Part-66 Module 1: the maths you need without a calculator

For category B1, Module 1 is 32 multiple-choice questions in 40 minutes with three choices each and a 75% pass mark. Most exams do not allow calculators, so the numbers are chosen to be worked by hand. Speed and accuracy with basic methods matter more than advanced theory.

Arithmetic

• Fractions: use a common denominator to add or subtract; multiply straight across; to divide, multiply by the reciprocal.
• Decimals and percentages: 3/8 = 0.375 = 37.5%. A percentage change is always based on the original value.
• Ratio and proportion: divide 60 in the ratio 2:3 by splitting into 5 parts. In inverse proportion, fewer workers take longer.
• Order of operations: brackets, powers, multiplication and division, then addition and subtraction.
• Conversions: 1 in = 25.4 mm, 1 ft = 0.3048 m, 1 kg = 2.2046 lb, 1 US gal = 3.785 L, 1 bar = 14.5 psi, °F = °C × 9/5 + 32, 1 NM = 1,852 m.
• Areas and volumes: circle πr², circumference πd, triangle ½ × base × height, cylinder πr²h, sphere 4/3 πr³. 1 litre = 1,000 cm³.

Algebra

• Solve linear equations by doing the same to both sides. Transpose formulas such as V = IR to R = V/I.
• Indices: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ, a^(1/2) = √a.
• Standard form: 0.00052 = 5.2 × 10⁻⁴.
• Logarithms: log₁₀ 1,000 = 3; log a + log b = log ab.
• Number systems: binary place values 1, 2, 4, 8…; 1011₂ = 11; hexadecimal 1F = 31; octal 17 = 15.
• Simultaneous equations: add or subtract to eliminate one unknown.
• Quadratics: factorise where possible; b² − 4ac < 0 means no real roots.

Geometry and trigonometry

• Angles in a triangle add to 180°, in a quadrilateral to 360°, in any polygon to (n − 2) × 180°.
• Pythagoras: c² = a² + b² (6, 8, 10 and 3, 4, 5 triangles appear often).
• SOH CAH TOA: sin 30° = 0.5, cos 60° = 0.5, tan 45° = 1, sin 60° ≈ 0.866.
• 180° = π radians, so 1 rad ≈ 57.3°.
• Polar to rectangular: x = r cos θ, y = r sin θ.
• In y = mx + c, m is the gradient and c the y-intercept. A straight line through the origin shows direct proportion; y = 1/x is a hyperbola.

Practise until each type takes under a minute: the exam allows about 75 seconds per question.