MCT Practice Problems and Review
Key Takeaways
- MCT success depends on fast concept recognition — you do not have time to derive formulas from scratch.
- The most common MCT topics are levers, gears, pulleys, hydraulics, and basic Ohm's Law circuits.
- Diagrams and visual problems are common — practice interpreting mechanical drawings quickly.
- When in doubt, use conservation principles: energy is conserved, momentum is conserved, work in equals work out.
- Build a mental formula sheet: F=ma, W=Fd, P=W/t, V=IR, P=IV, MA formulas for all six simple machines.
MCT Practice Problems and Review
Essential Formula Quick Reference
Commit these to memory before test day:
Forces and Motion
| Formula | What It Solves |
|---|---|
| F = ma | Force, mass, or acceleration |
| W = mg | Weight from mass |
| f = μN | Friction force |
| v = v₀ + at | Velocity with constant acceleration |
| d = v₀t + 1/2at² | Distance with constant acceleration |
| p = mv | Momentum |
Energy and Work
| Formula | What It Solves |
|---|---|
| W = Fd | Work done by a force |
| KE = 1/2mv² | Kinetic energy |
| PE = mgh | Gravitational potential energy |
| P = W/t | Power |
| Efficiency = output/input × 100% | Machine efficiency |
Simple Machines
| Machine | MA Formula |
|---|---|
| Lever | effort arm / load arm |
| Wheel & Axle | R_wheel / R_axle |
| Pulley | # supporting ropes |
| Inclined Plane | length / height |
| Wedge | length / width |
| Screw | 2πr / pitch |
Fluids
| Formula | What It Solves |
|---|---|
| P = F/A | Pressure |
| F₁/A₁ = F₂/A₂ | Hydraulic systems (Pascal) |
| A₁v₁ = A₂v₂ | Continuity (pipe flow) |
Electricity
| Formula | What It Solves |
|---|---|
| V = IR | Ohm's Law |
| P = IV | Electrical power |
| Series R: R_t = R₁+R₂ | Total series resistance |
| Parallel R: 1/R_t = 1/R₁+1/R₂ | Total parallel resistance |
Gears
| Formula | What It Solves |
|---|---|
| T₁ × RPM₁ = T₂ × RPM₂ | Gear speed relationships |
| Gear Ratio = T_driven / T_driving | Speed and torque ratio |
Mixed Practice Problems
These problems cover all MCT topics in random order, simulating the actual test experience. Try to answer each in under 30 seconds.
Problem Set Strategy
For the MCT, develop a quick mental checklist for each question:
- What concept is this? (Force? Gears? Fluids? Electricity?)
- What formula applies?
- Plug in numbers and solve
- Check: does the answer make physical sense?
Do not overthink. If you cannot identify the concept within 5 seconds, make your best guess and move on. Spending 2 minutes on one MCT question means skipping 3-4 others.
Common MCT Question Patterns
| Pattern | What to Recognize |
|---|---|
| "Which direction does gear X rotate?" | Count meshing gears: odd = same direction as first, even = opposite |
| "How much force to lift..." | Look for pulleys, levers, or inclined planes → calculate MA |
| "What happens if..." | Apply conservation laws or Newton's Laws qualitatively |
| "Which arrangement provides more/less..." | Compare series vs. parallel or different lever positions |
| "What is the pressure/voltage/speed..." | Direct formula application: P=F/A, V=IR, v=d/t |
30-Second Decision Framework
When time is running out:
| Seconds | Action |
|---|---|
| 0-5 | Read the question, identify the concept |
| 5-10 | Recall the relevant formula |
| 10-20 | Plug in numbers, calculate |
| 20-25 | Select answer |
| 25-30 | If stuck, eliminate 1-2 wrong answers and guess |
If you cannot identify the concept in 5 seconds, eliminate obviously wrong answers and make an educated guess. A quick guess that moves you to the next question is better than spending a minute on a problem you are unsure about.
A 2 kg ball is thrown upward at 15 m/s. What maximum height does it reach? (Use g = 10 m/s²)
A gear with 15 teeth drives a gear with 45 teeth at 600 RPM. What is the speed of the driven gear?
Water flows at 4 m/s through a pipe with area 20 cm². It enters a section with area 5 cm². What is the new speed?
Three resistors of 4Ω, 6Ω, and 12Ω are connected in series to a 44V battery. What is the total current?
A hydraulic lift has pistons of area 10 cm² and 200 cm². To lift a 4,000 N car, what force must be applied to the small piston?
A lever has the fulcrum 0.5 m from the load and 2 m from the effort. If the load weighs 800 N, what effort force is needed?
A crane lifts a 200 kg load 15 meters in 30 seconds. What power does the crane deliver? (Use g = 10 m/s²)
A block of wood (density 500 kg/m³) is placed in oil (density 800 kg/m³). What fraction of the wood is submerged?