Arithmetic
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Algebra - Expressions & Equations
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Algebra - Indices, Logs & Number Systems
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Geometry - Constructions & Graphs
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Trigonometry & Coordinates
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Quick Facts
- Exam
- Part-66 Module 1
- Credential
- Aircraft Maintenance Licence
- Questions
- 32 (Cat B1/B2)
- Time
- 40 min (Cat B1/B2)
- Pass
- 75% per module
- Format
- Multiple choice, 3-option
- Level
- Foundation module
- Blueprint
- Reg (EU) 2023/989
HCF vs LCM
HCF
- Largest shared factor
- Used to simplify fractions
LCM
- Smallest shared multiple
- Used to add fractions
Divides into vs divisible by
Which Operation to Apply
- Fraction plus fraction→Find common denominator first(Then add numerators)
- Percentage change wanted→Multiply base by percent(Add or subtract result)
- Ratio shares a total→Divide total by parts(Multiply per share)
- Need area of circle→π times radius squared
- Need volume of cylinder→π r² times height
- Need average of values→Sum values, divide by count
Fractions & Decimals
- 1/2
- 0.5 or 50%
- 1/4
- 0.25 or 25%
- 3/4
- 0.75 or 75%
- 1/8
- 0.125 or 12.5%
- 5/8
- 0.625 or 62.5%
- Add/subtract fractions
- Use common denominator first
- Multiply fractions
- Top times top, bottom times bottom
- Divide fractions
- Multiply by the reciprocal
Area vs Volume
Area
- Two dimensions only
- Measured in square units
Volume
- Three dimensions total
- Measured in cubic units
Flat surface vs solid space
Ratio, Percentage & Averages
- Ratio a:b
- Split total into a+b parts
- Percentage of X
- (part ÷ whole) × 100
- Increase by %
- Add the percentage amount
- Decrease by %
- Subtract the percentage amount
- Mean (average)
- Sum of values ÷ count
- HCF
- Highest common factor of numbers
- LCM
- Lowest common multiple of numbers
Areas, Volumes & Roots
- Rectangle area
- Length times width
- Triangle area
- Half of base times height
- Circle area
- π times radius squared
- Circle circumference
- 2 times π times radius
- Cylinder volume
- π times radius² times height
- Box volume
- Length times width times height
- Square/cube root
- Inverse of squaring or cubing
Units & Conversions
- 1 metre
- 1000 mm or 100 cm
- 1 kilogram
- 1000 grams
- 1 litre
- 1000 millilitres
- 1 tonne
- 1000 kilograms
- Scale 1:50
- Drawing length times 50
Order of Operations
Brackets, Indices, Divide, Multiply, Add, Subtract
Brackets firstThen indices/powersThen divide and multiplyThen add and subtract
Solving Equations Selector
- One unknown, one equation→Isolate the unknown
- Two unknowns, two equations→Elimination or substitution
- Brackets in expression→Expand brackets first
- Unlike terms present→Collect like terms only
- Fraction with unknown→Multiply to clear fraction
- Need to verify answer→Substitute back into equation
Algebraic Expressions
- Like terms
- Combine matching variables only
- Expand brackets
- Multiply each term inside
- Substitute value
- Replace the letter with number
- Algebraic fraction
- Cancel common factors first
- x² ÷ x
- Subtract powers, result is x
Linear & Simultaneous Equations
- Linear equation
- Solve for one unknown
- Isolate x
- Same operation on both sides
- Simultaneous equations
- Two unknowns, two equations needed
- Elimination method
- Add or subtract the equations
- Substitution method
- Substitute one equation into other
- Check your solution
- Plug values back into equations
Binary Place Values
Powers of two: 1, 2, 4, 8, 16, 32
Rightmost digit is onesEach place doubles leftwardHex A-F equal 10-15
Binary vs Hexadecimal
Binary
- Base 2
- Digits 0 and 1 only
Hexadecimal
- Base 16
- Digits 0-9 then A-F
Fewer digits vs more digits
Indices, Logs & Number Base Selector
- Multiplying same base powers→Add the indices
