PAF Aeronautical Engineering Initial Test Cheat Sheet

Intelligence Test

Not published of exam
Analogies + Classification Coding, Series + Logic Figure Series + Matrices Rotation + Spatial Rules

English

Not published of exam
Fixed Prepositions Voice, Tense + Agreement Sentence Completion + Collocation High-Frequency Spellings

Physics (FSc Level)

Not published of exam
Units + Measurement Mechanics Formulas Fluids + Flight Physics Heat + Thermodynamics Electricity + Magnetism Waves + Optics Modern Physics + Electronics

Mathematics (FSc Level)

Not published of exam
Algebra + Matrices Sequences + Binomial Trigonometry Calculus Conics + Vectors Counting + Probability

Route + Logistics

Not published of exam
What PAF Publishes Selection Sequence Centre Day Documents Source Tiers

Quick Facts

Course 108 Aeronautical Engineering Course
Stage 1 Intelligence test
Stage 2 E-test: English, Physics, Maths
Level FSc; Punjab Board Books I-II
Chemistry Eligibility only, not tested
Flying Aptitude Test GD Pilot only, not CAE
Questions Not published by PAF
Time Not published by PAF
Pass mark Not published by PAF
Only authority joinpaf.gov.pk active notice

Rotation Map IN

90° clockwise: up→right→down→left
180° = opposite side Anticlockwise reverses it Mirror ≠ rotation

Rotation vs Reflection IN

Rotation

Handedness preserved
Turn about a centre
90°, 180°, 270°

Reflection

Handedness reversed
Mirror across a line
Looks flipped
Mirrored option is reflection

Number Series Picker IN

Constant gap → Arithmetic rule ( Add d )
Gap changes steadily → Second differences
Constant ratio → Geometric rule ( Multiply by r )
Alternating jumps → Two interleaved series
Near squares or cubes → n² or n³ ± k
Nothing fits fast → Skip and return ( Pacing )

Analogies + Classification IN

Analogy Build one precise bridge sentence
Bridge test Narrow sentence if two fit
Odd-one-out Property excluding exactly one item
Classification Category, state, or numeric property
Synonym pairs Match register, not difficulty
Direction sense Sketch axes before counting turns
Verbal logic Only necessary conclusions count
Quantifier trap Some never supports all

Dice + Nets IN

Opposite faces sum to seven
Never both in view One gap = opposite face n folds → 2ⁿ holes

Coding, Series + Logic IN

Coding rule Derive from one letter
Confirm step Verify rule on second letter
Shift cipher Constant +1, -2 letter offset
Reversal cipher A↔Z, B↔Y mapping
Letter positions A=1 up to Z=26
Series order Differences, then ratios, then alternating
Second differences Try when first differences vary
Geometric jump Constant ratio: 2, 6, 18
Squares/cubes n² or n³ plus constant

Figure Series + Matrices IN

One attribute Track rotation, count, shading separately
Two cycles Most series run independent rules
3×3 matrix Check columns, not only rows
Overlay rule Sum, difference, or overlap
Second-line check Rule must repeat elsewhere
Odd figure One attribute breaks the set
Embedded figure Same size, same orientation, hidden

Rotation + Spatial Rules IN

90° clockwise Up→right→down→left→up
180° turn Every point to opposite side
Rotation test Handedness preserved, mirror is reflection
Mirror image Reflection, never a rotation
Paper folding n folds → 2ⁿ holes
Unfolding Reverse order, mirror each fold
Dice opposites Opposite faces sum to seven
Cube net One square gap = opposite face

Preposition Pairs EN

Consist of, comply with, differ from
depend on capable of responsible for superior to deprive of

Active vs Passive EN

Active

Subject acts
Technician calibrated instrument
Direct word order

Passive

Object becomes subject
be + past participle
Agent after 'by'
Tense must not drift

