so opposite divided by adjacent = 1.

Question 45

What are sin 0 degrees and cos 0 degrees?

Accepted Answer

sin 0 degrees = 0 and cos 0 degrees = 1. At 0 degrees there is no 'opposite' side (giving sine 0), while the adjacent side equals the hypotenuse (giving cosine its maximum value of 1).

Question 46

What are sin 45 degrees and cos 45 degrees, and why are they equal?

Accepted Answer

Both equal approximately 0.707 (exactly the square root of 2, over 2). They are equal because 45 degrees is its own complement (45 + 45 = 90), so sine and cosine of 45 degrees must match.

Question 47

State Pythagoras' theorem and what it is used for.

Accepted Answer

For a right-angled triangle, a squared + b squared = c squared, where c is the hypotenuse (the longest side, opposite the right angle). It lets you find any missing side of a right triangle when the other two are known.

Question 48

A right triangle has legs of length 3 and 4. What is the hypotenuse?

Accepted Answer

Using Pythagoras: c squared = 3 squared + 4 squared = 9 + 16 = 25, so c = square root of 25 = 5. This is the well-known 3-4-5 right triangle, a common shortcut for recognising right angles.

Question 49

What is the difference between rectangular and polar coordinates for locating a point?

Accepted Answer

Rectangular coordinates give a point's position as (x, y) along two perpendicular axes. Polar coordinates instead give a radius (distance from the origin) and an angle. Both describe the same point, just in different forms.

Question 50

How do you find the polar radius of a point given its rectangular coordinates (x, y)?

Accepted Answer

The polar radius equals the square root of (x squared + y squared), which is Pythagoras' theorem applied to the point's distance from the origin, using x and y as the two perpendicular legs.

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EASA Part-66 Module 01 — Mathematics

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