MCT Practice Problems and Review

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1 Introduction to the OAR

About the OAR Who Takes the OAR and Why Study Plan and Test-Day Strategy

2 Math Skills Test (MST)

Arithmetic Fundamentals Fractions, Ratios, and Proportions Percentages and Real-World Applications Algebra Essentials Geometry Foundations Word Problems, Statistics, and Data Interpretation

3 Reading Comprehension Test (RCT)

RCT Overview and Core Strategies Main Idea and Purpose Questions Detail, Fact, and Inference Questions Vocabulary in Context and Author Tone Advanced Reading Strategies and Passage Types RCT Practice Passages and Questions

4 Mechanical Comprehension Test (MCT)

Forces and Newton's Laws of Motion Energy, Work, and Power Simple Machines and Mechanical Advantage Gears, Belts, and Rotational Motion Fluids, Pressure, and Hydraulics Electricity, Circuits, and Magnetism Motion, Heat, and Thermodynamics MCT Practice Problems and Review

5 Full Practice Tests and Final Review

Practice Test: Math Skills Practice Test: Reading Comprehension Practice Test: Mechanical Comprehension Final Review and Test-Day Preparation

MCT Practice Problems and Review

Key Takeaways Explain This Topic AI

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.

Last updated: March 2026

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.