English Item Picker EN

Blank after verb → Fixed preposition list
'By' agent appears → Passive voice item
Subject far from verb → Ignore intervening phrase
Neither...nor present → Agree with nearer subject
Two synonyms offered → Pick standard collocation
If-clause given → Present tense after if

Fixed Prepositions EN

consist of Be made up of
comply with Follow a rule
differ from Be unlike something
depend on Be determined by
capable of Able to do
familiar with Know well
responsible for Accountable for
superior to Better than; never 'than'
insist on Demand firmly
deprive of Take away from
adhere to Stick to; follow
result in Cause; result from = caused

Voice, Tense + Agreement EN

Passive form be + past participle
Passive subject Old object becomes subject
Agent Old subject follows 'by'
Tense drift Passive keeps original tense
Each, every Always singular verb
Neither...nor Verb agrees with nearer subject
Intervening phrase 'The set of tools' ignored
Real condition If + present, then will
Will in if-clause Error in real conditions
Since vs for Point in time vs duration

Sentence Completion + Collocation EN

conduct research Standard academic collocation
carry out a test Standard technical collocation
accurate representation Register matches formal writing
Near-synonym trap Fits meaning, breaks the phrase
Read whole sentence Test each option in place
Signal words However, therefore set direction

High-Frequency Spellings EN

maintenance -ance, not -ence
occurrence Double c, double r
accommodate Double c, double m
necessary One c, double s
separate 'par' in the middle
recommend One c, double m
definitely No 'a'; finite inside
equipment Single p, no 'e'

Significant Figures PH

Multiply → sig figs; add → decimals
×,÷ least sig figs +,− least decimal places Check both sides

Isothermal vs Adiabatic PH

Isothermal

Constant temperature
ΔU = 0
Heat becomes work

Adiabatic

No heat flow
Q = 0
Expansion cools gas
Heat in vs temperature held

Physics Approach Picker PH

Forces, no acceleration → Both equilibrium conditions
Speed change asked → Work-energy theorem
Collision or impact → Impulse-momentum ( Ft = Δp )
Circular path → a = v²/r ( Toward centre )
Duct narrows → Continuity, then Bernoulli
Gas process named → First law with condition
Flux changing → Faraday plus Lenz
Light and frequency → Photoelectric equation

Units + Measurement PH

Sig figs (×,÷) Fewest sig figs wins
Sig figs (+,−) Fewest decimal places wins
Base units m, kg, s, A, K
Newton kg·m/s²
Pascal N/m²
Joule N·m = kg·m²/s²
Watt J/s
Dimensional check Both sides must match
Random vs systematic Averaging fixes random only

Gas Processes PH

Isothermal ΔU=0, adiabatic Q=0
Isobaric: W = PΔV Isochoric: no work Always use kelvin

Series vs Parallel PH

Series

Resistances add
Above largest resistor
Same current

Parallel

Reciprocals add
Below smallest resistor
Same voltage
Check against smallest resistor

Mechanics Formulas PH

F = ma Only when mass constant
F = Δp/Δt General second-law form
Impulse Ft = Δp; longer time, less force
Work-energy Net work = ΔKE
Power P = W/t = Fv
1st equilibrium ΣF = 0, no acceleration
2nd equilibrium Στ = 0, no spin
Centripetal a = v²/r, toward centre
Centrifugal Only in rotating frame
Projectile range R = v²sin2θ/g, max 45°
SHM condition a ∝ -x toward equilibrium
Pendulum period T = 2π√(l/g)
Mass-spring period T = 2π√(m/k)
Escape velocity v = √(2GM/R)

Fluids + Flight Physics PH

Continuity A₁v₁ = A₂v₂
Narrow duct Smaller area, higher speed
Bernoulli P + ½ρv² + ρgh constant
Bernoulli limits Steady, non-viscous, incompressible, one streamline
Lift explanation Faster flow, lower pressure
Terminal velocity Drag balances weight, zero acceleration
Stokes drag F = 6πηrv for spheres
Torricelli v = √(2gh) from orifice

