FEUCAT Abstract Reasoning — Mechanical ReasoningCheat Sheet
Mechanical Reasoning cheat sheet for FEUCAT aspirants. If you could only take one sheet of paper into your review session, this is what it would look like. Far Eastern University's most-tested concepts, all in one place.
Exam context
For the Far Eastern University College Admission Test, Far Eastern University tests Abstract Reasoning under a "Core" label, with Mechanical Reasoning in the 4th slot across 5 chapters. FEUCAT candidates must clear the Competitive overall score cut on the 2026 paper, which draws about a meaningful share of Abstract Reasoning questions. Date to watch: Q3–Q4 2026.
Mechanical Reasoning - Cheat sheet
Your last-minute revision companion for mastering mechanical reasoning principles and solving exam problems quickly.
Sections
Formulas
Formula
Speed Ratio = 1 / Size Ratio
Meaning
Speed of driven wheel = Speed of driver wheel ÷ Size ratio
Watch Out
Remember it's INVERSE - smaller wheels turn FASTER, not slower
When To Use
When calculating how fast one wheel turns relative to another
Formula
Turns = Driver turns × (Driver size ÷ Driven size)
Meaning
Number of complete turns made by driven wheel
Watch Out
Always divide driver size by driven size, not the other way around
When To Use
Finding exact number of rotations in gear problems
Section Title
Gears and Wheels
Important Facts
- Large wheel drives small wheel → small wheel turns FASTER
- Small wheel drives large wheel → large wheel turns SLOWER
- Same size wheels turn at same speed
- In gear trains, multiply ratios to find final speed
- Direction alternates in directly connected gears
Key Definitions
Term
Driving Wheel
Example
Motor-connected wheel that turns other wheels
Definition
The wheel that provides power and initiates motion
Term
Driven Wheel
Example
Wheel that rotates because another wheel turns it
Definition
The wheel that receives power from the driving wheel
Term
Gear Ratio
Example
6cm gear driving 3cm gear has 2:1 ratio
Definition
Comparison of sizes between two connected gears
Diagrams To Know
- Gear train diagrams showing multiple connected wheels
- Belt drive systems with pulleys of different sizes
- Wheel and axle mechanisms
Formulas
Formula
Fastest shaft = Smallest driving wheel + Largest driven wheel
Meaning
Best combination for maximum speed increase
Watch Out
Don't confuse driving wheel with driven wheel - they have opposite effects
When To Use
When asked which arrangement makes shaft turn fastest
Section Title
Belt Drive Systems
Important Facts
- Belts don't change direction of rotation (unlike direct gears)
- Belt can slip - less efficient than direct gear contact
- Smaller driving pulley = faster driven pulley
- Larger driving pulley = slower driven pulley
- Belt tension affects power transmission efficiency
Key Definitions
Term
Belt Drive
Example
Bicycle chain connecting pedal gear to wheel gear
Definition
System using flexible belt to transfer power between wheels
Term
Pulley System
Example
Car engine driving alternator through belt
Definition
Wheels with grooved rims connected by belt or rope
Diagrams To Know
- Pulley systems with belts
- Multiple pulley arrangements
- Belt drive speed calculations
Formulas
Formula
Pressure = ρgh
Meaning
ρ = fluid density, g = gravity, h = depth/height
Watch Out
Pressure increases with DEPTH, not height above surface
When To Use
Calculating pressure at different depths in fluids
Common Values
Value
101.3 kPa
Symbol
P₀
Quantity
Atmospheric pressure
Section Title
Fluid Pressure and Flow
Important Facts
- Deeper locations have greater pressure
- Pressure acts equally in all directions at same depth
- Fluid flows from high pressure to low pressure
- Pressure depends on fluid density and depth only
- Same depth = same pressure regardless of container shape
Key Definitions
Term
Fluid Pressure
Example
Water pressure increases as divers go deeper
Definition
Force per unit area exerted by liquid or gas
Term
Hydrostatic Pressure
Example
Pressure at bottom of swimming pool
Definition
Pressure in fluid at rest due to gravitational force
Diagrams To Know
- U-tube manometer readings
- Pressure variation with depth diagrams
- Fluid flow direction indicators
Formulas
Formula
MA = Effort arm ÷ Load arm
Meaning
MA = mechanical advantage, measures force multiplication
Watch Out
Longer effort arm = greater mechanical advantage, not shorter
When To Use
Finding how much force is multiplied by lever
Formula
Effort × Effort arm = Load × Load arm
Meaning
Balance condition for levers in equilibrium
Watch Out
Measure arms from fulcrum, not from ends of lever
When To Use
When lever is balanced or finding unknown forces
Section Title
Levers and Mechanical Advantage
Important Facts
- First class: fulcrum between effort and load (seesaw)
- Second class: load between fulcrum and effort (wheelbarrow)
- Third class: effort between fulcrum and load (tweezers)
- Longer effort arm = less force needed
- Mechanical advantage > 1 means force is multiplied
Key Definitions
Term
Fulcrum
Example
Pivot point of seesaw or crowbar
Definition
Fixed point around which lever rotates
Term
Effort Arm
Example
Distance from pivot to your hand on crowbar
Definition
Distance from fulcrum to where force is applied
Term
Load Arm
Example
Distance from pivot to object being lifted
Definition
Distance from fulcrum to load being moved
Diagrams To Know
- Three classes of levers with examples
- Force diagrams showing effort, load, and fulcrum
- Lever arm measurements
Must Remember
- Inverse relationship: Small driving wheel = Fast driven wheel
- Speed ratio = 1 ÷ Size ratio (not size ratio directly)
- Pressure increases with depth in fluids
- In gear trains, multiply individual ratios for final result
- Belt drives don't reverse rotation direction
- Mechanical advantage = Effort arm ÷ Load arm
- Longer effort arm = less force needed to lift load
- Same depth in fluid = same pressure everywhere
- Count gear teeth or use diameter for size ratios
- Direction alternates in touching gears, stays same with belts
Last Minute Tips
- Draw arrows on gears to track rotation direction - saves time and prevents errors
- For speed calculations, always ask 'Is the driver bigger or smaller?' first
- In pressure problems, find the deepest point - it always has highest pressure
- Label fulcrum, effort, and load clearly in lever problems before calculating
- When multiple gears connect, work step-by-step through each connection
Comparison Tables
Rows
Values
- Large
- Small
- Driven turns FASTER
- 6cm → 3cm: 2× faster
Property
Large to Small
Values
- Small
- Large
- Driven turns SLOWER
- 3cm → 6cm: 2× slower
Property
Small to Large
Values
- Same
- Same
- Same speed
- 3cm → 3cm: 1× speed
Property
Same Size
Columns
- Driving Gear
- Driven Gear
- Speed Change
- Example
Table Title
Gear Size vs Speed Relationship
Rows
Values
- Effort-Fulcrum-Load
- Seesaw, Crowbar
- Can be >1 or <1
Property
First Class
Values
- Fulcrum-Load-Effort
- Wheelbarrow, Nutcracker
- Always >1
Property
Second Class
Values
- Load-Effort-Fulcrum
- Tweezers, Fishing rod
- Always <1
Property
Third Class
Columns
- Class
- Arrangement
- Example
- Mechanical Advantage
Table Title
Lever Classes Comparison
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