EASA Part 66 · Module 1
Part 66 Module 1 maths formula cheat sheet
Every key formula and method for EASA Part 66 Module 1 (Mathematics) on one page — arithmetic, algebra, geometry and trigonometry. Free, no account needed. Grab the printable PDF and keep it beside you while you revise.
Module 1.1
Arithmetic
Order of operations & signs
- BIDMAS / BODMAS: Brackets → Indices → Division/Multiplication → Addition/Subtraction.
- Two like signs give +; two unlike signs give −. (−a)×(−b) = +ab.
- ≈ means approximately equal; = means exactly equal.
Fractions
- Add/subtract: put over a common denominator first.
- Multiply: a/b × c/d = ac/bd. Divide: multiply by the reciprocal — a/b ÷ c/d = a/b × d/c.
- Reciprocal of a fraction = flip it (a/b → b/a).
- Always cancel to lowest terms at the end.
Fractions ↔ decimals ↔ percentages
- Fraction → decimal: divide numerator by denominator.
- Decimal → fraction: write over a power of ten, then cancel.
- Percentage → fraction: write over 100 and cancel. Percentage → decimal: ÷ 100.
Factors & multiples
- HCF = largest number that divides both exactly.
- LCM = smallest number both divide into exactly.
- Prime = only factors are 1 and itself; composite has others.
Ratio & proportion
- Sharing in a ratio: add the parts → value of one part = total ÷ sum of parts → scale each.
- Simplify a ratio by dividing every part by their common factor.
- Direct proportion: cross-multiply to find the unknown.
Percentages
- Percentage of an amount: (% ÷ 100) × amount.
- Increase: add it on. Decrease: take it away.
- As a percentage: (part ÷ whole) × 100.
Averages
- Mean = sum of values ÷ number of values.
- Median = middle value when in order. Mode = most frequent value.
- Range = largest − smallest.
Powers, indices & roots
- Multiply same base: add indices (aᵐ × aⁿ = aᵐ⁺ⁿ). Divide: subtract (aᵐ ÷ aⁿ = aᵐ⁻ⁿ).
- Power of a power: multiply indices ((aᵐ)ⁿ = aᵐⁿ). a⁰ = 1.
- Negative index: a⁻ⁿ = 1 ÷ aⁿ. Fractional: a^(m/n) = ⁿ√(aᵐ).
- Squaring = n×n; cubing = n×n×n. A root reverses this.
Scientific / standard form
- Write as a number from 1 to <10 × a power of ten (e.g. 4.7 × 10³).
- Multiplying: multiply the fronts, add the powers, then renormalise the front to 1–9.99.
Units & conversions
- Multiply by the conversion factor — check which way it goes.
- Metric prefixes step in ×1000 (…milli → unit → kilo → mega…).
- Area units × (10ⁿ)²; volume units × (10ⁿ)³. e.g. 1 m² = 10 000 cm², 1 m³ = 1 000 000 cm³.
Areas, perimeters & volumes
- Rectangle = l × w. Triangle = ½ × base × height.
- Circle: area = π r²; circumference = 2 π r (= π d).
- Cuboid = l × w × h. Cube = side³. Cylinder = π r² × h.
- Sphere: volume = 4/3 π r³; surface area = 4 π r².
Denominated numbers
- Time: 60 min = 1 hour — carry/borrow at 60.
- Length: 12 inches = 1 foot — carry/borrow at 12.
- Angles: 60 minutes = 1 degree — carry/borrow at 60.
Module 1.2
Algebra
Expressions
- Collect like terms (same letter and power).
- Evaluate: substitute the numbers for the letters, then use BIDMAS.
- Expand a bracket: multiply the outside term by each inside term.
- Two brackets (FOIL): (a+b)(c+d) = ac + ad + bc + bd.
Algebraic fractions
- Same denominator: combine the numerators, then simplify.
- Different denominators: rewrite over a common denominator first.
- Simplify by factorising, then cancelling common factors.
Linear equations & transposition
- Expand brackets, gather the unknown on one side, then divide.
- Do the same operation to both sides to keep the balance.
- Rearranging a formula: undo each operation in reverse; square to clear a √, multiply up to clear a denominator.
Index laws (algebra)
- xᵐ × xⁿ = xᵐ⁺ⁿ; xᵐ ÷ xⁿ = xᵐ⁻ⁿ; (xᵐ)ⁿ = xᵐⁿ.
- x⁻ⁿ = 1/xⁿ; x^(1/n) = ⁿ√x; x⁰ = 1.
Simultaneous equations
- Eliminate one unknown by adding/subtracting the two equations…
- …or substitute one equation into the other, then solve.
Quadratics (second-degree)
- Factorise into two brackets, then set each = 0.
- Pure x²: isolate x², then take the square root of both sides (remember ±).
- Formula: x = (−b ± √(b² − 4ac)) / 2a.
- Discriminant = b² − 4ac (positive → 2 roots, 0 → 1, negative → none real).
Logarithms
- A log asks: base to what power gives this? logₐx = y ⇔ aʸ = x.
- log(ab) = log a + log b; log(a/b) = log a − log b; log(aⁿ) = n log a.
- ln = log base e; ln(e) = 1; ln(1) = 0.
Number systems
- Binary → decimal: add place values (1,2,4,8,16…) where there is a 1.
- Decimal → binary: divide by 2 repeatedly, read remainders bottom-up.
- Hex digits A–F = 10–15; each place is a power of 16. Octal uses powers of 8.
Rounding & significant figures
- Look at the next digit: 5 or more rounds up, otherwise down.
- Count significant figures from the first non-zero digit.
Module 1.3
Geometry & trigonometry
Angles & polygons
- Angles on a straight line = 180°; around a point = 360°.
- Angles in a triangle = 180°.
- Polygon interior angle sum = (n − 2) × 180°.
- Exterior angles sum = 360°; each one (regular) = 360° ÷ n.
Shape properties
- Equilateral = 3 equal sides & angles; isosceles = 2 equal; scalene = none.
- Lines of symmetry = the lines a shape reflects onto itself.
Pythagoras' theorem
- a² + b² = c², where c is the hypotenuse (longest side).
- Missing leg: rearrange → a = √(c² − b²).
- Right-angled if a² + b² = c² holds.
Trigonometry ratios
- SOH-CAH-TOA: sin = O/H, cos = A/H, tan = O/A.
- Find an angle: apply the inverse — sin⁻¹, cos⁻¹ or tan⁻¹.
Standard trig values
- sin: 0°=0, 30°=0.5, 45°=√2/2, 60°=√3/2, 90°=1.
- cos: the reverse (0°=1, 30°=√3/2, 45°=√2/2, 60°=0.5, 90°=0).
- tan: 0°=0, 30°=1/√3, 45°=1, 60°=√3, 90°=undefined.
Radians
- π radians = 180°.
- Degrees → radians: × π/180. Radians → degrees: × 180/π.
Coordinate geometry
- Straight line: y = mx + c (m = gradient, c = y-intercept).
- Gradient = change in y ÷ change in x.
- Midpoint = (average of x's, average of y's).
- Distance = √((x₂ − x₁)² + (y₂ − y₁)²).
Polar coordinates
- From (x, y): r = √(x² + y²).
- Angle θ = tan⁻¹(y / x).
Now put it into practice
Knowing the formulas is half the battle — the exam tests whether you can apply them under time. Practise 1,000+ original Module 1 questions, each with a full worked explanation, and take timed mock tests.
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