Heat + Thermodynamics PH

First law ΔU = Q - W
Isothermal ΔU = 0; heat becomes work
Adiabatic Q = 0; gas cools expanding
Isobaric Constant pressure; W = PΔV
Isochoric Constant volume; no work
Carnot efficiency 1 - T_cold/T_hot in kelvin
Second law Entropy of universe increases
Ideal gas PV = nRT
Kelvin rule Gas laws need absolute temperature

Electricity + Magnetism PH

Coulomb F ∝ q₁q₂/r²
Inverse square Triple distance → one ninth
Field vs force E depends on source charge
Series R Add; total exceeds largest
Parallel R Reciprocals; below smallest resistor
Two equal parallel Exactly half one resistor
Capacitors Opposite of resistor rules
Conductor force F = BIL sinθ
Moving charge F = qvB sinθ
Max vs zero force Perpendicular max, parallel zero
Faraday EMF ∝ rate of flux change
Lenz Induced current opposes change
RMS Peak/√2 ≈ 0.707 peak
220 V mains RMS; peak about 311 V

Waves + Optics PH

Wave equation v = fλ
New medium Frequency fixed, wavelength changes
Doppler Approach raises observed frequency
Young's fringes Δy = λL/d
Bright fringe Path difference = nλ
Dark fringe Path difference = (n+½)λ
Diffraction grating d sinθ = nλ
Polarisation Transverse only; not sound
Snell n₁sinθ₁ = n₂sinθ₂
Total internal reflection Dense → rare, beyond critical angle
Convex lens Positive focal length
Concave lens Negative focal length; virtual image
Lens power P = 1/f in dioptres

Modern Physics + Electronics PH

n-type Pentavalent dopant; electrons majority
p-type Trivalent dopant; holes majority
Doped crystal charge Still electrically neutral overall
Forward bias p to positive; current flows
Reverse bias Wide depletion; blocks current
Half-wave rectifier One diode; half cycle
Full-wave rectifier Four-diode bridge; both halves
Zener Reverse breakdown; voltage regulator
AND gate Output 1 only if both
NAND gate Universal gate; inverted AND
Photoelectric KE_max = hf - φ
Threshold frequency Below it, no emission ever
Intensity effect More electrons, same maximum energy
de Broglie λ = h/p
Half-life Fixed fraction, independent of amount
Mass defect Binding energy = Δmc²

Discriminant Signs MA

D>0 two, D=0 one, D<0 complex
D = b² - 4ac Perfect square → rational Negative → conjugate pair

Dot vs Cross Product MA

Dot

Scalar result
|a||b| cosθ
Zero when perpendicular

Cross

Vector result
|a||b| sinθ
Zero when parallel
Scalar vs vector

Maths Method Picker MA

Root nature asked → Discriminant only ( Skip solving )
Other root wanted → Sum and product rules
One coefficient wanted → Binomial general term
Limit gives 0/0 → Factor or rationalise
Composite function → Chain rule
Max or min asked → f'=0, then f''
Area under curve → Definite integral
Perpendicularity asked → Dot product zero
Order matters → nPr ( Else nCr )

Algebra + Matrices MA

Discriminant D = b² - 4ac
D > 0 Two distinct real roots
D = 0 One repeated real root
D < 0 Conjugate complex root pair
Perfect square D Roots are rational
Sum of roots -b/a
Product of roots c/a
Rebuild quadratic x² - (sum)x + product
Inverse exists Determinant non-zero (non-singular)
2×2 inverse 1/(ad-bc) × [[d,-b],[-c,a]]
Zero determinant No unique solution
Partial fractions Split proper rational expression
Log product log(ab) = log a + log b
Change of base log_b x = ln x/ln b

Conic Classifier MA

One square parabola, added ellipse, subtracted hyperbola
Equal coefficients → circle Read signs before algebra y² = 4ax → focus (a,0)

Permutation vs Combination MA

nPr

Order matters
Seating, ranking, codes
Always larger

nCr

Order ignored
Committees, teams, handshakes
Always smaller
nPr = nCr × r!

