Mathematics and Mechanical Reasoning
What this domain tests
Mathematics and Mechanical Reasoning tests practical arithmetic, unit conversion, speed, distance, time, and simple machine reasoning. Expect word problems tied to train movement, stopping distance, and equipment.
Core skills
- Convert units before calculating: feet to miles, seconds to hours, inches to feet.
- Use speed = distance divided by time; rearrange for distance or time.
- For stopping distance, add reaction distance and braking distance; do not use only one.
- For gears, the ratio is driven teeth divided by driver teeth. A larger driven gear increases torque and reduces speed.
- For levers, mechanical advantage = effort arm divided by load arm.
- Check whether the answer is reasonable: a subway train does not travel 300 mph in a station.
Worked example
A train travels 1,320 feet in 30 seconds. What is its average speed in miles per hour? 1,320 divided by 30 = 44 feet per second. 44 times 3,600 = 158,400 feet per hour. 158,400 divided by 5,280 = 30 mph. The answer is 30 mph. Notice the unit conversion: feet per second must be converted to feet per hour, then to miles per hour.
Traps
Mixing minutes and seconds; using diameter instead of radius in a lever problem; forgetting that average speed hides acceleration; and choosing a precise-looking answer that is physically impossible.