- Dividing same base powers→Subtract the indices
- Power of zero seen→Result is always 1
- Negative index shown→Take the reciprocal
- Fractional index (1/2)→Take the square root
- Base other than 10→Convert to decimal first
Indices & Powers Laws
- x^a × x^b
- Add the indices (a+b)
- x^a ÷ x^b
- Subtract the indices (a−b)
- x^0
- Always equals 1
- x^-a
- Reciprocal: 1 divided by x^a
- x^(1/2)
- Same as square root of x
- (x^a)^b
- Multiply the indices (a×b)
Number Systems
- Binary base
- 2, digits 0 and 1
- Octal base
- 8, digits 0 through 7
- Hexadecimal base
- 16, digits 0 through F
- Binary place values
- 1, 2, 4, 8, 16, 32
- Binary 1011
- Equals decimal 11
Logarithms & Quadratics
- log₁₀ 1000
- Equals 3 (10³ = 1000)
- Logarithm meaning
- Power needed to reach number
- log(ab)
- Add logs when multiplying
- x² = 9
- x equals plus or minus 3
Gradient vs Y-Intercept
Gradient
- Coefficient of x
- Steepness of the line
Y-intercept
- Constant term c
- Where line meets y-axis
Slope vs starting point
Geometric Constructions
- Right angle
- Exactly 90 degrees
- Bisect
- Divide into two equal parts
- Perpendicular lines
- Meet at 90 degrees
- Parallel lines
- Never meet, same direction
- Scale drawing
- Proportional to the real size
Graphs of Functions
- y = mx + c
- m is gradient, c is intercept
- Gradient
- Rise over run (slope)
- y-intercept
- Where the line crosses y-axis
- x-intercept
- Where y equals zero
- Distance-time graph
- Gradient equals speed
- Speed-time graph
- Gradient equals acceleration
SOH-CAH-TOA
Sin=Opp/Hyp, Cos=Adj/Hyp, Tan=Opp/Adj
Sin: opposite over hypotenuseCos: adjacent over hypotenuseTan: opposite over adjacent
Sine vs Cosine
Sine
- Opposite ÷ hypotenuse
- Rises 0 to 1
Cosine
- Adjacent ÷ hypotenuse
- Falls 1 to 0
Opposite side vs adjacent side
Trig & Coordinates Selector
- Know two triangle sides→Apply Pythagoras theorem
- Need opposite over hypotenuse→Use sine ratio
- Need adjacent over hypotenuse→Use cosine ratio
- Need opposite over adjacent→Use tangent ratio
- Point given as (x,y)→That is rectangular form
- Point given as radius/angle→That is polar form
Trig Ratios & Standard Angles
- SOH-CAH-TOA
- SOH-CAH-TOA (opp/adj/hyp)
- sin 30°
- Equals 0.5
- sin 45° = cos 45°
- Equals 0.707
- sin 60° = cos 30°
- Equals 0.866
- tan 45°
- Equals 1.0 exactly
- cos 0°
- Equals 1.0, maximum value
- sin 0°
- Equals 0
Standard Trig Values
Memorise sin 30, 45, 60 degrees
sin 30° = 0.5sin 45° = 0.707sin 60° = 0.866tan 45° = 1.0
Rectangular vs Polar Coordinates
Rectangular
- Uses (x, y) values
- Perpendicular axes
Polar
- Uses radius and angle
- Distance plus direction
Position vs distance and angle
Pythagoras & Coordinates
- Pythagoras
- a² + b² = c²
- 3-4-5 triangle
- Common right-triangle number set
- 5-12-13 triangle
- Another common right triple
- Rectangular coordinates
- Given as (x, y)
- Polar coordinates
- Given as radius and angle
- Polar radius
- Square root of x²+y²
Common Traps
Area ≠ Volume
Area is length times width ≠ Volume adds a third dimension
HCF ≠ LCM
HCF divides both numbers ≠ LCM is divisible by both
Sine ≠ Cosine
Sine uses opposite side ≠ Cosine uses adjacent side
Gradient ≠ Y-Intercept
Gradient is coefficient of x ≠ Intercept is the constant term
Add Indices ≠ Multiply Indices
Multiplying powers adds indices ≠ Raising a power multiplies indices
Rectangular ≠ Polar Coordinates
Rectangular uses x and y ≠ Polar uses radius and angle
Last Minute
- 1.32 questions, 40 minutes (B1/B2)
- 2.16 questions, 20 minutes (Category A)
- 3.75% pass mark per module
- 4.Real exam uses 3 options
- 5.Common denominator before adding fractions
- 6.Multiply indices when raising powers
- 7.Add indices when multiplying powers
- 8.Negative index means take reciprocal
- 9.SOH-CAH-TOA for right triangles
- 10.Gradient is coefficient of x
- 11.Pythagoras: a² + b² = c²
- 12.Hex digits A-F equal 10-15
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