Sequences + Binomial MA

AP nth term a + (n-1)d
AP sum n/2 [2a + (n-1)d]
GP nth term a r^(n-1)
GP sum a(1-rⁿ)/(1-r)
Infinite GP a/(1-r) only if |r|<1
AM (a+b)/2
GM √(ab) and AM ≥ GM
General term C(n,r)·a^(n−r)·b^r
Find coefficient Solve for r; skip expansion
Middle term n even → one middle term
Induction steps Base case, then step n+1

Independent vs Mutually Exclusive MA

Independent

Multiply probabilities
One does not affect other

Mutually exclusive

Cannot both occur
Add probabilities
Never both, unless zero

Trigonometry MA

sin(A±B) sinA cosB ± cosA sinB
cos(A±B) cosA cosB ∓ sinA sinB
Sign flip Cosine formula reverses the sign
sin 2A 2 sinA cosA
cos 2A cos²A - sin²A
cos 2A forms 1-2sin²A or 2cos²A-1
tan 2A 2tanA/(1-tan²A)
Pythagorean sin²θ + cos²θ = 1
Sine rule a/sinA = b/sinB
Cosine rule c² = a² + b² - 2ab cosC
arcsin range -90° to 90°
arccos range 0° to 180°
arctan range Strictly between -90° and 90°
General solution Add 360°n; tangent adds 180°n
Radian mode Calculus limits assume radians

Calculus MA

Product rule u'v + uv'
Quotient rule (u'v - uv')/v²
Quotient order Reversing numerator flips sign
Chain rule dy/du × du/dx
0/0 limit Indeterminate: factor or rationalise
sin x / x → 1 as x → 0
Stationary point f'(x) = 0
f'' < 0 Maximum
f'' > 0 Minimum
f'' = 0 Inconclusive; check f' signs
Power integral x^(n+1)/(n+1) + C
n = -1 case ∫dx/x = ln|x| + C
∫eˣ dx eˣ + C
∫sin x dx -cos x + C
Definite integral F(b) - F(a)
No +C Definite integrals drop the constant
Substitution limits Convert limits or revert x

Conics + Vectors MA

One square only Parabola
y² = 4ax Focus (a, 0)
Squares added Ellipse (unequal denominators)
Squares subtracted Hyperbola
Equal coefficients Circle
Classify first Read signs before algebra
Line gradient m = (y₂-y₁)/(x₂-x₁)
Perpendicular lines m₁m₂ = -1
Dot product |a||b| cosθ; a scalar
Dot = 0 Vectors are perpendicular
Cross product |a||b| sinθ; a vector
Cross = 0 Vectors are parallel
Anti-commutative a×b = -(b×a)
Unit vectors i×j = k, j×k = i

Counting + Probability MA

nPr n!/(n-r)!; order matters
nCr n!/(r!(n-r)!) order ignored
Relation nPr = nCr × r!
Which is larger Permutations always exceed combinations
Committee, team Combination
Seating, ranking Permutation
Independent events P(A∩B) = P(A)P(B)
Mutually exclusive P(A∩B) = 0
Addition rule P(A)+P(B)-P(A∩B)
Complement 1 - P(A)
Both at once Cannot be independent and exclusive

Test Order RO

Intelligence → English → Physics → Maths
Intelligence first English, Physics, Maths Maths is CAE-only No Chemistry

CAE vs GD Pilot RO

CAE

English, Physics, Maths
No Flying Aptitude Test
Engineering branch

GD Pilot

English and Physics
Flying Aptitude Test
Pilot branch
Maths only for CAE

Which Stage Applies RO

Applying for CAE → English, Physics, Maths
Applying GD Pilot → English and Physics
Told to prepare FAT → Not a CAE stage
Passed e-testing → Medical and interview
Shortlisted by PAF → ISSB, then final medical
Number seen online → Check the source tier

