Spatial and Mechanical Reasoning
What this domain tests
Spatial reasoning covers mental rotation, folding and unfolding nets, mirror images, and block counting. Mechanical reasoning covers levers, pulleys, gears, pressure, and basic physics intuition.
Concepts to master
- Mental rotation: track a distinctive feature (a notch, a coloured face) rather than the whole object.
- Nets and folding: opposite faces on a cube net never touch; a face adjacent in the net stays adjacent when folded.
- Levers: moment = force × distance from pivot; balance requires equal moments.
- Pulleys: a single fixed pulley changes direction only; a movable pulley halves the effort.
- Gears: meshed gears rotate in opposite directions; a larger gear turns more slowly (ratio of teeth).
- Pressure: pressure = force / area, so a smaller area gives greater pressure for the same force.
Traps to expect
- Mirror versus rotation in shape-matching items.
- Assuming effort equals load on pulley systems.
- Ignoring the pivot distance and comparing forces alone on levers.
- Gear direction errors when an idler gear sits between two gears (it reverses direction twice, so the outer gears turn the same way).
Rule of thumb
For levers, always measure distance from the pivot, not from the end of the beam. For gears, count the mesh points: each mesh reverses direction.
Worked example
A lever has a 200 N load 1 m from the pivot. How much effort is needed 4 m from the pivot on the other side? Moments balance: 200 × 1 = effort × 4, so effort = 50 N. A common wrong answer is 800 N, produced by multiplying instead of dividing.