What PAF Publishes RO

Intelligence test First stage; verbal, non-verbal
CAE academic test English, Physics, Mathematics
GD Pilot e-test English and Physics only
Maths section CAE only among officer courses
Syllabus level Punjab Textbook Board Books I-II
Chemistry Eligibility subject, never tested
Flying Aptitude Test GD Pilot only, not CAE
ISSB centres Kohat, Gujranwala, Malir, Quetta
Final medical CMH Lahore
Final selection Air Headquarters, overall merit
Training college CAE Risalpur; BE Aerospace/Avionics
Not published Counts, timing, weights, pass mark
Also not published Fee, retry rule, cutoffs
Only authority Active notice on joinpaf.gov.pk

Eligibility vs Tested RO

Eligibility

Chemistry required
Marks, age, height
Set by advertisement

Tested

English, Physics, Maths
Intelligence test first
No Chemistry
Entry rule ≠ test paper

Selection Sequence RO

1. Registration Online at joinpaf.gov.pk
2. Intelligence test Verbal and non-verbal
3. Academic e-test English, Physics, Mathematics
4. Initial medical At the selection centre
5. Interview At the selection centre
6. ISSB Shortlisted candidates only
7. Final medical CMH Lahore
8. Final selection Air Headquarters, overall merit

Initial Test vs ISSB RO

Initial test

One day
Academic and reasoning
At selection centre

ISSB

Multi-day board
Psychological, leadership tasks
Kohat, Gujranwala, Malir, Quetta
Knowledge vs personality

Centre Day Documents RO

Matric mark sheet Original plus attested copies
Intermediate mark sheet Original plus attested copies
NADRA Smart Card Token if not yet issued
Parents' CNICs Both, attested copies
Hope Certificate If result still pending
Registration slip Carries date, time, centre
Verification time Arrive early; queues are long
Missing document Can end the cycle

Published vs Reported RO

Published

Subjects and order
Syllabus books
Selection sequence

Reported

Question counts
Section minutes
Cutoff percentages
Plan on published only

Source Tiers RO

Tier 1 Active PAF induction advertisement
Tier 2 PAF training and portal pages
Tier 3 Candidate recall; unverified
Tier 4 Coaching tables; marketing claims
Height dispute 163 cm vs 165 cm online
Only your notice Settles eligibility for your intake
Leaked papers Recall or sales hook
Payment warning Never pay unverified channels

Common Traps

Chemistry

Eligibility subject ≠ Not on the test

GD Pilot material

English and Physics ≠ CAE adds Mathematics

Flying Aptitude Test

GD Pilot stage ≠ Never a CAE stage

SSC Engineering Branch

Needs BE and PEC ≠ Separate induction entirely

Coaching cutoffs

Candidate reports ≠ PAF publishes no cutoff

Initial test vs ISSB

Initial is academic ≠ ISSB is a later board

Will in if-clause

Present tense after if ≠ Will in main clause

Significant figures

Products use sig figs ≠ Sums use decimal places

Frequency at boundary

Wavelength changes ≠ Frequency stays fixed

Parallel resistance

Below smallest resistor ≠ Never above it

Centripetal force

Role of existing force ≠ Not an extra force

Quotient rule order

u'v minus uv' ≠ Reversing flips the sign

Last Minute

1. CAE test: English, Physics, Maths
2. Intelligence test comes first
3. Chemistry is eligibility, not tested
4. No Flying Aptitude Test for CAE
5. Syllabus = Punjab Board Books I-II
6. Counts, timing, cutoff: not published
7. Prepositions are highest-yield English topic
8. Passive = be + past participle
9. Discriminant positive means two real roots
10. Parallel resistance below smallest resistor
11. Frequency stays fixed at a boundary
12. Isothermal ΔU=0; adiabatic Q=0
13. Dot zero perpendicular, cross zero parallel
14. nPr when order matters, else nCr
15. Bring originals, attested copies, CNICs
16. Only joinpaf.gov.pk settles your rules

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